Physics Reports Room Temperature Magnetism in Ceo2—A Review

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Room temperature magnetism in CeO2—A review Karl Ackland, J.M.D. Coey * School of Physics and CRANN, Trinity College, Dublin 2, Ireland article info a b s t r a c t

Article history: Cerium dioxide clearly raises the question of whether spontaneous ferromagnetic order is Accepted 9 April 2018 possible at high temperatures without d- electrons. There are many reports in the literature Available online xxxx of a ferromagnetic-like response to an applied magnetic field at room temperature for bulk, Editor: F. Parmigiani nanocrystalline or thin film samples, with or without cation doping. Typical values of the saturation magnetization are very small, of order 0.1 kAm−1, but reports range from zero Keywords: up to 1000 kAm−1. The effect is somehow related to lattice defects – Ce3+ cations or oxygen Ferromagnetism d-zero magnetism vacancies – but it is a challenge to understand how electrons associated with these defects Exchange could order ferromagnetically at room temperature and above. Straightforward impurity Crystal defects effects are considered, and models based on conventional ferromagnetic superexchange Zero-point fluctuations or double exchange are discussed, as is exchange splitting of the 4f band or a defect- Giant orbital paramagnetism related impurity band. Results are also compared with a new model of athermal giant orbital paramagnetism that involves no spontaneous ferromagnetic order. A key issue is the fraction, if any, of the volume of the CeO2 samples that is spontaneously ferromagnetic. Detailed analysis of the magnetic properties suggests that the conventional explanations of the magnetism of CeO2 are untenable, and directions for further research are suggested. © 2018 Elsevier B.V. All rights reserved.

Contents

1. Introduction...... 2

2. Magnetism in undoped CeO2 ...... 5 2.1. Bulk CeO2 ...... 5 2.2. Nanoparticles and nanostructures...... 7 2.3. Thin films...... 11

3. Magnetism in doped CeO2 ...... 13 3.1. Bulk...... 13 3.2. Nanoparticles and nanostructures...... 14 3.3. Films...... 18 4. Discussion...... 20 4.1. What fraction of the volume is spontaneously ferromagnetic?...... 22 4.2. Electronic structure calculations...... 23 4.3. Models...... 28 4.3.1. Superparamagnetism...... 28 4.3.2. Heisenberg superexchange...... 29 4.3.3. Zener double exchange...... 29 4.3.4. Stoner ferromagnetism...... 29 4.3.5. Modulated ferromagnetism...... 29

4.3.6. Giant orbital paramagnetism...... 30 5. Conclusions...... 31 Acknowledgements...... 32 References...... 33

1. Introduction

This review addresses the puzzle of d-zero magnetism in oxides by focussing on the best-documented example of a material with no unpaired d-electrons that exhibits a ferromagnetic-like response to an applied magnetic field at room temperature. Ferromagnetism at room-temperature and above has traditionally been the preserve of materials that are rich in 3d electrons, whether delocalized in bands or localized in atomic levels. Spontaneous magnetic order is a consequence of interatomic exchange interactions involving the electron spins. The magnetism follows an m:J paradigm, where Coulomb correlations lead to the appearance of magnetic moments m that are more or less localized in the vicinity of the atomic sites. The spin moments at neighbouring sites are coupled by an exchange interaction J that is positive for ferromagnetic coupling (parallel spin alignment) and negative for antiferromagnetic coupling (antiparallel spin alignment). The negative exchange interactions may give rise to antiferromagnetic or ferrimagnetic order, depending on lattice type. The histogram for oxides in Fig. 1 is based on an early compendium of data on magnetic ordering temperatures [1]. No oxide orders magnetically above 1000 K and in 90% of cases the order is antiferromagnetic or ferrimagnetic, rather than ferromagnetic, which indicates that J is much more frequently negative than positive. There are few ferromagnetic oxides 5 with a Curie temperature TC above 500 K. Ordering temperatures tend to be highest in oxides containing the 3d cations, 2+ 3+ Mn or Fe , for which the spin angular momentum takes its greatest value of 5/2 h¯ . The ferric antiferromagnet αFe2O3 for example, has a Néel temperature of 960 K, and the ordering temperature of ferrimagnetic γ Fe2O3 is estimated to be a little higher, but it transforms to the α phase beforehand. Nevertheless, there are persistent reports of weak, high-temperature magnetism in a wide variety of materials with no unpaired 3d electrons, including zinc oxide nanoparticles [2–4], hafnium dioxide thin films [5], alkaline earth hexaboride films [6], gold, silver and copper nanoparticles capped with dodecanethiol [7], graphene [8] and even severed Teflon tape [9], The reproducibility of the data is generally poor; results are controversial and often influenced by trace impurities or measurement artefacts [10–15]. Many more reports exist of high-temperature magnetism in dilute magnetic oxides (DMOs) containing only a few percent of 3d ions, which have been intensively investigated in the quest for a useful dilute magnetic semiconductor (DMS) [16–20] but these too are problematic in the light of Fig. 1. The magnetic ordering temperature for a magnet with an atomic fraction x of uniformly-distributed 3d impurities is expected to vary as x or x1/2 [21] so if x = 5% the magnetic ordering temperature should never exceed 200 K. We focus this review on a single material CeO2 (ceria) because there are so many reports of weak room-temperature ferromagnetism in this oxide in its various forms, undoped or doped, and it fits the profile of a d0 magnet [16] perfectly. Although the data are only marginally reproducible, there is enough qualitative agreement among them to establish the existence of a puzzling phenomenon that merits explanation. Pure, stoichiometric ceria is an insulating pale-yellow oxide with the cubic fluorite structure, space group Fm3¯m and −3 lattice parameter a0 = 541.1 pm [22]. The X-ray density is 7220 kg m . The molecular weight is 0.17212 kg/mol and the molar volume is 23.85 10−6 m3/mol. Each Ce4+ cation (formally 4f0) is coordinated by eight equivalent O2− anions at the corners of a cube, and each O2− is coordinated in turn by a tetrahedron of Ce4+ ions. The crystal structure, illustrated in Fig. 2, can tolerate a wide range of oxygen deficiency in the form of oxygen vacancies, represented as CeO2−x where 0 < x < 0.28 [23]. A series of ordered oxygen vacancy superstructures is found for larger values of x, ending with Ce2O3, x = 0.5, a sesquioxide that crystallizes in the related hexagonal bixbyite structure. Various cerium oxide structures are reviewed in [24]. There is no mixed cerium valence in CeO2, but rather covalent bonding involving O(2p) and Ce(4f) 3+ 1 orbitals [25,26]. On the other hand, the cerium in Ce2O3 is in an ionic Ce , 4f state [27]. Vacancies in CeO2 occur principally in the oxygen planes, and the non-stoichiometric material exhibits good anionic conductivity. It is very difficult to image the surface of nanoparticles or thin films of CeO2 in ambient conditions with atomic resolution, although this is what we would really like to do in order to understand both its magnetic and catalytic properties. We therefore depend on theoretical calculations and measurements such as scanning tunnelling microscopy (STM) on clean surfaces in vacuum to have an idea about what is going on. STM experiments on (111) surfaces [28,29] have revealed the formation of triangles, pairs, and linear clusters of surface oxygen vacancies, 2–7 oxygen sites long, with associated subsurface vacancies, which are known to be stable in ceria nanoparticles [24]. In a reduced sample, these vacancy strings could form percolation paths across the surface. Calculations have shown that isolated vacancies are more stable than pairs on {100} and {110} surfaces, but pairs are stable on {111} surfaces [30]. Early calculations also established that the energies of relaxed vacancy structures are lower than the unrelaxed structures [31] and structural relaxation is now a routine feature of density functional theory (DFT) calculations. Associated with the oxygen vacancies are the Ce3+ ions whose f electrons form small polarons that contribute activated electronic conductivity [32]. The ionic radius of Ce3+ (115 pm) exceeds that of Ce4+ (101 pm), leading to lattice expansion associated with the oxygen vacancies [33]. It has been calculated that it requires 4.55 eV to form a single oxygen vacancy

Fig. 1. Magnetic transition temperatures for oxides. The histogram illustrates the distribution of Curie and Néel temperatures for a thousand magnetically- ordered oxides. None of them exceed 1000 K. Ferromagnets are shown in blue, ferrimagnets in pink and antiferromagnets in red. Data are based on [1].

Fig. 2. Schematic of the fluorite crystal structure of CeO2; Ce cations (purple) are located at the corners and face centres of a cube, and O anions (red) at the centre of tetrahedral cerium cages.

3+ in pure CeO2, but only 0.26 eV when the vacancy is next to a pair of Ce ions in the CeO2 matrix [34]. Multiple oxygen vacancies have a tendency to align along ⟨111⟩ directions [35]. Nanometric ceria is known to undergo lattice expansion with decreasing nanoparticle size 2r, as evidenced by transmission electron microscopy (TEM) [36] and corroborated by X-ray diffraction (XRD) [37,38]. The surface/volume ratio of nanoparticles increases as 1/r, which leads to an increase in Ce3+ associated with unsaturated Ce–O bonds at the surface. X-ray Photoelectron Spectroscopy (XPS) measurements confirm that the Ce3+ content increases with decreasing nanoparticle size [39]. Ceria and its applications are the topic of a thousand publications a year, and they were recently the subject of a wide- ranging review [40]. The main application is in oxidative catalysis, particularly in automotive catalytic converters [41], thanks to the ability of non-stoichiometric ceria to readily absorb or release oxygen depending on the ambient partial oxygen

3+ Fig. 3. Schematic of the electronic structure of CeO2. In nonstoichiometric material, there are localized Ce donor states in the gap (as indicated), or occupied 4f states in the 4f (Ce) conduction band.

pressure. Catalytic activity is directly related to the number of oxygen vacancy defects, particularly at the oxide surface. Nanoparticles of metals such as Pd are efficient catalysts when present on ceria surfaces [42], or when ceria-coated [43]. The mixed conductivity produced by oxygen vacancies makes ceria a candidate electrolyte in solid-oxide fuel cells [44]. It also is used in thermochemical water splitting to produce hydrogen. Another application is as an abrasive for glass polishing [45] and in the chemical mechanical polishing process for planarization of dielectric layers [46]. It serves as a useful buffer layer between Si and SrTiO3 for oxide electronics. No application has been found for its magnetic properties. Stoichiometric CeO2 is an insulating wide-bandgap oxide, with a large static dielectric constant of 26. The primary O 2p–Ce 5d bandgap is about 7 eV, but a narrow empty Ce 4f band lies in the gap, about 3 eV above the 2p band edge [25,26,47–49]. A simple scheme of the energy bands is presented in Fig. 3. Ce3+ levels introduced by oxygen vacancies act as donors, lying below the 4f band edge.

In terms of magnetic properties, the subject of this review, pure CeO2 might be expected to exhibit temperature- independent orbital diamagnetism since it is composed of nominally closed-shell ions with no unpaired electrons. Never- theless, well-crystallized stoichiometric CeO2 is typically found to be weakly paramagnetic [50–54] with a dimensionless SI susceptibility χ of order 10×10−6. The intrinsic susceptibility is temperature-independent, but 4f1 Ce3+ ions associated with oxygen vacancies or pentavalent substitutions in the structure would be expected to contribute Curie-law paramagnetism 2 varying as 1/T, with an effective moment peff = 2.54µB corresponding to the F5/2 Hund’s-rule ground state multiplet 1 2 of the 4f ion (S = 1/2, L = 3, J = 5/2). The first excited multiplet, F7/2 lies 0.28 eV higher in energy on account of the spin–orbit interaction [55]. The cubic crystal field at the Ce3+ site splits the 2F multiplet further into a lower Γ √ √ √ 5/2 √ 8 quartet [|±1/2⟩; { (5/6)|±5/2⟩ + (1/6)|∓3/2⟩}] and an upper Γ7 doublet {− (1/6)|±5/2⟩ + (5/6)|∓3/2⟩} separated 1 by ∆cf = 75 K in the dilute limit [54]. The end-member sesquioxide Ce2O3, where all cerium is 4f , is hexagonal and antiferromagnetic, with a very low Néel temperature (TN ∼ 9 K) [22]. Superexchange for these paramagnetic ions is very weak. Doping with a trivalent rare earth extends the stability of the ceria lattice. The fluorite crystal structure is maintained up to 55 at.% La doping for example [56], and there is an extended ionic conductivity range compared to the undoped dioxide. In this review, we present the magnetic properties that have been found for ceria in its various forms, and discuss them in terms of the defect structure of the oxide. Data on undoped and doped material are first presented, in separate sections. Then the extensive experimental data sets are subjected to broad-brush analysis before discussing electronic structure calculations and various physical models that might explain the results. The problem is a challenging one, because CeO2 appears to defy expectations of how magnetically-dilute systems should behave. The behaviour captures the essence of d-zero magnetism [16] and it is related to the wider issue of dilute magnetic oxides [17,18,57]. Since the magnetism of CeO2 is more reproducible than that of other dilute magnetic oxide systems, it offers a great opportunity to advance understanding of these knotty problems. Readers uninterested in the details of the numerous experimental studies set out in the next two Sections may scan the tables and figures, before jumping on to Section4.

Fig. 4. Magnetization data analysis. A representative SQUID measurement of the magnetic moment of a CeO2 powder sample mounted in a diamagnetic gelcap is shown on the left. After correcting for the high-field slope, both the susceptibility of the gelcap and that of the CeO2 powder are removed, leaving the nonlinear saturating room-temperature magnetic (RTM) signal.

2. Magnetism in undoped CeO2

We first review results for room-temperature magnetism (RTM) in undoped CeO2. There is enormous variability according to the preparation method and the form of the sample. Stoichiometry, purity and surface-to-volume ratio all appear to −1 be significant considerations. The saturation magnetization Ms at room temperature is often small, of order 100 Am . It is important to put this number into perspective. A ferromagnetic moment of 1 µB per formula unit corresponds to a −1 2 −1 −1 magnetization Ms = 234 kAm (specific magnetization σs = 32.5 Am kg ), so 100 Am corresponds on average to barely 5 × 10−4 Bohr magnetons, per formula unit. If uniform, this is an extraordinarily small value, but the distribution of magnetic moments in the samples could be quite inhomogeneous. To put the number into perspective, a particle of radius 10 nm with a surface layer having a magnetic moment of 1 µB per unit cell would have an average magnetization of −1 2 −1 9.5 kAm (1.3 Am kg ). Just 45 point defects, each with a moment of 1 µB in such a particle would provide a magnetization of 100 Am−1 if they were ferromagnetically aligned. However, 100 ppm by weight of iron in the form of magnetite impurity −1 −4 2 −1 1 would give a magnetization Ms = 66 Am (92 × 10 Am kg ), so we must beware of magnetic impurities. Experimentally, a magnetic measurement of a powder or thin film will include the sample itself, as well as a sample holder or substrate, which can be measured separately and subtracted from the total data. Long plastic straws are used in SQUID measurements, with powders best mounted between diamagnetic gelatine capsules (gelcaps). By subtraction, the high-field susceptibility of the powder and any intrinsic nonlinear, saturating ‘ferromagnetic’ component with magnetization Ms is determined.2 Furthermore, the linear susceptibility of the powder may depend on temperature, and it too can be subtracted off directly, leaving just the nonlinear contribution, shown in Fig. 4. The additivity assumed in the data reduction process needs to be critically scrutinized in the case of thin films, where the substrate may not be simply passive, but interact with the CeO2 film by mechanical strain or electronic interface reconstruction, thereby modifying its magnetic properties. We mention here at the outset that the anhysteretic, easily saturated ferromagnetic-like magnetization curves should not be taken as evidence of superparamagnetism, because they are athermal (temperature-independent). Magnetization of a superparamagnet should scale as H/T, as discussed in Section 4.3.1 and illustrated in Fig. 18.

2.1. Bulk CeO2

Before discussing RTM, it is useful to have a benchmark for the magnetic susceptibility of defect-free CeO2 at room temperature. Since the stoichiometric oxide contains no paramagnetic species, it is expected to exhibit the underlying closed- shell orbital diamagnetism of an ionic compound like NaCl. The expected, temperature-independent value is χ = −22 × 10−6 [58,59]. There are many ways of expressing susceptibility in the literature; here we systematically convert everything −3 to dimensionless SI susceptibility, using the X-ray density of 7220 kg m for CeO2 (the expected molar diamagnetic −10 −6 susceptibility is −5.1 × 10 ). In fact, except for a value of −3 × 10 reported in [60] for one CeO2 powder, ceria usually exhibits temperature-independent paramagnetism. This paramagnetism is not attributable to traces of Ce3+ ions, which

1 To avoid confusion, we adopt SI units consistently throughout. Convenient cgs conversions are 1 kAm−1 is equivalent to 1 emu/cc (or 1 Gauss); 1 Am2 kg−1 is equivalent to 1 emu/g; the dimensionless SI susceptibility is numerically 4π times greater than its cgs counterpart; 1 Am2 is equivalent to 1000 emu; 1 Am−1 is equivalent to 4π/1000 Oe and 1 mT is equivalent to 10 G. 2 We distinguish saturation magnetization Ms determined from the M (H) curves after correction for the high-field slope with no necessary implication of ferromagnetic ordering, from the spontaneous magnetization that can arise in zero field in a ferromagnetically-ordered domain or region of a sample.

Please cite this article in press as: K. Ackland, J.M.D. Coey, Room temperature magnetism in CeO2—A review, Physics Reports (2018), https://doi.org/10.1016/j.physrep.2018.04.002. 6 K. Ackland, J.M.D. Coey / Physics Reports ( ) – would produce a Curie law upturn of susceptibility at low temperature. Lipp et al. [52] found the susceptibility of CeO2 powder to be positive χ = 88 × 10−6 and temperature-independent, except for an upturn below 50 K due to a 0.5% trace of Ce3+. Two further examples are 13 × 10−6 [61] and 40 × 10−6 [62]. The handbook value is χ = 14 × 10−6 [63]. Bonding in 4+ CeO2 is covalent, involving hybridization of the empty 4f(Ce) orbitals of formally Ce cations and the filled 2p(O) orbitals of the O2− anions. A static magnetic field mixes the occupied, lower-energy bonding level in second-order perturbation theory with the empty, higher-energy antibonding level to produce temperature-independent Van Vleck paramagnetism. −6 Analogous behaviour is found in TiO2 (rutile), which is diamagnetic for an annealed single crystal χ = −12× 10 (although the susceptibility is less negative than expected for core orbital diamagnetism) but paramagnetic and temperature- −6 independent for a TiO2 powder χ = +3.4× 10 [64], increasing when the powder is slightly oxygen-deficient. Positive −6 susceptibility, also found in anatase (χ = +0.3× 10 ), is ascribed to van Vleck paramagnetism [65]. In TiO2, as in CeO2, all the ions in their formal valence states have closed shells, but the sign and the value of the temperature-independent susceptibility varies greatly with the state of the sample. The origin of the variability in paramagnetism is not really explained, but it could reflect the influence of defects on the covalent bonds or it might possibly be a Pauli contribution from electrons in narrow bands associated with the defects. −6 A CeO2 single crystal was found to be paramagnetic, with χ = +12× 10 and no significant RTM [61], but there are reports of RTM in undoped CeO2 microparticles and microcrystals. The first evidence for micropowders (1–3 µm size) was obtained after grinding down a piece of the aforementioned paramagnetic single crystal, when a magnetization of 35 Am−1 was measured at room temperature [61]. Grinding induces oxygen vacancies. Upon oxygen annealing, the ferromagnetic CeO2 powder became paramagnetic again, so the authors suggested an oxygen-vacancy-related origin, similar to the explanation in the original report of Sundaresan et al. for CeO2 nanoparticles [2] that is discussed in the next section. −1 Elsewhere, weak RTM of 20 Am measured for undoped CeO2 microparticles 0.5–1 µm in size [66], was attributed to surface defects in the small particles. The value corresponds to a moment of about 0.1 µB per unit cell in a surface layer. Another report found a small magnetization of 6 Am−1 at room temperature for a finely-ground as-received powder of 99.99% (4N) nominal purity [67]. The powder became purely paramagnetic upon annealing in O2, so the authors again invoked oxygen vacancies induced by grinding as an explanation for the weak RTM. For 4N (99.99% pure) as-received powder annealed in −1 −1 vacuum or a reducing hydrogen atmosphere, Ms values of 300 Am [62] or 18 Am [68] were measured respectively; for both cases, the powder is paramagnetic before any annealing treatment, and re-annealing the ferromagnetic powder in air destroys the magnetism and recovers the original paramagnetism. All of their experiments point to oxygen vacancies as somehow responsible for the RTM effect. ◦ It has also been found that bulk CeO2 pellets, prepared by sintering powder at 1400 C, that are weakly paramagnetic at −1 320 K, become magnetic when irradiated with 200 MeV swift heavy Xe ions (range ∼12.5 µm) and exhibit Ms = 380 Am 13 2 for an irradiation fluence of 2 × 10 ions/cm [69]. Successively higher doses decrease the value of Ms. The magnetism vanishes when the irradiated samples are annealed in air. Magnetization curves virtually superpose at 320 K and 20 K, showing temperature independent-magnetism below room temperature, which would be compatible with a very high Curie temperature. We will see that this temperature independence of the magnetization curve is a recurrent feature of the RTM.

The measured lattice constant of CeO2 increases by about 0.2% from its unirradiated value when the oxide is irradiated in a fluence of 1.5 × 1013 ions/cm2, which is correlated with an enhanced Ce3+ content previously measured both by XAS (14% for 2 × 1013 ions/cm2)[70] and XPS [71]; since the RTM again vanishes upon annealing in air, the ion-irradiation was thought to induce RTM via oxygen vacancies. The effect is attributed to the magnetic moments of localized 4 f electrons on Ce3+ ions. Irradiation with Xe ions was shown by TEM analysis to introduce structural disorder in the form of numerous ion tracks of 3+ diameter 5–7 nm in CeO2 [72], which are postulated to create the sub-stoichiometry required for Ce and oxygen vacancy formation; upon irradiation at higher doses of ≥ 1013 ions/cm2, overlap of radiation damage tracks is purported to enhance the lattice disorder, which may be related to the reduction in Ms upon irradiation at higher fluences. Elsewhere, a structural + analysis of a CeO2 film irradiated with 2 MeV He ions of varying flux density also showed oxygen vacancy creation and 3+ enhanced Ce content [73], up to 20%. CeO2 pressed powder pellets irradiated with 10 MeV Iodine ions (ion range ∼2.5 µm) −1 13 2 exhibit Ms = 535 Am for a fluence of 1.2 × 10 ions/cm [74]; oxygen vacancies and interstitials are proposed to mediate the magnetism, and as with the 200 MeV swift Xe ion-irradiation, the magnetism appears to be destroyed at higher ion fluences due to enhanced lattice disorder and expansion.

It is noted that L3 edge X-ray absorption spectroscopy (XAS) measurements of high-purity bulk CeO2 micropowder (Cerac 99.99%) in transmission mode revealed at least 5% Ce3+ impurities [75], a value representative of the whole sample volume due to the transmission of X-rays throughout the bulk, indicating that it is not uncommon to detect Ce3+ in bulk-like particles using this method. Table 1 summarizes results on undoped bulk material, listing the maximum RTM for each sample in each report. Sample purity is stated whenever it is mentioned. It emerges clearly that bulk CeO2 is normally paramagnetic unless it has received 2 −1 some treatment such as grinding, vacuum annealing or ion-irradiation. Specific magnetization σs in Am kg (emu/g) is −1 −3 converted to Ms in units of Am using the X-ray density of CeO2, 7220 kg m . −1 However, commercial powders of 99.9% nominal purity show Ms ∼23 Am for 35 nm grain-sized samples, and Ms ∼2.3 Am−1 for 200 nm grain-sized samples [78]; the iron impurity content measured by X-ray fluorescence is ∼0.01 wt%

(100 ppm). This leads us to the magnetism of CeO2 nanoparticles, of which there are many examples.

Table 1 Maximum room temperature magnetization for undoped CeO2 bulk samples. −1 Sample + treatment Ms (A m ) Ref Single crystal 2 [61] Powder (99.9%) 0 [52] Powder (99.99%) 0 [62] Powder (no treatment)q 4 [76] Powder (99.99%) finely ground 6 [67] Powder (99.99%) (Alfa Aesar, no treatment)a 6 [77] Powder (99.99%) — H2 annealed 18 [68] Powder (no treatment) 20 [66] Powder ground from single crystal 35 [61] Powder (99.99%) — vacuum annealed 300b [62] Pellet (pressed from sintered powder) — irradiated 380c [69] (200 MeV Xe ions, 2 × 1013 ions/cm2) Pellet (pressed from sintered powder) — irradiated 535 [74] (10 MeV I ions, 1.2 × 1013 ions/cm2)

a −1 Crystallite size = 0.11 µm –Ms increases slightly to 11 A m upon argon annealing. b As received powder is paramagnetic; re-annealing powder in air (8 h) recovers paramagnetism, Ms = 0. c Pellet is paramagnetic before irradiation. q Powder contains 230 ppm Fe.

Fig. 5. Room temperature magnetization curves for undoped CeO2 nanoparticles from the first report of RTM, by Sundaresan et al. [2] (reproduced with permission). The particle diameter is indicated.

2.2. Nanoparticles and nanostructures

The first experimental report of RTM in undoped CeO2 was published in 2006 by Sundaresan et al. [2] for nanoparticles (NPs) precipitated during the reaction of solutions of cerium nitrate and hexamethylenetetramine (HMTA). It was found that NPs of 7 and 15 nm diameter had room temperature saturation magnetization values of 7 and 11 Am−1 respectively, whereas larger 500 nm sized particles only exhibited a paramagnetic signature at room temperature, similar to the temperature independent paramagnetism exhibited by pure crystalline CeO2 [52]. The magnetization curves are shown in Fig. 5. RTM was also measured for Al2O3, ZnO, In2O3 and SnO2 NPs of 7–30 nm diameter, and it was suggested by the authors that RTM is a universal feature of very fine oxide nanoparticles. A noticeable feature of the magnetization curves is their marked lack of hysteresis, with typical coercive fields of only a few mT. Powders lost their RTM, and became paramagnetic after sintering at 1000 ◦C in air or oxygen. The authors suggested that (ferro)magnetism arose from exchange interactions between localized electron spin moments resulting from oxygen vacancies at the NP surfaces. After Sundaresan’s report on undoped nanoparticles [2], there was a rapid growth in experimental investigations of all kinds of CeO2 nanostructures. An account of some of these experiments is now presented, and the magnetization data are

Fig. 6. Magnetization curves for 4 nm diameter CeO2 nanopowders of different purity [96]. The samples are synthesized by a sol–gel method [95,96] using 99% (2N) or 99.999% (5N) cerium nitrate precursors, where the 2N precursor contains ∼1 wt% La impurities. Data are corrected for the diamagnetism of the gelcap sample holder and the high-field susceptibility of the nanopowder. Significant RTM is measured for the impure CeO2 nanopowder but not for the pure nanopowder.

summarized in Table 2, grouped by synthesis method and particle size. It is emphasized that pure, well-crystallized material is weakly paramagnetic with little or no magnetization, but quite variable susceptibility from sample to sample. Precipitation: Undoped NPs synthesized by the self-propagating room temperature (SPRT) synthesis method that involves continually mixing the cerium nitrate and NaOH precursors, followed by exposure of the mixture to air, suspension in water and extraction of the CeO2 nanopowder by centrifugation and washing with water/ethanol, have magnetizations of 40–140 Am−1(3–15 nm diameter particles) [79–82], with no apparent correlation between magnetization and particle diameter. Other undoped NPs synthesized by similar co-precipitation processes without use of surfactant (when surfactants −1 are used in this review the process is denoted as ‘sol–gel’) have Ms values in the range 3–125 Am (2–15 nm particles) [82–89]. In one of the reports [89] the magnetization increases from 30 Am−1 (10 nm) to 45 Am−1(22 nm) upon annealing at 700 ◦C in a reducing atmosphere. Sol–gel: Sol–gel precipitation is one of the most common synthesis methods for growing small CeO2 NPs of narrow size distribution. Measured magnetization values are 15 Am−1 (7 nm particles) [90] and 0.7 Am−1 (5.7 nm particles) [91], the former being synthesized by reduction of cerium nitrate in an inorganic solvent, and the latter using NaOH/cerium nitrate/PEG. For the latter sample however, the authors ascribe the small magnetization of their undoped NPs to ferromagnetic impurities (20 ppm of Fe as measured by ICP-OES). Magnetization values of 8 Am−1 are reported elsewhere for as-prepared NPs (10 nm diameter) using citric acid as a complexing agent [92], which increases to 11 Am−1 upon annealing in forming gas to create oxygen vacancies. Cyclical oxidation/reduction anneals are shown to repeatedly reduce/enhance the magnetization. Interestingly, for NPs synthesized by the sol–gel method and subject to subsequent microwave irradiation [93] (termed the −1 ‘microwave-refluxing’ method) the maximum Ms for undoped material is noticeably larger, 135 Am , compared to the reports just mentioned above. In contrast to many other reports concerning RTM in undoped CeO2, Liu et al. [94] did not find a correlation with oxygen −1 vacancies. They reported a rather large Ms of 550 Am for small nano-needles (length 5 nm, diameter 1 nm) synthesized by a sol–gel process involving the reduction of cerium nitrate by NaOH in a solution of polyethyleneglycol (PEG) and water. When either ethanol or pure water was employed as the solvent, spheres of size 5–20 nm or 200–500 nm were obtained respectively, neither of which exhibited any RTM. Upon annealing the magnetic nano-needles in oxygen, which should remove oxygen vacancies, the RTM vanishes. However upon annealing the ferromagnetic sample in a reducing atmosphere, which should create oxygen vacancies, the RTM also vanishes, from which these authors inferred that oxygen vacancies were not responsible. The significance of the purity of the reagents used in the synthesis has to be highlighted. This is not just to eliminate the possibility of contamination by ferromagnetic elements. Traces of nonmagnetic dopants can completely change the RTM. To illustrate this point, we show in Fig. 6 the magnetization curve of 4 nm CeO2 NPs synthesized by a PEG sol–gel process using 99% (2N) pure cerium nitrate [95,96]. There is a clear magnetization, which can reach 150 Am−1. However, when 99.999% (5N) pure cerium nitrate was used instead, RTM is practically absent. The impurity present in the 2N reagent is largely lanthanum, and the effects of doping with La or other trivalent rare earths are discussed in Section 3.2. The RTM of CeO2 NPs therefore depends critically on the purity of the cerium reagent used, in a way that was not anticipated.

Table 2 Maximum room temperature magnetizations reported for undoped CeO2 nanostructures. Samples are in the form of equiaxed nanoparticles unless stated otherwise. −1 Synthesis Diameter (nm) Ms (A m ) Ref

Thermal decomposition method + air anneal (20% PO2) 9.5 1800 [99] Hydrothermal synthesis 150–300a 1300 [107] Hydrothermal synthesis 750 × 25b 1280 [100], [101] Hydrothermal synthesis 200–400c 895 [108] Thermal decomposition method 3.5 760 [97] Hydrothermal synthesis 750 × 200d 580 [103] Sol–gel (PEG) 5 × 1e 550 [94] Thermal decomposition method — Argon anneal 800 ◦C 60 475 [98] Hydrothermal synthesis 90 × 45f 230 [104] Hydrothermal synthesis 350 × 45g 230 [113] Hydrothermal synthesis 6–10 230 [131] Hydrothermal synthesis 400 × 15b 190 [102] Hydrothermal synthesis 500–700h 190 [110] Hydrothermal synthesis 500h 185 [111] Thermal decomposition method — air anneal 500 ◦C 10 175 [98] Hydrothermal synthesis + UV irradiation (24 h) 200i 145 [119] Self-propagating room temperature synthesis (SPRT) 6 140 [81] Pulsed electron beam evaporation 3 137q [76] Microwave Refluxing (sol–gel + MW irradiation) 5 135 [93] co-precipitation 15.4 125 [83] PVP assisted hydrothermal method 9.2 120 [116] Auto-combustion (citric acid + nitrates) + anneal 700 ◦C 19 70 [123] co-precipitation 14 70 [132] Polymer pyrolysis 15 65 [127] Auto-combustion (citric acid + nitrates) 21 62 [124] Hydrothermal synthesis ∼10000 × 40g 52 [114] Hydrothermal synthesis ∼1000j 50 [109] co-precipitation 28 50 [133] Hydrothermal synthesis 16 47 [117] co-precipitation + annealed in H2/Ar 22 45 [89] SPRT 10 45 [79] SPRT 6 45 [82] Cerium nitrate + Oleic acid /tert-butylamine/toluene 5.3i 43 [118] SPRT 3 40 [80] Polymer pyrolysis 30 38 [128] Pulsed electron beam evaporation 326 34q [76] Hydrothermal synthesis 1000 × 100k 30 [112] co-precipitation 5.4 25 [84] Microwave-induced combustion 24 23 [126] Hydrothermal synthesis 5 20 [134] PVP assisted hydrothermal method 20 20 [115] Cerium nitrate/NH4OH 7 15 [135] Sol–gel (using inorganic solvent) 7 15 [90] co-precipitation 2–3 15 [85] Thermal decomposition method — air anneal 450 ◦C 7.4 14 [136] Auto-combustion (citric acid + nitrates) 22 12.5 [125] co-precipitation 8 12 [86] cerium nitrate/HMTA 15 11 [2], [137] Sol–gel (citric acid) + anneal in H2/N2 14 11 [92] co-precipitation 9.2 10 [87] co-precipitation 28 6.3 [138] Sol–gel (ethylene glycol) 3 6 [139] Sol–gel (ethylene glycol) 3 5.3 [140] Hydrothermal synthesis 280× 10l 5 [141] Hydrolysis 4 5m [129] Solution combustion using glycine 14 n 5 [122] Cerium nitrate/NH4OH 8 4.5 [142] co-precipitation 7 4 [143] co-precipitation 4 4 [82] co-precipitation 4 3o [88] Solution combustion using L-glutamic acid 8 1.5 [121] (continued on next page)

Thermal decomposition: RTM with a value of 760 Am−1 [97] has been reported for 3.5 nm NPs synthesized by a thermal decomposition method involving heating a mixed solution of cerium(III) acetylacetonate hydrate, 1,2-dodecanediol (stabilizer), and octyl-ether to 100 ◦C, followed by addition of surfactants (oleic acid and oleylamine) and further heating

Table 2 (continued)

−1 Synthesis Diameter (nm) Ms (A m ) Ref Hydrothermal synthesis 10.7 0.8 [144] Sol–gel (PEG) + annealed in air 5.7 0.7r [91] Sol–gel (ethylene glycol) 4 0.6 [145] microwave-assisted hydrothermal method 70 × 10p 0 p [106] a ‘popcorn’- shaped particles. b ‘poles/rods’ (average length l × diameter d). c ‘flower’- shaped particles. d ‘wire bundles’ (avg. l × d). e ‘needles’ (avg. l × d). f ‘columns’ (avg. l × d). g ‘sheets’ (avg. size × thickness). h Octahedrons. i Cubes. j ‘gear’- shaped particles. k ‘rods’ (avg. l × d) which form bowtie-shaped agglomerates of overall length 10 µm and diameter 3 µm. l ‘wires’ (avg. l × d). m Nanocrystals with short ‘nanorod’ shapes, approx. diameter given. n Mesoscale structure is porous-sponge-like. o −1 Synthesized using cerium nitrate or chloride; Ms = 1 A m for NPs synthesized using cerium ammonium nitrate. p ‘rods’ (l × d) for which diamagnetism only is measured (no RTM). q −1 Contains ∼150 ppm Fe (note; Ms for 1 ppm of metallic Fe is 1.7 A m ). r Attributed to Fe impurities. to reflux at 300 ◦C before final separation of the precipitate by centrifugation. The magnetic signals for the NPs synthesized by this method were attributed to enhanced Ce3+ content (40%) at the NP surface and correlated with oxygen vacancies, 3+ which create more Ce , as measured by X-ray absorption near edge spectroscopy (XANES) at the Ce M4,5 absorption edge. The authors [97] also find that excess Ce3+ content (48%) at the surface may suppress the magnetic signal. It is noted that −1 −1 the maximum measured Ms of 760 Am [97] is larger than that typically found (∼10–100 Am ), and is comparable in magnitude to the largest previously reported value of 550 Am−1 for the nano-needles synthesized by Liu et al. [94]. In a later report using a simpler variant of the thermal decomposition method (Cerium(III)acetate hydrate precursor used only, −1 −1 without surfactants or refluxing step) smaller Ms values of 175 Am (10 nm) and 475 Am (60 nm) were measured for NPs calcined in air at 500 ◦C and in argon at 800 ◦C respectively [98]. The largest RTM values reported to date for undoped CeO2 nanostructures are for nanocrystals synthesized by the thermal decomposition method (as reported in [97]) and subsequently annealed under various conditions by Chen et al. [99]. The as-prepared NPs were paramagnetic, only exhibiting RTM after annealing. The largest magnetization measured was ∼1800 −1 ◦ Am for 9.5 nm NPs that were subsequently annealed at 500 C for 2 h in an oxygen partial pressure (PO2) of 20%. The ◦ use of higher oxygen partial pressures (50%) and/or lower annealing temperatures (300 C) resulted in smaller values of Ms −1 3+ ∼750–1700 Am , but still larger than any reported previously. Although no clear correlation between Ms and the total Ce content was found, by considering the effect of particle size and by calculating the surface Ce3+ content only, the authors attributed the large magnetization to a narrow range of surface Ce3+ concentration ratio ρ, as measured by XANES at the Ce L edge (0.40 < ρ < 0.45), similar to the explanation given in their earlier report [97], and they further suggest from X-ray magnetic circular dichroism (XMCD) measurements performed in fluorescent yield mode that the 4f electrons of Ce (but not O) bear the magnetic moments. By fitting the Ce XAS spectra [97], it is estimated that the as-prepared (paramagnetic) NPs 3+ ◦ 3+ contain 28% Ce , and that those annealed at 300 C in air, N2 or O2 contain 17%, 35% or 10% Ce respectively. As the electron escape depth exceeds the NP diameter (3–10 nm), the estimated Ce3+ content is attributed to the entire NP volume. Hydrothermal synthesis: RTM has been recently been measured for elongated CeO2 nanostructures, variously referred to as ‘poles’, ‘rods’, ‘columns’, ‘spindles’, ‘wires’ and ‘bundles’ among others, a series of terms that loosely reflect their aspect ratio. −1 Nanopoles of length 0.5–1 µm and diameter 20–30 nm have Ms = 1280 Am [100,101] and similarly-shaped nanorods −1 of length 0.2–0.6 µm and diameter 10–20 nm have Ms = 190 Am [102]. Nanowire bundles of length 0.5–1 µm and −1 bundle/individual diameter ∼200/20 nm have Ms = 580 Am [103] while nanocolumns of length 60–120 nm and diameter −1 30–60 nm have Ms = 230 Am [104]. The nanopoles/nanorods are grown by a hydrothermal synthesis whereby an aqueous solution of NaOH is added gradually to a cerium chloride aqueous solution after which ethylenediamine (which acts as a complexing agent) is added drop-wise. The solution is then heated in an autoclave at 180 ◦C for several days, after which the precipitate is separated, washed and dried. The nanocolumns are synthesized in a similar way, except that a mixed ethanol/H2O solution is used instead of H2O alone, N2H4· H2O (aq. hydrazine) is used as a base instead of NaOH, and the duration of heating in the autoclave is only 8 h. The nanowire bundles are grown similarly, with NaH2PO4· 2H2O used instead of NaOH. It appears that for nanostructures prepared in a similar way, those with higher aspect ratio have larger Ms, with the larger Ms values perhaps related to the larger surface areas of CeO2; for example, it has been shown using nitrogen gas

Please cite this article in press as: K. Ackland, J.M.D. Coey, Room temperature magnetism in CeO2—A review, Physics Reports (2018), https://doi.org/10.1016/j.physrep.2018.04.002. K. Ackland, J.M.D. Coey / Physics Reports ( ) – 11 adsorption that ceria rods and spindles have larger surface areas than spheres of equivalent crystallite size [105]. The larger surface areas may have more structural oxygen vacancies associated with them, yet other nanorods (70 nm length, 10 nm diameter) synthesized by a microwave-assisted hydrothermal method, exhibit diamagnetism at room temperature, which the authors ascribe to oxygen vacancies located in the bulk rather than at the surface [106]. Other discrete particles with shapes variously described as ‘popcorn’ [107] or ‘flower’ like [108], have quite large Ms values −1 −1 of 1300 and 895 Am respectively, while ‘gear’ (cog) shaped particles of ∼1000 nm size have a smaller Ms of 50 Am [109]. Such varied morphologies are typically produced by changing the reagent concentrations and heating time/temperature used in the hydrothermal synthesis. In all such cases, defect-rich particles are produced, and it is to the defects that the magnetism is attributed. For 500–700 nm octahedrons synthesized by hydrothermal synthesis using trisodium phosphate [110], irregularly- −1 shaped octahedrons have the largest Ms, up to 190 Am , approximately twice as large as is measured for regularly shaped −1 octahedrons in the same report. A similar Ms value of 185 Am is obtained by others for octahedrons of similar size [111]. Bowtie-shaped CeO2 agglomerates (3 µm diameter, 10 µm length) consisting of bundled nanorods of 100 nm diameter and 1 −1 µm length synthesized by a hydrothermal route (using CTAB and urea) have Ms = 30 Am [112]. Hexagonal nanosheets of 300–400 nm diameter and 40–50 nm thickness also synthesized by the hydrothermal method (using ethylenediamine) have −1 Ms = 230 Am [113], while larger 10 µm sized nanosheets ∼40 nm thick synthesized by a hydrothermal method using −1 citric acid have Ms = 52 Am [114]. NPs synthesized using a polyvinylpyrrolidone (PVP) assisted hydrothermal method ◦ (mix PVP with H2O, then add cerium nitrate solution and heat in an autoclave at 160–200 C for 12 h) have maximum magnetization values of 20 Am−1(20 nm) [115] and 120 Am−1 (9.2 nm) [116]. Other NPs synthesized by the hydrothermal −1 method (using citric acid and hydrazine hydrate) have Ms = 47 Am for 16 nm particles [117]. Nanostructures of different morphology (cubes) are found to exhibit size-dependent magnetism, 5 Am−1 for 100 nm cubes compared to 43 Am−1 for 5.3 nm cubes [118]. As in many other reports, oxygen vacancies and enhanced Ce3+ character at surfaces of samples of smaller dimension are suggested to account for the magnetism. Nanocubes of 200 nm size synthesized by a hydrothermal method have a room temperature saturation magnetization of 25 Am−1, which increased to 145 Am−1 after UV irradiation for 24 h [119], and here the authors propose that the increased magnetic signal is due to UV excitation of two electrons in an oxygen vacancy which forms a triplet state in the 4f orbitals of two neighbouring Ce ions. One benefit of using NPs with different morphologies is that the surfaces feature different crystallographic planes of the fluorite structure. For example nanocubes have {001} facets, whereas nano-octahedra have {111} facets and nanorods have {110} facets. This aspect is important for catalysis, since oxygen vacancies favour particular surfaces, but it has only recently been considered in the context of magnetism. The vacancy structures and corresponding magnetic defects depend on the surface [120]. Other methods: NPs synthesized by solution combustion using L-glutamic acid (8 nm diameter) exhibit very small Ms of −1 −1 ∼1.5 Am when undoped [121] and Ms of ∼5 Am when using glycine (14 nm) [122]; the latter has a porous sponge-like structure at the mesoscale. An auto-combustion synthesis in which citric acid and metal nitrate act as fuel and oxidizer respectively variously −1 −1 −1 produced NPs with Ms of 70 Am (19 nm) [123], 62 Am (21 nm) [124] and 12.5 Am (22 nm) [125], Undoped NPs synthesized by microwave-induced combustion, in which solutions of cerium nitrate and urea are mixed − −1 and irradiated with microwaves to induce combustion (and during which urea generates OH ions) exhibit Ms = 23 Am (24 nm) [126]. For undoped NPs synthesized by polymer pyrolysis, which involves the mixing of the metal nitrate solution with acrylic −1 −1 acid followed by stirring/heating of the solution to dryness and final calcination, Ms = 65 Am (15 nm) [127] and 38 Am (30 nm) [128]. Other undoped nanocrystals (4 nm) synthesized by (forced) hydrolysis exhibit small RTM values of 5 Am−1 (using polyacrylic acid) and 1.5 Am−1 (using trioctylphosphine oxide) [129], where the weak magnetism is claimed to be due to electron transfer between the nanocrystals and surfactants. For undoped nanopowders synthesized by pulsed electron beam evaporation of ceramic targets [76], smaller sized −1 −1 particles (3 nm) have larger Ms values (137 Am ) than larger 327 nm particles (Ms = 34 Am ); however there are doubts about iron impurity contamination with this method.Fig. 7 displays some Transmission electron microscopy (TEM) images of a selection of different undoped ceria nanostructures, all of which exhibit RTM to some extent. Table 2 provides a list of RTM data for undoped CeO2 nanostructures, mostly NPs, in order of decreasing maximum −1 magnetization measured. As in Table 1, Ms is given in units of Am . There does not appear to be any clear correlation between NP diameter and Ms. Although some NPs exhibit RTM directly after synthesis, others only exhibit RTM after being post-treated in some way, typically by a reducing anneal. Data for NPs with a variety of morphologies are included in Table 2. The differences may reflect the different morphologies, but also cerium nitrate purity [95,96], concentration [105], or different sodium hydroxide concentrations [130]. In order to relate morphology to magnetism convincingly, it would be helpful to be able to alter it, while keeping everything else the same.

2.3. Thin films

By far the largest magnetic signals for undoped CeO2 have been found in electrodeposited films. Electrodeposition is an attractive method for making micro- and nano-structured ceramic oxide films as it offers the advantages of low-temperature processing, simplicity and voltage or current control.

Fig. 7. Selection of TEM images of undoped CeO2 nanostructures which exhibit RTM; A = nanocolumns [104], B = nanocubes [118], C = nanoparticles [99], D = nanowire bundles [103], E = nanoneedles [94]. Their respective Ms values are presented in Table 2.

Fernandes et al. present RTM in thin compact nanocrystalline films in a series of papers. Very large RTM values of up to ∼120 kA m−1 – 70 times larger than any in Table 2 – were initially reported for ∼30 nm thick oxygen-deficient films grown 3+ on p-type Si (001) substrates [146]. Hydrogen peroxide (H2O2) is sometimes added to modify the oxidizing conditions (Ce content) of the films with more stoichiometric films obtained at higher H2O2 concentrations. Electrodeposition does not occur in the dark, so the electrolyte/Si interface is illuminated with a halogen lamp [147]. The cerium precursor used in 3+ all of the syntheses is 99.8% CeCl3.7H2O (Merck) with a Ce concentration of 22.7% as estimated by XPS. Thicker films −1 (250 nm) display a similarly large value of Ms ∼100 kAm , and despite an exponential-like decay of Ms from 100 to 7 kAm−1 over a 1 year timespan for this thicker film, the magnetization is then stable at room temperature for 1 year −1 thereafter. The Ms values are even larger, ∼160 kAm , for thinner 20 nm films, and increase up to a maximum of ∼450 kAm−1 (similar to that of ferromagnetic nickel, 490 kAm−1) upon irradiation with 30 keV Ne+ ions at a fluence of 2 × 1016 ions/cm2 [148]. The authors suggest that their large magnetic signals are mostly associated with point defects (Ce and O vacancies) in the structure. The effect of ion-irradiation is to create more vacancies, and hence to enhance the Ce3+ content 3+ from 22.7% before irradiation to 47.2% after irradiation; it is found that Ms continuously increases with Ce concentration, despite the significant amorphization of the films upon irradiation. Such huge values would require two Ce3+ ions or half a cerium vacancy per formula unit. In a subsequent paper 20 nm thick granular oxygen-deficient nanocrystalline films were deposited on SiO2/Si substrates, without removing the native oxide layer [149]; these films exhibited extraordinary anisotropy of the RTM (Fig. 8); the in-plane magnetization is 280 kAm−1, but the out-of-plane magnetization reaches 1150 1 −1 kAm , the latter value being the largest measured to date for any CeO2 system, exceeding that of nickel (490 kAm ) and even approaching that of cobalt (1440 kAm−1). The large anisotropy cannot be explained in terms of the usual combination of in-plane shape anisotropy and perpendicular surface or magnetocrystalline anisotropy (PMA) because the in-plane and perpendicular curves do not tend to the same saturation value. It seems as if there is a very large perpendicular magnetization due to in-plane orbital motion of the electrons. We return to this idea in Section 4.3.6. Compared to the oxygen-deficient films, relatively smaller (but still very large) anisotropic magnetization values of 91 kAm−1 and 117 kAm−1 for in-plane and out-of-plane measurements respectively are found for near-stoichiometric films (3.8% Ce3+). The large magnetic signals and anisotropy were attributed to oxygen vacancy pairs lying along the (111) axes of the fluorite structure. No other group has yet published anything similar. 20 nm films of strongly-magnetic, highly oxygen-deficient CeO2 electrodeposited on a Co/Pt multilayer with an Au buffer were found to exhibit the strong perpendicular magnetic anisotropy [150], with in- and out-of-plane RTM of ∼200 kAm−1 and ∼900 kAm−1 respectively. The films switch in a field of several tens of mT. −1 A more modest, but still impressive Ms value of 8 kAm has been measured for 150 nm thick magnetron sputtered −1 films on Si (100) [151]. A similar Ms value (7 kAm ) is measured elsewhere for RF sputtered films, 290 nm thick, on Si (111) [152]. Weak RTM was also found in rough polycrystalline CeO2 films composed of multiply stacked nanosheets and porous microstructures synthesized by electrodeposition on copper substrates [153]. The stacked sheets were ∼5 µm thick overall (as estimated from electron micrographs) with individual nanosheet thicknesses of 60 nm, several µm across, while the porous microstructures were ∼2 µm thick and composed of pores of ∼2 µm size with ∼0.6 µm thick walls. Morphology was modified by changing the concentration of the cerium nitrate precursor used during electrodeposition. The Ms values were very small, 5 Am−1 for pores and 6 Am−1 for sheets; enhanced magnetism at 4 K was associated with paramagnetic Ce3+ as detected by XPS. Elsewhere for ∼0.5 µm thick nanoporous films electrodeposited from 99.999% (5N) nominal purity

Fig. 8. Strong, anisotropic magnetization of 20 nm thick oxygen-deficient electrodeposited CeO2 thin films. Source: Adapted from [149], reproduced with permission.

Table 3 Representative magnetization values measured for undoped CeO2 films. In-plane Ms is displayed unless stated otherwise. Note that Ms here is given in kA m−1. Films are listed in order of decreasing film thickness. −1 Synthesis Thickness (nm) Ms (kAm ) Ref Electrodeposited (ED) on Cu substrate (99.99%) ∼5000a 0.006 [153] ED on Cu substrate (99.99%) ∼2000b 0.005 [153] ED on Si (using 99.999% (5N) cerium nitrate) ∼500 <0.002 Unpublishedc RF sputtering on Si(111) 290 7 [152] ED on Si (22.7% Ce3+) 250 100 [146] Magnetron sputtering on Si(100) 150 8 [151] ED on Si (22.7% Ce3+) 30 120 [146] ED on Si (22.7% Ce3+) 20 245 [148] ED on Si (3.3% Ce3+) 20 159 [148] ED on Si (22.7% Ce3+) + irradiated with 30 keV Ne+ (2×1016 ions/cm2) 20 450 [148] (Ce3+content = 47.2%) 3+ ED on SiO2/Si (3.8% Ce ) 20 91∥ 117⊥ [149] 3+ ED on SiO2/Si (24.2% Ce ) 20 280∥ 1150⊥ [149], [154] ED on SiO2/Pt/Co-Pt/Au 20 200∥ 900⊥ [150] a Stacked ‘nanosheets’. b Porous microstructures. c Same synthesis/authors as [95]. See Fig. 13. cerium nitrate solution no distinct RTM signals were observed, however when 99% (2N) cerium nitrate solution containing −1 ∼1 wt% La impurities was used Ms values of up to 600 Am were measured [95] (see Section 3.3 and Table 6). Magnetization values for undoped films are summarized in Table 3.

3. Magnetism in doped CeO2

RTM has been reported for a host of different doped CeO2 samples, where the dopant is a 3d transition metal in the majority of cases and a magnetic or nonmagnetic rare-earth element in some others. When the transition-metal dopants are ferromagnetic (Fe, Co, Ni), the magnetism is usually found to be large. The magnetization in most tables in this section is also given in units of Bohr magnetons per dopant atom.

3.1. Bulk

Experimental reports for RTM in doped bulk CeO2 are listed in Table 4. Maximum magnetization values are listed in −1 descending order. The largest Ms values (>8 kAm ) are for samples subject to reducing anneals. Samples not subject to vacuum annealing mostly have intermediate values, while those annealed in air typically have the smallest Ms values (<0.5 kAm−1). The moments per cobalt or iron atom never exceed that of the ferromagnetic metal, which raises the question

Table 4 Maximum room temperature magnetization values per dopant reported for doped CeO2 bulk samples (all in micropowder form). Note that Ms here is given in kA m−1. −1 Synthesis Dopant (at.%) Ms (kA m ) Moment Ref (µB/atom)

Solid state reaction (SSR) + H2/Ar anneal 3% Co 8.5 1.12 [158] SSR + H2/N2 anneal 3% Co 8.4 1.06 [156] SSR 2.7% Fe 7.6 1.15 [159] SSR 5% Co 7.5 0.62 [160] q SSR + H2/N2 anneal 3% Co 4.7 0.65 [155] SSR + H2/Ar anneal 3% Co 3.7 0.51 [157] SSR 2.1% Co 3.6 0.35 [61] SSR 2% Co 3.0 0.61 [161] SSR 3% Co + 10% Y 2.7 0.40 [162] Obtained from sintered 10 nm nanocrystals 25% Y + 0.25% Gd 0.57 0.01 [163] Chemical solution method (with citric acid) + calcined in air 20% Nd 0.38 0.007 [164] SSR 3% Fe 0.3 0.04 [67] Sol–gel (coconut water) + calcined in air 10% Zn 0.23 0.01 [165] SSR + calcined in air +Ar anneal 10% Gd 0.07 0.003 [166] Sol–gel (coconut water) + calcined in air 10% Co +10% Zn 0.007r <0.001 [167] SSR 5% Cr 0.006 <0.001 [77] q Attributed to Co clusters. r Contains Co3O4 clusters. of whether the magnetism should be attributed a nanocrystalline secondary metallic phase. In at least one case, the as- prepared powder was paramagnetic, χ = 35 × 10−6 [155], and the ferromagnetic phase formed after treatment in a reducing atmosphere was shown to contain nanocrystalline cobalt particles that were magnetically blocked below 400 K. In other cases, for example [156,157], the reducing anneal is shown to create oxygen vacancies and Ce3+ ions. It is suggested that spin-polarized electrons trapped in the vacancies (F+-centres) are responsible for exchange coupling the Co2+ dopant ions, leading to a high Curie temperature. The RTM associated with nonmagnetic or rare-earth doping is one or two orders of magnitude smaller than it is with 3d doping.

3.2. Nanoparticles and nanostructures

A summary of literature reports for RTM in doped CeO2 nanostructures (mostly NPs) is given in Table 5. The maximum magnetization value reported for each reference is listed in order, starting with the largest. XRD analysis typically suggests that the dopants are incorporated into the fluorite lattice of the ceria, at least at the lower doping concentrations, although XRD has limited ability to detect traces of secondary phases at the 1% level. From the data, there appears to be little correlation between the magnetization values and either particle size or the specific dopant used. In some cases RTM is measured for −1 doping with non-ferromagnetic elements such as Cu, La, Pr, and Sm but the magnetization is then small, Ms ∼100 Am . The majority of the reports attribute the enhanced magnetization to oxygen vacancies induced by doping with divalent or trivalent cations. Whenever a series of dopant concentrations are measured, the RTM signal is usually found to go through a maximum and to decrease at larger dopant concentration [81,96]. No magnetization is reported for doping with pentavalent Nb5+, which is expected to generate Ce3+ with no oxygen vacancies [54]. Although most of the Ms values for doped NPs in Table 5 are larger than those for undoped NPs in Table 2, there are only a few reports of magnetizations in excess of 1 kAm−1. The largest value, 35 kAm−1, is surprisingly for 6 nm NPs doped with 9 at.% copper synthesized by a solvothermal route using hexamethylene triperoxide diamine (HMTD) [168]. The 9 2+ moment, equivalent to 1.58 µB/Cu, exceeds the 1.0 µB spin-only moment of the 3d Cu ion, and would suggest a significant contribution of Ce3+, or of spin-polarized electrons in trapped in oxygen vacancies. In another report for Cu-doped samples with up to 5 at.% Cu, nanorods (70 nm length, 10 nm diameter) synthesized by a microwave-assisted hydrothermal method, showed room temperature paramagnetism (not RTM), which the authors ascribe to the oxygen vacancies being located in the bulk where they are unable to mediate RTM, rather than at the surface [106]. Another large magnetization of 14.5 kAm−1 is measured for 10 nm NPs doped with 15 at.% Fe and synthesized by a gel-combustion reaction [169]. The coercivities measured are ≤ 50 mT, and the authors claim from magnetization, XRD, TEM and Raman data that their samples are free of iron or iron oxide clusters, and therefore they attribute the magnetism to defects and/or oxygen vacancies. At higher doping, there is increased magnetization but an αFe2O3 phase appears in XRD. Their undoped NPs are diamagnetic. Elsewhere, it is reported that the iron solubility limit in ceria is between 10 and 20 at.% for doped NPs synthesized by the co-precipitation method [189]. All of the other reports for NPs with magnetizations >1 kAm−1 in Table 5 are for samples subject to reducing anneals, suggesting that samples richer in oxygen vacancies have enhanced magnetization compared to those which are not vacuum annealed after synthesis. An XAS study of Fe-doped CeO2 NPs performed in transmission mode on the O K, Fe L and Ce M edges reveals that the relative Ce3+ content does not vary monotonically with Fe doping concentration [190]. At lower doping concentrations 3+ 3+ (below 5–7 at.% Fe) the proposed defect structure is Fe –VO–Ce which allows charge transfer between the Ce and Fe

Table 5 Maximum room temperature magnetization values per dopant reported for doped CeO2 nanostructures (nanoparticles unless stated). −1 Synthesis Diameter (nm) Dopant (at.%) Ms (Am ) Ref Solvothermal synthesis 6 9% Cu 35000 [168] Gel-combustion (glycine + nitrates) 10 15% Fe 14500 [169] co-precipitation + vacuum anneal 7 9% Co 6100 [170] co-precipitation + vacuum anneal 17 5% Co 3000 [171] Microwave-induced combustion 16 11.1% Dy 2670 [126] ◦ co-precipitation + VSM activated anneal in N2 at 450 C 8 8% Ni 2100 [172] Hydrothermal synthesis 25 0.05% Mn 2000 [173] co-precipitation 6 3% Mn 910 [135] Sol–gel using coconut water 45 1% Fe 840 [174] Pulsed electron beam evaporation 5 0.54% Fe 765 [76] Electrospinning + calcined at 800 ◦C ∼10000 × 60a 4% Fe 705 [175] Auto-combustion (citrate + nitrates) 15 5% Er + 5% Co 620 [125] Microwave refluxing 5 3% Cr 610 [93] Pulsed electron beam evaporation 4 1% Cu 500 [76] Auto-combustion (citrate + nitrates) 14 5% Er + 5% Fe 455 [125] b b b b Ag mixed with cerium nitrate/reflux 50 Ag, 7 CeO2 Ag@CeO2NPs 390 [143] co-precipitation 41 7% Mn 350 [176] ◦ co-precipitation + N2 anneal at 500 C 5 5% Co 310 [177] co-precipitation 22 7% Ni 270 [133] Hydrothermal synthesis 800 × 15c 6% Co 250 [102] Hydrothermal synthesis 500d 2% Co 240 [111] co-precipitation 13 7% Co 230 [132] Thermal decomposition method + 7 5% Ni 230 [136] air anneal 450 ◦C co-precipitation 6 6% Co 210 [142] Solution combustion (glycine) + calcined at 500 ◦C 7 8% Fe + 1% Eu 205 [122] Sol–gel with citric acid 9 4% Cr 190 [178] Auto-combustion (citric acid + nitrate) 19 5% Er + 5% Ni 185 [125] Pulsed electron beam evaporation 5 0.84% C 175 [76] Sol–gel (PEG) 99% (2N) Ce nitratee 4 1.2% La 40–150 [95,96] Self-prop. room temp. synth. (SPRT) 3–10 12% Fe3+ 150 [79,80] Composite Hydroxide Mediated (CHM) synthesis 3000-7000 × 55f Mn (% not given) 150 [66] Auto-combustion (citric acid + nitrate) 26 5% Ndg 135 [123] Auto-combustion (citric acid + nitrate) 22 5% Er 125 [125] co-precipitation 6 7% Ni 125 [87] Polymer pyrolysis 12 5% Sm + 5% Sr 100 [128] co-precipitation 7.5 7% Fe 100 [179] co-precipitation 22 7% Fe 95 [138] co-precipitation 11 1% Fe 90 [180] Polymer pyrolysis 20 15% Sm 90 [127] Microwave refluxing 40 × 7c 3% Cu 90 [181] SPRT 4 1% Pr 75 [81] co-precipitation 8 3% Co 75 [182] co-precipitation 7.2 3% Co 65 [86] Hydrothermal synthesis + Gd ion irradiated at 40 keV, 3 × 1016 25 4.6% Gd 60 [134] ions/cm2 + 500 ◦C anneal co-precipitation 2–3 11% Cr 60 [85] Auto-combustion (citric acid + nitrate) 19 5% Pr 46 [124] Sol–gel with citric acid 10 3% Cr 45 [183] Sol–gel (ethylene glycol) 3 9% La 45 [184] Sol–gel with PVP 15 3% Co 45 [115] Sol–gel (PVA) + calcined at 600 ◦C 25 3% Fe 45 [185] Sol–gel (ethylene glycol) 2 5% Fe 30 [139] As-received powder (99.9% purity) 35 0.1% Mn 23 [186] Sol–gel (ethylene glycol) 3 15% Sm 23 [140] ◦ co-precipitation + N2 anneal at 200 C 3 5% Ni 22 [177] co-precipitation 10 25% Y, 0.25% Gd 15 [163] Hydrothermal synthesis 23h 5% Fe 15 [187] co-precipitation 4 20% Fe 11 [88] Hydrothermal synthesis 243 × 10i 4% Mg 11 [141] co-precipitation 7 4% Ni 9 [188] Hydrothermal synthesis 6.8 1 CeO2: 2 CuO 8 [144] (continued on next page)

Table 5 (continued)

−1 Synthesis Diameter (nm) Dopant (at.%) Ms (Am ) Ref Sol–gel (PEG) + calcined at 400 ◦C 6.6 10% Cu 5.5 [91] co-precipitation 4 9% Y 2.5 [145] Solution combustion (L-glutamic acid) 4 10% Ca 1.7 [121] As-received powder (99.9% purity) 150 0.1% Mn 1.5 [186] a ‘fibres’ (average length l × diameter d). b −1 15 nm-thick shell of 7 nm sized CeO2 NPs deposited onto 50 nm sized Ag NPs. Ms is reduced to 175 A m when shell thickness is increased to 35 nm. Further details are given in a subsequent paragraph. c ‘rods’ (avg. l × d). d Octahedrons (edge length). e −1 NPs synthesized using 99.999% (5N) cerium nitrate and which exhibit no distinct RTM, when doped with 1 wt% La have Ms ∼50 A m [96]. f ◦ ‘rods’ (avg. l × d); CHM synthesis involves adding CeO2/MnCl2 to a basic solution (KOH + NaOH) and heating to 200 C for 72 h. g −1 Further co-doping with either 5% of Zn, Cr or Cu increases Ms to 160, 195 or 210 Am respectively. h ‘nanocubes’; for >15% doping, RTM is attributed to an Fe2O3 secondary phase. i ‘wires’ (avg. l × d).

3+ 3+ and facilitates RTM, while for higher doping levels of up to 11 at.% Fe the defect structure is Fe –VO–Fe , which is antiferromagnetic and is hence proposed to reduce the RTM signal in this case. For 6 at.% Co-doped NPs [142] XANES measurements reveal that Co substitutes on Ce sites, resulting in a change of valency from Ce4+ to Ce3+, but the concentration of oxygen vacancies may not be high enough to form a delocalized impurity band that could enhance magnetic percolation in undoped and Co-doped CeO2 samples. In an article on Cr-doped CeO2NPs of 2–3 nm diameter [85], authors of the undoped CeO2 XMCD study of Chen et al. [99], using similar measurement conditions in a 1 T applied field, find an XMCD signal for the Ce L edge, but not for the Cr K edge; hence the magnetism is associated with Ce3+ rather than the Cr3+ dopant. Furthermore, it is postulated that the effect of Cr-doping is to reduce the distance between magnetic Ce3+ ions thereby increasing the density of defects and promoting RTM. For Fe-doped NPs, XMCD also reveals that 3+ 3+ 3+ 3+ the magnetism is associated with cerium [139], and that the defect structures (a) Fe -VO-Ce and (b) Fe -VO-Fe are likely responsible for (a) enhancing and (b) decreasing the saturation magnetization respectively as the iron concentration increases. A study of Fe-doped NPs (4–8 nm in size, with 0–7.2 at.% Fe doping) synthesized by co-precipitation reports a low temperature saturating ferromagnetic/paramagnetic magnetization signal at 5 K, but no RTM. The low-temperature 3+ 2− magnetism is mediated by oxygen vacancies in the form of Fe -VO complexes, and the signal is not ascribed to iron clusters or secondary phases from either XPS, magnetization or Mössbauer measurements [191]. Doping with magnetic or nonmagnetic rare earths produces small magnetizations, typically <100 Am−1. For Y doped NPs [145], XANES measurements reveal that Y3+ substitutes for Ce4+ in the ceria lattice, creating oxygen vacancies, but the RTM is associated mainly with cerium (rather than O or Y) from XMCD measurements, specifically with surface Ce3+. In a report on Pr doped NPs [81], the authors find that Pr doping actually suppresses the magnetic signal that they measure compared to their undoped CeO2 sample. A similar result showing suppression of Ms with increased Pr doping concentration in nanoparticles was later measured by other authors [124]. A novel recent study investigates the magnetic properties of 7 nm CeO2 NPs deposited onto larger 50 nm sized Ag NPs [143]. The experimental method involves first spin-coating TiO2 prepared by a sol–gel route onto a Si substrate to form a film. Ag NPs are then deposited by thermally-assisted photoreduction (of silver nitrate) onto the TiO2 film. The resultant Ag NPs are removed and suspended in water for CeO2coating, realized by mixing with cerium nitrate hexahydrate and heating ◦ −1 −1 to reflux at 200 C for 4 h. The CeO2 NPs alone have Ms = 4 Am , while the Ag NPs alone exhibit Ms = 52 Am . The key −1 −1 result however is that upon coating the Ag NPs with a 35 nm shell of CeO2 NPs Ms is increased to 175 Am , or 390 Am 3+ when the CeO2 shell thickness is reduced to 15 nm. The Ce content is measured during TEM imaging by energy electron loss spectroscopy (EELS) to be 40% at the Ag/CeO2 interface, It is proposed that electron transfer at the interface from Ag p to Ag d and Ce 4f orbitals mediates the magnetization, which is enhanced due to a thinner CeO2 shell having increased surface or interface area to volume ratio. In one case, as-received nanopowders, with 99.9% nominal purity powder containing 0.1 at.% Mn impurity exhibit RTM −1 −1 with Ms values of 23 Am (35 nm) and 1.5 Am (150 nm) [186]. Electron paramagnetic resonance (EPR) analysis of the powders ruled out iron contamination as a cause of the RTM, but detected Ce3+ instead. The set of magnetization curves shown in Fig. 9 are for 4 nm NPs, containing ≈ 1 at.% La. The fit to these data is discussed in Section 4.3. By comparison, the NPs made using 5N pure cerium nitrate are essentially paramagnetic (Fig. 6). The remarkable feature is that the curves are practically anhysteretic, and there is no temperature-dependence of the magnetization curve up to 380 K. Measurements at higher temperatures lead to a progressive evolution of the nanopowder, so direct measurement of a Curie temperature is impractical. If one exists, its magnitude is estimated to be of order 1000 K, from a mean-field or Bloch T3/2 law extrapolation of the maximum possible variation of magnetization between 4 and 380 K consistent with the experimental data in Fig. 9. The 58 Am−1 RTM of Fig. 9 is rather stable over time, decaying by 20% after 2 years, but on annealing in air for 3 h durations at successively higher temperature, Ms measured at 300 K decreases by 5% at 470 K (5 nm), 20% at 670 K (6 nm), 40% at 870 K (12 nm) and 60% at 1070 K (40 nm). The particle size (nm) evolves on annealing,

Fig. 9. Temperature independence of the magnetization curves of low purity 4 nm CeO2 nanoparticles [95,96]. The curves measured between 4 K and 380 K superpose, showing the athermal nature of the magnetic response. The main impurity in the 99% (2N) cerium nitrate precursor is ∼ 1% La.

Fig. 10. Effect of doping high purity CeO2 nanoparticles with La [96]. 4 nm nanoparticles are synthesized using 5N cerium nitrate precursor (99.999% purity) with added pure lanthanum nitrate; the largest Ms measured at 1 wt% La agrees with that found for the 2N precursor in Fig. 6.

and the magnetization is correlated with the particle size. Samples which are not ferromagnetic in the bulk often exhibit RTM when in nanoparticulate form, and there are a number of reports that the magnetism of CeO2 is size dependent, for example [2,94,118], and is likely to be related to surface to volume ratio, and surface oxygen vacancies associated with Ce3+. The NP surface acts as an extended defect due to the unsaturation of chemical bonds there compared to saturated bonds in the interior. The effect of deliberately doping CeO2 NPs made from the highly pure 5N cerium nitrate (which initially exhibits no distinct RTM, Fig. 6) with La3+ is shown in Fig. 10. The RTM is turned on by the nonmagnetic La3+, reaching a maximum for a doping of 1 wt% (1.2 at.%), and decreasing for higher La doping [96]. A similar effect is found for doping with Pr3+. The results of Figs. 6,9 and 10 are important because they reveal that the surface oxygen vacancies in nanoparticles of pure ceria are not sufficient to create RTM. A trace of trivalent rare earth is necessary, which may alter the nature of the conductivity of the surface states. However, the most remarkable feature of the magnetism of ceria nanoparticles is its dependence on the degree of agglomeration of the powder [96]. The magnetism exhibited by closely-packed 4 nm powder is reduced by dispersing the powder with nanocrystalline alumina, or microcrystalline sugar. The latter has the advantage that it can be dissolved, and

Fig. 11. Evidence for a characteristic magnetic length scale in CeO2 nanopowder, reproduced with permission from [96]. (a) Magnetization curves for 4 mg samples of 4 nm CeO2 nanoparticles that are mixed with various amounts of 15 nm γ Al2O3 nanoparticles. (b) TEM image showing that the dispersion with alumina separates the CeO2 nanoparticles into clumps about 100 nm in size. (c) Effects of dilution with different dispersants. (d) Appearance of UV absorption associated with magnetism in three CeO2 powder samples.

the magnetism is found to return when the CeO2 nanoparticles re-agglomerate. Since the diluent is in direct contact with only a small fraction of the ceria nanoparticles, its effect is to destroy continuity between the nanoparticles on a length scale of order 100 nm. The results are illustrated in Fig. 11. The weak magnetic response of ceria therefore not only has a high characteristic temperature, of order 1000 K as shown by the temperature-independence of the magnetization curve, but there is also a characteristic length scale of order 100 nm. This behaviour is not unprecedented, as there have been other reports of magnetism in both undoped oxides [137] and dilute magnetic oxides [192] depending on the state of agglomeration of the sample. A further manifestation of the syndrome is the appearance of a peak in the UV absorption of magnetic CeO2 nanoparticles around 4 eV that is absent in nonmagnetic micropowder, and weak in the nanoparticles made from the 5N precursor, Fig. 11(d).

3.3. Films

The first report of RTM in any form of CeO2 was by Tiwari et al. [193] for cobalt-doped CeO2 films. Crystalline films of thickness ∼500 nm doped with 3 at.% Co were grown by pulsed laser deposition (PLD) on LaAlO3 (001) substrates. The magnetization curves are virtually anhysteretic, as shown in Fig. 12, with a large RTM signal of ∼45 kAm−1, equivalent to a remarkable magnetic moment of 6 µB/Co. The magnetism cannot therefore be entirely due to cobalt inclusions, since the 2+ best that can be expected from Co is a spin moment of 3 µB, plus a small unquenched orbital contribution. The magnitude of the moment remained unchanged from 300 K down to 5 K. Superparamagnetism can be ruled out as an explanation, due to its characteristic temperature dependence. In superparamagnets, the magnetization follows a Langevin function, and it scales as H/T (see Fig. 18(a)). + An F -centre mediated exchange mechanism, originally proposed by one of the present authors for SnO2 films doped with Fe3+ [194], was suggested by Tiwari et al. [193] as an explanation for ferromagnetic ordering. An F+-centre consists

Fig. 12. First magnetization curves showing RTM in a CeO2 film. The film, grown on a 100 LaAlO3 substrate by PLD, contains 3 at.% Co [193] (reproduced with permission).

of a single electron in an oxygen vacancy; earlier EPR studies had shown the presence of these electrons trapped at vacant oxygen sites rather than occupying states in the 4f band [195]. In a later report by Tiwari on similar films grown on SrTiO3 −1 (001) substrates [196], the magnetization was smaller, 18 kAm (2.4 µB/Co), and there was a significant superparamagnetic contribution; XAS and XPS showed that in this case 85% of the cobalt was phase-separated in small clusters rather than homogeneously incorporated into the CeO2 lattice, as it was in the initial report [193]. A large number of other publications followed the initial work. RTM signals of similar magnitude appeared in films with 3 at.% Co grown by PLD on Si (111) or glass substrates [197]. Others found similar magnetizations of up to 16 kAm−1 for 4.5 at.% Co doped PLD grown films on either Si or SrTiO3 [198]. The presence of oxygen during the growth or annealing reduces the ferromagnetism drastically, reinforcing the idea that oxygen vacancies play a key role in magnetic coupling between Co ions. Of course oxidation of metallic cobalt clusters would also reduce Ms, since neither CoO nor Co3O4 is ferromagnetic at room temperature [199]. Use of ferromagnetic 3d dopants inevitably raises doubt about the origin of the RTM. Non-magnetic dopants are a better tool to investigate the defect-, rather than impurity-related origins of RTM. One such example are electrodeposited nanoporous films synthesized from 99% (2N) cerium nitrate which contain ∼1 wt% La [95]. The size of the magnetic signal depends on the overpotential used during the electrodeposition, which in turn alters the degree of porosity of the electrodeposits; some ferromagnetic films can be made virtually non-magnetic simply by varying the overpotential. Films produced without PEG and those with smaller magnetization are smoother and have fewer grain boundaries or defects than those produced using PEG. The RTM signals are tentatively associated with grain boundaries/surfaces of nanopores and/or the small quantities of La in the films. For films electrodeposited from a 5N cerium nitrate precursor no RTM was measured whatever the deposition conditions, but the RTM signal could be ‘turned on’ by additional non-magnetic dopants, as shown in Fig. 13. It is noted that the pores for the magnetic films have a similar morphology to undoped films grown elsewhere [153], but the pores here [95] are about 10 times smaller in size and the Ms values are ∼100 times larger than those in [153] (see Table 3). The effect of doping the very-strongly magnetic CeO2 films electrodeposited on oxidized (001) silicon [154] is quite different. Doping 20 nm thick films with ∼ 3 at.% Fe, Mn, Co or Cu reduces the magnetization of 290 kAm−1 in that order, with the largest remaining value of 220 kAm−1 for Fe and the smallest value of 80 kAm−1 for Cu. Elsewhere although a modest Ms is measured for 0.5 µm thick Co-doped films composed of nanorods electrodeposited on a 99.99% Cu substrate (80 Am−1 for 5% doping), the authors report a Curie temperature of 870 K for the sample [200]. Other than this, we are unaware of any other report of RTM where the authors attempt to measure TC. A summary of literature reports for RTM in doped CeO2 films is provided in Table 6, where the majority of the dopants are 3d transition elements. Murugan et al. [221–224] used RF magnetron sputtering to deposit a series of Ni, Mn, and Co doped CeO2 films with −1 t∼0.5 µm on glass, but in all cases Ms was practically zero, ≤ 0.1 Am . There is also a report for Fe-doped (2, 6 wt %) films with t = 200 nm, grown at 550 ◦C by PLD on Si (100) [225], where XPS measurements show that Ce ions are in a mixed valence state and that Fe ions are in a 2+ state; hence ferromagnetic metallic iron clusters were ruled out. There is no systematic correlation in Table 6 of magnetization with film thickness or substrate used, although as in the case of undoped CeO2, the largest magnetizations for doped CeO2 are found in some of the thin electrodeposited films.

Fig. 13. Doped nanoporous films prepared electrochemically from 5N (99.999%) cerium nitrate (unpublished) following [95] for different charges (C) and various non-magnetic dopants. The undoped film does not exhibit RTM, whereas doped films do. Typical film morphology for a doped film with M s = 280 Am−1 is shown on the right.

Large moments are also found for some films prepared by PLD. Since the moments per dopant atom are unphysically large, for example 7.2 µB/Co [210] or 6 µB/Co [193,197], it is again clear that the magnetism cannot be attributed directly to ferromagnetic 3d dopants in these cases. Instead combined contributions of spin polarized Co, Ce, and O atoms with enhancement from O vacancies have been proposed, for example in [210]. Other notably large magnetizations of ∼100 kAm−1 are also reported for Co doped films [207,208], but in the latter case, the magnetism is attributed to Co clusters. RTM of 12 kAm−1 has been induced in films by irradiation with non-magnetic elements such as N [216]. Fe-doped films electrodeposited on a 99.99% purity Cu plate [211] have a structure of nanospheres or nanopores with nanosphere diameters of 250–400 nm (composed of 16 nm grains), or nanopores with pore diameters of 27 nm. The morphology of the nanostructures is varied by changing the current density. The largest values of Ms measured are 65 and 50 kAm−1 for the nanospheres and nanopores respectively, with magnetization measured perpendicular to the Cu substrate plane. The coercivities of these samples (∼ 330–660 mT) are markedly larger than usual for d0 systems or dilute magnetic oxides (usually a few mT), but the authors argue from XRD and XPS measurements that all of the iron is substitutional in the CeO2 lattice, and the magnetic signal is attributed to oxygen vacancies. For the Fe-doped (1–3 at.%) CeO2 polycrystalline thin films, ∼200 nm thick, grown by PLD on LAO (001) substrates [204], XMCD measurements of the Fe L2,3 edge performed in fluorescence yield mode reveal enhanced Fe2+ character in a mixed valence Fe2+-Fe3+ environment with increased Fe doping concentration. The authors propose that the reason why the magnetization of the system is reduced is related to the relative decrease in the Fe3+ contribution proposed to mediate the magnetism as compared to the Fe2+ contribution. For the Pr doped thin films [217], XANES measurements reveal that oxygen vacancies are created by Pr3+ doping while 4+ cerium remains in a Ce charge state, and Ms is strongly correlated with the number of oxygen vacancies. Trivalent cation substitution induces nonstoichiometry in the dioxide, via vacant anion sites.

4. Discussion

The problem of room-temperature magnetism of CeO2 epitomizes two open questions that have been at the forefront of research in magnetism since the beginning of this century, relating to dilute magnetic oxides (DMOs) and d0 magnetism. The first question is how can traces of 3d dopants apparently turn nonmagnetic oxides such as ZnO or TiO2 into room- temperature ferromagnets? The second is how can similar effects can be achieved by using nonmagnetic dopants or defects in systems with no unpaired d-electrons? The use of 3d dopants in the first case in an effort to realize a dilute magnetic semiconductor deflected attention from the second question, which may be more fundamental and challenging. Every material known to order magnetically well above room-temperature had been an element or compound possessing a high density (>1028 m−3) of 3d transition elements with unpaired spin, sometimes in the company of other d-group or 4f elements. High-temperature ferromagnetism is thought to require a density of ferromagnetic exchange energy that is not easy to achieve. The histogram for oxides in Fig. 1 was based on a compendium of data on magnetic ordering temperatures [1], but the histogram for Curie and Néel temperatures of a larger group that includes non-oxide magnetic materials looks similar. There are then a few points above 1000 K, but a century of research has not come up with a higher magnetic ordering temperature than that of cobalt (Curie temperature of 1360 K). Examples of spontaneous magnetic order become increasingly sparse at higher temperatures.

Table 6 Maximum room temperature magnetization values per dopant for CeO2 films, grouped according to method of fabrication. The largest Ms value is displayed for each reference. Magnetic measurements are in-plane and all films are polycrystalline unless stated otherwise.

Growth method Thickness Dopant Ms Moment Ref −1 (nm) (at.%) (kA m ) (µB/atom) a PLD on Al2O3 (0001) 1000 3% Co 14.3 ∥ 1.9 µB/Co [201,202] a PLD on Al2O3 (0001) 1000 3% Co 12 ⊥ 1.6 µB/Co [201,202]

PLD on LAO (001) ∼500 3% Co 45 6 µB/Co [193]

PLD on LAO (001) ∼500 3% Cu 8.3 1.1 µB/Cu [203] PLD on LAO (001) 200 1% Fe 0.38 0.15 [204] µB/Fe PLD on LAO (001) 200 5% Co 0.5q 0.04 [205] µB/Co

PLD on MgO (100) 262 10% Co 31 1.2 µB/Co [206]

PLD on MgO (100) 953 25% Co 105 ⊥ 1.5 µB/Co [207]

PLD on STO (001) 520 3% Co 7 1 µB/Co [196] q PLD on STO (001) 350 15% Co ∼100 ⊥ 2.5 µB/Co [208]

PLD on STO (001) 400–500 4.5% Co 16 ⊥/∥ 1.4 µB/Co [198,209]

PLD on Si (111) or glass ∼100 nm 3% Co 45 6 µB/Co [197]

PLD on Si (111) ≥ 100 12% Co 230 7.2 µB/Co [210] 2 Electrodeposited (ED) on Cu at 1 mA/cm 5% Fe 65 ⊥ 5 µB/Fe [211] b

2 ED on Cu at 3 mA/cm 10% Fe 50 ⊥ 1.9 µB/Fe [211] c

ED on Si (001) 5–20 13.2% Co 35 1.0 µB/Co [212]

ED on SiO2/Si (001) 20 3% Fe 220 29 µB/Fe [154]

ED on SiO2/Si (001) 20 3.2% Mn 140 17 [154] µB/Mn

ED on SiO2/Si (001) 20 2.7% Co 90 13 µB/Co [154]

ED on SiO2/Si (001) 20 3.4% Cu 50 5.8 µB/Cu [154] ED on Si (001) ∼500 23% Co 1.3 0.02 [213] 10% Zn µB/Co ED on Si (111) ∼500 1.2% La 0.6 ∼0.16 [95] µB/La ED on Si (111) ∼500 2.5% Mg 0.28 ∼0.04 (see 0.5% Zn µB/Mg Fig. 13) ED on Si (111) ∼500 2% Mg 0.16 ∼0.02 (see 0.3% Bi µB/Mg Fig. 13) ED on 99.99% Cu ∼500d 5% Co 0.08 0.006 [200] µB/Co

Magnetron sputtering (MS) on Al2O3 (0001) 1000 3% Co 38 5 µB/Co [214] + e MS on Al2O3 (0001) + Ar sputter 10 min 1000 3% Co 24.2 3.2 µB/Co [215] MS on Si (100) 150 6% Sn 21.74 1.46 [151] µB/Sn

MS on Si (111) + N ion-irradiation (80 keV, ∼300 N irradi- 12 µB/N [216] 1 × 1015 ions/cm2) ated % unknown unknown

RF sputtering on Si(111) + C ion-irrad. (70 290 7.8% C 27 µB/C [152] keV, 6 × 1016 ions/cm2) unknown Molecular beam epitaxy on Si (111) 24 20% Pr 13.5 0.28 [217] µB/Pr Spin coating (from sol–gel) on LAO (001) 210 7% Mn 31.5 1.75 [218] µB/Mn

(continued on next page)

Table 6 (continued)

Growth method Thickness Dopant Ms Moment Ref −1 (nm) (at.%) (kA m ) (µB/atom) Spin coating (from sol–gel) on Si (100) Not given 5% Mn Not given 1.12 [219] µB/Mn Spin coating (from sol–gel) on LAO (001) 216 5% Co 13.9 1.09 [220] µB/Co a After subtraction of moment due to magnetic phase-separated Co clusters. b Films are not compact (of defined thickness) but composed of nanospheres of 250–400 size. c Films are nanoporous (27 nm pores). d Films are composed of nano-‘rods’ of size 600 × 25 (avg. l × d). e + −1 Before Ar ion sputtering, Ms = 7.5 kAm (1µB/Co). q Magnetism attributed to Co clusters.

Fig. 14. Representative magnetization curves for thin films of dilute magnetic oxides. The three doped oxides are measured at room temperature. Reproduced with permission from [21]. Ms and H0 denote the saturation magnetization and field obtained by extrapolating the initial susceptibility to zero, respectively, defined as shown for the Ti0.99Fe0.01O2 film.

As mentioned in the Introduction, the conventional framework for thinking about magnetism in solids is the m:J paradigm, where interatomic exchange interactions J couple the spins of 3d electrons that are more or less localized by interelectronic Coulomb correlations to produce the atomic moments m. Ferromagnetic order is relatively uncommon in oxides; J is usually negative and short-range, hence most oxides are ferrimagnetic or antiferromagnetic. The main oxide families of spinels, garnets, hexaferrites and mixed-valence perovskites all date from the heydays of the 1950s. It is therefore astonishing that an oxide doped with a few percent of magnetic or nonmagnetic ions could order magnetically above room temperature, as originally suggested in 2001 for thin films of Co-doped TiO2 by Matsumoto et al. [226] and Co-doped ZnO by Ueda et al. [227]. Some representative data on thin films of three DMOs presented in Fig. 14 show that the behaviour is by no means limited to CeO2. A big problem, alleviated to a certain extent in the case of CeO2 as we have seen in the preceding sections, has been reproducibility of data. Although there clearly is something to be explained, a scrupulously-critical experimental mindset must be maintained in view of well-documented artefacts [10–15,19], especially for thin film samples and particularly for those with cobalt doping. The sobriquet ‘phantom ferromagnetism’ inspired by dilute magnetic oxide thin films captures the reproducibility problem. Cerium dioxide, undoped or with nonmagnetic dopants, allows us to address the simpler but more puzzling open question of d0 magnetism.

4.1. What fraction of the volume is spontaneously ferromagnetic?

A key question, in view of the presence of crystallographic defects at the surface or in the bulk is, what proportion, if any, of the volume of these samples is really ferromagnetic? If we assume that only a fraction f of the volume of the nanoparticles or thin films is spontaneously ferromagnetic in the normal sense, then it is possible to give a rough answer to the question, provided the hysteresis is negligible [228]. For this purpose, it is useful to plot M (H) curves using the same units (Am−1) for both M and H, so the shape of the curve has an obvious meaning. The magnetization of any region in a ferromagnet is ′ governed by the internal magnetic field H , which is the sum of the applied field H and the demagnetizing field Hd. The latter is approximately related to the local magnetization Mloc by a demagnetizing factor N, where Hd = −NMloc. In equilibrium

′ during the initial stages of the magnetization process, H should be zero everywhere, otherwise domain walls will move to make it so. N take values of ∼1/3 for isolated particles or roughly isometric samples, ∼1/6 for polycrystalline samples where only the grain boundaries are ferromagnetic [228] (a grain boundary foam [3]) or 1 for thin films magnetized out-of-plane. The slope of the initial magnetization curve is 1/N, so Mloc = H0/N can be deduced from the intercept H0 of this line with the saturation magnetization Ms (see Fig. 14). The ferromagnetic volume fraction is then given by [228].

f = Ms/Mloc = NMs/H0 (1)

Applying this method to the thin films of dilute magnetic oxides featured in Fig. 14, for example, and taking N ≈ 1/3, gives −1 values of Mloc of about 300 kAm , and f of 3%–10%. The films therefore cannot be uniformly magnetized. Separate Ms vs H0 plots are shown in Fig. 15 for both undoped and doped samples of CeO2. We also include on the plots, for reference, data on three examples of well-characterized particles. These are magnetite nanoparticles, iron microparticles, and a sample of iron nanoparticles dispersed on a silicon substrate, where the iron is only a tiny fraction of the total sample volume [229]. Data on the first two examples lie on the sloping lines plotted for fully-dense material, drawn for different demagnetizing factors. The dilute iron nanoparticles fall in a completely different region of the plot, six orders of magnitude below the iron micropowder, with a ferromagnetic volume fraction f ∼ 0.0001%. These results confirm the validity of this semiquantitative approach to answering the question posed at the outset of this section. The undoped electrodeposited CeO2films have f ∼ 3%–30%, but the volume fractions for the micropowder and thin films are much lower, falling between 0.005% and 1%. The conclusion is that only a tiny fraction of the volume of CeO2 micro- and nano-particles can be ordered ferromagnetically. If the samples were uniformly magnetized, the anhysteretic magnetization would saturate in far lower fields, on account of the weak demagnetizing fields created by the sample. It must be emphasized that this analysis is based on normal spontaneous ferromagnetic order, where the saturation is controlled by the demagnetizing field in a multidomain structure. Other models of the magnetic response discussed in Section 4.3 based on helimagnetic order or giant orbital paramagnetism give different explanations of the nonlinear anhysteretic magnetization curves. Turning to the data on doped CeO2 in Fig. 15(b), the picture is rather similar, although average f values are a bit higher. Thin films show the largest ferromagnetic fractions, ranging from 1%–100%, microparticles are around 1% and nanostructures range from 1–0.005%.

4.2. Electronic structure calculations

Next we turn to electronic structure calculations for some atomic-scale insight into the problem. Many calculations carried out on pure, defective and substituted CeO2 provide information on stability of various lattice defects in the fluorite structure, and their possible relevance to the room-temperature magnetism. The calculations are almost all based on density- functional theory (DFT) of small supercells with oxygen vacancies [32,35,117,230–235], cerium vacancies [146,235,236], oxygen interstitials [234,237], or doping with trivalent cations [238,239], ions of the 3d transition metals Fe [240], Co [156,210,241,242] or Ni [243], or other elements (Sn, C, N, Cu) [151,244–246], including rare earths [206,207,223–225]. These calculations provide data on the structural stability, electronic structure, magnetic moment formation and magnetic order, albeit in small supercells with periodic boundary conditions. The local density approximation (LDA) for a free electron gas with exchange and correlation energy works rather well for metals and intermetallic compounds, but it has to be corrected with an ad hoc Hubbard-like U parameter in order to account for the strong electronic correlations and insulating behaviour found in non-stoichiometric oxides [230,247]. A small oxygen deficiency does not create neutral vacancies with two electrons that immediately populate the 4f-band to form a metal, but as suggested in Fig. 3, localized 4f1 states appear instead in the 2p–4f gap. Different values of U are appropriate for the 4f and 5d electrons of Ce, or the 2p electrons of oxygen, and no single choice will simultaneously account for the band gap(s) and the positions of defect levels within the gap. Furthermore, different choices are appropriate for different implementations of DFT, in the LDA or GGA (generalized gradient approximation). Appropriate choices of U can be controversial, but ranges are:

5 ≤ U4f ≤ 8 eV, U5d ∼ 5 eV and U2p ∼ 7 eV. Calculations frequently reveal unpaired electrons that are somehow related to the point defects, but further stability analysis of ordered ferromagnetic or antiferromagnetic configurations relative to a disordered paramagnetic configuration is essential before concluding anything about room-temperature ferromagnetism from the presence of these moments m. More recently, hybrid functionals have been developed that can lead to improved agreement with experimentally- determined bandgaps in insulators. Electronic structure calculations by Skorodumova et al. [49] and Gillen et al. [48] using a variety of methods provide a summary of the electronic band-gaps for both CeO2 and Ce2O3, with the principal bandgap of ceria ranging from 5.5–8 eV for the O 2p–Ce 5d transition, and 1.5–4.2 eV for the O 2p–Ce 4f transition. Some examples of a calculated band structure of ceria for different functionals are shown in Fig. 16. Although the 4f electrons may be at the Fermi level in the 4f band, in photoemission spectroscopy experiments they can appear about 2 eV below the Fermi level due to final-state effects. Fig. 17 illustrates the main possible defects in CeO2. The stability of the defects and their effects on the electronic structure can differ according to whether they are located in the bulk or at the surface. Oxygen vacancies: Oxygen vacancies (VO) are the most common point defects in undoped ceria, but there is no consensus among the calculations that they necessarily cause ferromagnetism. No clear connection between oxygen vacancies and

Fig. 15. Room temperature saturation magnetization Ms plotted against the local magnetization Mloc deduced from the saturation field H0 with 1 −1 demagnetizing factor N = /3 for undoped (a) and doped (b) CeO2. Data are taken from many literature reports, omitting most samples with Ms < 5 Am . Most error bars are removed in (b) for clarity of display. Reference data for iron and magnetite particles are discussed in the text. The volume fractions lie in the range 0.001%–1% for all except the electrodeposited films of Fernandes et al. [146–150,154,212]. Open circles denote iron (oxide) reference samples, as labelled in (a); the additional open circles in (b) denote doped samples in which authors explicitly ascribe the magnetic signals to ferromagnetic impurities.

room-temperature magnetism based on the electronic spins has been generally established in the DFT calculations [241]. The inference that oxygen vacancies cause magnetism is usually made from experiments that treat the samples in oxidizing

Fig. 16. DFT (density functional theory) electronic structure calculations for CeO2 [48] (reproduced with permission) using screened exchange (PBE) and hybrid exchange–correlation functionals (HSE06 and sX-LDA). The grey dashed line (right panels) corresponds to experimental data on a CeO2 film on graphite [26] for comparison.

or reducing conditions, and while there is a strong body of evidence that oxygen vacancies are involved, they may not by themselves be sufficient [210]. The two electrons associated with a neutral vacancy (an F-centre) in a d0 oxide may form a singlet or a triplet state, depending on whether the vacancy is in the bulk, at the surface of a nanoparticle or at the interface of a thin film [248]. Surface oxygen vacancies are more likely to be magnetic [249]. Furthermore the magnetic state may depend on the crystallographic surface involved [120]. Depending on the strength of interatomic electronic correlations, the Ce 4f electrons introduced by oxygen vacancies may be expected to form localized mid-gap states [247], or enter localized or delocalized states at the bottom of the 4f conduction band [250]. A GGA calculation for a Ce4O7 unit cell that does not include a large U parameter predicts that removal of an oxygen atom from pristine CeO2 will introduce electrons directly into the narrow 4f band which spontaneously splits to form a half-metallic ferromagnetic state with a net magnetic moment of 2 µB per formula unit [250]. An early calculation using LDA+U (U 4f = 5–6 eV) for undoped ceria found that VO defects do produce magnetic signals which are enhanced at the surface compared to in the bulk [118]. Moments of 1.41 µB, 1.87 µB and 1.98 µB per (2×2×2) supercell were calculated for one VO in the bulk, one VO at the surface and for two VO at the surface respectively. These calculations appear to be consistent with some of the experimental reports for ferromagnetism in undoped ceria nanoparticles and thin films, where the surface to volume ratio is greatly enhanced compared to the bulk and where surfaces can readily accommodate oxygen vacancies. However, the calculations must be approached with caution because moments of order 1 µB per defect and defect concentrations of ∼ 0.1 per unit cell give moments that are about 100 times larger than usually measured. We must accept that most oxygen defects, including those at the surfaces of nanoparticles, make no contribution to the magnetism. Of course, no moment is ever measured for the pristine, bulk, defect-free, stoichiometric phase, and it is seen in Section 2.1 that ‘ferromagnetism’ can

3+ Fig. 17. Defects in CeO2. (a) An oxygen vacancy, that may be neutral (two electrons may reside in the vacancy, or else produce two Ce ions), or charged (one electron resides in the vacancy) and form an F-centre or an F+-centre, respectively. (b) A cerium vacancy may give rise to four 2p holes on nearby 2− oxygen ions. An adjacent pair of 2p holes produce an O2 peroxide ion. (c) An oxygen/cerium antisite (d) An oxygen or a cerium interstitial.

be produced in undoped bulk ceria by grinding [61,67], irradiation [69,74] or vacuum annealing [62] which create defects and especially oxygen vacancies at the surface. However, pure nanocrystalline samples, which are likely to have a large surface area are not necessarily ferromagnetic. A calculation, performed in the local spin density approximation (LDA) + U scheme, using U = 8 eV, found that with increasing oxygen deficiency, the electrons left behind when oxygen is removed localize not only on the Ce 4f orbitals, but also in the vacant oxygen site itself, leading to ferromagnetic superexchange and spin polarization in the case of heavily defective material (up to 25% VO)[231]. However, a paper was published soon afterwards by Keating et al. [232] hotly contesting that result, finding that VO concentrations of up to 12.5% do not cause localization in the vacancy site, and thus cannot be responsible for enhanced ferromagnetism on any (111), (110) or (100) ceria surfaces; These authors use GGA + U with a smaller U 4f value of 5 eV, and consider that the value used in [231] was too large, as U values >6 eV have been shown to give a a delocalized solution similar to that seen for small values of U, which leads to the appearance of an erroneous density of states in the vacancy position. Furthermore, they note further that the absence of electron density in the vacancy position is no surprise, as ceria is known not to behave as a strongly ionic oxide where F+-centres accompany vacancy formation [232]. Instead, the localization of the remaining electrons on the neighbouring Ce sites to form Ce3+ is well characterized elsewhere [233], and small polaron formation is widely accepted [32]. An F+-centre coupling mechanisms due to oxygen vacancy formation is therefore questionable as the reason for reported enhanced ferromagnetic behaviour in undoped CeO2 samples. The authors then reported that intrinsic ferromagnetism cannot be accounted for by defects in nanosized CeO2 from further GGA+U calculations [234]. Nevertheless, a later GGA + U calculation persisted in using U = 7 eV to calculate moments of 1.21 µB for a single VO, and 1.97 µB for a VO pair [119]. Fernandes et al., who prepared the strongly ferromagnetic CeO2 films by electrodeposition, both undoped [146–150] and Co doped [154,212], consider that oxygen vacancies contribute significantly to the magnetism of their films [146]

(assuming U 4f = 5 eV) and they relate the strong anisotropy of the magnetism to the orientation of VO–VO pairs [149]; divacancies located along the (110) directions gave no net moment, but VO–VO pairs along the (100) and (111) directions showed moments of 0.04 µB/VO and 2.67 µB/VO, respectively [149]. Another calculation with U 4f = 5 eV reports 0.26 µB per oxygen vacancy and 0.73 µB per oxygen divacancy [117]. It is evident from this summary that the question of whether oxygen vacancies mediate ferromagnetism in undoped ceria is still keenly debated among theorists who use DFT calculations, and it would appear that the contradictory results are due at least in part to the sensitivity of the band structure to the particular DFT method used, the functional and particularly the choice of U in these ‘first principles’ calculations. We emphasize that RTM requires not only unpaired spin moments m, but a strong exchange interaction J to couple them together. Without the exchange, localized spin moments will simply exhibit Curie-law susceptibility, which is not usually observed. Extended line defects such as ⟨111⟩ strings of oxygen vacancies that could give rise to a nearly-free-electron-like impurity band have not been considered in supercell calculations. Defect moment calculations. Hamiltonian-based methods have also been used to analyse the magnetic state of 4f electrons arising from an oxygen vacancy, with an appropriate choice of U [120]. Isolated vacancies on {100} surfaces, and vacancies in the bulk lead to the formation of nonmagnetic singlets, whereas there is a net moment associated with vacancies on {110} or {111} surfaces, or with vacancy pairs on {111} surfaces [120]. The latter are thought to lead to Nagaoka ferromagnetism [251], namely spontaneous spin splitting of a nearly half-filled impurity band with a large Hubbard U, with Tc ∼ 100 K. These methods can predict the appearance of defect-related moments, but can only offer rough estimates of the Curie temperatures.

Cerium vacancies: First suggestions that a cation vacancy in a dioxide could produce a high-spin defect from 2p holes on neighbouring oxygen ions was by Pemmaraju and Sanvito for the case of HfO2 [252]. Elfimov et al. [253] had already pointed out in 2002 that the two oxygen holes created by a Ca vacancy in CaO form a triplet state due to strong Coulomb correlations in the 2p shell (U 2p = 5–7 eV), and they suggested that half-metallic ferromagnetism was possible at defect concentrations as low as 3%. Calculations for undoped CeO2 by Fernandes et al. [146] indicated that both Ce vacancies (VCE) and O vacancies (VO) are consistent with a ferromagnetic state for a 3%–25% VOconcentration, with calculated maximum moments of 4 µB/Ce vacancy (associated with O 2p holes) and 2 µB/O vacancy (associated with Ce 4f holes). The authors use U 4f = 5 eV within the LDA + U or GGA + U schemes, which should not result in a delocalized solution. A similar calculation using GGA+U with U4f = 5 eV also finds that Ce vacancies can induce a magnetic moment in undoped ceria that arises mainly from a 2p hole on a nearest-neighbour O atom with a moment of 1 µB/O [236]. Yet another LDA calculation indicates that oxygen interstitials, oxygen antistites and cerium vacancies can induce magnetism in CeO2, while cerium interstitials, cerium antisites and oxygen vacancies cannot [235]. Radiation damage: Swift heavy ions tend to introduce high-energy defects such as antisites and interstitials. Calculations using the GGA + U 4f method (U 4f = 5.5 eV) [254] by some of the authors of the experimental irradiation paper on sintered 3+ pellets exposed to 200 MeV swift heavy Xe ions [69] indicate that for defective CeO2, Ce ions originate not only from the oxygen vacancies but also from oxygen vacancy — interstitial Frenkel pairs; hence reduction is not the only means of 3+ producing Ce ions but displacement of oxygen from its sublattice position to an interstitial region IO can have the same effect. Furthermore, an interstitial oxygen ion expelled from its lattice position and an adjacent oxygen lattice ion can form 2− a dimer, calculated to possess a moment of 1.8 µB [254], that may behave as an O2 peroxide molecule, a bonded state that 2− can also produce excess electrons and trivalent cerium cations in cerium dioxide. Peroxide ions, O2 , may also be more stable surface defects than oxygen vacancies on oxygen-rich (100) and (110) surfaces of CeO2, especially when doped with La3+ [238]. 3d doping: One of the earlier DFT calculations, on Co-doped CeO2, attributes the rather strong ferromagnetism observed in this system to the combined contributions of spin polarized Co, Ce, and O ions as well as oxygen vacancies in a cell where the concentrations of both Co and VO are 12.5% [210]; the magnitudes of the moments are 2.68 µB for Co d electrons, 1.48 µB for Ce and 0.17 µB for spin polarized O. Similar findings for Co doped ceria are reported in a later paper, where the U4f is fixed at 5.3 eV, and it is proposed that VO defects may promote strong ferromagnetic exchange coupling between nearest- + neighbouring Co ions, via electrons trapped in VO (F -centre mediated exchange) [241]. Besides these two reports which find oxygen-vacancy-mediated magnetism in Co-doped ceria, but not in undoped ceria, another calculation using GGA calculates that Co polarizes the neighbouring Ce and O atoms with a maximum moment of ∼4 µB/supercell or 2.82 µB/Co for 6.25% Co doping and a 6.25% VOconcentration [156]; like many others, they find that there is no ferromagnetism in pure CeO2 due to oxygen vacancies, but in Co-doped ceria, the oxygen vacancies enhance the ferromagnetic coupling between the spins of Ce3+ ions, as well as those of the 3d magnetic impurities. For the ferromagnetic ground state, the F+-centre exchange mechanism involving a spin-polarized electron trapped at an oxygen vacancy is again suggested. A subsequent calculation for the same material reports a transition from antiferromagnetic to ferromagnetic coupling as the VO concentration increases, with maximum calculated moments of 5 µB per (2 × 2 × 2) supercell with 2 VO and both 6.25 and 12.5% Co doping, corresponding to ∼2.5 µB/Co and ∼0.95 µB/Ce [242]. The authors note that the calculated magnetic moments per cell depend on the degree of reduction, which could explain the wide spread of magnetization values measured by experiment. In the case of Co-doped ceria at least, there does seems to be a consensus that oxygen vacancies do mediate the magnetism.

Turning to iron dopants, a GGA+U calculation (U 4f = 5.3 eV) for Fe doped ceria predicts the emergence of ferromagnetism with or without oxygen vacancies, attributable to an F+-centre or double exchange mechanism, respectively [240]; a large calculated moment of ∼4.0 µB/Fe dopant is almost entirely associated directly with the Fe ion, with or without VO and for both 6.25% and 12.5% Fe doping levels. The result of this calculation is different to those just mentioned for Co-doped ceria, [156,210,241,242] where oxygen vacancies are thought to mediate the ferromagnetism. Finally in a calculation for

12.5% Ni doped CeO2 using GGA+U with U4f = 5.3 eV, a total moment of ∼2 µB is calculated [243], and similar to the calculation for Fe doping [240], the moment is not associated with the oxygen vacancy, but rather with the 3d dopant. Nonmagnetic doping: Calculations have been also performed for ceria doped with non-ferromagnetic elements. Using the LDA + U method (U 4f = 5.3 eV), for carbon doping, a moment of 2 µB/supercell has been observed for one carbon atom/supercell, equivalent to 0.65 µB/C [244] (the supercell contains four unit cells in this case). The magnetism is attributed to hole-mediated long-range magnetic coupling (double exchange) between local magnetic moments attributed to the collective effects of the p–p, p–d, and p–f hybridization between C and neighbouring O or Ce atoms. In addition, the authors calculate that an oxygen vacancy results in the disappearance of the magnetism in C-doped CeO2, since the two electrons left behind by removing an oxygen atom compensate the two holes provided by the C dopant, eliminating the magnetism as hole-doping is purported to stabilize the ferromagnetic ground state. For nitrogen-doped ceria, a half-metallic ground state with ∼1 µB/N impurity is calculated (0.4 µB associated directly with the N atom itself, ∼0.25 µB due to next-nearest neighbouring O atoms) using either GGA or LDA, both with and without U, where U 4f = 5.3 eV, for N doping levels of either 3% or 6% [245]. The ferromagnetism is attributed to a hole-mediated long-range exchange mechanism similar to that for carbon doped ceria [244]. A GGA calculation for Cu-doped ceria yields a moment of 1 µB per CuCe-VO complex (or 0.5 µB/Cu), where U = 8 eV is chosen [246]; however this result should be treated with caution in view of the large U value chosen, as flagged by Keating et al. [232]. It is proposed that the defect complex formed by substitution of Cu for Ce (CuCe) and a nearest neighbour oxygen

Fig. 18. Magnetization of a superparamagnet is a function of H/T. (a) Data for 2 nm superparamagnetic iron nanoparticles suspended in mercury, measured at 77 K and 200 K scale with H/T [260]. (b) Data for 4 nm CeO2 nanoparticles are temperature independent, and do not scale with H/T. They cannot be superparamagnetic.

vacancy (VO) has a low formation energy, and that strong ferromagnetic coupling between the defect complexes may be attributed to a magnetic coupling chain formed by the strong p–d interactions between the Cu and O atoms. For DFT-LSDA calculations (again with U = 8 eV) applied to Sn doped CeO2 (3.125 at.%) [151], Sn doping is predicted to induce oxygen vacancy formation which can create magnetic order, but the magnitude of the moment is not stated. Substitution of Ce by a tripositive rare earth ion has been examined for La [238,239,255] and other members of the rare- earth series [239,256]. These dopants contribute to both ionic and electronic conductivity [257] and they may promote reactivity by increasing the tendency towards oxygen vacancy formation at the surface. DFT calculations suggest the formation of oxygen holes [255] or peroxide ions [238] at the surface under oxygen-rich conditions, but oxygen vacancy formation under oxygen-poor conditions. The defect structure is primarily dependent on the cation’s ionic radius. For Sc and the small, heavy rare earths, the charge-compensating vacancy tends to lie beside the dopant, but for La, Pr and the other light rare earths, it is pushed away to a next-neighbour position. Ce4+ is less likely to be reduced to Ce3+ in the presence of these dopants, and ionic rather than polaronic conductivity is enhanced. Finally it is noted that the magnitudes of the magnetic moments per dopant atom which are calculated for doped CeO2 in small supercells, typically 1–5 µB/dopant, correspond to many of the moments experimentally measured for several at.% doped films listed in Table 6; however, some of the high moments experimentally measured for electrodeposited films exceed these values, suggesting that the magnetism there may not be due to the dopant atom alone. A local magnetization of order 300 kAm−1 could be accounted for by dopants, but the analysis in Section 4.1 indicates that the dopants must be quite inhomogeneously distributed. For the majority of nanoparticles it is evident that the moments per dopant atom are generally much lower than those for films, typically ≪ 1 µB per dopant, and are generally much less than any of the values obtained by calculation.

4.3. Models

Next we consider mesoscopic physical models that can shed some light on mesoscopic aspects of the CeO2 problem.

4.3.1. Superparamagnetism The anhysteretic room-temperature magnetization curves shown in Figs. 4–6,8,9, 11(a) and 12–14 resemble those of a superparamagnet above its blocking temperature Tb, but the resemblance is misleading, because temperature dependence of a superparamagnet is entirely different to that observed. A superparamagnet is composed of weakly-interacting ferromagnetic nanoparticles each with moment mp, which undergo spontaneous thermal fluctuations between Tb and the Curie temperature TC. The superparamagnet exhibits no hysteresis, but its magnetization follows a Langevin function that scales with H/T, so long as the initial susceptibility does not exceed the demagnetizing limit 1/N. A classical example is illustrated in Fig. 18(a). M (H) curves for iron nanoparticles measured at different temperatures above Tb look quite different, but when plotted as a function of H/T, they superpose. For CeO2 nanoparticles [96], the magnetization curves at different temperatures superpose (Fig. 9) and, as seen in Fig. 18(b), so they cannot possibly scale with H/T. Furthermore, they show no sign of blocking down to temperatures as low as 2 K. The magnetic response of CeO2, and other d-zero systems such as SrTiO3 micropowder [258] or nanoporous amorphous alumina [259] is essentially athermal. The d0 magnets are definitely not superparamagnetic.

Fig. 19. Examples of possible defect-rich sites with which d0 magnetism may be associated, after [267].

4.3.2. Heisenberg superexchange High-temperature ferromagnetism based on ferromagnetic superexchange of Ce3+ ions via O2− anions would be a tall order. Exchange coupling in oxides is usually antiferromagnetic (Fig. 1) and Curie or Néel temperatures scale with the square of the local moment. The Néel temperature of Gd2O3 is 17 K [261]. That of Ce2O3 is smaller [22].

4.3.3. Zener double exchange A strong ferromagnetic interaction arises in 3d mixed-valence oxides due to hopping of 3d electrons from one cation site to the next with spin memory. The textbook examples are the mixed-valance manganites, which exhibit Curie temperatures up to 400 K [262]. Oxygen deficient ceria contains cerium in 3+ and 4+ valence states. Ce–Ce distances (383 pm) are comparable to the Mn–Mn distances in perovskites, but the smaller radius of the 4f shell compared to the 3d shell makes the direct overlap of 4f wavefunctions negligible, so the hopping should involve an intervening oxygen vacancy site (F+-centre mechanism). Another plausible idea is hopping of 2p holes from one anion site to the next with spin memory. We have seen that there is some evidence for cation vacancies and oxygen holes or peroxide ion formation in CeO2, where 2p–2p overlap is sufficient to allow the holes at the top of the oxygen 2p band to hop around. Nonetheless, it has not been established that this mechanism can deliver the high-temperature ferromagnetism we seek. Although the oxygen molecule itself has a triplet ground state, superoxides such as CsO2 where the magnetism is associated with peroxide ions are antiferromagnets with Néel temperatures of order 10 K [263]. There is evidence of short-range ferromagnetic order in nonstoichiometric RbO2, but only up to 50 K [264].

4.3.4. Stoner ferromagnetism The alternative to the strongly-correlated m:J paradigm is Stoner’s model of spontaneous spin-splitting of uncorrelated electrons in narrow bands — exchange without correlation. In the case of CeO2, the bands would have to be associated with the defects; either an impurity band associated with mid-gap states due to electrons trapped in oxygen vacancies (F+-centres), or 4f electrons associated with Ce3+. The former seems more likely, because hydrogenic orbitals of electrons trapped in the oxygen vacancies will gave strong overlap and weak correlations on account of the large dielectric constant of ceria, whereas the 4f electrons occupy small orbitals and form polarons that will be easily localized by disorder in the lattice. This model of a half-metallic impurity band formed from hydrogenic orbitals has been proposed for doped CaB6 [265]. Furthermore, the 4f and hydrogenic electron reservoirs may communicate, and electrons could be transferred from Ce to the oxygen vacancies or vice versa in order to gain energy by satisfying the Stoner criterion. This is the model of charge- transfer ferromagnetism [266,267], proposed originally for mixed-valence dilute magnetic oxides. The Curie temperature in the Stoner model is determined by the bandwidth, and it can therefore be very high. Magnetization can be quite variable, as it depends on the band occupancy. Micromagnetism will apply in the same way as for any other form of ferromagnetic order, but cubic crystal field effects on the 4f electrons would impede the approach to saturation, and underestimate the ferromagnetic fraction inferred from H0 in (1). The model does not account for the aggregation effect, Fig. 11(a). What is clear experimentally is that there are few unpaired or weakly-coupled paramagnetic electron spins present in the system, either associated with electrons trapped in oxygen vacancies or with Ce3+ ions. If present, they would give rise to a Curie–Weiss upturn in susceptibility, and the magnetization would saturate at a higher value in large fields at low temperature, which is not observed. In the models we have been discussing, practically all unpaired electron spins are fully invested in the high-temperature ferromagnetic phase, although it may only occupy a tiny fraction of the sample volume. Some possible schemes for defect segregation are illustrated in Fig. 19. The fact is that there are very few unpaired electrons or inactive Ce3+ ions outside the ferromagnetic fraction, which is a significant constraint both on the defects supposedly responsible for the magnetism, and on their spatial distribution in the ceria samples. They have to be perfectly segregated.

4.3.5. Modulated ferromagnetism The analysis that led to the conclusion that only a small fraction of the volume of the nanoparticles or thin films could be ferromagnetic was based on the approach to saturation. If the approach to saturation is not governed by internal demagnetizing fields, but by other factors such as magnetocrystalline anisotropy or competing exchange interactions producing a long-wavelength-modulated magnetic structure such as a chiral (spiral, helical) structure or Overhauser’s spin

Please cite this article in press as: K. Ackland, J.M.D. Coey, Room temperature magnetism in CeO2—A review, Physics Reports (2018), https://doi.org/10.1016/j.physrep.2018.04.002. 30 K. Ackland, J.M.D. Coey / Physics Reports ( ) – density wave [268], the magnetization process would then correspond to unwinding the spin texture in an applied magnetic field of order 1 T, and the magnetic fraction deduced from (1) would be an underestimate. DFT calculations for small blocks of unit cells cannot capture the effects; the thermal stability of these electronic spin structures induced by exchange and spin– orbit interactions among single electrons with partial 4f character is uncertain; the possibility of a long-period modulated spin texture having a very high magnetic ordering temperature but a very small saturation magnetization might account for anhysteretic saturating magnetization curves. The possibility merits investigation, but it is still difficult to see how this could be the collective magnetic ground state for a system of weakly-coupled nanoparticles. Why would a weakly-polarized spin density wave propagate coherently in such a sample? A serious difficulty with all the exchanged-based models for spin magnetism in nanoparticulate systems is that there is little evidence of the finely-divided nature of the samples to be found in the magnetic data. It may be argued that only in a −1 small fraction of the volume are conditions just right for the appearance of a local magnetization Mloc = H0/N ≈ 300 kAm , but what of the remainder? If the ferromagnetism originates in oxygen vacancies at the surfaces of the nanoparticles, and conditions are favourable in a few spots for interparticulate coupling to form extended regions, what becomes of the disordered spins in particles that are left out? We see no sign of decoupled particle moments m of order VpMloc ≈ −20 2 10 Am ≈ 1000 µB. Such moments would be easily saturated at 4 K, and they should contribute a paramagnetic 2 −3 −1 susceptibility of µ0 nm /3 kT ≈ 3 × 10 at 300 K. The magnetization in a field of 1 MAm should be 60 times greater at 4 K than at 300 K. In fact the increase is only about a factor of two [96]. It seems that the appearance of a moment and the appearance of a ferromagnetic-like state involving all the moments are inextricably linked.

4.3.6. Giant orbital paramagnetism We find that almost any explanation of spontaneous ferromagnetic order of electron spins in CeO2 runs into formidable obstacles, especially in nanoparticles. The last, and most radical suggestion to explain the athermal magnetic response in CeO2 is to abandon that track altogether, and admit that our saturation magnetization curves may have nothing to do with collective spontaneous ferromagnetism. The key experimental observation here is that the magnetic response can be reversibly disrupted by dispersing nanopowder on a mesoscopic scale in a nonmagnetic matrix. This is not anticipated on the basis of any of the models of spin-based ferromagnetism, other than superferromagnetism [269] – the stabilization of superparamagnetic fluctuations by interparticle dipole–dipole interactions such as are found, for example, in magnetotactic bacteria, – but the magnetic CeO2 nanoparticles are too small and the dipolar interactions are several orders of magnitude too weak [96]. The idea is that ceria is not ferromagnetic at all. There is no collective, high-temperature spin ordering, but instead the oxide exhibits an unusual type of saturating, temperature-independent paramagnetism. The moment is entirely field- induced, not field-aligned, and it originates from coherent orbital electronic currents circulating in mesoscopic domains. This picture has previously been evoked in the context of Au thin films and nanoparticles [270,271] and ZnO [272–274] nanoparticles. A theory of these coherent electron states has been developed, and they are found to be potentially stable in quasi-two-dimensional systems with a large surface-to-volume ratio [275]. The model is based on the formation of coherent states of large numbers of electrons (assumed to be spinless, for the sake of simplicity) in response to zero-point fluctuations of the vacuum electromagnetic field. The doping that is essential for the effect (Fig. 10) is electronic, not magnetic, and sparse electrical rather than magnetic continuity between nanoparticles is all that is required. The magnetic aspect of the theory has been calculated, in the context of CeO2 [96], where it is given in the supplemental information to that paper. According to the magnetic version of the theory, magnetization curves should be fitted to the theoretical expression

2 1/2 M = Ms[x/(1 + x ) ] (2) where x = CB. The function in square brackets resembles the tanh x function often used to represent magnetization curves. −1 −1 In CeO2, fitting yields values of C of 9.4 ± 0.7 T for samples with Ms ≈ 60 Am . The length scale in the problem is set by a characteristic excitation frequency ω of CeO2 which is resonant with the zero-point vacuum fluctuations. The corresponding wavelength is λ = 2πc/ω, and the volume of the coherent domain is about (π/6) λ3. The characteristic wavelength is given by

1/4 λ = [(C/Ms)(6hcf¯ c)] (3) where fc is the fraction of the sample volume that is electronically coherent. Identifying the enhanced optical absorption at λ = 300 nm (Fig. 11(d)) with the characteristic excitation frequency gives fc = 28%. This corresponds to a moment 6 −20 3 of 6.6 × 10 µB per coherent domain, of volume 1.4 × 10 m [96]. Dispersion of the nanoparticles on a scale of 100 nm (Fig. 11(c)) then disrupts the coherent electronic domains, and destroys their giant orbital paramagnetic response to the applied field, providing an explanation of the remarkable behaviour illustrated in Fig. 11. There is no temperature- dependence and no net exchange of energy with the vacuum at the characteristic frequency, but the energy levels of the system are perturbed by the zero-point fluctuations, and by an applied magnetic field. The theory in its present form treats the electrons as spinless fermions [96], but it can be developed. A schematic image of the field-induced orbital paramagnetism in a nanoparticle cluster is shown in Fig. 20. The development of the orbital moment in response to the applied field just depends on the possibility of establishing a conducting path through a sample on the appropriate lengthscale λ. This avoids many of the objections we have raised to

Fig. 20. Schematic of collective paramagnetism due to the orbital moment of a coherent domain (a large clump of nanoparticles) >100 nm size. r is the radius of a nanoparticle, λ is the coherence (wave)length, which is in effect the clump size. If the clump is broken up, so also are the coherent domains, and the magnetism disappears because the wavelength of the electromagnetic excitation can no longer be accommodated in the nanoparticle clump.

the spin-based magnetic models 2.1–2.5. It is easier to envisage a charge current percolating around a loop of surface oxygen vacancies, than is to envisage stable high-temperature collective spin ferromagnetism in such a one-dimensional geometry. The loops in thin films will tend to lie in the plane of the film, leading to a highly-anisotropic, perpendicular orbital moment, but in nanoparticle clusters the moments will be isotropic. The conducting paths are likely to be based on oxygen vacancies, but the presence of a small amount of rare earth or other trivalent ions seems to be necessary to ensure conductivity. 0 The model has been applied to other d systems, including SrTiO3 surfaces [258] and nanoporous alumina membranes [259]. It is worth noting that there has been a recent increase in the number of examples in molecular and materials science where hybrid light–matter states appear that depend only on the zero-point energy [276]. CeO2 is the first example where magnetic effects of these interactions have been identified.

5. Conclusions

Our overview of the copious literature on magnetism in defective CeO2, covering both undoped, and chemically-doped material has established that the magnetic signals cannot generally be attributed to faulty experimental procedure or extraneous ferromagnetic elements and phases. The magnetization is generally enhanced in thin films and nanostructures compared to the bulk, and it can be induced by doping with nonmagnetic elements. No 3d element needs to be involved. This is in contrast to claims of high temperature ferromagnetism in nonmagnetic oxides with dilute 3d dopants [20], that are based almost entirely on measurements on this films with moments <10−8 Am2, some of which have not survived 0 critical scrutiny [13]. The claims of d magnetism in CeO2 are more secure, thanks to the somewhat larger magnetic signals, −8 2 generally >10 Am , and the diversity of samples that exhibit the effect. The five orders of magnitude span of values for Ms reported by various groups is impressive. There is an urgent need to confirm the most extreme results on electrodeposited thin films by Fernandes et al. [146–150,154,212], who report a saturation magnetization that is highly anisotropic, with values comparable to that of nickel or cobalt. The next steps should take us from measuring the magnetic properties of yet more CeO2 samples, to designing experiments that can provide answers to specific questions (some of them quite obvious), such as: Is there spontaneous ferromagnetism? And if so, are there domains? What is the Curie point? Is the magnetism principally of spin or orbital character? A strongly-enhanced moment in thin films when the field is applied perpendicular to the plane would be strong evidence for the mesoscopic orbital moments envisaged in the theory of giant orbital paramagnetism. How do magnetic interactions propagate between nanoparticles? Does the magnetism persist in artificially-patterned thin films? Where exactly are the moments located? (samples sufficiently large for neutron diffraction can be obtained, with some labour; films can be studied by advanced X-ray and electron scattering methods [19]. Is it possible to modulate the magnetism with light? Is there really a continuity from the weak magnetization found in nanoparticles to the strong magnetism reported in certain electrodeposited films? Is it just the same d-zero phenomenon occupying an increasing fraction of the sample volume? The unparallelled sensitivity of SQUID magnetometry is a precious asset that should continue to be extensively deployed, in full awareness of the possible associated pitfalls and artefacts [10–15,19]. Hysteresis and time-dependence of the magnetism need to be carefully examined. Any magnetic study should include data taken as a function of temperature.

Fig. 21. Plot of Ms versus Mloc for over 200 samples of CeO2. The grey band marks the uniformly-magnetized concentrated limit.

There are fairly strong indications that the magnetism, like the catalytic properties of CeO2, originates at nanoparticle surfaces, but nothing has been done yet to relate the two properties, trying to correlate magnetism with catalytic activity and investigating magnetic field effects on catalysis. There are opportunities to investigate the magnetism and photocatalytic activity of CeO2 films in resonant cavities [276]. Theranostic applications must await the development of nanoparticles with a much larger saturation magnetization. This review has demonstrated how a big-data approach can be applied to a problem in condensed matter physics, beginning to make sense of a situation where at first sight the inconsistencies in the data are daunting. Our analysis of a mass of scattered and apparently contradictory experimental results with error bars less than the separation of the points has signposted an approach to treating these disparate data sets. More than 200 measurements from Fig. 15 are reproduced in Fig. 21 as a plot of Ms versus Mloc. Their ratio is just the magnetically-ordered volume fraction in the sample, assuming that we are dealing with conventional spontaneous ferromagnetic order, an assumption that we have seen raises as many questions as it answers. The problem of identifying magnetic interactions that can couple discrete nanoparticles without a trace of superparamagnetism is a serious hurdle from that point of view.

The idea that CeO2 is not ferromagnetic, but exhibits giant orbital paramagnetism is a fresh approach to an intractable problem. The theory at present is fairly rudimentary, based on a simplified treatment of electrons as spinless fermions [96]. Introducing spin and spin–orbit coupling may extend the stability of the coherent electronic domains, and bring in hysteresis. Despite the emphasis we have placed on the ‘practically anhysteretic’ nature of the phenomenon, especially in the absence of 3d dopants, there may indeed be a little hysteresis in many cases. Precautions are necessary to measure such hysteresis correctly and avoid trapped flux after saturating a small magnetic sample in a high magnetic field produced by a superconducting magnet [13]. In doped systems, hysteresis is usually the sign of segregation of a 3d impurity phase. Focus should be on the role of nonmagnetic dopants such as La or Y, and the role that small amounts, ∼1%, of these elements play in modifying the surface electronic structure of the CeO2 nanoparticles, and promoting surface conductivity. Whether the correct explanation is giant orbital paramagnetism, or a half-metallic impurity band related to electrons trapped in oxygen vacancies, or something else again, it seems certain that CeO2 is pointing us to something new in magnetism, beyond the m:J paradigm. Things will eventually become clear and then hindsight will allow the story of this review to be condensed onto a page. In the meantime, we must proceed thoughtfully, with care, imagination and awareness of what we do not understand.

Acknowledgements

The authors are indebted to M. Venkatesan for performing a multitude of magnetization measurements and for general advice. The authors would also like to acknowledge Lorena M.A. Monzon for many early electrodeposition experiments, while the subsequent contributions of Amir S. Esmaeily and Asra S. Razavian to the electrodeposition are also kindly appreciated. We thank Siddhartha Sen and Plamen Stamenov for numerous helpful theoretical discussions. This work was supported by Science Foundation Ireland (SFI) as part of the NISE project, contract 10/IN1.I3006.

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Please cite this article in press as: K. Ackland, J.M.D. Coey, Room temperature magnetism in CeO2—A review, Physics Reports (2018), https://doi.org/10.1016/j.physrep.2018.04.002.