Physics Reports ( ) – Contents lists available at ScienceDirect Physics Reports journal homepage: www.elsevier.com/locate/physrep 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 – Ce3C 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 * Corresponding author. E-mail address: [email protected] (J.M.D. Coey). https://doi.org/10.1016/j.physrep.2018.04.002 0370-1573/' 2018 Elsevier B.V. All rights reserved. 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. 2 K. Ackland, J.M.D. Coey / Physics Reports ( ) – 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, 2C 3C Mn or Fe , for which the spin angular momentum takes its greatest value of 5=2 hN . 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 D 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