materials

Article Magnetic Hysteresis in Nanocomposite Films Consisting of a Ferromagnetic AuCo Alloy and Ultrafine Co Particles

Federico Chinni 1, Federico Spizzo 1, Federico Montoncello 1, Valentina Mattarello 2, Chiara Maurizio 2, Giovanni Mattei 2 and Lucia Del Bianco 1,*

1 Dipartimento di Fisica e Scienze della Terra and CNISM, Università di Ferrara, I-44122 Ferrara, Italy; [email protected] (F.C.); [email protected] (F.S.); [email protected] (F.M.) 2 Dipartimento di Fisica e Astronomia and CNISM, Università di Padova, I-35131 Padova, Italy; [email protected] (V.M.); [email protected] (C.M.); [email protected] (G.M.) * Correspondence: [email protected]; Tel.: +39-0532-974225

Received: 14 June 2017; Accepted: 26 June 2017; Published: 28 June 2017

Abstract: One fundamental requirement in the search for novel magnetic materials is the possibility of predicting and controlling their magnetic anisotropy and hence the overall hysteretic behavior. We have studied the magnetism of Au:Co films (~30 nm thick) with concentration ratios of 2:1, 1:1, and 1:2, grown by magnetron sputtering co-deposition on natively oxidized Si substrates. They consist of a AuCo ferromagnetic alloy in which segregated ultrafine Co particles are dispersed (the fractions of Co in the AuCo alloy and of segregated Co increase with decreasing the Au:Co ratio). We have observed an unexpected hysteretic behavior characterized by in-plane anisotropy and crossed branches in the loops measured along the hard magnetization direction. To elucidate this phenomenon, micromagnetic calculations have been performed for a simplified system composed of two exchange-coupled phases: a AuCo matrix surrounding a Co cluster, which represents an aggregate of particles. The hysteretic features are qualitatively well reproduced provided that the two phases have almost orthogonal anisotropy axes. This requirement can be plausibly fulfilled assuming a dominant magnetoelastic character of the anisotropy in both phases. The achieved conclusions expand the fundamental knowledge on nanocomposite magnetic materials, offering general guidelines for tuning the hysteretic properties of future engineered systems.

Keywords: magnetic hysteresis; magnetic anisotropy; exchange interaction; nanocomposite material; SQUID magnetization measurements; micromagnetic modeling

1. Introduction The dominant issue in the search for innovative magnetic materials is the creation of nanocomposite systems consisting of at least two different magnetic phases. This approach adds some degrees of freedom to single-phase materials and allows them to overcome their intrinsic limits. Some well-known examples are the Fe-rich [1] and the NdFeB-based [2] crystalline alloys composed of two different ferromagnetic phases so intimately mixed at the nanoscale as to be coupled by magnetic exchange interaction, which results in outstanding soft and hard magnetic properties, respectively. For magneto-recording and spintronic applications, magnetic nanocomposite systems are fabricated in the form of films. For instance, the magnetic exchange interaction between a ferromagnetic layer and an antiferromagnetic one is efficiently exploited to tune the anisotropy of the former and, thus, to control the magnetization reversal process, which is a strategic goal in the construction of modern magnetoresistive devices [3–5]. For the same purpose, ferromagnetic soft-hard composites

Materials 2017, 10, 717; doi:10.3390/ma10070717 www.mdpi.com/journal/materials Materials 2017, 10, 717 2 of 16 are among the most investigated systems: the inter-phase exchange coupling allows the hard phase anisotropy to be controlled both in strength and direction and favors a faster magnetization switching as well as a reduction of the switching field [6,7]. In layered materials, the substrate itself can be considered as a main component of the system, able to affect the magnetic behavior of the on-top magnetic film. Properly engineered architectures of substrate plus underlayers are employed to govern the film growth and the microstructure and, hence, the magnetic properties [8]. This is the case of Co-based crystalline films for recording applications, typically consisting of nanograins with a robust ferromagnetic character separated by weakly ferromagnetic boundaries, which modulate the intergrain magnetic interaction [9]. A different scenario is that in which a mechanical stress is produced in the magnetic film due to the bonding with the substrate [10], opening the possibility of exploiting the magnetoelastic coupling to tune the magnetic anisotropy [11–13]. Tailoring the anisotropy is crucial in the field of magnetic sensors where, moreover, flexible substrates are now often employed [14,15]. Indeed, the study of the magnetic behavior of nanocomposite materials does not stop drawing increasing interest because of their intriguing fundamental properties and prospective applications. In this rich context, we have studied the magnetic properties of a set of three typical films made of Au and Co in different concentration ratios, grown by the magnetron sputtering co-deposition technique. By this method, a bimetallic compound of Au and Co, which are immiscible as bulk phases [16], is formed and the samples can be modeled as consisting of a prevalent ferromagnetic AuCo alloy and of segregated ultrafine Co particles, the two phases being well intermixed. It is worth noting that alloys and intermetallic compounds of Au with magnetic 3d elements are fascinating materials of great scientific interest for their magnetic, magneto-optical, magneto-plasmonic, and catalytic properties [17–22]. This article is fully focused on the magnetism of these AuCo samples, which exhibit a peculiar and unexpected hysteretic behavior, showing in-plane anisotropy and loops with crossed branches when measured along the hard magnetization direction. Micromagnetic calculations have been carried out to elucidate such a complex phenomenology. The results indicate that the main features of the hysteresis process can be qualitatively well reproduced assuming the existence of two different exchange-coupled ferromagnetic phases, identified with the AuCo alloy and the embedded Co particles, with almost orthogonal anisotropy axes. We will indicate specific requirements that the magnetic configuration of this composite system must fulfill in order for the described hysteretic behavior to be predicted or intentionally produced also in other nanocomposite magnetic materials.

2. Experimental Methods

2.1. Production and Composition of the AuCo Samples AuCo films have been deposited at room temperature on natively oxidized (100)-silicon substrates by the magnetron sputtering technique, using a custom built apparatus in which the metal targets are tilted at ~30◦ with respect to the axis normal to the sample plane, allowing a simultaneous deposition of the two metals. A rotating sample-holder has been employed, grounded to the deposition chamber, to favor a uniform coverage of the substrate. Argon has been the processing gas (working pressure = 5 × 10−3 mbar) and the deposition rate was ~1.5 Å/s. In this article, we address a set of three typical films, with nominal thickness ~30 nm and Au:Co concentration ratios of 2:1, 1:1, and 1:2, labeled as Au2Co1, Au1Co1, and Au1Co2, respectively; they have been coated in the same deposition batch with a SiO2 cap layer (~80 nm thick), in order to prevent environmental contamination and oxidation. A continuous Co film, with thickness (22 ± 1) nm and SiO2 cap layer, has been also deposited to be used as a reference sample. The film composition has been determined by Rutherford Backscattering Spectrometry (RBS) (Table1). The RBS analysis together with SEM observations in cross-section mode also provided information on their thickness (Table1). Information on the structure and composition of the films Materials 2017, 10, 717 3 of 16 has been mainly acquired by Extended X-ray Absorption Fine Structure (EXAFS) investigation [23,24]. To provide a full description of this analysis is beyond the scope of the present research work. Here, we just summarize the principal conclusions. EXAFS experiments have been performed at both Au L3-edge and Co K-edge at T = 80 K (Italian Beamline BM08 of the European Synchrotron ESRF, Grenoble, France). The typical spectra for the Au1Co2 sample are displayed in Figure1a.

Table 1. Column 1: labels of the samples. Columns 2 and 3: Au and Co content in the films. Column 4: thickness of the films. Columns 5–7: volume fractions of the AuCo alloy, with its composition, and of

segregatedMaterials Co 2017 and, 10 Au, 717 (to convert atomic fractions to volume fractions, elemental atomic3 weightsof 17 and densities have been used). L3-edge and Co K-edge at T = 80 K (Italian Beamline BM08 of the European Synchrotron ESRF, Grenoble, France). The typical spectra for the Au1Co2 sample are displayed in Figure 1a. Composition Thickness Volume Fractions Sample TableAu (at%)1. Column 1: labels Co (at%) of the samples. Columns(nm) 2 and 3: Au Alloyand Co content (vol%) in the films. Co Column (vol%) 4: Au (vol%) thickness of the films. Columns 5–7: volume fractions of the AuCo alloy, with its composition, and of Au2Co1 segregated69 ± 1 Co and Au 31 (to± convert1 atomic fractions 30 ± 2 to volume Au fractions,80Co20 elemental89 ± 7 atomic weights 10 ± and3 1.0 ± 0.8 Au1Co1 densities49 ± have1 been used). 51 ± 1 28 ± 1 Au73Co27 74 ± 10 25 ± 5 1.0 ± 0.8 Au1Co2 33 ± 1Composition 67 ± 1 Thickness 28 ± 1 Au57CoVolume43 64 Fractions± 9 35 ± 5 1.0 ± 0.9 Sample Au (at%) Co (at%) (nm) Alloy (vol%) Co (vol%) Au (vol%) Au2Co1 69 ± 1 31 ± 1 30 ± 2 Au80Co20 89 ± 7 10 ± 3 1.0 ± 0.8 In the spectraAu of1Co all1 three 49 ± 1 films, 51 the± 1 EXAFS 28 ±analysis 1 Au has73Co27 evidenced 74 ± 10 25 a ± Au-Co5 1.0 interatomic ± 0.8 correlation signal unambiguouslyAu1Co2 revealing 33 ± 1 67 the ± 1 formation 28 ± 1 of the Au57 AuCoCo43 64 ± 9 alloy. 35 A± 5 low 1.0first ± 0.9 shell coordination number has beenIn inferred,the spectra comparedof all three films, to bulk the EXAFS Au and analysis Co, andhas evidenced no significant a Au-Co signal,interatomic except for that from the firstcorrelation intermetallic signal atomicunambiguously coordination, revealing hasthe formation been detected. of the AuCo These alloy. results A low are first consistent shell with an amorphous-likecoordination or poorly number nanocrystalline has been inferred, structure. compared Theto bulk AuCo Au and alloy Co, isand the no prevalent significant signal, phase in all of the except for that from the first intermetallic atomic coordination, has been detected. These results are films. However,consistent the EXAFSwith an analysisamorphous-like has alsoor poorly indicated nanocrystalline the presence structure. of segregatedThe AuCo alloy cobalt is the in the form of structurally disorderedprevalent phase particles in all of the (~2 films. nm However, in size) the dispersed EXAFS analysis within has thealso alloyedindicated the AuCo presence matrix, of in general agreement withsegregated what cobalt was inobserved the form of structurally in similar disord samplesered particles [22]. (~2 The nm estimatedin size) dispersed volume within fractionsthe of the alloyed AuCo matrix, in general agreement with what was observed in similar samples [22]. The different phasesestimated inthe volume films fractions are reported of the different in Table phases1. in Both the films the are percentage reported in ofTable Co 1. in Both the the alloy and the fraction of segregatedpercentage of Co Co increasein the alloy with and the decreasing fraction of segregated the Au:Co Co ratio.increase A with very decreasing small amount the Au:Co of segregated Au (~1 vol%)ratio. has A been very small also amount considered of segregated in the Au fit (~1 of thevol%) EXAFS has been spectra also considered of all threein the films.fit of the EXAFS spectra of all three films.

(b)

Figure 1. EXAFS spectra (a) and bright-field TEM image (b) for the Au1Co2 composition. Figure 1. EXAFS spectra (a) and bright-field TEM image (b) for the Au1Co2 composition. Other structural investigation techniques are quite unable to provide more precise information. For instance, in Figure 1b we show a typical in-plane view by transmission electron microscopy in Other structuralbright-field (BF-TEM) investigation for the techniquesAu1Co2 composition are quite (analysis unable performed to provide with a Field more emission precise FEI information. For instance,TECNAI in Figure F20 Super1b we Twin show FEG (S) a typicalTEM). The in-plane BF-TEM contrast view is by quite transmission uniform with some electron black and microscopy in white spots of a few nanometers in size: considering the abovementioned poorly crystalline nature bright-field (BF-TEM) for the Au1Co2 composition (analysis performed with a Field emission FEI of the films evidenced by the EXAFS analysis, the BF-TEM contrast is dominated by mass-contrast TECNAI F20with Super negligible Twin contribution FEG (S) TEM).from diffraction-contrast. The BF-TEM Therefore, contrast we is quitecan qualitatively uniform interpret with somethe black and white spots ofBF-TEM a few image nanometers as arising from in size: a composite considering film, made the byabovementioned some segregated Au-rich poorly nanostructures crystalline nature of the films evidenced(dark spots) by and the some EXAFS Co-rich analysis, nanostructures the BF-TEM(white spots), contrast both embedded is dominated in a AuCo byalloy, mass-contrast which with constitutes the dominant phase. Similar conclusions can be drawn for the other investigated compositions. negligible contribution from diffraction-contrast. Therefore, we can qualitatively interpret the BF-TEM image as arising from a composite film, made by some segregated Au-rich nanostructures (dark spots) Materials 2017, 10, 717 4 of 16 and some Co-rich nanostructures (white spots), both embedded in a AuCo alloy, which constitutes the dominant phase. Similar conclusions can be drawn for the other investigated compositions.

2.2. Magnetic Methods The magnetic properties of the AuCo films have been studied in the 6–300 K temperature range using a superconducting quantum interference device (SQUID) magnetometer (maximum applied field H = 50 kOe). For the SQUID analysis, the sputtered samples have been cleaved according to the crystallographic orientation of the substrate, so as to obtain pieces of about (5 × 5) mm2. The hysteresis loops have been corrected for the diamagnetic contributions of the Si substrate and SiO2 cap layer. The saturation magnetization MS has been determined as the magnetic moment/sample volume. MS of the reference Co film has been also measured at T = 6 K and 300 K. Micromagnetic simulations have been carried out using the object-oriented micromagnetic framework (OOMMF) code from NIST [25]. In the following, to facilitate the comparison, loops measured along orthogonal in-plane directions and simulated loops are shown normalized to MS.

3. Results and Discussion

3.1. Sample Magnetization

Table2 reports the values of M S for the AuCo samples, measured at temperature T = 6 K and 3 300 K in H = 50 kOe. In the reference Co film, at T = 6 K MS = (1250 ± 60) emu/cm and it does not depend appreciably on temperature in the investigated range, within the error; it is lower than the literature value of bulk Co (1446 emu/cm3 at T = 0 K), in general agreement with other results on thin Co films [26]. MS increases with increasing the Co content in the films. One can easily realize that the MS values are higher than the magnetization contributions provided by the Co particles (we have attributed the MS of the reference Co film to the segregated cobalt for this calculation). Hence, in all the samples, the AuCo alloy has a net magnetization, namely is ferromagnetic. Based on the volume fractions in Table1, calculated values of saturation magnetization for the AuCo alloy at T = 6 K are 3 3 3 ~230 emu/cm for sample Au2Co1, ~280 emu/cm for Au1Co1, and ~500 emu/cm for Au1Co2 (the relative error associated to these values ranges between 20% and 35%).

Table 2. Column 1: labels of the samples. Column 2: saturation magnetization (MS) measured at temperature T = 6 K in H = 50 kOe. Column 3: MS at T = 300 K. The main error source is the uncertainty of the sample thickness.

3 3 Sample MS at T = 6 K (emu/cm )MS at T = 300 K (emu/cm )

Au2Co1 325 ± 22 232 ± 15 Au1Co1 523 ± 20 480 ± 18 Au1Co2 755 ± 28 733 ± 27

3.2. Measured Hysteretic Properties

First, let us consider the sample Au1Co2. Figure2a shows the loops measured at T = 20 K along two in-plane orthogonal directions corresponding to the sides of the sample. Along one direction, the loop appears highly squared, with the ratio between the remanent magnetization and saturation magnetization Mr/MS ~ 0.97; the loop measured in the orthogonal direction has a lozenge shape with a smaller squareness ratio (Mr/MS ~ 0.41) and shows a very peculiar feature, namely the crossing of the two branches (Figure2a, inset). Hence, the magnetic behavior is clearly anisotropic and the direction corresponding to the high-remanence loop is a preferential magnetization axis, that we conventionally indicate as the easy axis; accordingly, the orthogonal direction is indicated as the hard axis. The same hysteretic behavior is observed at higher temperature, up to 300 K (the loops for Materials 2017, 10, 717 5 of 16

T = 100 K are displayed in Figure2b). The curves of H C and Mr/MS vs. T, measured along the easy and hardMaterials axes, 2017 are, 10 shown, 717 in Figure2c,d. 5 of 17

Materials 2017, 10, 717 5 of 17

Figure 2. In-plane hysteresis loops measured on sample Au1Co2 at T = 20 K (a) and T = 100 K (b), along Figure 2.twoIn-plane orthogonal hysteresis directions loops indicated measured as easy on(triangl samplees) and Au hard1Co2 (circles).at T =20 The K curves (a) and are T normalized = 100 K (b ), along

two orthogonalto the saturation directions magnetization indicated M ass. The easy inset (triangles) of frame (a) and is an hard enla (circles).rged view The of the curves hard axis are loop, normalized to the saturationFigurehighlighting 2. In-plane magnetization the crossing hysteresis of loopsth Me twos. measured The branches. inset on ofCoercivity sample frame Au (a)H1Coc ( isc2 )at anand T = enlarged squareness20 K (a) and view ratio T = 100 ofMr /M theK (Sb (), hardd )along vs. axisT; loop, twothe valuesorthogonal measured directions along indicated the easy andas easy hard (triangl axes ares)e displayed and hard (in (circles). some cases, The curves the error are bar normalized is smaller highlighting the crossing of the two branches. Coercivity Hc (c) and squareness ratio Mr/MS (d) vs. T; to the saturation magnetization Ms. The inset of frame (a) is an enlarged view of the hard axis loop, the valuesor comparable measured to along the symbol the easy size; and solid hard lines axes are guides are displayed for the eye). (in some cases, the error bar is smaller highlighting the crossing of the two branches. Coercivity Hc (c) and squareness ratio Mr/MS (d) vs. T; or comparable to the symbol size; solid lines are guides for the eye). theSample values Au measured1Co1 exhibits along the a easyvery and similar hard axesmagnetic are displayed behavi (inor. someTypical cases, hysteresis the error barloops, is smaller measured alongor comparablethe orthogonal to the directions, symbol size; are solid di linessplayed are guides in Figure for the 3a eye). (T = 100 K); HC and Mr/MS vs. T are Samplereported Au in1Co Figure1 exhibits 3b,c. aIn verythis similarsample we magnetic can also behavior. distinguish Typical an easy hysteresis magnetization loops, axis, measured correspondingSample Au to1Co the1 exhibits direction a veryalong similar which magnetic the high-remanence behavior. Typical loops arehysteresis measured, loops, and measured the loops along the orthogonal directions, are displayed in Figure3a (T = 100 K); H C and Mr/MS vs. T alongmeasured the orthogonal along the hard directions, axis present are di crossedsplayed branches. in Figure 3a (T = 100 K); HC and Mr/MS vs. T are are reportedreported in in Figure Figure3 b,c.3b,c. In this sample sample we we can can also also distinguish distinguish an easy an easymagnetization magnetization axis, axis, correspondingcorresponding to the to directionthe direction along along which which the high-remanence high-remanence loops loops are measured, are measured, and the and loops the loops measuredmeasured along along the hardthe hard axis axis present present crossed crossed branches.

Figure 3. (a) In-plane hysteresis loops measured on sample Au1Co1 along the easy and hard

orthogonal axes at T = 100 K (normalized to the saturation magnetization Ms), Coercivity Hc; and

(b) squareness ratio Mr/MS; (c) vs. T, along the easy and hard axes. Figure 3. (a) In-plane hysteresis loops measured on sample Au1Co1 along the easy and hard Figure 3. (a) In-plane hysteresis loops measured on sample Au1Co1 along the easy and hard orthogonal orthogonal axes at T = 100 K (normalized to the saturation magnetization Ms), Coercivity Hc; and axes at T = 100 K (normalized to the saturation magnetization M ), Coercivity H ; and (b) squareness (b) squareness ratio Mr/MS; (c) vs. T, along the easy and hard axes. s c ratio Mr/MS;(c) vs. T, along the easy and hard axes.

Materials 2017, 10, 717 6 of 16

◦ ◦ As for sample Au2Co1, the loops measured at 0 and 90 at T = 6 K are shown in Figure4a. In this case, the film appears isotropic in the plane, but it turns to anisotropic with rising temperature. In fact, at T = 100 K, hysteretic properties similar to those found in Au1Co2 and Au1Co1, even if less pronounced, are observed (Figure4b), which persist at higher temperature. H C and Mr vs. T are Materialsshown 2017 in Figure, 10, 7174 c,d. At the lowest temperature, H C is higher than in the other investigated samples6 of 17 and it strongly decreases with increasing T especially up to ~100 K (there is no substantial difference As for sample Au2Co1, the loops measured at 0° and 90° at T = 6 K are shown in Figure 4a. In this in HC along the easy and hard magnetization directions); Mr exhibits a similar decreasing trend (the case,values the measured film appears along isotropic the easy in axis the are plane, obviously but it larger turns than to anisotropic those measured with alongrising thetemperature. hard axis). In fact, at T = 100 K, hysteretic properties similar to those found in Au1Co2 and Au1Co1, even if less Hence, the magnetic behavior of sample Au2Co1 is somewhat different compared to the other films pronounced,and, in this respect, are observed a remarkable (Figure difference 4b), which is also persist a clear at non-saturationhigher temperature. tendency HC ofand the M loops,r vs. whichT are shown in Figure 4c,d. At the lowest temperature, HC is higher than in the other investigated samples becomes more pronounced with increasing temperature (hence, for this sample, the values of MS andin Table it strongly2, taken decreases as those with measured increasing in H T = especially 50 kOe, may up to be ~100 slightly K (there underestimated; is no substantial however, difference the insaturation HC along magnetization the easy and hard values magnetization will lie within directions); the indicated Mr errorexhibits bar, a reasonably).similar decreasing This effect trend is (the well valuesvisible measured in Figure5 aalong showing the easy the firstaxis quadrant are obviously of the larger loop at than T = thos 300 Ke measured (at high field, along the the trend hard of axis). M vs. Hence,H does the not magnetic visibly depend behavior on theof sample measurement Au2Co1 direction). is somewhat It should different also compared be noted thatto the a reductionother films of and, in this respect, a remarkable difference is also a clear non-saturation tendency of the loops, which MS of ~30% is experienced with increasing the temperature from 6 K to 300 K, whereas it is not larger becomesthan 8% inmore the pronounced other samples with (Table increasing2). temperature (hence, for this sample, the values of MS in TableIn 2, thistaken class as of those samples, measured the magnetic in H = exchange 50 kOe, couplingmay be slightly of the Co underestimated; particles with the however, surrounding the saturationmatrix is expected magnetization to result values in an will increase lie within of their the effective indicated magnetic error bar, size, reasonably). with respect This to theeffect structural is well visiblesize. Moreover, in Figure 5a since showing the fraction the first of quadrant Co particles of the in theloop films at T increases= 300 K (at with high decreasing field, the trend the Au:Co of M vs.ratio H does (Table not1) andvisibly their depend interdistance on the measurement reduces and possibly direction). vanishes, It should the also exchange be noted interaction that a reduction may be oftransmitted MS of ~30% to is neighboring experienced particles with increasing through the te ferromagneticmperature from matrix, 6 K leadingto 300 K, to whereas the formation it is not of largermagnetically than 8% coupled in the other clusters samples (i.e., aggregates(Table 2). of Co particles).

Figure 4. In-plane hysteresis loops measured on sample Au2Co1 along the easy and hard orthogonal Figure 4. In-plane hysteresis loops measured on sample Au2Co1 along the easy and hard orthogonal axes at T = 6 K (a) and T = 100 K (b) (normalized to the saturation magnetization Ms). Inset of frame axes at T = 6 K (a) and T = 100 K (b) (normalized to the saturation magnetization Ms). Inset of frame (b): enlarged view of the hard axis loop. Coercivity Hc (c) and squareness ratio Mr/MS (d) vs. T along (b): enlarged view of the hard axis loop. Coercivity Hc (c) and squareness ratio Mr/MS (d) vs. T along thethe easy easy and and hard hard axes. axes.

Materials 2017, 10, 717 7 of 16 Materials 2017, 10, 717 7 of 17

Figure 5. (a) First quadrant of the loop measured on sample Au2Co1 at T = 300 K; (b) Zero-field-cooling Figure 5. (a) First quadrant of the loop measured on sample Au2Co1 at T = 300 K; (b) Zero-field-cooling (ZFC) and field-cooling (FC) magnetization as a function of temperature, measured on Au2Co1 in an (ZFC) and field-cooling (FC) magnetization as a function of temperature, measured on Au2Co1 in an applied magnetic field Happl = 20 Oe. applied magnetic field Happl = 20 Oe.

In this class of samples, the magnetic exchange coupling of the Co particles with the surrounding However, in Au Co the segregated cobalt is just a small fraction (~10 vol%) and the AuCo alloy matrix is expected to result2 1 in an increase of their effective magnetic size, with respect to the structural has a weaker ferromagnetism compared to the matrix in the other films, being richer in Au. Hence, size. Moreover, since the fraction of Co particles in the films increases with decreasing the Au:Co we hypothesize a weaker magnetic coupling between the Co particles and the AuCo matrix and ratio (Table 1) and their interdistance reduces and possibly vanishes, the exchange interaction may between neighboring Co particles in this sample, compared to Au Co and Au Co , which results be transmitted to neighboring particles through the ferromagnetic matrix,1 2 leading1 to1 the formation in Co clusters with smaller magnetic size. This can account for the larger H of Au Co at T = 6 K of magnetically coupled clusters (i.e., aggregates of Co particles). C 2 1 (~235 Oe), compared to the other films. However, in Au2Co1 the segregated cobalt is just a small fraction (~10 vol%) and the AuCo alloy With increasing temperature, the strong thermal dependence of M and the marked non-saturation has a weaker ferromagnetism compared to the matrix in the other films,S being richer in Au. Hence, tendency of the hysteresis loops suggest that the smallest Co clusters undergo a magnetic relaxation we hypothesize a weaker magnetic coupling between the Co particles and the AuCo matrix and process, similar to superparamagnetism [27]. In order to better elucidate this point, the magnetization between neighboring Co particles in this sample, compared to Au1Co2 and Au1Co1, which results in M has been measured for increasing temperature in the 6–300 K range in Happl = 20 Oe, after cooling Co clusters with smaller magnetic size. This can account for the larger HC of Au2Co1 at the sample from room temperature down to 6 K both without an external field (zero-field-cooling, T = 6 K (~235 Oe), compared to the other films. ZFC) and in Happl (field-cooling, FC). With increasing temperature, the strong thermal dependence of MS and the marked non- The result is shown in Figure5b: a magnetic irreversibility effect, i.e., a difference between FC saturation tendency of the hysteresis loops suggest that the smallest Co clusters undergo a magnetic and ZFC magnetization, is clearly observed from T = 6 K up to ~215 K, confirming our hypothesis relaxation process, similar to superparamagnetism [27]. In order to better elucidate this point, the of magnetically relaxing Co clusters [27,28]. Accordingly, HC reduces strongly with increasing magnetization M has been measured for increasing temperature in the 6–300 K range in Happl = 20 Oe, temperature, especially in the 6–100 K range (H ~ 20 Oe at T = 100 K, Figure4c). A similar, even after cooling the sample from room temperature Cdown to 6 K both without an external field (zero- if less marked, decrease of HC at low temperature is also visible in Au1Co2 and Au1Co1 (Figures2c field-cooling, ZFC) and in Happl (field-cooling, FC). and3b). Hence, we cannot exclude the possibility that a very small fraction of relaxing Co clusters The result is shown in Figure 5b: a magnetic irreversibility effect, i.e., a difference between FC also exists in these two samples, although the coercivity trend would be the only appreciable hint and ZFC magnetization, is clearly observed from T = 6 K up to ~215 K, confirming our hypothesis of of this. Similar values of HC are measured in the three samples for T ≥ 100 K. This suggests that, magnetically relaxing Co clusters [27,28]. Accordingly, HC reduces strongly with increasing above this temperature, the magnetic behavior of Au2Co1 is also ruled by the AuCo matrix and by the temperature, especially in the 6–100 K range (HC ~ 20 Oe at T = 100 K, Figure 4c). A similar, even if fraction of the non-relaxing Co clusters and, for this reason, hysteretic properties emerge similar to less marked, decrease of HC at low temperature is also visible in Au1Co2 and Au1Co1 (Figures 2c and 3b). those observed in the other samples. Hence, we cannot exclude the possibility that a very small fraction of relaxing Co clusters also exists in3.3. these Micromagnetic two samples, Simulations although ofthe the coercivity Hysteresis trend Loops would be the only appreciable hint of this. Similar values of HC are measured in the three samples for T ≥ 100 K. This suggests that, above this temperature,We have the ascribed magnetic the observedbehavior hystereticof Au2Co1 behavior, is also ruled especially by thewell AuCo visible matrix in theand samples by the fraction Au1Co2 ofand the Au non-relaxing1Co1, to the Co coexistence clusters an ofd, two for different this reason, magnetic hysteretic phases, properties that we emerge have identified similar to with those the observedAuCo matrix in the and other the samples. Co clusters. The two phases are intimately mixed and the magnetization process is expected to be governed by the subtle interplay between the strength and directions of their 3.3.magnetic Micromagnetic anisotropy, Simulati strengthons of of the the Hysteresis exchange Loops interaction, and the external applied field. Since most of these parameters cannot be experimentally determined and because of the inherent complexity We have ascribed the observed hysteretic behavior, especially well visible in the samples Au1Co2 of the system, to achieve a full comprehension of the magnetization process in the investigated and Au1Co1, to the coexistence of two different magnetic phases, that we have identified with the samples is a quite difficult task. We have obtained valuable information by considering a simplified AuCo matrix and the Co clusters. The two phases are intimately mixed and the magnetization process model of a ferromagnetic two-phase system and performing micromagnetic calculations by OOMMF. is expected to be governed by the subtle interplay between the strength and directions of their magnetic anisotropy, strength of the exchange interaction, and the external applied field. Since most of these parameters cannot be experimentally determined and because of the inherent complexity of the system, to achieve a full comprehension of the magnetization process in the investigated samples

Materials 2017, 10, 717 8 of 16

OOMMF employs the finite difference method, which requires discretization of a chosen geometry over a gridMaterials of 2017 identical, 10, 717 prism-cells in which the magnetization is supposed to be uniform.8 of 17 In our case, we have considered the geometry shown in Figure6: a squared element hosting a circularis disk a quite at thedifficult center, task. both We have discretized obtained usingvaluable cells information with abasis by considering of (1.25 ×a simplified1.25) nm model2 and of height of a ferromagnetic two-phase system and performing micromagnetic calculations by OOMMF. × 2 10 nm. InOOMMF particular, employs the the squared finite difference element method, consists which of 14 requires14 cellsdiscretization and, hence, of a chosen its area geometry is 306.25 nm in the x-yover plane a grid and of identical the thickness prism-cells along in which the z the direction magnetization is 10 nm.is supposed The central to be uniform. disk is also 10 nm-thick and occupiesIn aour volume case, we corresponding have considered to the 26.5% geometry of that shown of the in Figure squared 6: a element.squared element The simulations hosting a have been carriedcircular out disk using at the 2D center, periodic both discretiz boundaryed using conditions, cells with which a basis meansof (1.25 that× 1.25) the nm geometry2 and height in of Figure 6 is periodically10 nm. In replicated particular, the in thesquared whole element x-y planeconsists so of as 14 to × 14 simulate cells and, an hence, infinite its area film. is 306.25 Hence, nm the2 in central the x-y plane and the thickness along the z direction is 10 nm. The central disk is also 10 nm-thick element represents a Co cluster (i.e., an aggregate of smaller Co particles) of 10 nm in size and the and occupies a volume corresponding to 26.5% of that of the squared element. The simulations have squaredbeen one carried represents out using the 2D portion periodic of boundary surrounding conditions, AuCo which matrix. means Thethat the precise geometry definition in Figure of 6 such a system hasis periodically been dictated replicated by a in number the whole of x-y concomitant plane so as to factors. simulate The an Coinfinite cluster film. shapeHence, isthe cylindrical central and the diameterelement is represents equal to the a Co height cluster in (i.e., order an aggregate to increase of thesmaller symmetry Co particles) of the of structure10 nm in size preventing, and the at the same time,squared shape one anisotropy represents the effects portion and of keeping surrounding the computation AuCo matrix. timeThe precise under definition control; theof such choice a of the 10 nm sizesystem is strictly has been intertwined dictated by a number to the dimension of concomitan oft thefactors. prism-cells. The Co cluster In fact, shape to is avoid cylindrical the occurrenceand the diameter is equal to the height in order to increase the symmetry of the structure preventing, at of fictitious effects, the side of the cells has been set so as to fulfill two main requirements: (i) to the same time, shape anisotropy effects and keeping the computation time under control; the choice smoothof the the jagged 10 nm perimetersize is strictly of theintertwined cylinder to andthe dimension (ii) to manage of the anprism-cells. even number In fact, of to cells,avoid preventingthe any artificialoccurrence symmetry-breaking of fictitious effects, in the the side simulations. of the cells has Moreover, been set so we as to demanded fulfill two main that requirements: the relative volume fractions(i) of to the smooth cylindrical the jagged and perimeter squared elementsof the cylinder approximately and (ii) to manage corresponded an even tonumber the volume of cells, fractions preventing any artificial symmetry-breaking in the simulations. Moreover, we demanded that the of the Co and AuCo phases in Au1Co1 (Table1). relative volume fractions of the cylindrical and squared elements approximately corresponded to the Coherently with the data for Au1Co1 reported in Section 3.1, we have assigned saturation volume fractions of the Co and AuCo phases in Au1Co1 (Table 1). magnetization values M = 280 emu/cm3 to the AuCo matrix and M = 1250 emu/cm3 Coherently withS_alloy the data for Au1Co1 reported in Section 3.1, we have assignedS_Co saturation to the Comagnetization cluster. The values magnetic MS_alloy exchange= 280 emu/cm stiffness3 to the AuCo for Co matrix is A Coand= M 3S_Coµerg/cm, = 1250 emu/cm corresponding3 to the Co to the literaturecluster. value The (provided magnetic byexchange the OOMMF stiffness for database Co is ACo [25 = ]),3 µerg/cm, whilst A correspondingalloy was arbitrarily to the literature set to a value one ordervalue of magnitude(provided by smallerthe OOMMF to take database account [25]), of whilst the Co Aalloy dilution was arbitrarily in the alloyedset to a value phase one [29 order]. With this of magnitude smaller to take account of the Co dilution in the alloyed phase [29]. With this choice of 1/2 choice of Aalloy the ferromagnetic exchange length of the AuCo phase Lalloy = (Aalloy/Kalloy) is Aalloy the ferromagnetic exchange length of the AuCo phase Lalloy = (Aalloy/Kalloy)1/2 is ~3 nm. This implies ~3 nm. This implies that, given the geometry in Figure6, the matrix does not transmit the exchange that, given the geometry in Figure 6, the matrix does not transmit the exchange interaction to interactionneighboring to neighboring Co clusters Co because clusters Lalloy because is shorter L alloythan isthe shorter Co clusters’ than interdistance the Co clusters’ [30]. interdistance [30].

Figure 6. Scheme of the system simulated in the micromagnetic analysis. The squared element Figure 6. Scheme of the system simulated in the micromagnetic analysis. The squared element represents the AuCo matrix and the central disk represents a Co cluster. In this geometry, the volume representsfraction the AuCooccupied matrix by the andCo cluste ther central is 26.5%. disk The representsdotted lines are a Co the cluster. anisotropy In thisdirections geometry, for the thetwo volume fractionphases: occupied the byCo theanisotropy Co cluster (KCo) isforms 26.5%. an angle The dottedθ with linesthe x areaxis theand anisotropythe AuCo anisotropy directions (K foralloy) the two phases:forms the Co an angle anisotropy δ with the (K Coy axis.) forms See the an text angle for details.θ with the x axis and the AuCo anisotropy (Kalloy) forms an angle δ with the y axis. See the text for details. Materials 2017, 10, 717 9 of 16

Materials 2017, 10, 717 9 of 17 The stiffness of the exchange interaction between the two phases has been set to 1.6 µerg/cm, i.e., 6 3 intermediateThe stiffness between of A theCo andexchange Aalloy interaction. The anisotropy between coefficients the two phases are K Cohas= been 5 × 10set erg/cmto 1.6 µerg/cm,for the Co 6 36 3 element,i.e., intermediate corresponding between to the ACo literature and Aalloy value. The anisotropy [31], and K coefficientsalloy = 2.4 ×are10 KCoerg/cm = 5 × 10 forerg/cm the AuCo for the alloy, aboutCo halfelement, of the corresponding former. We to have the literature considered value that [31], the and anisotropy Kalloy = 2.4 × axes 106 erg/cm of both3 for phases the AuCo lie inalloy, the x-y planeabout as schematizedhalf of the former. in Figure We 6have: the considered Co anisotropy that th directione anisotropy is defined axes of byboth the phases angle lieθ init formsthe x-y with theplane x axis as whereas schematized the AuCo in Figure anisotropy 6: the Co direction anisotropy is direction defined byis defined the angle by δtheit angle forms θ with it forms the with y axis. the x axis whereas the AuCo anisotropy direction is defined by the angle δ it forms with the y axis. We have carried out simulations of hysteresis loops measured by applying the magnetic field H We have carried out simulations of hysteresis loops measured by applying the magnetic field H along the x and y axes; they will be shown as normalized, in ordinate, to the saturation magnetization along the x and y axes; they will be shown as normalized, in ordinate, to the saturation magnetization and, in abscissa, to the anisotropy field of the matrix H = 2K /M . and, in abscissa, to the anisotropy field of the matrix HKK = 2Kalloyalloy/MS_alloyS_alloy. ◦ In aIn first a first set set of of simulations, simulations, we we have have setset δ = 0° 0 (namely,(namely, the the AuCo AuCo anisotropy anisotropy direction direction is along is along y) y) ◦ ◦ andandθ has θ has been been varied varied between between 0 0°and and 9090°.. Selected results results are are shown shown in inFigure Figure 7a–f:7a–f: for foreach each θ, theθ , the loopsloops measured measured along along y y and and along along x x are are displayed.displayed. At At all all θθ valuesvalues an an anisotropic anisotropic hysteretic hysteretic behavior behavior is observedis observed and and the the high-remanence high-remanence looploop isis measured along along the the y yaxis, axis, namely namely along along the theanisotropy anisotropy directiondirection of the of AuCothe AuCo matrix. matrix. Hence, Hence, we we indicate indicate the the y axis y axis as theas the easy easy magnetization magnetization axis axis of theof the system. Forsystem.θ 6= 90 ◦For, non-zero θ ≠ 90°, remanencenon-zero remanence is measured is measured along the alon hardg the magnetization hard magnetization direction, direction, i.e., alongi.e., x. along x.◦ For θ = 90°, namely when Kalloy and KCo are parallel, the loop measured along y is perfectly For θ = 90 , namely when Kalloy and KCo are parallel, the loop measured along y is perfectly squared whereassquared no whereas hysteresis no ishysteresis observed is observed in the x directionin the x direction (Figure (Figure7f). This 7f). behavior This behavior is very is very close close to that to that modeled by Stoner and Wohlfarth for a single-domain magnetic element with uniaxial modeled by Stoner and Wohlfarth for a single-domain magnetic element with uniaxial anisotropy [32]. anisotropy [32]. For small θ values, the loops measured along x show a crossing of the branches. The For small θ values, the loops measured along x show a crossing of the branches. The effect is well visible effect is well visible in Figure 7 for θ = 5°, 15°, and 20° (the best similarity with the experimental θ ◦ ◦ ◦ in Figureresults7 isfor obtained= 5 , for 15 the, and smallest 20 (the θ, actually). best similarity No crossing with the is observed experimental at higher results θ (Figure is obtained 7e). The for the smallest θ, actually). No crossing is observed at higher θ (Figure7e). The same results are obtained same results are obtained for negative values of θ, namely imposing a negative slope to the KCo axis. for negativeThen, we valueshave studied of θ, namely the case imposingof θ = 0° and a negative variable slopeδ. Selected to the results KCo axis.are shown Then, in we Figure have 7g–i: studied for the ◦ ◦ caseδ of= 5°,θ = the 0 andloop variablewith higherδ. Selected remanence results is measured are shown along in Figurey and 7crossedg–i: for branchesδ = 5 , theare loopfound with in the higher remanenceloop along is measuredx; for δ = 15° along the highest y and remanence crossed branches is measured are in found the x indirection the loop (the along loops x; have for δsimilar= 15◦ the highestremanence remanence actually) is measured and no branch-crossing in the x direction is visible; (the loops as expected, have similar for δ = remanence 90°, a Stoner–Wohlfarth actually) and no branch-crossingtype behavioris is visible;produced. as expected, for δ = 90◦, a Stoner–Wohlfarth type behavior is produced.

Figure 7. (a–i) Simulated hysteresis loops obtained for the indicated values of θ and δ, with magnetic Figure 7. (a–i) Simulated hysteresis loops obtained for the indicated values of θ and δ, with magnetic field H applied along the y axis (continuous line) and the x axis (line with circles). H values are field H applied along the y axis (continuous line) and the x axis (line with circles). H values are normalized to the anisotropy field HK of the AuCo matrix. normalized to the anisotropy field H of the AuCo matrix. K Materials 2017, 10, 717 10 of 16

Hence, key ingredients for observing anisotropic hysteretic behavior and the branch-crossing effect are that the AuCo matrix has a well-defined anisotropy direction (the y axis, in our reference frame in Figure6) and that the Co clusters’ anisotropy lies almost orthogonally to that of the matrix, i.e., it is just slightly misaligned with respect to the x axis. Now, the point is whether these requirements can be fulfilled in real samples. The possibility that the anisotropy ruling the magnetic behavior has a magnetocrystalline origin appears unlikely. In fact, the AuCo alloy presents a poorly crystalline structure, which implies a distribution of locally varying easy axes, possibly resulting in a vanishingly small averaged anisotropy [33]. In this view, we are not able to account for the appearance of a net uniaxial magnetocrystalline anisotropy of the matrix. As for the Co clusters, if the prevalent type of anisotropy was the magnetocrystalline one, they should possess a preferential crystallographic orientation in the plane of the film so that their anisotropy vectors would lie within a cone of limited angular width. However, the structural analyses exclude an in-plane texturing of the Co phase [23]. We must consider a different scenario and we propose that both phases have dominant magnetoelastic anisotropy. The magnetoelastic anisotropy energy is expressed by the relation 2 E = 3/2λSσsin ϕ, where λS is the magnetostriction, σ is the mechanical stress, and ϕ is the angle between the stress axis and the magnetization [31]. Cobalt is a magnetostrictive material and the AuCo alloy is likely to possess the same property (no information can be found in literature on this point). As for σ, it is well known that all films have a state of residual stress due to extrinsic factors (typically, the mismatch in the thermal expansion coefficients of the film and of the substrate) and to intrinsic factors (growth processes, grain structure, substitutional or interstitial impurities) [10]; in the case of composite films, lattice and thermoelastic mismatch among the different phases must be also taken into account [34,35]. Several of these factors may operate simultaneously so that the final stress distribution in the film results from their balance. Despite the fact that most of the models on the mechanical properties of film-substrate systems, such as the well-known Stoney theory [36], assume a spatial stress uniformity, a non-uniform stress distribution is much more likely to occur in practice [37] due, for instance, to the deviation between the ideal isotropic properties of the substrate and the real properties. A non-uniform stress distribution may be settled in our films, which implies that the average stress along two orthogonal directions may be different [10,38,39]. Although, at present, we are not able to unambiguously account for a non-uniform stress state in our samples, the observation that easy and hard magnetization axes are along the sample sides in all the three cases suggests that the stress distribution originates from the reproducible intervention of precise factors, presumably connected with the silicon substrate and/or with the production procedure of the samples. The item certainly deserves further attention also in the perspective of achieving a control of the stress state and thus governing the magnetoelastic anisotropy. A small difference between the stresses acting along y and along x on AuCo (σy_alloy and σx_alloy, respectively) and Co (σy_Co, and σx_Co) is sufficient to generate the inherent anisotropic character that emerges in the hysteretic magnetic behavior, depending on the interplay between their strength and sign and λS. Two main pictures can be drawn. In the first one, the Co and AuCo alloy have magnetostriction constants of different signs. Since Co has negative λS [31], a positive λS is assigned to AuCo. We hypothesize that along the y axis the two phases are subjected to a stress with the same sign—taken as positive to preserve the coherence with the coordinate system adopted in Figure6—and that σy_alloy > σx_alloy and σy_Co > σx_Co. In this way, the anisotropy axis of the AuCo matrix is along the y direction and the anisotropy of the Co clusters preferentially lies along the x direction. In the second picture, both Co and AuCo have negative λS. We hypothesize that, along the y axis, a negative stress acts on AuCo and a positive stress acts on Co and that |σy_alloy| > |σx_alloy| and σy_Co > σx_Co. In this way too, the anisotropy directions for the AuCo matrix and for the Co clusters are along y and x, respectively. In this framework, the required small misalignment of KCo with respect to the x axis, may be accounted for in terms of the competition between the dominant magnetoelastic anisotropy and the magnetocrystalline anisotropy, presumed to act on the Co clusters along random directions. Materials 2017, 10, 717 11 of 16

MaterialsHence, 2017, 10 by, 717 assuming that the anisotropy of AuCo and Co has a prevalent magnetoelastic character,11 of 17 different situations can be envisaged, which fulfill the requirements indicated by the micromagnetic micromagneticstudy. By the study. light of By this the statement, light of ourthis initialstatement, choice our of settinginitial KchoiceCo to of the setting magnetocrystalline KCo to the magnetocrystallineanisotropy of bulk anisotropy cobalt may of appear bulk notcobalt appropriate may appear (also not in appropriate consideration (also of thein consideration poor crystallinity of theof thepoor Co crystallinity phase in real of samples)the Co phase and in also real the samples) choice of and Kalloy alsohas the been choice arbitrary. of Kalloy Calculationshas been arbitrary. carried Calculationsout using different carried out values using of different KCo and values Kalloy, of but KCo in and the K samealloy, but relationship, in the same produce relationship, similar produce results, similarindicating results, that theindicating outcomes that do the not outcomes strictly depend do not on strictly the assigned depend anisotropy on the coefficients.assigned anisotropy Moreover, coefficients.Figure8a shows Moreover, the loops Figure obtained 8a shows imposing the loops both ob totained the AuCo imposing matrix both and to the AuCo Co element matrix the and same to 6 3 6 3 theanisotropy Co element (Kalloy the= KsameCo = anisotropy 2.4 × 10 erg/cm (Kalloy =), whereasKCo = 2.4 in × Figure 106 erg/cm8b,c, K3),alloy whereas= 5 × 10in Figureerg/cm 8b,c,and 6 3 KKalloyCo == 5 2.4 × 10×6 10erg/cmerg/cm3 and K(namely,Co = 2.4 × compared 106 erg/cm to3 (namely, the previous compared simulations, to the previous the anisotropy simulations, values the for ◦ ◦ anisotropyAuCo and values Co have for been AuCo exchanged). and Co have In bothbeen cases,exchanged). we have In setbothδ = cases, 0 and weθ have= 5 , asset inδ Figure= 0° and7b. θThe = 5°, main as in features Figure of7b. the The hysteretic main features behavior of the are stillhysteretic visible. behavior However, are the still remanent visible. However, magnetization the remanentmeasured magnetization along x is substantially measured smaller along thanx is substantially in Figure7b, asmaller characteristic than in that Figure worsens 7b, a thecharacteristic qualitative thatagreement worsens with the qualitat the experimentalive agreement results. with the experimental results.

FigureFigure 8. 8. SimulatedSimulated hysteresis hysteresis loops loops obtained obtained for δ for = 0°δ =and 0◦ θand = 5°θ with= 5◦ magneticwith magnetic field H field applied H applied along the y axis (line) and the x axis (line with circles). In (a) Kalloy = KCo = 2.4 × 106 erg/cm3; in (b6 ) Kalloy = 35 × 106 along the y axis (line) and the x axis (line with circles). In (a)Kalloy = KCo = 2.4 × 10 erg/cm ; in (b) erg/cm3 and KCo 6= 2.4 × 1036 erg/cm3; Frame (c) is6 an enlarged3 view of the loop along x as shown in (b). Kalloy = 5 × 10 erg/cm and KCo = 2.4 × 10 erg/cm ; Frame (c) is an enlarged view of the loop along x as shown in (b). Finally, we have addressed the case of a sample with a higher Co content. For this purpose, we have reduced the extension of the squared element drawn in Figure 6, down to a size of 12 × 12 cells. Finally, we have addressed the case of a sample with a higher Co content. For this purpose, we In this way, the volume occupied by the Co inclusion is ~35%, corresponding to the fraction that exists have reduced the extension of the squared element drawn in Figure6, down to a size of 12 × 12 cells. in sample Au1Co2 (Table 1). Accordingly, we have assigned a magnetization MS_alloy = 500 emu/cm3 to In this way, the volume occupied by the Co inclusion is ~35%, corresponding to the fraction that exists the AuCo matrix (see Section 3.1). All the remaining parameters are unchanged with respect to the in sample Au Co (Table1). Accordingly, we have assigned a magnetization M = 500 emu/cm3 simulations in 1Figure2 7. In particular, in Figure 9 we present the results obtainedS_alloy for δ = 0° and θ = 5°. to the AuCo matrix (see Section 3.1). All the remaining parameters are unchanged with respect to the In this case, the high-remanence loop is measured along x and the cross-branching effect is visible in simulations in Figure7. In particular, in Figure9 we present the results obtained for δ = 0◦ and θ = 5◦. the loop along y. Hence, the easy and hard axes are exchanged with respect to Figure 7b, a situation In this case, the high-remanence loop is measured along x and the cross-branching effect is visible in that cannot be distinguished by experiments on the real samples. the loop along y. Hence, the easy and hard axes are exchanged with respect to Figure7b, a situation that cannot be distinguished by experiments on the real samples. Regarding sample Au2Co1, the simulation approach used for the other two samples is affected by the difficulty of assessing the fractions of non-relaxing and relaxing Co clusters, which should actually be treated as two different magnetic phases. However, the loops calculated for a smaller Co element

Materials 2017, 10, 717 12 of 16 in Figure6 (corresponding to a volume fraction of ~10%, Table1) and with the appropriate value of

MaterialsMS_alloy 2017, show, 10, 717 basic characteristics close to those found for sample Au1Co1. 12 of 17

Figure 9. Hysteresis loops obtained by simulating a system slightly different from that in Figure 6, Figure 9. Hysteresis loops obtained by simulating a system slightly different from that in Figure6, namelynamely in whichwhich thethe volume volume fraction fraction of of the the Co Co cluster cluster is higher is higher (~35%). (~35%). Loops Loops are calculated are calculated for θ = for 5◦ θand = 5°δ and= 0◦ δwith = 0° magneticwith magnetic field Hfield applied H applied along along the y the axis y(line) axis (line) and theand x the axis x (lineaxis (line with with circles). circles).

Regarding sample Au2Co1, the simulation approach used for the other two samples is affected 4. Conclusions by the difficulty of assessing the fractions of non-relaxing and relaxing Co clusters, which should actuallyWe be have treated studied as two the different magnetic magnetic properties phas ofes. AuCo However, films, the with loops different calculated atomic for a ratios smaller of theCo elementconstituent in Figure metals, 6 prepared (corresponding by co-sputtering to a volume deposition. fraction Theof ~10%, samples Table consist 1) and of anwith almost the appropriate amorphous valueAuCo of alloy MS_alloy in, whichshow basic nanosized characteristics Co particles close to are those dispersed. found for Indeed, sample the Au1 magneticCo1. analysis can be a valuable tool to gain structural information, hardly accessible otherwise. Our study has 4.nicely Conclusions revealed the composite magnetic structure of the samples, disclosing, in particular, an unexpected hysteretic behavior, characterized by in-plane anisotropy and branch-crossing in the We have studied the magnetic properties of AuCo films, with different atomic ratios of the loop measured along the hard magnetization direction. In fact, these characteristics have been constituent metals, prepared by co-sputtering deposition. The samples consist of an almost satisfactorily reproduced by micromagnetic calculations relative to a simplified system representing amorphous AuCo alloy in which nanosized Co particles are dispersed. Indeed, the magnetic analysis two exchange-coupled ferromagnetic phases—a matrix embedding a different element—with almost can be a valuable tool to gain structural information, hardly accessible otherwise. Our study has orthogonal anisotropy axes. The two phases have been identified with the AuCo alloy and with nicely revealed the composite magnetic structure of the samples, disclosing, in particular, an a Co cluster. Different scenarios have been discussed in order to explain how the requirement of unexpected hysteretic behavior, characterized by in-plane anisotropy and branch-crossing in the loop orthogonal anisotropy axes can be fulfilled. In particular, we have assumed a dominant magnetoelastic measured along the hard magnetization direction. In fact, these characteristics have been character of the anisotropy of the two phases, which implies that both of them must be magnetostrictive satisfactorily reproduced by micromagnetic calculations relative to a simplified system representing and subjected to a non-uniform stress distribution. In the perspective of creating novel magnetic two exchange-coupled ferromagnetic phases—a matrix embedding a different element—with almost architectures, for which flexible substrates are now more and more often employed, the latter condition orthogonal anisotropy axes. The two phases have been identified with the AuCo alloy and with a Co can be intentionally induced, so as to obtain a control of the anisotropy and hence of the loop cluster. Different scenarios have been discussed in order to explain how the requirement of shape, particularly of the remanence state and of the approach to saturation. In this view, the orthogonal anisotropy axes can be fulfilled. In particular, we have assumed a dominant particular hysteretic features that we have described could become the fingerprint of the existence of magnetoelastic character of the anisotropy of the two phases, which implies that both of them must (almost)-orthogonal anisotropy axes. be magnetostrictive and subjected to a non-uniform stress distribution. In the perspective of creating Samples Au Co and Au Co have been preferably addressed in the micromagnetic study. novel magnetic architectures,1 1 for1 which2 flexible substrates are now more and more often employed, The simulation approach for Au Co is made complicated by the difficulty in estimating the fractions of the latter condition can be intentionally2 1 induced, so as to obtain a control of the anisotropy and hence the stable Co clusters and of the magnetically relaxing ones, which strongly affect the overall magnetic of the loop shape, particularly of the remanence state and of the approach to saturation. In this view, behavior, especially for T < 100 K. the particular hysteretic features that we have described could become the fingerprint of the existence The micromagnetic analysis has succeeded in attaining general guidelines regarding how the of (almost)-orthogonal anisotropy axes. observed hysteretic properties may originate in the investigated material. The obtained results Samples Au1Co1 and Au1Co2 have been preferably addressed in the micromagnetic study. The contribute to expanding the fundamental comprehension of nanocomposite magnetic systems and simulation approach for Au2Co1 is made complicated by the difficulty in estimating the fractions of offer interesting implications for the creation of future composite materials. the stable Co clusters and of the magnetically relaxing ones, which strongly affect the overall magneticAcknowledgments: behavior,L.D.B. especially acknowledges for T < 100 Ferrara K. University for financial support provided through ‘Fondo per l’IncentivazioneThe micromagnetic alla Ricerca—FIR analysis 2016’. has succeeded in attaining general guidelines regarding how the observed hysteretic properties may originate in the investigated material. The obtained results contribute to expanding the fundamental comprehension of nanocomposite magnetic systems and offer interesting implications for the creation of future composite materials.

Materials 2017, 10, 717 13 of 16

Author Contributions: The authors from Ferrara University carried out the magnetic study. In particular, F.C. performed the magnetic measurements, under the supervision of F.S. and L.D.B., and the micromagnetic simulations, under the supervision of F.S. and F.M.; all of them analyzed and discussed the results. The authors from Padova University (V.M., C.M., and G.M.) prepared the samples and provided the structural and compositional data. L.D.B. wrote the manuscript that was discussed and finally approved by all the authors. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A To gain a deeper insight into the hysteresis process affected by branch-crossing, let us examine in more detail the simulated loop obtained for δ = 0◦, θ = 5◦ and the magnetic field applied along x, already shown in Figure7b. Each point of the hysteresis loop corresponds to a specific configuration of the magnetization (magnetization map) of the system, modeled by the grid of cells in Figure6. In Figure A1, the simulated loop is displayed (central frame) together with eight magnetization maps relative to the points indicated on the loop itself. The arrow, visible in each cell of the maps, indicates the orientation of the magnetization (as already explained above, the magnetization is supposed to be uniform in each cell). The color of each cell provides information about the projection of the magnetization along x (Mx), namely in the direction of the applied magnetic field: blue and red designate the sign of Mx (positive and negative, respectively) and the color intensity is proportional to the magnitude of |Mx|. To mimic the experimental loop measurement procedure, our calculation of the simulated loop starts from the positive magnetic saturation state, namely from map (a) (different shades of blue characterize the matrix and the Co cluster because of the different values of MS_alloy and MS_Co). With decreasing the applied field, i.e., moving to point (b) and then to the positive remanence state (c), the interplay between the matrix-cluster exchange coupling and the anisotropies’ strengths and directions—the misalignment θ of KCo plays a particularly crucial role—favors an upward orientation of the magnetization arrows in the cells. This means that the projection of the magnetization along y (My) is positive. At point (d), the negative field, applied along x, has been sufficient to reverse the largest fraction of the magnetization of the system. Hence, Mx < 0, whereas My is still positive, even in the Co cluster. In fact, the exchange coupling with the matrix dominates on KCo that here is forcing the Co magnetization downward, because of the misalignment θ. With further decreasing the field, a magnetic configuration settles on with arrows pointing downward, which results in My < 0 (this map is not shown, but the configuration is qualitatively similar to that visible also in frame (f), along the ascending branch of the loop). A sudden jump in M/MS marks this passage from My > 0 to My < 0. Then, a negative saturation is achieved at point (e), where My = 0. Point (e) marks the end of the descending branch of the loop (from positive to negative saturation). On the ascending branch of the loop (from negative to positive saturation), point (f) is analogous to point (b). In this case, KCo and the matrix-cluster exchange coupling cooperate to produce a downward orientation of the magnetization arrows (i.e., Mx < 0 and My < 0). Point (g) is the negative remanence state. In point (h), analogous to (d), Mx > 0 and My < 0. Points (d) and (f) correspond to the same negative value of the applied magnetic field. The comparison of the corresponding maps reveals that the slope of the magnetization arrows with respect to the x axis, especially those of the Co cluster, is larger in map (f) than in map (d). As a consequence, |Mx| calculated in (f) is smaller than in (d). Similarly, points (b) and (h) correspond to the same positive field. The slope of the arrows in (b) is larger than in (h) and, hence, Mx in (b) is smaller than in (h). The following general behavior emerges from the analysis of the maps: at any field within the range where the branch-crossing effect occurs in the third (first) quadrant of the loop, the slope of the Co magnetization and the slope of KCo have the opposite sign along the descending (ascending) branch and have the same sign along the ascending (descending) one. Materials 2017, 10, 717 14 of 16

Materials 2017, 10, 717 14 of 17

Figure A1. Central frame: hysteresis loop calculated for δ = 0°, θ = 5° ◦and H applied◦ along the x axis Figure A1. Central(already frame: shown in hysteresisFigure 7b); the descending loop calculated branch (from for positiveδ = to 0 negative, θ = saturation) 5 and His the applied black along the x axis (already shownline, whereas in Figure the ascending7b); the branch descending (from negative branch to positive (from saturation) positive is the to green negative line (in saturation)the is the regions where the two branches are superposed, only the green line is visible). The magnetization black line, whereasmaps corresponding the ascending to the indicated branch points (from of the negative loop are shown: to positive they are labelled saturation) with letters is from the green line (in the regions where(a) to the (h). twoThe key branches frame on the are bottom-left superposed, corner indica onlytes thethat the green blue and line red is colors visible). in the maps The magnetization maps correspondingdesignate to the the sign indicated of the projection points of the of magnetization the loop arealong shown: the x axis, theyMx (positive are labelled and negative, with letters from respectively); no specific color is assigned to the magnetization projection along the y axis, My. See (a) to (h). The keythe text frame for further on theexplanation. bottom-left corner indicates that the blue and red colors in the maps designate the sign of the projection of the magnetization along the x axis, Mx (positive and negative, The following general behavior emerges from the analysis of the maps: at any field within the respectively);range no where specific the branch-crossing color is assigned effect tooccurs the in magnetization the third (first) quadrant projection of the along loop, the the slope y axis, of the M y. See the text for furtherCo magnetization explanation. and the slope of KCo have the opposite sign along the descending (ascending) branch and have the same sign along the ascending (descending) one.

Appendix B Appendix B In Figure A2 we show the simulations obtained for the system in Figure 6, for θ = 5° and δ = 5° ◦ ◦ In Figure A2and we10°. Given show the the results simulations for θ = 5° and δ obtained = 0° (Figure 7b), for the the branch-crossing system in effect Figure is seen6, to for reduceθ = 5 and δ = 5 and 10◦. Givenmore the resultsand more forwithθ increasing= 5◦ and δ (noδ effect= 0◦ is(Figure observed7 forb), δ > the 10°). branch-crossing effect is seen to reduce more and more withIf we increasing focus the attentionδ (no on effect the simulations is observed presenting for δthe> branch-crossing 10◦). and consider the ratio between the remanence measured along y (Mry) and that measured along x (Mrx), we obtain: If we focusMry the/Mrx attention~ 1.32 for δ = on0° and the θ simulations= 5° (Figure 7b); presentingMry/Mrx ~ 1.11 for the δ = branch-crossing5° and θ = 0° (Figure 7g); and consider the Mry/Mrx ~ 1.17 for δ = 5° and θ = 5° (Figure A2). Thus, the misalignment of Kalloy is detrimental not only ratio between the remanence measured along y (Mry) and that measured along x (Mrx), we obtain: for the branch-crossing◦ effect ◦but also for the anisotropic character of the hysteretic behavior,◦ as it ◦ Mry/Mrx ~ 1.32tendsfor toδ smooth= 0 andthe differenceθ = 5 between(Figure the7 easyb); and M hardry/M axes.rx ~ 1.11 for δ = 5 and θ = 0 (Figure7g); ◦ ◦ Mry/Mrx ~ 1.17 for δ = 5 and θ = 5 (Figure A2). Thus, the misalignment of Kalloy is detrimental not only for the branch-crossing effect but also for the anisotropic character of the hysteretic behavior, as it tends to smoothMaterials 2017 the, 10 difference, 717 between the easy and hard axes. 15 of 17

1.0 H along y 1.0 H along x 0.5 0.5

S S (b) 0.0 (a) 0.0

M / M M / M -0.5  = 5° -0.5  = 5°  = 5°  = 10° -1.0 -1.0 -1.0 -0.5 0.0 0.5 1.0 -1.0 -0.5 0.0 0.5 1.0 H / H H / H K K Figure A2.FigureSimulated A2. Simulated hysteresis hysteresis loops loops obtained obtained forfor θθ == 5° 5 and◦ and for forthe indicated the indicated values of values δ, with of δ, with magnetic field H applied along the y axis (line) and the x axis (line with circles). magnetic field H applied along the y axis (line) and the x axis (line with circles). References

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