Magnetic moment orientation and in-depth distribution of dysprosium near the surface of DyCo4.6 thin films from x-ray circularly polarized absorption

PHYSICAL REVIEW B 104, 054439 (2021) Magnetic moment orientation and in-depth distribution of dysprosium near the surface of DyCo4.6 thin films from x-ray circularly polarized absorption J. Díaz *and C. Blanco-Roldán Universidad de Oviedo, Calle Federico García Lorca, 18, Oviedo 33007, Spain and CINN (CSIC-Universidad de Oviedo), 33940 El Entrego, Spain (Received 18 March 2021; revised 22 July 2021; accepted 5 August 2021; published 30 August 2021) We have investigated the dysprosium distribution and its magnetic moment orientation at the region near the surface of DyCo4.4and DyCo4.6ferrimagnetic amorphous films with perpendicular magnetic anisotropy. X-ray magnetic circular dichroism spectroscopy of the films at the Dy M4,5and Co L2,3edges using total electron yield (TEY) detection was performed at 2 K and 300 K temperatures, and at sample orientations ranged from 0◦to 70◦with respect to the normal to the sample. The measurements showed an apparent partial decoupling between the cobalt and dysprosium magnetic sublattices. At RT, the magnetic moment per atom of dysprosium was below the minimum value expected if all dysprosium moments were Antiferromagnetic (AF) coupled to cobalt. At 2 K, the cobalt sublattice presented a surprisingly stronger magnetic anisotropy than the dysprosium sublattice. A detailed analysis of the circularly polarized spectra of the Dy M5edge, based on the deconvolution of the spectra in their related parallel, antiparallel, and transverse to Jzspectral components, demonstrates that the spectra are composed by dysprosium with different magnetic moment distributions. The fit of the Dy M5 spectra using the Jzspectral components evidenced a gradation of dysprosium concentration due to segregation at the region probed by TEY. The topmost layer was magnetically uncoupled from cobalt. At RT, 25% of the dysprosium magnetic moments in the underlayer were found averaged oriented in the same direction of cobalt. The expected weak magnetic coupling of these dysprosium atoms to cobalt should explain the surprisingly lower magnetic anisotropy of the dysprosium sublattice compared to that of cobalt probed by TEY at 2 K. DOI: 10.1103/PhysRevB.104.054439 I. INTRODUCTION Rare earth-transition metal (RE-TM) alloys are wellknown magnetic materials since decades ago [1,2], constituting a key component in a variety of industrial and technological applications. A renewed interest in these materials has grown because of their richness in magnetic behaviors and their relative flexibility for tailoring their properties to fit in specific magnetic applications and devices. RE-TM alloys are present in spring magnets [3–5], magnetic topological formations [6–8], spin-wave functional devices [9], and all optical magnetic switching [10–12]. Their use is also favored by its simple thin-film preparation process, which can be done at RT. The extraordinary magnetic properties of these alloys are based on the strength of the TM-TM exchange coupling, the high magnetic moment of the RE, and their RE-TM indirect exchange coupling interaction. The high orbital moment of its unquenched 4forbital and the high energy of its spin-orbit coupling makes the RE act as a strong and localized magnetic moment whose orientation depends on the interatomic exchange and the crystal field at its particular local atomic environment. These two interactions are mainly provided by their TM neighbors whose RE-TM interaction energies overwhelm those of RE-RE. Since the RE-TM magnetic exchange *[email protected] coupling is antiferromagnetic in spin, RE-TM alloys are ferrimagnetic for heavy REs like dysprosium. This interaction is usually treated as a molecular field whose intensity is calculated to be of the order of 200 T for crystalline DyCo5 [13]. The energy of this interaction is, at least, one order of magnitude smaller than the TM-TM exchange. This range of values is comparable to kBTenergies, giving rise to different magnetic configurations as a function of temperature and RE concentration. A characteristic parameter that defines these ferrimagnetic alloys is their compensation temperature, Tcomp, the temperature where the magnetic moment of the RE and TM sublattices cancel to each other. Given the radical different magnetic behavior of the RE and the TM, the understanding of the magnetism of these alloys requires a precise characterization of the magnetic moment and anisotropy of the RE and TM sublattices separately. The perfect technique to do so is x-ray magnetic circular dichroism (XMCD) spectroscopy. The magnetic properties of the RE and TM sublattices can be studied separately by tuning the incident circularly polarized x rays to the corresponding absorption edges of the RE (M4,5, probing its 4forbital) and the TM (L2,3, probing its 3dorbital) [14–16]. This is actually the technique of choice for the study of RE-TM alloys in the form of thin films because it allows ex situ sample preparation and it can be sensitive to regions at different depths of the sample by changing the way the x-ray absorption spectra is detected. Surface sensitivity is attained using total electron yield (TEY) detection, with probed depths of the order of 2469-9950/2021/104(5)/054439(18) 054439-1 ©2021 American Physical Society J. DÍAZ AND C. BLANCO-ROLDÁN PHYSICAL REVIEW B 104, 054439 (2021) 2 to 3 nm, whereas fluorescence yield or x-ray transmission are more bulk-sensitive techniques. The simultaneous use of these two detection modes has been proven to be important for a correct understanding of these alloys. The different Tcomp measured in these alloys using TEY and bulk detection [5], together with the reported RE segregation at their surface [17,18], has been used as an argument to explain interesting phenomena that occur at temperatures near their Tcomp when the applied magnetic field is intense enough. The hysteresis loops of some DyCo alloys of similar concentration than the samples used in this study presented side wing loops at high applied fields as presented in some spring magnetlike bilayer structures [3,4,19]. The effect was explained as derived from the effective different RE concentrations at the bulk and the region near the surface, which will yield two different Tcomp for each region [5,20]. In these studies, the Tcomp at the region near the surface was estimated from the magnetic moments of cobalt and dysprosium deduced by XMCD measurements done using TEY detection. In all the cases, the analysis has always assumed the presence of a single dysprosium magnetic phase. However, due to the structural disorder of these alloys, different grades of intensity in the magnetic exchange interaction between dysprosium and cobalt are expected. Such effects should be stronger at the surface whose assumed larger RE concentration is driven by RE-RE bonding preference. Previous XMCD studies in NdCo alloys conducted by us using TEY detection [21] reported a substantial proportion of RE atoms that behaved as if they were paramagnetic, indicating that not all the RE atoms probed might have the same exchange interaction strength with the TM and, therefore, the same magnetic orientation distribution. Although those experiments were sensitive to the surface, their exact distribution was not demonstrated. Actually, Extended X-ray Absorption Fine Structure spectroscopy (EXAFS) experiments performed by us in similar samples deduced the possible presence of RE segregation in thebulkaswell[22]. The possible existence of paramagnetic RE atoms nonexchange coupled to the TM due to disorder or/and RE segregated would contribute to overestimate the Tcomp at the surface because its average magnetic moment orientation would be in the same direction of the applied field. This effective bilayer interpretation of the side wing loops in DyCo films has been contested by others who consider that the observed effect is due to a spin flop phase transition [23]. The range of temperatures and fields under which this transition is produced can be predicted by the H−T(applied field Htemperature) phase diagram of the alloy which is built by considering all the interactions present in the alloy. These studies show that the relative magnetic anisotropy of the RE and TM sublattices [23] and the interaction of the alloy at the interface with other metals [23] are key to understanding these spin-flop transitions. It is clear, then, the importance of having a good characterization of the magnetism of these alloys at the region near the surface or at their interface with other materials whose magnetic structure could be complex. The purpose of the experiment presented in this paper is to improve the spectroscopical tools to understand the magnetic behavior of the TM and the RE sublattices, their mutual interaction, and their magnetic anisotropy using the information extracted from the x-ray absorption spectra of the RE atoms, and consider their possible inhomogeneous distribution in depth at the region probed by TEY. For this experiment, we prepared DyCo thin films anisotropically uniaxial with high perpendicular magnetic anisotropy (PMA) energies. Their anisotropy fields at 2 K, HK, were well above the range of available field intensities in the experiment. Measurements were done at 2 K and RT. These two temperatures were distant enough from the Tcomp of the alloys to avoid possible spin flip (and flop) effects. Also, it permitted us to measure in the regions where each of the sublattices were magnetically dominant (cobalt at RT and dysprosium at 2 K). At 2 K, thermal disorder was reduced to a minimum. The ferrimagnetic character of DyCo alloys permits us to detect dysprosium atoms magnetically uncoupled from cobalt since they will be oriented in the opposite direction than their counterpart exchange-coupled dysprosium atoms at temperatures above Tcomp, where the cobalt sublattice is magnetically dominant. Their detection requires a deconvolution of the RE M4,5spectra in their parallel, antiparallel, and transverse components of Jzwhich are specially well defined in dysprosium. This deconvolution has been presented before in DyCo films [24] but it was not linked to the moment orientation of the dysprosium magnetic moments as done and explained in detail in this paper. Also, we use the XMCD spectra to deconvolve these components from the circularly polarized spectra instead of relying completely on their theoretically calculated shapes, as the mentioned work tried. We show the potential of this technique in the study of the interaction between RE and cobalt atoms at the region probed by TEY by measuring at different orientation angles under a strong PMA. This technique is able to detect the presence of a RE segregated layer that affects in a significant way the measured moment of the RE. The presence of this layer seems intrinsic to the thin film growth in RE-TM alloys. Even removing the effect of this layer, the proportion of dysprosium atoms directly engaged in the PMA anisotropy of the alloy probed by TEY was not majority, possibly due to the extended thickness of the cobalt-depleted layer caused by the dysprosium segregation. The paper is organized as follows: First, sample preparation and experimental details for XMCD data acquisition are described. Next, after showing the VSM magnetometry characterization of the measured films, the XMCD experimental results for each elemental sublattice are presented and discussed separately. This is followed by a section dedicated to explain how the deconvolution of the Dy M5spectra is made, with the calculation details shown in an Appendix section. After this explanation, a model to fit the Dy M5of the measured samples using the deconvolved spectral components is proposed, which consisted of two layers with different dysprosium moment distributions. The results of the fits are presented and discussed. The final section is the conclusion of the paper. II. EXPERIMENT The two studied DyCo thin films were prepared at RT by magnetron sputtering at a base pressure of 10−8mbar 054439-2 MAGNETIC MOMENT ORIENTATION AND IN-DEPTH … PHYSICAL REVIEW B 104, 054439 (2021) and 10−3mbar Ar pressure. They were grown onto silicon wafer substrates using two separate magnetron guns set at normal (cobalt gun) and at 30◦angle incidence (dysprosium) with respect to the normal to the sample. Dysprosium and cobalt concentrations were calibrated using a quartz balance. The deposition method was different for each sample. A sample called DCC was prepared by codeposition of cobalt and dysprosium. A sample called DCM was grown by the alternate deposition of cobalt and dysprosium layers. The nominal thickness of the cobalt and dysprosium layers was 4.9 Å and 2.8 Å, respectively. The topmost deposited layer was cobalt. This second preparation method was intended as a way to estimate the importance of the interdiffusion between the elements forming the alloy in their structure and magnetic properties. All the samples were protected with a 20-Åaluminum capping layer. The mean atomic concentration in the alloys was determined by electron-induced fluorescence spectroscopy. The difference in concentration between both films was relatively small. Sample DCC contained more dysprosium (DyCo4.4±0.05) than the DCM film (DyCo4.6±0.05). Their nominal thickness was 35 nm. The structure of the alloys, deduced from x-ray diffraction measurements, was noncrystalline. Pure cobalt grain texture peaks disappeared at the RE concentrations of the analyzed samples, indicating the known amorphization effect of the RE on cobalt [25]. NdCo alloys studied by EXAFS, prepared in similar conditions and with the same concentrations of the analyzed samples, showed an extremely disordered atomic environment for the RE, whereas cobalt atoms seemed to cluster in grains of few atoms [22]. A similar structure is expected for the DyCo alloys due to the similar chemistry of Nd and Dy with cobalt. X-ray circularly polarized absorption spectra were obtained at the HECTOR endstation [26] of the BOREAS BL-29 beamline at the ALBA synchrotron using TEY detection. HECTOR has a cryomagnet that can apply up to ±6 T along the x-ray beam direction at different sample orientations, which in our case ranged from normal incidence (0◦) to near grazing incidence (70◦). The cryomagnet works at ultrahigh vacuum conditions (pressure within the 10−10 mbar range). A liquid He cryostat permits fixing the sample temperature between 2 K and 350 K. Circularly polarized light was produced by an APPLE II elliptical undulator. Each XMCD spectra was the result of four spectra taken at opposite circular polarization helicities and magnetic field orientations. III. EXPERIMENTAL RESULTS AND DISCUSSION A. Magnetometry Both samples presented PMA even at RT. Figure 1shows vibrating sample magnetometer (VSM) measurements of the variation with the temperature of the coercive field and the magnetization in remanence of samples DCC and DCM, together with their hysteresis loops obtained at 2 K. The values of the magnetization in remanence were obtained after magnetic saturation of the films with a field of 9 T at 5 K applied normal to their plane [27]. The remanent magnetization at 2 K was 75% and 83% of the saturation magnetization in samples DCM and DCC, respectively. Table Isummarizes these magFIG. 1. Magnetic properties of samples DCC and DCM: (a), (b) are the variation in the coercive field as a function of the temperature of samples DCC and DCM, respectively, (c) is the magnetization in remanence as a function of the temperature for the two samples, (d) shows the hysteresis loop of samples DCC (red line, smaller coercive field) and DCM (blue line, bigger coercive field). netic properties of the two samples at the two temperatures measured by XMCD (RT and 2 K) and their compensation temperatures, Tcomp.Tcomp wassmallerinsampleDCM(90K) than in sample DCC (125 K). These values agree with their different RE concentrations, and with that expected by comparing with the reporting by others in DyCo alloys of similar concentrations [5,20], assuming a linear relationship between Tcomp and the atomic concentration of the alloy [18]. The higher cobalt concentration in sample DCM causes a marked lower magnetic remanence at 10 K than in sample DCC. This explains the large difference between the coercive fields measured at 10 K, higher in sample DCM (3.5 T) than in sample DCC (1.9 T). However, sample DCM has a higher HCat RT, when its MSis higher. X-ray reflectometry shows rougher surfaces in DCM than in DCC thin films, suggesting that the larger HCof the DCM thin film is probably caused by its higher density of domain-wall pinning defects. The response to the magnetic field of the analyzed samples differed from those reported in DyCo thin films of similar concentration [5,20]. The coercive fields of both samples were notoriously higher and the loops were not squared at temperatures below RT, indicating that their internal structure, which is responsible for the way cobalt and dysprosium sublattices magnetically interact, was somehow different. TABLE I. Compensation temperature, Tcomp, Magnetic remanence, MR, and coercive field, HC, of samples DCC and DCM at 2 K and RT [27]. Sample Tcomp Temperature MR(emu/cm3)HC(T) DCC 125 K 2 K 125 1.9 300 K 250 0.2 DCM 90 K 2 K 75 3.5 300 K 275 0.4 054439-3 J. DÍAZ AND C. BLANCO-ROLDÁN PHYSICAL REVIEW B 104, 054439 (2021) FIG. 2. Hysteresis loops taken at the Dy M5(pink) and Co L3 (blue) edges at RT: (a) normal orientation, (b) grazing incidence (70◦). The hysteresis loop of the dysprosium sublattice multiplied by −1 has been drawn in red behind the cobalt loop for comparison. (c) Dysprosium hysteresis loop taken at 2 K at grazing incidence (70◦). The shape of the hysteresis loops measured by VSM along the perpendicular axis of the sample rapidly evolved with decreasing temperature from square loops at RT to wasp-waist shaped loops, as shown in Fig. 1, starting at 240 K. There are different ways to obtain this kind of loop [28]. Most of them require an AF interaction between magnetic phases with contrasting coercivities or anisotropies [29], indicating a possible nonuniform distribution of cobalt and dysprosium in the films. As will be shown, such a structure agrees with the results obtained from the analysis of their TEY spectra. This might explain the relatively large coercive fields of the analyzed samples and the absence of triple hysteresis loops at fields below 6 T at temperatures close to their Tcomp,as reported in samples of similar concentration and thickness [5,20]. B. XMCD hysteresis loops Figure 2shows the hysteresis loops of sample DCC at RT and 2 K for the cobalt and dysprosium sublattices obtained by measuring the intensity of the Co L3peak and the Dy M5peak, respectively. Their change in shape with field orientation at RT [Figs. 2(a) and 2(b)], from squared at 0◦ orientation to S shaped at 70◦field orientation, shows that the samples had PMA, as observed by VSM magnetometry. The loops of the cobalt and dysprosium sublattices are nearly identical. A small decoupling between both sublattices is only noticeable at high fields. The magnetization of cobalt remains constant at high fields up to 6 T whereas that of dysprosium seems to decrease steadily with the increasing field from zero field. A similar kind of decoupling, although more pronounced than in the present case, has been observed in NdCo films [21]. The effect was caused by a portion of Nd that was paramagnetic. In the present case, the reduction in the dysprosium magnetization must come from dysprosium atoms which must be AF oriented at the saturation field. This should be paramagnetic dysprosium, but also dysprosium which is poorly AF coupled to cobalt. At 2 K, only the hysteresis loop of the dysprosium sublattice in sample DCM was taken at near the plane field orientation (70◦), shown in Fig. 2(c). The shape of the loop shows that the films were far from being magnetically saturated up to 6 T, indicating that the PMA energy of the samples was strongly increased at this temperature. The lack of a coercive field in the loop shows that the measured magnetic moments experienced a progressive rotation with the applied field intensity. The loop shows a shape asymmetry between the positive and negative branches. C. XMCD Cobalt The magnetic moments of cobalt were deduced from their L2,3spectra. The method used to extract the cobalt absorption coefficient to correctly apply the XMCD sum rules [30,31] is fully described in Ref. [21] and it considers saturation effects [32]. The number of holes was calculated comparing their unpolarized absorption spectra with that of a pure cobalt reference sample deposited in similar conditions as the rest of the films. The number of holes for this reference sample was set to the tabulated for pure cobalt, 2.49, yielding a magnetic moment at 2 K of 1.79 ±0.02μB, which is similar to that measured by others (1.77 μB)[33]. As can be observed from Figs. 3(a) and 3(b), the shape of the spectra was almost identical to the cobalt reference except in their intensity, which was lower and almost independent of the sample orientation angle or temperature. Their number of holes reduced to approximately 91% those of pure cobalt. The total magnetic moment of the samples together with the related orbital and spin components and orbital to spin ratios are shown in Table II. The total magnetic moment of the two alloys at 2 K and normal incidence (easy magnetic axis) was similar within the error, of the order of 1.33 ±0.03μB.This value is in agreement with that expected from those observed in NdCo alloys as a function of the number of holes [21], and they would correspond to a RE concentration higher than the nominal, of the order of DyCo3.5. The magnetic moment obtained at RT (only measured at normal incidence in DCC) was practically the same than at 2 K, 1.34 ±0.03μB. The anisotropy of the orbital moment and the dipolar moment [14,34]weremL=m0◦−m70◦=−0.04 and −0.013μB, respectively. These values are small. They discard cobalt as the source of PMA in the films. The negative sign indicates an in-plane anisotropy for the cobalt sublattice at RT [14,35,36]. This is in coincidence with what we observed in NdCo alloys [21] and it is the expected behavior if dysprosium 054439-4 MAGNETIC MOMENT ORIENTATION AND IN-DEPTH … PHYSICAL REVIEW B 104, 054439 (2021) FIG. 3. X-ray absorption (XAS) spectra obtained at the Co L2,3 edge of a pure cobalt thin film compared with the spectra of cobalt in (a) DCC and (b) DCM thin films taken at 2K and 0◦(blue), 20◦ (green),45◦(orange), and 70◦(red) beam incidence angles (magnetic field orientation angle) with respect to the normal to the sample. The most intense spectrum (black line) is from pure cobalt. In the inset, the XMCD spectra taken at different orientation field angles, using the same code color. causes the observed PMA of the samples because of the oblate shape of its 4forbital. The total magnetic moment measured at 2 K is displayed in Fig. 4as a function of the field orientation angle. It decreases in both samples with increasing field angle orientations because of the uncompleted magnetic saturation of the alloy at the 6 T applied field. The dashed curve displayed in Fig. 4is the fit of the averaged magnetic moments of the two samples using a cosine function plus a constant. The constant could be interpreted as the portion of the cobalt magnetic moment that it is oriented parallel to the field. This constant is only 10% of the total intensity, indicating that most of the cobalt magnetic moments were fixed at the easy axis direction. The orbital magnetic moment at 0◦field orientation increased a small quantity in both samples with respect to their value at RT, from 0.12 μBto 0.16μB(sample DCC). For the rest of the field-orientation angles, only the orbital to effective spin moments ratio can be compared because of the uncompleted magnetic moment saturation of the films. This ratio is the highest at 0◦and it decreases in both samples, from 0.14 at normal orientation to 0.09 (0.10 at 70 ◦in sample DCC). This decrement was small but the effect appeared in both samples. It might indicate that the PMA of the alloy involves either an anisotropy in the orbital moment of cobalt in the same direction of the easy axis or a larger effective spin component at angles far from the easy axis, which might come from cobalt atoms in more isotropic locations. TABLE II. Total magnetic moment (mtot), efective spin (m∗ s) moment, orbital (mo) moment, and its ratio mo/m∗ s, of cobalt obtained by XMCD in DyCo alloys (samples DCC and DCM) and YCo alloys (YCC and YCM). All moments are given in μBunits. m∗ sand, therefore, mtot have not been corrected by the mTz term, the dipole moment of spin. Error bars are of the order of 2% for msand mo. As a reference, pure cobalt (thin film) at 2 K: ms=1.58 μB; mo=0.21 μB;m tot =1.79 μB Sample T Field orientation angle 0◦20◦45◦70◦ DCC RT m∗ s1.22 −−1.11 mo0.12 −−0.16 mtot 1.34 −−1.25 mo/m∗ s0.09 −−0.12 2K m ∗ s1.17 1.15 0.91 0.41 mo0.16 0.10 0.08 0.06 mtot 1.33 1.25 0.99 0.50 mo/m∗ s0.14 0.09 0.09 0.10 DCM RT m∗ s−−−1.08 mo−−−0.16 mtot −−−1.24 mo/m∗ s−−−0.15 2K m ∗ s1.15 1.10 0.79 0.54 mo0.15 0.10 0.06 0.04 mtot 1.30 1.20 0.85 0.58 mo/m∗ s0.13 0.09 0.08 0.09 YCC 2 K m∗ s1.28 −1.24 1.28 mo0.14 −0.19 0.16 mtot 1.42 −1.43 1.44 mo/m∗ s0.11 −0.16 0.13 YCM 2 K m∗ s1.26 −1.18 1.22 mo0.07 −0.18 0.17 mtot 1.33 −1.36 1.39 mo/m∗ s0.06 −0.15 0.14 FIG. 4. Total magnetic moment of cobalt (solid dots) and dysprosium (empty dots) in samples DCC (red dots) and DCM (blue dots) measured at 2 K. The black dashed line in (a) is the fit to a cosine function plus a constant. Black dots and triangles are cobalt moments measured at RT. The estimated error of the measurement is the width of the dots. 054439-5 J. DÍAZ AND C. BLANCO-ROLDÁN PHYSICAL REVIEW B 104, 054439 (2021) FIG. 5. Dy M5spectra of sample DCM obtained at RT [spectra at (a), (b)] and 2 K [spectra (c), (d)]. The spectra taken with rightcircular polarization are (a), (c). (b), (d) are the spectra taken using left-circular polarization. RT spectra were taken at 0◦(dark blue line) and 70◦(red line) incident angles. 2 K spectra were taken at 0◦(dark blue line), 20◦(light blue line), 45◦(orange line), and 70◦(red line) incident angles. To discard that the observed anisotropy of the cobal magnetic moment was only caused by the chemical bonding to the RE, YCo films deposited in similar conditions of concentration, film thickness and deposition process were measured by XMCD. The chemical interaction of yttrium is equivalent to that of RE, with a nearly empty 4dband but without an occupied 4forbital, i.e., with no 4fmagnetic moment. Actually, the YCo phase diagram is very similar to that of DyCo [37,38]. Therefore, the atomic structure of the YCo alloy should be similar to that of DyCo. The magnetic moments of cobalt in YCo measured at RT (normal orientation only) and 2 K are displayed in Table II. The values are about 10% smaller in the multilayer than in the continuous film and they increase in both films when temperature goes from RT to 2 K, in contrast to the observed in the DyCo alloys where there was almost no difference. The YCo alloys were magnetically soft and their magnetic anisotropy was in the plane. Their orbital to effective spin ratios were similar to that found at normal orientation in the DyCo films but they did not show the strong decrease in their value with the increasing orientation angle as observed in DyCo. This fact, together with the cosinelike variation in the total magnetic moment of cobalt in the DyCo films, indicates that their probed cobalt atoms are mostly located at magnetically anisotropic environments. By comparison with the YCo alloy, the magnetic anisotropy found in the cobalt sublattice of the DyCo films must be induced by the magnetic interaction with the dysprosium atoms. Therefore, a similar angle variation in the magnetic moment of the dysprosium sublattice as that found in cobalt would be expected. D. XMCD Dy In dysprosium, the most relevant changes in the spectra occur in the Dy M5edge. Figure 5shows the Dy M5taken in sample DCM at RT and 2 K for the two circular polarizations at different angles. Sample DCC showed similar changes. The Dy M5spectral shape is defined by three intense TABLE III. Efective spin moment,m∗ s, orbital moment, mo, dipole moment of spin, mTz, and total magnetic moment, mtot,of dysprosium obtained by XMCD in samples DCC and DCM. All moments are given in μBunits. The estimated error bars is of 2% in m∗ s,m o,andm Tz.m Tz=mo 6[m∗ s mo−ms mo][15], using the theoretical value of ms mo=0.475 [16]. mtot =mo+(m∗ s-6mTz). Sample T Field orientation angle 0◦20◦45◦70◦ DCC RT m∗ s−1.92 −−−1.92 mo−1.42 −−−1.41 mTz −0.09 −−−0.10 mtot −2.78 −−−2.74 2K m ∗ s2.78 2.51 2.19 1.46 mo4.19 3.81 3.42 2.23 mTz 0.26 0.23 0.19 0.13 mtot 8.18 7.43 6.67 4.35 DCM RT m∗ s−−−−0.91 mo−−−−1.44 mTz −−−−0.07 mtot −−−−2.81 2K m ∗ s2.84 2.64 2.14 1.61 mo4.21 3.93 3.17 1.61 mTz 0.28 0.26 0.21 0.15 mtot 8.2 7.66 6.19 4.73 peaks, marked in the figure as peaks AP, TR, and PP, which are located at photon energies 1294.5 eV, 1296.7 eV, and 1298.6 eV, respectively. Their relative intensity changes with the polarization sign and with the field orientation angle. At RT, the changes with the angle are small, but they are very evident at 2 K. At this temperature, peak PP is the most intense at C+polarization and normal incidence. Within the same polarization, peak PP decreases in intensity as the field orientation angle (incident x-ray beam angle) increases. The opposite is observed using C−polarization. In this case, the peak marked AP is the most intense at normal incidence. For both polarizations, peak TR increases in intensity when the incident angle increases. As will be shown, peaks PP, AP and TR are associated to electronic transitions to states where the magnetic moment of the related 4forbital is parallel, antiparallel, or transverse to the circularly polarized x-ray beam wave vector, respectively. It is important to note that, at RT, peak PP is also the most intense in C−polarization. This is opposite to what happens at 2 K, especially at 70◦, where the measured magnetic moment of dysprosium is the lowest and comparable to that measured at RT. The XMCD spectra of the Dy M4,5edge were analyzed following the process explained in Ref. [21]. Table III shows the magnetic moments of dysprosium in each of the samples at RT and 2 K. The relative weakness of the AF interaction with cobalt and the structural disorder of the alloy makes the magnetic moment of the dysprosium atoms be dispersed in its orientation with respect to the cobalt magnetic moment, forming what is called an asperomagnet [39]. The moment orientation of the RE atoms when the alloy is magnetized in the easy axis is usually taken as uniform and symmetrically distributed around this axis within a cone with a half opening 054439-6 MAGNETIC MOMENT ORIENTATION AND IN-DEPTH … PHYSICAL REVIEW B 104, 054439 (2021) angle θC(for instance, θC=π/2 represents the distribution of moments in a semisphere). For field orientations away from the easy axis, a dispersion in the shape and opening angle of the cone is expected. In this case, we assume that the resulting distribution of the dysprosium can be approximated by a cone that has its symmetry axis deviated from the field direction, an angle ϕC. The magnetic moment measured is the averaged sum within the cone of the magnetic moment component along the field orientation axis. At the easy axis, this sum is MDy cos2θC/2, where MDy is 9.8μB, the dysprosium magnetic moment of its 4forbital. The magnetic anisotropy would then change the value of the measured magnetic moment by opening the cone angle and changing its symmetry axis orientation. At RT, the dysprosium magnetic moment has almost no difference at both orientations, as expected from the hysteresis loops. The PMA of dysprosium doesn’t have enough energy to distort its magnetic moment distribution cone at RT. There is not a significant variation between the values obtained in both samples, which are about −2.8μB(sample DCM only measured at 70◦field orientation). This quantity is small. The lowest magnetic moment that can be measured assuming that all dysprosium atoms are AF coupled to Co, i.e., uniformly distributed within a cone of half opening angle θC=π/2 (semisphere), is MDy/2=−4.9μB, i.e., half the value of its total magnetic moment. This means that there should be dysprosium atoms with their moment orientation opposite to that of those AF coupled to cobalt. Theoretical calculations estimated that the averaged magnetic moment of Dy decays to half its value at about 300 K in crystalline DyCo5 [40]. The lower values observed in the present case should have to do with the intrinsic disorder of the measured alloys, with dysprosium atoms distributed in different atomic environments where, in some of them, the exchange coupling to cobalt should be weaker than in crystalline DyCo5or possibly nonexistent. The analysis of the Dy M5spectra exposed in a later section searches to understand how these dysprosium atoms are distributed through the depth proved by TEY and how this can affect the TEY measurements, including the possible presence of segregated dysprosium at the interface with the aluminum capping layer. Figure 4(right-side scale) displays the variation of the dysprosium magnetic moment as a function of the field orientation angle at 2 K compared to that of cobalt. Both samples have similar values which decay with the angle at a slower pace than in the cobalt sublattice. This magnetically less anisotropic behavior of dysprosium is somehow contrary to what was expected: the magnetic moment of the RE should be, compared to cobalt, the one fixed with the highest energy to the easy axis since the PMA in these alloys must stem from it, as deduced from the analysis done in the previous section (Sec. III C). The total magnetic anisotropy of the alloy should depend on the distribution of the crystal field orientation at the RE sites [2] and its influence on the magnetic moment of the bonding TMs at each RE site. Following the single ion anisotropy model [2], both crystal field and RE-TM indirect exchange are expected to be tightly related. Therefore, the RE environments that most contribute to the magnetic anisotropy of the alloys should be strongly exchange coupled to the TM as well. The magnetically less anisotropic character of the measured dysprosium sublattice indicates that only a portion of the dysprosium atoms probed by TEY should be active magnetic anisotropy generators. The magnetic field felt by dysprosium is the sum of the external applied field and the molecular field, which is mainly provided by the interatomic exchange interaction with cobalt atoms, whose strength can be estimated in, at least, more than 150 T [21]. As has been observed, the rotation of the cobalt moment at grazing orientations is small. Therefore, the effective molecular field felt by the dysprosium should be closer to that of the applied field at those sample orientation angles, meaning that a portion of the probed dysprosium should be somehow decoupled or poorly coupled to cobalt, as stemming from the analysis done at RT. One of the challenges in the analysis of the Dy M5spectra, shown in the next sections, is to determine the location of the dysprosium which are apparently weakly interacting to cobalt. A way to compare the magnetization measured in the bulk with the magnetization measured near the surface (XMCD using TEY) is to evaluate how these magnetic moments found by XMCD fit with those deduced from VSM, shown in Table I. When the magnetic moment of the cobalt used to calculate the total magnetization of the alloy is that obtained by XMCD, 1.33μB, the magnetic moment of dysprosium that it is needed to match the magnetization measured by VSM at RT is 3.8μB, 1μBabove that measured by XMCD. This value is still below the expected if all dysprosium magnetic moments were AF coupled to cobalt. When the same estimation is done at 2 K, the magnetic moment expected for dysprosium is 7.3μB, close to 1μBsmaller than that found by XMCD. These differences between bulk (VSM) and surface (XMCD) are similar to the reported by Chen et al. [5] and Luo et al. [20]. The explanation given to this effect in those cited reports was the presence of a higher dysprosium concentration at the region near surface than in the bulk due to RE segregation in their samples. If that was happening in our samples, their cobalt and dysprosium moments in the bulk should be higher than that measured by XMCD. For instance, if the cobalt moment in the bulk raised to 1.50 μB, the related dysprosium moment should be 4.7μB, which is almost 2 μBhigher than that measured by XMCD. This would set the surface at a higher Tcomp than in the bulk. The Tcomp of a ferrimagnetic RE-TM alloy essentially depends on the magnetic exchange strength between the RE and the TM atoms. If the segregated RE atoms at the region near the surface do not bond tight to cobalt, their exchange interaction will weaken. The effect, in terms of magnetic moments, will be similar to an increase of the Tcomp because, above this temperature, there will be dysprosium moments that will not be AF coupled to cobalt, reducing the total moment of the dysprosium sublattice. Below Tcomp, the effect will be the opposite, i.e., they will add up in moment to the moment of the AF coupled-to-cobalt dysprosium. This is not an unlikely situation regarding the magnetic moments of dysprosium measured by XMCD, which are well below the expected if all RE atoms were AF coupled to cobalt. Moreover, if RE segregation occurs it is because it favors RE-RE metallic bonding. To demonstrate the presence of these two kinds of RE atoms requires a technique able to detect them. 054439-7 J. DÍAZ AND C. BLANCO-ROLDÁN PHYSICAL REVIEW B 104, 054439 (2021) The next section shows a way to do it in a quantitative way by analyzing the circularly polarized Dy M5spectra. Dysprosium is especially well adapted for this kind of analysis, although it should be applicable to most REs, with the exception of those with L=0 like Gd+3. IV. SPECTRAL ANALYSIS METHOD FOR THE DY M4,5 SPECTRA A. Decomposition of the Dy M4,5spectrum Like most REs, the electrons in the 4forbital of dysprosium are well screened by the valence band orbitals and they behave as in an isolated atom. Actually, the Dy M4,5 edge spectrum, which involves electronic transitions form the 3dto the 4forbital, is practically insensitive to the dysprosium chemical environment and is well fitted by calculating it using only intratomic interactions [41,42]. The intensity of these transitions can be notably influenced by the bonding with other magnetic atoms through its indirect exchange magnetic interaction and the resulting crystal field. The relative weakness of these interactions permits us to treat them as perturbations whose most important effect is to break the degeneracy of the quantum number Mof the 4fangular moment component Jz. When the interaction is magnetic, this effect consists of orienting the magnetic moment of the 4forbital along a specific direction. Therefore, to a good approximation, only the intensity, but not the shape, of the Dy M4,5lines are modulated by the orientation of the total angular moment of the 4forbital with respect to the direction of the polarized x ray. The allowed transitions in the dipole approximation are those in which J=0,±1. If light is circularly polarized, only m=±1 transitions are allowed. Therefore, if the beam is perfectly oriented parallel (antiparallel) to the magnetic moment of the 4forbital, the resulting M4,5spectrum will be built with only those excitations where J=0,±1 and m=1(−1). We will call these spectral components PP if m=−1 and AP when m=1. The circular dichroism spectrum, XMCD, is the difference between these two spectrum. The sum rules related to these transitions give rise to the XMCD sum rules that permit determining both the magnetic spin and orbital moments of the 4forbital. m=0 transitions occur when the light is linearly polarized along the magnetic moment direction. This spectral component is not present in the XMCD spectrum because it depends on M2[42]. We will call this component TR. The excitations of all three spectral components PP, AP, and TR occur when the 4fmagnetic moment and the incident circularly polarized light are not parallel. This is because the electric field felt by the 4felectrons is equivalent to the sum of two circularly polarized fields with opposite helicities, and a linear polarized field aligned in the direction of the magnetic moment. The detailed calculation of the amplitude of these fields is explained in Appendix. The dependency of the amplitude of these polarized field with the magnetic moment orientation angle θis P=e±iϕ √2(cos θ±1) √2P−1 zm+(cos θ∓1) √2P1 zm+P0 zmsin θ. (1) FIG. 6. Angle coefficients for PP, AP and TR as a function of (a) magnetic moment orientation angle with respect to the circularly polarized incident beam, θ, and (b) cone half opening angle θC. P−1 zm,P1 zm, and P0 zmare the dipole operators for rightand left-circular polarizations, and linear polarization along the z axis, respectively. ϕis an arbitrary phase. Taking into account the previous expressions, the modulation of the intensity of each of the spectral components (PP, AP, and TR) with the orientation angle θis given by the following expression (see Appendix): PP +AP +TR =(cos θ±1)2 4A−1 JJ+(cos θ∓1)2 4A1 JJ+sin2θ 2A0 JJ, (2) where Aq JJare the reduced angular integers. They are directly related to the transitions J=0,±1 and q=m. The distribution in energy and intensity of these transitions is well tabulated, both theoretically and experimentally [41–43]. Figure 6(a) displays the coefficients that multiply to the angular integers Aq JJshown in Eq. (2) as a function of the magnetic moment orientation angle θwith respect to the incident beam. As expected, the coefficients that multiply to the TR (A0 JJ) and AP (A1 JJ) components increase their value only at angles closer to π/2. The most common situation found in the studied alloys, which have no defined crystal structure, is the one in which the orientation of the magnetic moment of dysprosium is not well defined but is distributed over a range of angles due to structural and thermal disorder. This distribution is assumed to be uniform and symmetrical with respect to the axis of a cone with a half opening angle θC. This distribution modifies the coefficients of the angular integers. The new coefficients in this situation are obtained by averaging the angle coefficients defined in Eq. (2) for each component within the cone angle θC, resulting in the following expression as a function 054439-8 MAGNETIC MOMENT ORIENTATION AND IN-DEPTH … PHYSICAL REVIEW B 104, 054439 (2021) of θC: PP +AP +TR =1 31−cos6θC 2 sin2θC 2 A−1 JJ+1 3sin4θC 2A1 JJ +1 3 (cos3θC−3 cos θC+2) 1−cos θC A0 JJ.(3) Figure 6(b) shows the coefficients of each excitation component as a function of the cone half-opening angle θC.The coefficients of the TR and AP components increment its value at large angles, but not as fast as in the case of a defined angle orientation. This is better observed when the ratio between the TR and AP components, shown in both figures, are compared. These ratios are substantially smaller in the cone angle coefficients [Fig. 6(b)]. When the cone has an inclination angle ϕCwith respect to the beam direction, the components PP’, AP’, and TR’ of the magnetic moment in the cone are projected in the beam axis following expression Eq. (2), substituting the angle θ by ϕC. The PP’ component is calculated using Eq. (3), the AP’ component is the same as Eq. (2) but interchanging the factors A−1 JJby A1 JJ, and the TR’ component is calculated by multiplying TR by sin2θC/2. Since the cross-section values of the angular integers are tabulated [41,42] and the angle dependent modulation of the PP, AP and TR components are known [Eqs. (2) and (3)], it is possible to determine the orientation of the magnetic moment of any RE in any chemical environment just by identifying their PP, AP, and TR components and checking their relative intensities. This is something that can be inferred also by comparing the magnetic moment deduced from the application of the XMCD sum rules and comparing it with the total magnetic moment of the RE. But this is only valid if there is a single magnetic form of dysprosium. Things become more complicated if the analyzed material contains RE in different magnetic states, i.e., RE with different magnetic moment orientation distributions. The deconvolution of the spectra in their PP, AP, and TR components is then required. This could be done by their direct calculation using numerical methods as the employed by Thole et al. [41]. This is the approach used in Ref. [24], but it is important to note that the build of the RE M4,5spectrum only requires, to a good approximation, the shape of the spectral component, which can be isolated by spectral methods. The Dy M5spectrum is especially suited for this kind of analysis. Due to the large value of the orbital moment, L,ofthe 4forbital in dysprosium, the splitting between the PP and AP components in the M5edge is the largest among the RE. Dy is the RE that has the lowest overlap between these two sets of excitations, which is estimated in less than 5% [42]. This eases the extraction of both spectral components from any XMCD spectra at the Dy M5edge. Figure 7shows the XMCD spectrum for Dy M5. Only the PP and AP components are in the spectra, which are well distinguished because they have opposite signs. These two spectral shapes can be taken, as a first approximation, to the PP and AP true components of the spectra. The TR spectral component is extracted by subtraction of these two approximated components to the related circularly polarized spectra. For the subtraction, each FIG. 7. (a) XMCD spectrum of the DCC sample at RT and normal incidence and its related PP and AP components; (b) C− polarized spectrum of DCC sample taken at RT and normal incidence with their related PP, AP, and TR components; (c) C+polarized spectrum of DCC sample taken at RT and normal incidence with their related PP, AP, and TR components of the components must be multiplied by a coefficient which is related to its relative spectral intensity, which depends on the sum of all the RE magnetic moment orientation distributions probed. These coefficients must be the same in both circularly polarized spectra, bearing in mind that the PP and AP components are interchanged in the two polarizations when the spectra are taken at the same magnetic field direction. The determination of the value of these coefficients is not precise, since it depends on how well the shape of the TR component is known. In our approach, we used the spectral line shape theoretically calculated by Thole et al. [41]. This so-extracted TR component contains the overlap region between the PP and AP components. This produces some shape differences between the TR obtained at different beam orientation angles because the proportion of the TR component respect to the PP and AP components changes. In our case, the spectra 054439-9 J. DÍAZ AND C. BLANCO-ROLDÁN PHYSICAL REVIEW B 104, 054439 (2021) No. FIS2016-76058 (AEI/FEDER, EU) and No. PID2019104604RB/AEI/10.13039/501100011033. APPENDIX: ORIENTATION DEPENDENCE OF LIGHT ABSORPTION This Appendix shows the details of the calculation of the intensity absorbed by circularly polarized light when the orientation of the angular moment of the 4forbital forms an angle θwith the direction of the wave vector  kwhich is chosen parallel to the zaxis. The components of the electric field of the circularly polarized light in the frame of the 4f angular moment, with its zmaxis along its quantization axis, are calculated by making a first rotation of an angle ϕin the xy polarization plane (zaxis as the rotation axis) followed by a rotation of an angle θaround the resulting yaxis after the first rotation: ⎛ ⎝ xm ym zm ⎞ ⎠=⎛ ⎝ cos ϕ−sin ϕ0 sin ϕcos ϕ0 001 ⎞ ⎠⎛ ⎝ cos θ0−sin θ 01 0 sin θ0 cos θ⎞ ⎠⎛ ⎝ x y z⎞ ⎠. (A1) Therefore, for right (−) and left (+) circular polarization: ⎛ ⎝ xm ym zm ⎞ ⎠=e±iϕ √2⎛ ⎝ cos θ ∓i sin θ⎞ ⎠.(A2) By using this result, the electric dipole operator Pwritten in the frame of the 4forbital read P=e±iϕ √2P0 xmcos θ∓iP0 ym+P0 zmsin θ.(A3) The superscript in the dipole operator indicates the polarization state of the electric field in the frame of the 4f orbital: 0 is lineal, 1 left circular, and +1 right circular. The electric dipole operator can be expressed in the components parallel to the quantization axis zmof the 4forbital using the relations P0 xm=1 √2P−1 zm+P1 zm(A4) and P0 ym=i √2P−1 zm−P1 zm.(A5) Then P=e±iϕ √2(cos θ±1) √2P−1 zm+(cos θ∓1) √2P1 zm+P0 zmsin θ. (A6) The absorption cross section for the excitation from a state |αmJto a state |αmJis, in the dipole approximation, σαmJ−→αmJ=4π2α0¯hω|αmJ|P|αmJ|2.(A7) The cross section for circular polarized light is obtained substituting Eq. (1)inEq.(2), σαmJ−→αmJ=4π2α0¯hωSαJαJ(cos θ±1)2 4A−1 JJ +(cos θ∓1)2 4A1 JJ+sin θ2 2A0 JJ,(A8) where SαJαJis the radial integer and Aq JJare the angular integers. Under the assumption of a weak crystal field, as happens in dysprosium, the values of the radial and angular integers do not change. Only the relative orientation of the moment with respect to incident beam changes. We redefine the angular integers as the absorption cross sections for the corresponding situation in which the polarized beam and the magnetization are parallel (q=0,±1). Then, the θ-dependent functions that multiply to each of the related q=0,±1 cross sections are the coefficients for the TR (q=0), PP (q=−1) and AP (q=+1) components: PP +AP +TR =(cos θ±1)2 4A−1 JJ+(cos θ∓1)2 4A1 JJ+sin2θ 2A0 JJ. (A9) [1] K. H. J. Buschow, Intermetallic compounds of rare-earth and 3d transition metals, Rep. Prog. Phys. 40, 1179 (1977). [2] R. Skomski and D. Sellmyer, Anisotropy of rare-earth magnets, J. Rare Earths 27, 675 (2009). [3] C. Blanco-Roldán, Y. Choi, C. Quirós, S. M. Valvidares, R. Zarate, M. Vélez, J. M. Alameda, D. Haskel, and J. I. Martín, Tuning interfacial domain walls in GdCo/Gd/GdCo’ spring magnets, Phys. Rev. B 92, 224433 (2015). [4] R. Morales, J. I. Martín, and J. M. Alameda, Domain walls and macroscopic spin-flip-like metamagnetism in GdxCo1−x/GyCo1−yexchange-coupled double layers, Phys. Rev. B 70, 174440 (2004). [5] K. Chen, D. Lott, F. Radu, F. Choueikani, E. Otero, and P. O, Observation of an atomic exchange bias effect in DyCo4film, Sci. Rep. 5, 18377 (2015). [6] C. Blanco-Roldán, C. Quirós, A. Sorrentino, A. HierroRodríguez, L. M. Álvarez-Prado, R. Valcárcel, M. Duch, N. Torras, J. Esteve, J. I. Martín, M. Vélez, J. M. Alameda, P. E., and S. Ferrer, Nanoscale imaging of buried topological defects with quantitative x-ray magnetic microscopy, Nat. Commun. 6, 8196 (2015). [7] L. Caretta, M. Mann, F. Büttner, K. Ueda, B. Pfau, C. M. Günther, P. Hessing, A. Churikova, C. Klose, M. Schneider, D. Engel, C. Marcus, D. Bono, K. Bagschik, S. Eisebitt, and G. S. D. Beach, Fast current-driven domain walls and small skyrmions in a compensated ferrimagnet, Nat. Nanotech. 13, 1154 (2018). [8] A. Hierro-Rodríguez, C. Quirós, A. Sorrentino, L. M. AlvarezPrado, J. I. Martín, J. M. Alameda, S. McVitie, E. Pereiro, M. Vélez, and S. Ferrer, Revealing 3d magnetization of thin 054439-16 MAGNETIC MOMENT ORIENTATION AND IN-DEPTH … PHYSICAL REVIEW B 104, 054439 (2021) films with soft x-ray tomography: Magnetic singularities and topological charges, Nat. Commun. 11, 6382 (2020). [9] D. Markó, F. Valdés-Bango, C. Quirós, A. Hierro-Rodríguez, M. Vélez, J. I. Martín, J. M. Alameda, D. S. Schmool, and L. M. Alvarez-Prado, Tunable ferromagnetic resonance in coupled trilayers with crossed in-plane and perpendicular magnetic anisotropies, Appl. Phys. Lett. 115, 082401 (2019). [10] S. Mangin, M. Gottwald, C-H. Lambert, D. Steil, V. Uhlíˇ r, L. Pang, M. Hehn, S. Alebrand, M. Cinchetti, G. Malinowski, Y. Fainman, M. Aeschlimann, and E. E. Fullerton, Engineered materials for all-optical helicity-dependent magnetic switching, Nat. Mater. 13, 286 (2014). [11] C. Schubert, A. Hassdenteufel, P. Matthes, J. Schmidt, M. Helm, R. Bratschitsch, and M. Albrecht, All-optical helicity dependent magnetic switching in an artificial zero moment magnet, Appl. Phys. Lett. 104, 082406 (2014). [12] J. Becker, A. Tsukamoto, A. Kirilyuk, J. C. Maan, T. Rasing, P. C. M. Christianen, and A. V. Kimel, Ultrafast Magnetism of a Ferrimagnet Across the Spin-Flop Transition in High Magnetic Fields, Phys.Rev.Lett.118, 117203 (2017). [13] K. Hummler and M. Fähnle, Full-potential linear-muffin-tinorbital calculations of the magnetic properties of rare-earth– transition-metal intermetallics. I. Description of the formalism and application to the series RCo5(R=rare-earth atom), Phys. Rev. B 53, 3272 (1996). [14] J. Stöhr, Exploring the microscopic origin of magnetic anisotropies with X-ray magnetic circular dichroism (XMCD) spectroscopy, J. Magn. Magn. Mater. 200, 470 (1999). [15] S. P. Collins, D. Laundy, C. C. Tang, and G. van der Laan, An investigation of uranium M4,5 edge magnetic x-ray circular dichroism in US, J. Phys.: Condens. Matter 7, 9325 (1995). [16] Y. Teramura, A. Tanaka, B. Thole, and T. Jo, Effect of Coulomb interaction on the x-ray magnetic circular dichroism spin sum rule in rare earths, J. Phys. Soc. Jpn. 65, 3056 (1996). [17] N. Bergeard, A. Mougin, M. Izquierdo, E. Fonda, and F. Sirotti, Correlation between structure, electronic properties, and magnetism in CoxGd1−xthin amorphous films, Phys.Rev.B96, 064418 (2017). [18] E. Haltz, R. Weil, J. Sampaio, A. Pointillon, O. Rousseau, K. March, N. Brun, Z. Li, E. Briand, C. Bachelet, Y. Dumont, and A. Mougin, Deviations from bulk behavior in TbFe(Co) thin films: Interfaces contribution in the biased composition, Phys. Rev. Materials 2, 104410 (2018). [19] L. Baczewski, D. Givord, J. Alameda, B. Dieny, J. Nozieres, J. Rebouillat, and J. Prejean, Magnetism in rare-earth-transition metal systems. magnetization reversal and ultra-high susceptibility in sandwiched thin films based on rare-earth and cobalt alloys, Acta Phys. Pol. A 83, 629 (1993). [20] C. Luo, H. Ryll, C. Back, and F. Radu, X-ray magnetic linear dichroism as a probe for non-collinear magnetic state in ferrimagnetic single layer exchange bias systems, Sci. Rep. 9, 18169 (2019). [21] R. Cid, J. M. Alameda, S. M. Valvidares, J. C. Cezar, P. Bencok, N. B. Brookes, and J. Díaz, Perpendicular magnetic anisotropy in amorphous NdxCo1−xthin films studied by x-ray magnetic circular dichroism, Phys. Rev. B 95, 224402 (2017). [22] J. Díaz, R. Cid, A. Hierro, L. M. Álvarez-Prado, C. Quirós, and J. M. Alameda, Large negative thermal expansion of the Co subnetwork measured by EXAFS in highly disordered Nd1-xCox thin films with perpendicular magnetic anisotropy, J. Phys.: Condens. Matter 25, 426002 (2013). [23] M. D. Davydova, K. A. Zvezdin, J. Becker, A. V. Kimel, and A. K. Zvezdin, h−tphase diagram of rare-earth–transitionmetal alloys in the vicinity of the compensation point, Phys. Rev. B 100, 064409 (2019). [24] K. Chen, D. Lott, F. Radu, F. Choueikani, E. Otero, and P. Ohresser, Temperature-dependent magnetic properties of ferrimagnetic DyCo3alloy films, Phys. Rev. B 91, 024409 (2015). [25] C. Quirós, I. Popa, O. Robach, D. Wermeille, J. Díaz, R. Felici, and S. Ferrer, Stacking dependent disordering processes in Gd/Co/Pt(111) studied with surface x-ray diffraction, Phys. Rev. B 78, 195406 (2008). [26] A. Barla, J. Nicolás, D. Cocco, S. M. Valvidares, J. HerreroMartín, P. Gargiani, J. Moldes, C. Ruget, E. Pellegrin, and S. Ferrer, Design and performance of BOREAS, the beamline for resonant x-ray absorption and scattering experiments at the ALBA synchrotron light source, J. Synchrotron Radiat. 23, 1507 (2016). [27] C. Blanco-Roldán, Magnetic interactions in rare earth-transition metal systems and their study by synchrotron radiation techniques PhD thesis, Universidad de Oviedo, 2017. [28] L. H. Bennett and E. Della Torre, Analysis of wasp-waist hysteresis loops, J. Appl. Phys. 97, 10E502 (2005). [29] M. V. Sapozhnikov, Y. V. Petrov, N. S. Gusev, A. G. Temiryazev, O. L. Ermolaeva, V. L. Mironov, and O. G. Udalov, Artificial dense lattices of magnetic skyrmions, Materials 13,99 (2020). [30] M. Altarelli, Orbital-magnetization sum rule for x-ray circular dichroism: A simple proof, Phys.Rev.B47, 597 (1993). [31] P. Carra, B. T. Thole, M. Altarelli, and X. Wang, X-Ray Circular Dichroism and Local Magnetic Fields, Phys. Rev. Lett. 70, 694 (1993). [32] R. Nakajima, J. Stöhr, and Y. U. Idzerda, Electron-yield saturation effects in L-edge x-ray magnetic circular dichroism spectra of Fe, Co, and Ni, Phys. Rev. B 59, 6421 (1999). [33]C.T.Chen,Y.U.Idzerda,H.-J.Lin,N.V.Smith,G.Meigs, E. Chaban, G. H. Ho, E. Pellegrin, and F. Sette, Experimental Confirmation of the X-Ray Magnetic Circular Dichroism Sum Rules for Iron and Cobalt, Phys. Rev. Lett. 75, 152 (1995). [34] J. Stöhr and H. König, Determination of Spin-and Orbital-Moment Anisotropies in Transition Metals by Angle-Dependent X-Ray Magnetic Circular Dichroism, Phys. Rev. Lett. 75, 3748 (1995). [35] G. Van Der Laan, Microscopic origin of magnetocrystalline anisotropy in transition metal thin films, J. Phys.: Condens. Matter 10, 3239 (1998). [36] Y. Suzuki and S. Miwa, Magnetic anisotropy of ferromagnetic metals in low-symmetry systems, Phys. Lett. A 383, 1203 (2019). [37] C. H. Wu and Y. C. Chuang, The Co-Y (cobalt-yttrium) system, J. Phase Equilib. 12, 587 (1991). [38] H. Okamoto, Supplemental Literature Review of Binary Phase Diagrams: Ag-Ho, Ag-Tb, Ag-Y, Cd-Na, Ce-Sn, Co-Dy, CuDy, Cu-Sn, Ir-Pt, Mg-Pb, Mo-Ni, and Sc-Y, J. Phase Equilib. Diffus. 35, 208 (2014). 054439-17 J. DÍAZ AND C. BLANCO-ROLDÁN PHYSICAL REVIEW B 104, 054439 (2021) [39] J. M. D. Coey, Magnetism in amorphous solids, in Amorphous Solids and the Liquid State,editedbyN.H.March,R.A.Street, and M. P. Tosi (Springer US, Boston, MA, 1985), pp. 433–466. [40] C. E. Patrick and J. B. Staunton, Rare-earth/transition-metal magnets at finite temperature: Self-interaction-corrected relativistic density functional theory in the disordered local moment picture, Phys. Rev. B 97, 224415 (2018). [41] B. T. Thole, G. van der Laan, J. C. Fuggle, G. A. Sawatzky, R. C. Karnatak, and J.-M. Esteva, 3d x-ray-absorption lines and the 3d94fn+1multiplets of the lanthanides, Phys.Rev.B32, 5107 (1985). [42] J. Goedkoop, X-Ray Dichroism of Rare Earth Materials (Krips Repro, Meppel, 1989). [43] J. B. Goedkoop, B. T. Thole, G. van der Laan, G. A. Sawatzky, F. M. F. de Groot, and J. C. Fuggle, Calculations of magnetic x-ray dichroism in the 3d absorption spectra of rare-earth compounds, Phys.Rev.B37, 2086 (1988). [44] G. van der Laan, E. Arenholz, A. Schmehl, and D. G. Schlom, Weak anisotropic x-ray magnetic linear dichroism at the Eu M4,5edges of fFerromagnetic EuO(001): Evidence for 4f-state Contributions, Phys. Rev. Lett. 100, 067403 (2008). [45] B. Das, R. Choudhary, R. Skomski, B. Balasubramanian, A. K. Pathak, D. Paudyal, and D. J. Sellmyer, Anisotropy and orbital moment in Sm-Co permanent magnets, Phys. Rev. B 100, 024419 (2019). [46] K. P. Shinde, V. M. Tien, L. Huang, H.-R. Park, S.-C. Yu, K. C. Chung, and D.-H. Kim, Magnetocaloric effect in Tb2O3and Dy2O3nanoparticles at cryogenic temperatures, J. Appl. Phys. 127, 054903 (2020). [47] N. A. Anderson, Q. Zhang, M. Hupalo, R. A. Rosenberg, J. W. Freeland, M. C. Tringides, and D. Vaknin, Magnetic properties of Dy nano-islands on graphene, J. Magn. Magn. Mater. 435, 212 (2017). [48] J. M. Tonnerre, M. De Santis, S. Grenier, H. C. N. Tolentino, V. Langlais, E. Bontempi, M. García-Fernández, and U. Staub, Depth Magnetization Profile of a Perpendicular Exchange Coupled System by Soft-X-Ray Resonant Magnetic Reflectivity, Phys. Rev. Lett. 100, 157202 (2008). 054439-18