Disentanglement of magnetic contributions in multi-component systems by using X-ray magnetic circular dichroism at a single absorption edge

X-ray magnetic circular dichroism (XMCD) has become in recent years an outstanding tool for studying magnetism. Its element specificity, inherent to core-level spectroscopy, combined with the application of magneto-optical sum rules allows quantitative magnetic measurements at the atomic level. These capabilities are now incorporated as a standard tool for studying the localized magnetism in many systems. However, the application of XMCD to the study of the conduction-band magnetism is not so straightforward. Here, it is shown that the atomic selectivity is not lost when XMCD probes the delocalized states. On the contrary, it provides a direct way of disentangling the magnetic contributions to the conduction band coming from the different elements in the material. This is demonstrated by monitoring the temperature dependence of the XMCD spectra recorded at the rare-earth L₂-edge in the case of RT₂ (R = rare-earth, T = 3d transition metal) materials. These results open the possibility of performing element-specific magnetometry by using a single X-ray absorption edge.

1. Introduction

The possibility of disentangling the magnetic contribution of different atomic species within the same material has been a challenge for a long time. Most of the experimental techniques aimed at studying the magnetic properties of materials are sensitive to the total magnetization of the measured system and, consequently, they cannot discern between the contributions of different atoms in the material. Within this scenario, X-ray magnetic circular dichroism (XMCD), the difference in absorption of left- and right-circularly polarized X-rays by a magnetized sample, emerges as an outstanding tool for studying magnetism by incorporating the element specificity of core-level spectroscopies (Funk et al., 2005; Lovesey & Collins, 1996; Stöhr, 1999).

The advantage of X-rays over optical techniques such as the Kerr effect lies in the fact that the absorption edges from a core level have energies which are characteristic for each element and, owing to the dipole selection rules, final states with different symmetries can be probed by choosing the initial state. In this way, as each element can be probed separately by appropriately choosing the absorption edge, XMCD opens the possibility of performing element-specific magnetic hysteresis measurements (Chen et al., 1993), magnetic domain imaging etc. (Kortright et al., 1999). However, while the capabilities of XMCD are squeezed in the case of localized states carrying a magnetic moment [f-states of lanthanides and actinides (M_4,5-edges), d-states of transition metals (L_2,3)], the same does not hold when the delocalized states are being probed. While atomic calculations reproduce quantitatively the XMCD signal in the soft X-ray range, the theoretical description is more difficult to handle in the hard X-ray domain (Schütz et al., 1987, 1988; Wang et al., 1993; Harmon & Freeman, 1974). As a consequence, most of these selective magnetometry experiments are limited to the soft X-ray energy in which the surface sensitivity may affect the magnetic characterization of the samples. Moreover, in the case of materials containing both transition metal and heavier elements such as lanthanides or noble metals, the XMCD characterization of these heavy elements has to be performed in the hard X-ray region which implies a dramatic change of the probing depth. As a consequence, the magnetic properties of the different components of the material cannot be obtained under the same experimental conditions. This scenario leads us to look for a new experimental method aimed at obtaining the magnetic characterization of complex magnetic systems by using XMCD in the hard X-ray region. The fact that the energy of the X-rays is raised from the soft to the hard X-ray region has the main advantages of avoiding surface effects, of guaranteeing that the XMCD becomes a real bulk probe and, in addition, the flexibility of the sample environment is enhanced allowing studies under extreme conditions of temperature, applied magnetic field and applied pressure (Ishimatsu et al., 2007).

We have performed in the past a systematic study of rare-earth (R) and transition metal (T) R–T compounds by means of XMCD at the L-edges and the K-edge of rare-earth and the transition metals, respectively. By recording the XMCD at these absorption edges, the conduction-band 4p states of transition metals and the 5d states of rare-earths are probed. These delocalized states propagate the magnetic interaction between the R-4f and T-3d electrons coupling the magnetic properties of both magnetic sublattices and determining the magnetic behaviour of the material. We and others have shown in previous works that in the case of multi-component magnetic systems such as R–T intermetallics both atomic species influence the XMCD spectra recorded at the L₂-edge¹ of the rare-earth (Laguna-Marco, 2007; Laguna-Marco et al., 2005a,b, 2008a,b; Giorgetti et al., 2004; Chaboy et al., 2007b; Ishimatsu et al., 2007) and at the K-edge of the transition metal (Laguna-Marco et al., 2005a; Ishimatsu et al., 2007; Chaboy et al., 1996, 1998b, 2004, 2007a,c; Rueff et al., 1998). These experimental results have been accounted for in terms of the R(5d)–T(d) hybridization (Laguna-Marco et al., 2008a; Chaboy et al., 2007b). Therefore, despite the atomic selectivity inherent to the X-ray absorption, the transition metal also contributes to the rare-earth XMCD spectra and, conversely, there is a non-negligible contribution of the lanthanide metal to the K-edge XMCD spectra of the transition metal. Beyond this, information is of fundamental importance in order to obtain a correct interpretation of the R L₂- and T K-edge XMCD signals; it also opens the possibility of disentangling the magnetic contribution of different atomic species within the same material by using a single X-ray absorption edge.

In this way we show here that, when a delocalized final state is probed by the absorption process, XMCD is a simultaneous fingerprint of both the rare-earth and the transition metal even when only a single absorption edge of an atomic element is tuned. This does not mean that the atomic selectivity is lost. On the contrary, it provides the possibility of studying at the same time the magnetic behaviour of different magnetic species. In particular, by tuning the X-ray absorption either at the L₂-edge of the rare-earth or at the K-edge of the transition metal, it is possible to disentangle, using only this edge, the magnetization of both rare-earth and transition metal. This is shown here in the case of different RFe₂ and RCo₂ compounds through the temperature regime between 4.2 K and room temperature. The main advantages of this new method of performing atom-specific magnetometry by using a single X-ray absorption edge lie in the fact that the magnetic characterization of the different elements is obtained exactly under the same experimental conditions. Moreover, this being a hard X-ray method, it avoids all the inherent difficulties of using soft X-rays and it broadens the experimental conditions especially regarding the possibility of performing the magnetic characterization under applied pressure.

2. Experimental

ErAl₂, ErCo₂, ErFe₂, Er(Fe_0.75Al_0.25)₂, Er(Fe_0.5Al_0.5)₂, HoCo₂ and HoAl₂ samples were prepared by arc-melting the pure elements under Ar protective atmosphere. The ingots were annealed at 1123 K for one week. Structural characterization was performed at room temperature by means of powder X-ray diffraction by using a rotating-anode Rigaku diffractometer in the Bragg–Brentano geometry, with Cu Kα radiation. All the samples are single phase and show the MgCu₂-type (C15) Laves structure (Laguna-Marco, 2007). The macroscopic magnetic measurements were performed following standard methods in magnetic fields up to 50 kOe, by using a commercial SQUID magnetometer (Quantum Design MPMS-S5).

XMCD experiments were performed at beamline BL39XU of the SPring-8 facility (Maruyama, 2001). XMCD spectra were recorded in transmission mode at the rare-earth L_2,3-edges by using the helicity-modulation technique (Suzuki et al., 1998). The sample is magnetized by an external magnetic field applied in the direction of the incident beam and the helicity is changed from positive to negative each energy point. The XMCD spectrum corresponds to the spin-dependent absorption coefficient obtained as the difference of the absorption coefficient μ_c = (μ⁻ − μ⁺) for antiparallel, μ⁻, and parallel, μ⁺, orientation of the photon helicity and the magnetic field applied to the sample. For the sake of accuracy, the direction of the applied magnetic field is reversed and XMCD, now μ_c = (μ⁺ − μ⁻), is recorded again by switching the helicity. The subtraction of the XMCD spectra recorded for both field orientations cancels, if present, any spurious signal.

For the measurements, homogeneous layers of the powdered samples were made by spreading fine powders of the material on adhesive tape. The thickness and homogeneity of the samples were optimized to obtain the best signal-to-noise ratio. The XMCD spectra were recorded at T = 5 K and μ₀H = 5 T. In all cases the origin of the energy scale was chosen at the inflection point of the absorption edge, E₀ (9263 and 8918 eV for the Er and Ho L₂-edge, respectively). Consequently, all the comparisons are referred to the E − E₀ scale. The XAS spectra were normalized to the averaged absorption coefficient at high energy (E − E₀ ≃ 50 eV).

3. Results and discussion

The rare-earth L₂-edge XMCD spectra of ErAl₂ and HoAl₂ recorded at T = 5 K are shown in Fig. 1. In both cases the spectral profile consists of a main negative peak (A) at ∼1 eV above the edge and a positive structure (B) located at ∼7 eV above the edge. In addition, the ratio of the intensity of these main peaks is also the same, I_A/I_B ≃ −3, in both the Er and Ho L₂ XMCD spectra. Moreover, both absorption edges show a shoulder-like feature at the low-energy side of the main negative peak. This feature is due to a quadrupolar (2p → 4f) transition that accompanies the main dipolar (2p → 5d) transitions at the L₂-edge (Chaboy et al., 1998a). The simultaneous presence of both quadrupolar and dipolar transitions (Carra et al., 1991; Lang et al., 1995) and the need to include the 4f–5d intra-atomic exchange interaction (Jo & Imada, 1993; Matsuyama et al., 1997; van Veenendaal et al., 1997) points out the crucial role of the 4f electrons in determining the L₂-edge XMCD even when the empty 5d band is probed. Within this framework the similarity of the spectral shape observed for both ErAl₂ and HoAl₂ compounds is in agreement with the atomic-like picture used to account for the XMCD at the rare-earth L-edges (Matsuyama et al., 1997; van Veenendaal et al., 1997). As a consequence, no significant modification of this absorption profile is expected if Al is substituted by a 3d metal. Surprisingly, the Er L₂-edge XMCD spectra recorded through the Er(Fe_xAl_1−x)₂ series are quite different from those of ErAl₂. A similar modification with respect to the RAl₂ case is observed when Al is substituted by Co in both ErCo₂ and HoCo₂. When the magnetic (Co or Fe) 3d metal is placed in the RT₂ lattice, both the shape and the amplitude of the negative XMCD contribution at the edge, peak A, are modified in comparison with those of RAl₂. The amplitude of this peak is strongly reduced by factors of ∼40% and ∼25% for the Fe and Co compounds, respectively, with respect to the RAl₂ case. In addition, the spectral shape evolves from a single negative peak in RAl₂ to a more structured profile showing two components when the 3d metals are present. In this respect, the case of ErFe₂ is of special significance as a positive peak emerges at the energy at which the XMCD spectrum of ErAl₂ shows the negative peak A.

Figure 1 Normalized XMCD spectra recorded at the Er L2-edge in (a) ErFe2, (b) Er(Fe0.75Al0.25)2, (c) Er(Fe0.5Al0.5)2 and (d) ErCo2, together with those at the Ho L2-edge XMCD from HoCo2 and HoAl2 (e): T = 5 K (red, filled circles), 70 K (green, open circles), 150 K (blue, filled squares) and 300 K (purple, open squares). The dotted line in each panel shows the spectrum from the RAl2 compound (R = Er and Ho) measured at T = 5 K. In all of the cases the applied magnetic field was 5 T. Panel (f) shows the extracted Er L2 XMCD spectra from ErFe2, obtained by subtracting that of ErAl2.

This behaviour, showing a different XMCD shape for RT₂ compounds with different transition metal (Al, Fe and Co), cannot be explained in terms of the current knowledge of the rare-earth XMCD signals at the L-absorption edges. All these ferromagnetic compounds exhibit the same C15-Laves crystal structure. More importantly, the 4f magnetic moments are close to the free-ion values under the working conditions of temperature T = 5 K and applied magnetic field μ₀ = 5 T (Laguna-Marco, 2007; Burzo et al., 1990; Purwins et al., 1976). Therefore, it is difficult to account for the observed behaviour in terms of the variation of the 4f magnetism or the intra-atomic 4f–5d interaction through the three series. What is expected is that all these spectra are similar to the XMCD spectra of the RAl₂ compounds as they can be considered as corresponding to a pure rare-earth metal as no magnetism is carried by the Al atoms. The fact that the magnetic properties of the R counterpart (Al, Fe and Co) are clearly different suggests that the origin of such a behaviour stems from an unexpected contribution arising from the T sublattice. According to previous systematic experiences, this contribution is related to the magnetic contribution of the specific transition metal in the compound even when the rare-earth is being probed by the X-rays (Laguna-Marco, 2007; Laguna-Marco et al., 2005a,b, 2008a,b).

This result suggests that XMCD at the L₂-edge of the rare-earth in this class of R–T materials is a simultaneous fingerprint of the magnetism of both the rare-earth and the transition metal even when only an atomic element is tuned. The question to answer is whether this peculiarity can also provide quantitative information about the magnetic properties of both sublattices separately. To this end we have studied the dependence on temperature of the XMCD signals recorded at the R-L₂ absorption edge. The behaviour of the temperature dependence of the Er L₂-edge XMCD spectrum in ErFe₂ is a paradigmatic case. As noted above, a positive peak emerges at the absorption edge and its intensity increases with temperature. This behaviour is not envisaged at all. In principle, one expects that the amplitude of the XMCD signal decreases as temperature increases, reflecting the weakening of the Er magnetic moment as temperature increases. To account for such anomalous behaviour we have considered that the XMCD at the L₂-absorption edges is not exclusively due to the rare-earth being probed itself, but there is also a contribution from the neighbouring magnetic transition-metal atoms. In this way the XMCD signal can be decomposed as the addition of two contributions,

one exclusively owing to the rare-earth, XMCD_R, and the second owing to the transition metal, XMCD_T. Within the atomic picture discussed above, the rare-earth contribution to the L₂-edge XMCD spectra is mainly determined by the 4f electrons. Because they are close to the free-ion values, we can assume that in the case of the RT₂ compounds the rare-earth XMCD_R contribution to the XMCD spectrum corresponds to the whole XMCD spectrum of the RAl₂ compound as Al atoms do not carry magnetic moment and thus XMCD_T should be zero. Under these assumptions it is possible to isolate the contribution of the transition metal to the R L₂ XMCD by subtracting from each recorded dichroic spectrum that of RAl₂ with the same R, i.e. XMCD_T = XMCD_RT2 − XMCD_RAl2. It should be noted that this procedure also cancels any contribution stemming from the atomic-like quadrupolar transition to the R(4f) states as these 4f states are not affected by the substitution at the T sites.

We show in Fig. 1 the result of applying this procedure in the case of ErFe₂. Similar results are found in the cases of Er(Fe_0.75Al_0.25)₂, Er(Fe_0.5Al_0.5)₂, ErCo₂ and HoCo₂ compounds. The extracted XMCD_T contribution shows an intense positive peak at the absorption edge. The profile is basically the same regardless of the rare-earth or the transition metal. Therefore, one can conclude that the contribution of the transition metal to the dichroism of the rare-earth is mainly limited to the absorption edge, i.e. to the energy region where the negative peak (A) appears, while the higher-energy region, peak B, is significantly less affected. For example, in the case of ErFe₂ at 5 K, the intensity of the subtracted signal at the B peak is one order of magnitude smaller than at the A peak, and it becomes 20 times smaller at room temperature. This result opens the possibility of disentangling the thermal dependence of both contributions from the XMCD spectra: the intensity of peak B recorded as a function of temperature should reflect the temperature dependence of the rare-earth sublattice magnetization, M_R(T), while the intensity of peak A contains the dependence on temperature of the magnetization of both the rare-earth and transition-metal sublattices. Then, we have derived M_R(T) from the intensity of peak B as

We have assumed free ion values at low temperature and then M_R(T = 5 K) equals 9μ_B and 10μ_B for Er and Ho compounds, respectively. The next step in determining the temperature dependence of the transition-metal magnetization, M_T(T), from the rare-earth L₂-edge XMCD spectrum is to determine the XMCD_T(T) term from equation (1). To this end we have applied the subtraction method described above, as the dependence in temperature of the pure rare-earth contribution, XMCD_R(T), should be the same as for the RAl₂ compound. However, the magnetic ordering temperatures of both RT₂ (T_C ≃ 600 K) and RAl₂ (T_C ≃ 13 K) compounds significantly differ. Thus, it is not possible to identify XMCD_R(T) with XMCD_RAl2(T). For this reason we have considered that XMCD_R(T) is given by the signal recorded at T = 5 K for the RAl₂ compound factorized by the reduction of the rare-earth magnetization,

where f(T) = M_R(T)/M_R(T = 5 K) has been derived from the temperature dependence of the intensity of peak B according to equation (2). Then, M_T(T) is obtained as

where the values at T = 5 K are determined from the magnetization measured under the same conditions by applying a two-sublattices model ( = + ) in which the free-ion values (μ_R = gJ) are assumed for the rare-earth magnetic moments. In this way the same absorption edge yields the temperature dependence of the magnetization of both sublattices M_R(T) and M_T(T). The result of applying this procedure is reported in Figs. 2 and 3. The total magnetization built up (Fig. 2) from the values determined from the XMCD spectra (Fig. 3 and Table 1) shows a remarkably good agreement with the experimental values of the magnetization measured in a commercial SQUID magnetometer under the same experimental conditions (temperature and applied magnetic field). It should be noted that this remarkable agreement holds throughout both the ferromagnetic (FM) and paramagnetic (PM) regimes. Indeed, while ErFe₂ shows FM ordering from 4.2 K to room temperature (T_C = 582 K), the magnetic ordering temperature decreases as the Al content increases through the R(Fe_1−xAl_x)₂ series. In this way T_C is 140 K and 60 K for Er(Fe_0.75Al_0.25)₂ and Er(Fe_0.5Al_0.5)₂, respectively. As shown in Fig. 2, the values of the magnetization obtained from the XMCD data match well the bulk magnetization measurements at both FM and PM ordering regimes.

Table 1
Temperature dependence of the magnetization in an applied field of 5 T, M_Exp, and that derived from the rare-earth L₂-edge XMCD spectra, M_Calc; M_R and M_T are the magnetization of the rare-earth and transition-metal sublattices, respectively

T (K)	M (μB/f.u.)	ErFe2	Er(Fe0.75Al0.25)2	Er(Fe0.5Al0.5)2	ErCo2	HoCo2
5	MExp	6.00	6.26	6.72	7.65	8.20
	MCalc	6.00	6.26	6.72	7.65	8.2
	MR	9.00	9.00	9.00	9.00	10.00
	MT	−3.00	−2.74	−2.28	−1.35	−1.8
70	MExp	5.50	4.88	3.56	2.18	6.45
	MCalc	5.83	5.13	3.53	2.32	6.43
	MR	9.12	8.15	5.41	3.07	8.94
	MT	−3.29	−3.01	−1.88	−0.76	−2.51
150	MExp	4.03	2.46	0.97	0.86	1.47
	MCalc	3.84	2.44	1.10	1.17	1.88
	MR	6.90	4.30	1.53	1.65	2.44
	MT	−3.06	−1.85	−0.44	−0.49	−0.57
300	MExp	1.82	0.46	–	0.41	0.52
	MCalc	1.79	0.48	–	0.48	0.37
	MR	4.94	0.68	–	0.60	0.52
	MT	−3.15	−0.20	–	−0.12	−0.15

Figure 2 Comparison of the temperature dependence of the magnetization measured at 5 T by using a standard SQUID magnetometer (dotted lines) and that derived from the rare-earth L2-edge XMCD spectra (open symbols) in the case of ErFe2 (black, squares), Er(Fe0.75Al0.25)2 (red, circles), Er(Fe0.5Al0.5)2 (green, triangles), ErCo2 (blue, inverted triangles) and HoCo2 (purple, diamonds).

Figure 3 Temperature dependence of the magnetization of the rare-earth (solid symbols) and transition-metal (open symbols) sublattices, MR and MT, determined from the rare-earth L2-edge XMCD spectra: ErFe2 (black, squares), Er(Fe0.75Al0.25)2 (red, circles), Er(Fe0.5Al0.5)2 (green, triangles), ErCo2 (blue, inverted triangles) and HoCo2 (purple, diamonds). The dotted lines are a guide for the eye.

Moreover, this method provides additional information not affordable from macroscopic tools such as the temperature dependence of both μ_R and μ_Co in the RCo₂ compounds. In these systems the Co 3d-band states appear near the critical conditions for the Co moment formation (Duc & Goto, 1999). The R magnetic moment is essentially constant in the whole phase diagram while the Co magnetic moment is generally thought to be developed as the rare-earth sublattice undergoes the magnetic transition. Then, the Co subsystem is magnetically ordered (μ_Co ≃ 1μ_B) in zero external magnetic field owing to the effect of the molecular field, B_eff, created by the R moments acting on the Co sites. However, recent work calls for the existence of an intrinsic Co moment in the paramagnetic phase of ErCo₂ (Herrero-Albillos et al., 2007), that opens again the debate concerning the existence or not of an intrinsic Co magnetic moment in RCo₂ systems (Duc & Goto, 1999). To date, no direct information regarding the behaviour of both R and Co sublattices can be obtained separately under the same experimental conditions. In contrast, our method fills this lack of knowledge as the temperature dependence of the magnetization of both sublattices M_R(T) and M_T(T) has been determined from the same experimental spectrum in the case of ErCo₂ (T_C = 32 K) and HoCo₂ (T_C = 78 K). As shown in Fig. 3, the magnetic ordering transition is visible in the disentangled M_R(T) and M_Co(T) curves of both ErCo₂ and HoCo₂ compounds. As shown in the figure, magnetization of the Co sublattice suddenly drops and almost disappears above T_C, in agreement with the expected destabilization of the itinerant d subsystem as the molecular field created by the R moments becomes ineffective in inducing the appearance of Co moment.

The results reported in Figs. 2 and 3 show the success in disentangling the magnetic contribution of different atomic species by using a single X-ray absorption edge. The addition of both individual sublattice magnetizations according to their ferrimagnetic coupling reproduces fairly well the temperature dependence of the macroscopic magnetization. As discussed above, the temperature dependence of the rare-earth magnetization has been derived from the modification of the intensity of the higher-energy B peak (∼7 eV above the edge). In an attempt to confirm the validity of our results we have followed a different approach to determine M_R(T). In this way we have determined this dependence by using the XMCD spectra recorded at the K-edge of the transition metal as a function of the temperature. Systematic XMCD studies performed at the K-edge of the transition metal in both R-Fe (Laguna-Marco et al., 2005a; Chaboy et al., 1996, 1998b, 2004, 2007c) and R-Co (Rueff et al., 1998; Ishimatsu et al., 2007; Chaboy et al., 2007a) intermetallic compounds demonstrate that the dichroic signal measured at this absorption edge carries magnetic information not only of the T ions but also of the R ions. The influence of the rare-earth, owing to the effect of the molecular field acting on the T sites, is especially important in the case of the RFe₂ Laves phase compounds in such a way that the amplitude of the rare-earth contribution hinders the signal coming from the transition metal. This can be seen in Fig. 4 where we compare the XMCD spectra recorded at the Fe and Co edges in the compounds under study and in the cases of YFe₂ and Y(Co_0.85Al_0.15)₂. For the Fe K-edge XMCD spectrum of YFe₂, the XMCD spectrum closely resembles that of Fe metal (Schütz et al., 1987). It shows a narrow positive peak at the absorption threshold, a ∼12 eV-wide negative dip hindered by the presence of a small superimposed peak, and a broad positive resonance at higher energies. Despite the fact that the magnetic properties of the Fe sublattice in YFe₂, ErFe₂ and HoFe₂ compounds are thought to be similar, their Fe K-edge XMCD spectra present noticeable differences. As shown in Fig. 4, the Fe K-edge XMCD spectrum of ErFe₂ exhibits a narrow and intense peak at the edge (A) but, in addition, a second peak of similar intensity but broader grows up at ∼15 eV above the edge. This peak was not present in the case of YFe₂ nor in Fe foil. A similar situation occurs when the Co K-edge is considered. The Co K-edge of ErCo₂ is similar to the Fe K-edge of ErFe₂, presenting both A and B peaks. In contrast, the XMCD spectrum of Y(Co_0.85Al_0.15)₂, similar to that of hexagonal-close-packed cobalt, presents a single negative dip. These results indicate that the magnetism of the rare-earth not only influences but dominates the spectral shape of the XMCD recorded at the transition-metal K-edge. The same behaviour is found for the whole set of compounds studied here. It is concluded from these results that the intensity of the main peaks (A and B) reflects the magnetization of the rare-earth sublattice. However, whereas both T and R contribute to the shape and intensity of peak A, only the latter is responsible for peak B. Consequently, the temperature dependence of its intensity would be a measure of the temperature dependence of the rare-earth magnetization, M_R(T).

Figure 4 Temperature dependence of the normalized XMCD spectra recorded at the Fe K-edge in the case of ErFe2 (a), Er(Fe0.75Al0.25)2 (d) and Er(Fe0.5Al0.5)2 (e), and at the Co K-edge in ErCo2 (c) and HoCo2 (f): T = 5 K (blue, inverted triangles), 70 K (green, triangles), 150 K (red, circles) and 300 K (black, squares). For the sake of completion, the Fe and Co K-edge XMCD spectra recorded at the same applied field in YFe2 and Y(Co0.85Al0.15)2, respectively, are shown in panel (b).

Then, we have derived M_R(T) from the intensity of this peak as indicated in equation (2) and by assuming also the free ion values at T = 5 K for the rare-earth magnetic moments. In this way, M_R equals 9μ_B and 10μ_B at T = 5 K for the Er and Ho compounds, respectively. This dependence has been included as the factor f in equation (3). Then, we have applied again the subtraction procedure to the L₂-edge by using this thermal dependence of the rare-earth contribution but now extracted from the transition-metal K-edge XMCD. Finally, the temperature dependence of the transition-metal magnetization has been obtained from the isolated XMCD_T(T) contribution according to equations (2) and (4). The results of applying this procedure are shown in Fig. 5. As in the case of using only the L₂ data, the disentangled determination of the magnetization of both sublattices obtained from the combination of both K-edge and L₂-edge XMCD spectra provides a good reproduction of the macroscopic magnetization data. The agreement between the M_R(T) and M_T(T) values derived by using both L₂-edge (Table 1) and combined L₂ + K edges (see Table 2) methods is better than 10% over the ferrimagnetic regime for all the studied compounds. Consequently, the results presented here show the capability of this new approach to obtain the disentanglement of the magnetic contribution of different atomic species in R-T compounds by using XMCD at a single X-ray absorption edge.

Table 2
Temperature dependence of the magnetization in an applied field of 5 T, M_Exp, and that derived from the XMCD spectra, M_Calc; the magnetization of the rare-earth, M_R, and transition-metal, M_T, sublattices have been derived from the K-edge and L₂-edge XMCD data, respectively

T (K)	M (μB/f.u.)	ErFe2	Er(Fe0.75Al0.25)2	Er(Fe0.5Al0.5)2	ErCo2	HoCo2
5	MExp	6.00	6.26	6.72	7.65	8.20
	MCalc	6.00	6.26	6.72	7.65	8.2
	MR	9.00	9.00	9.00	9.00	10.00
	MT	−3.00	−2.74	−2.28	−1.35	−1.8
70	MExp	5.50	4.88	3.56	2.18	6.45
	MCalc	5.41	4.78	3.80	2.31	6.12
	MR	8.54	7.39	5.31	2.67	8.38
	MT	−3.13	−2.61	−1.51	−0.36	−2.26
150	MExp	4.03	2.46	0.97	0.86	1.47
	MCalc	3.99	2.18	1.21	0.95	1.45
	MR	7.10	3.74	1.51	1.13	1.66
	MT	−3.11	−1.56	−0.30	−0.18	−0.21
300	MExp	1.82	0.46	–	0.41	0.52
	MCalc	1.49	0.53	–	0.59	0.57
	MR	4.52	0.78	–	0.67	0.67
	MT	−3.03	−0.25	–	−0.09	−0.10

Figure 5 (a) Comparison of the temperature dependence of the magnetization measured at 5 T by using a standard SQUID magnetometer (dotted lines) and that derived by combining both the rare-earth L2-edge and the transition-metal K-edge XMCD spectra (open symbols) in the case of ErFe2 (black, squares), Er(Fe0.75Al0.25)2 (red, circles), Er(Fe0.5Al0.5)2 (green, triangles), ErCo2 (blue, inverted triangles) and HoCo2 (purple, diamonds). (b) Temperature dependence of the magnetization of the rare-earth (solid symbols) and transition-metal (open symbols) sublattices, MR and MT, determined from XMCD spectra: ErFe2 (black, squares), Er(Fe0.75Al0.25)2 (red, circles), Er(Fe0.5Al0.5)2 (green, triangles), ErCo2 (blue, inverted triangles) and HoCo2 (purple, diamonds). The dotted lines are a guide for the eye.

4. Summary and conclusions

In this work we have reported on an XMCD study performed as a function of the temperature at the rare-earth L₂-edge in the case of RT₂ (R = rare-earth, T = 3d transition metal) materials. According to previous works the analysis of the R L₂-edge XMCD spectra shows the presence of a magnetic contribution coming from the transition metal even when the rare-earth is probed. These results show that the atomic selectivity is not lost when XMCD probes the delocalized states. On the contrary, XMCD is a simultaneous fingerprint of the magnetic contributions to the conduction band coming from the different elements in the material. Taking advantage of this peculiarity we have proposed a direct method of disentangling these contributions. As a consequence we have demonstrated that it is possible to perform element-specific magnetometry by using a single X-ray absorption edge.

Footnotes

¹While the effect of the magnetism of the transition metal is notorious in the L₂-edge XMCD spectra, no significant effect is detected in the XMCD recorded at the Er L₃-edge. A detailed discussion can be found by Chaboy et al. (2007b).