Origin of the X-ray magnetic circular dichroism at the L-edges of the rare-earths in RxR1−x′Al2 systems

Chaboy, J.; Laguna-Marco, M.Á.; Piquer, C.; Boada, R.; Plugaru, N.; Maruyama, H.; Kawamura, N.

doi:10.1107/S0909049509009807

research papers

JOURNAL OF
SYNCHROTRON
RADIATION

ISSN: 1600-5775

Volume 16| Part 3| May 2009| Pages 405-412

doi:10.1107/S0909049509009807

Origin of the X-ray magnetic circular dichroism at the L-edges of the rare-earths in R_xR_1−x′Al₂ systems

Jesús Chaboy,^a,^b ^* María Ángeles Laguna-Marco,^c Cristina Piquer,^a,^d Roberto Boada,^a,^b Neculai Plugaru,^d,^e Hiroshi Maruyama ^f and Naomi Kawamura ^g

^aInstituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, 50009 Zaragoza, Spain, ^bDepartamento de Fisica de la Materia Condensada, Universidad de Zaragoza, 50009 Zaragoza, Spain, ^cAdvanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA, ^dDepartamento de Ciencia y Tecnología de Materiales y Fluidos, Universidad de Zaragoza, 50009 Zaragoza, Spain, ^eNational Institute of Materials Physics, PO Box MG-07, Bucharest, Romania, ^fGraduate School of Science, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, Japan, and ^gJapan Synchrotron Radiation Research Institute/SPring-8, 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan
^*Correspondence e-mail: jchaboy@unizar.es

(Received 9 January 2009; accepted 17 March 2009; online 1 April 2009)

An X-ray magnetic circular dichroism (XMCD) study performed at the rare-earth L_2,3-edges in the R_xR_1−x′Al₂ compounds is presented. It is shown that both R and R′ atoms contribute to the XMCD recorded at the L-edges of the selected rare-earth, either R or R′. The amplitude of the XMCD signal is not directly correlated to the magnetization or to the value of the individual (R, R′) magnetic moments, but it is related to the molecular field acting on the rare-earth tuned in the photoabsorption process. This result closes a longstanding study of the origin of the XMCD at the L-edge of the rare-earths in multi-component systems, allowing a full understanding of the exact nature of these signals.

Keywords: X-ray magnetic circular dichroism; rare-earth L-edges.

1. Introduction

In recent years the advent of new synchrotron radiation sources has led to the development of magnetic studies on the microscopic scale by using X-ray core-level spectroscopies such as X-ray circular magnetic dichroism (XMCD) (Lovesey & Collins, 1996 ; Stöhr, 1999 ; Kortright et al., 1999 ; Funk et al., 2005 ). The great advantage of using X-rays lies in the fact that each element can be probed separately since the energy of the X-ray absorption edges is characteristic for each element. XMCD combined with the so-called sum rules may provide element-specific information about the orbital (Thole et al., 1992 ) and spin (Carra et al., 1993 ) magnetic moments of the states of the absorbing atom probed in the absorption process.

In this way, XMCD has been mostly applied to those cases in which the final states are localized, such as the d-states (L_2,3-edges) of the late transition metals like Co and Ni (Lovesey & Collins, 1996; Stöhr, 1999; Kortright et al., 1999; Chen et al., 1993 ). However, the application of the spin sum rule (Carra et al., 1993) worsens in other cases because of two main problems: the unknown value of the magnetic dipole operator T_z and the need for a large L_2,3-edge spin–orbit splitting. This 2p spin–orbit splitting is strongly reduced for light transition metals, and quantum mechanical mixing of j_3/2 and j_1/2 excitations is present. This mixing reduces the observed XMCD related spin and magnetic dipole term contributions and prevents the direct application of XMCD spin sum rules (Goering, 2005 ; Crocombettey et al., 1996 ). Moreover, the strong electron core-hole correlations in the early 3d transition metals lead to dramatic changes in the spectral intensities and a severe deviation of the spin sum rule (Scherz et al., 2004 ).

The problem of extracting quantitative magnetic information from the XMCD spectra increases in those cases in which the final states are delocalized, such as the 4p states (K-edge) of the 3d transition metals (T) and the 5d states (L_2,3-edges) of the rare-earths (R). Initially, the Fe K-edge XMCD was thought to be proportional to the p-projected spin density of states (Schütz et al., 1987 ). However, this interpretation failed to account for the cases of Co and Ni (Schütz & Wienke, 1989 ; Schütz et al., 1989 ; Stähler et al., 1993 ). According to Igarashi & Hirai, who pointed out the critical role of the hybridization of the 4p states with the 3d states at neighbouring sites (Igarashi & Hirai, 1994 , 1996 ), the shape of the XMCD spectrum near the K-edge of the ferromagnetic metals such as Fe, Co and Ni is determined by the 3d-projected orbital magnetization density of states. On the other hand, two main problems limit the use of XMCD for studying the magnetic properties of the 5d states of the rare-earths by using XMCD at the R L_2,3-edges. Both the contribution of quadrupolar transitions (Carra et al., 1991 ; Lang et al., 1992 , 1994 , 1995 ; Chaboy et al., 1998a ) and the spin dependence of the radial matrix elements of the dipolar transitions (Wang et al., 1993 ) affect both the shape and the sign of the XMCD signals. The appearance of these effects prevents the determination of the 5d magnetic moments from the simple application of the sum rules and, moreover, the correct determination of the sign of the magnetic coupling (Schütz et al., 1988 ).

These problems become more acute when both localized and delocalized moments are present in the material, as in the case of R–T intermetallics (Laguna-Marco, 2007 ). Several works have shown that the rare-earth contributes to the XMCD spectrum recorded at the T K-edge (Chaboy et al., 1996 , 1998b , 2003 , 2004 , 2007a ,d ; Laguna-Marco et al., 2005a , 2007; Ishimatsu et al., 2007 ; Rueff et al., 1998 ) and, conversely, the transition metal contributes to the XMCD signals recorded at the rare-earth L_2,3-edges (Laguna-Marco et al., 2005b , 2008a ,b ; Giorgetti et al., 2004 ; Chaboy et al., 2008 ; Boada et al., 2009a ). The systematic work performed to date has demonstrated the universality of this behaviour within the R–T intermetallics. However, while the shape of these contributions does not depend significantly on the particular R/T stoichiometry, especially at the R L-edges, their amplitude shows a strong variation through different series. Indeed, in several cases of pure RT₂ compounds (T = Fe, Co) the rare-earth contribution to the T K-edge XMCD spectra is so large as to hinder that of the T 4p states that, however, are still present as demonstrated in the (R_xLu_1−x)Fe₂ series by diluting the magnetic rare-earth with a non-magnetic one (Boada et al., 2009b ). This contribution is associated with the exchange interaction with the rare-earth, being mainly determined by the magnitude of the molecular field that the rare-earth magnetic moments cause at the T sites (Laguna-Marco et al., 2009 ). A similar scheme was applied to the case of the T contribution to the rare-earth L_2,3-edges XMCD. Our results have shown that it is possible to establish a relationship between the T contribution to the rare-earth L_2,3-edges XMCD and the molecular field acting on the absorbing sites (Chaboy et al., 2007b ). These results suggest the possibility of extracting quantitative magnetic information from the analysis of the rare-earth L_2,3-edges XMCD, especially regarding both the exchange interaction between the 5d moments and those of the matrix, and also on the R(5d)–T(d) hybridization.

The experiments above have been performed in systems in which there is competition between the localized 4f magnetism of the rare-earth and the itinerant magnetism of the transition metal, and in which the R(5d)–T(d) hybridization plays a fundamental role into governing the magnetic properties of the compounds (Campbell, 1972 ; Yamada et al., 1984 ; Yamada & Shimizu, 1985 ). However, similar behaviour has been observed in the R(Al_1−xT_x)₂ Laves phases (Laguna-Marco, 2007; Laguna-Marco et al., 2007a ,b , 2009) in which the magnetism shows an evolution from RKKY-like to itinerant magnetism. Therefore, we have tailored the study of the relationship between the XMCD signals recorded at the L_2,3-edges of the rare-earths and the magnetic properties of systems in which no T-3d magnetic moment and, consequently, no R(5d)–Fe(3d) hybridization are present. In this way, the systematic XMCD study performed on the RAl₂ series has shown that there is a clear relationship between the rare-earth L₂-edge XMCD and the molecular field coefficients n_RR (Laguna-Marco et al., 2008b). More specifically, our results showed that the intensity of the R L₂ XMCD spectra remarkably mimics the modification of the n_RR coefficient through the RAl₂ series, which suggests that analysis of the XMCD signal can be used to obtain valuable information about the R(4f )–R(5d) exchange.

In order to go further in this subject we have extended our previous studies to the case of the substituted R_1−x $[R_{x}^{\,\prime}]$ Al₂ compounds. Here we present an XMCD study performed at the rare-earth L_2,3-edges in the R_x $[R_{1-x}^{\,\,\prime}]$ Al₂ compounds. The magnetic behaviour of these systems is accounted for in terms of the RKKY interaction and, consequently, it is not expected that the hybridization of the 5d states plays a significant role. However, our results show that in the case of the substituted Gd_1−x $[R_{x}^{\,\prime}]$ Al₂ compounds (with R′ = Dy, Ho, Er) the amplitude of the Gd L_2,3-edge XMCD spectra decreases upon doping despite the magnetization of the system increasing. In contrast, the substitution of Gd by R′ entails a strong modification of the magnetic ordering temperature, which indicates that the exchange interaction is strongly modified with respect to that of the undoped RAl₂ compounds. In this work it is shown that the observed decrease in the amplitude of the Gd L_2,3-edge XMCD is due to an R′ contribution, whose intensity is correlated with the molecular field that the R′ atoms exert on the Gd sublattice. Hence, our experimental findings provide a deeper insight into the interpretation of the L_2,3-edge XMCD spectra of the rare-earths by showing that the amplitude of the XMCD signals can be quantitatively related to the magnetic properties of the systems under study. In this way we have proven that these signals are determined not only by the magnetization of the probed sublattice but also by the other magnetic moments present in the material which should be considered in terms of the molecular field acting on the absorbing sites. These results open the possibility of using XMCD at the rare-earth L_2,3-edges to extract experimentally quantitative magnetic information.

2. Experimental

RAl₂ compounds (R = Pr, Nd, Sm, Gd, Tb, Dy, Ho and Er) were prepared by melting the pure elements in a high-frequency induction furnace, under Ar protective atmosphere. The as-cast alloys were wrapped in Ta foil and enclosed in silica tubes, under Ar gas. All the alloys were annealed at 1073 K for 100 h and then quenched to room temperature. A similar procedure was applied to the synthesis of the Gd_1−xR_xAl₂ compounds (R = Dy, Ho, Er and Lu) that were annealed at 1023 K for one week. Structural characterization was performed at room temperature by means of powder X-ray diffraction, using a rotating-anode Rigaku diffractometer in the Bragg–Brentano geometry, with Cu Kα radiation. The magnetic measurements were performed by using a commercial SQUID magnetometer (Quantum Design MPMS-5s). Magnetic isotherms were measured on loose powders in applied magnetic fields H ≤ 5 T.

XMCD experiments were performed at the beamline BL39XU of the SPring-8 facility (Maruyama, 2001 ). For the measurements, homogeneous layers of the powdered samples were made by spreading fine powders of the material onto adhesive tape. The thickness and homogeneity of the samples were optimized to obtain the best signal-to-noise ratio, giving a total absorption jump of ∼1 at about 150 eV above the edge. In all of the cases, the origin of the energy scale, E₀, was chosen at the inflection point of the absorption edge, and the XAS spectra were normalized to the averaged absorption coefficient at high energy. The XMCD spectra were recorded at different fixed temperatures in the transmission mode using the helicity-modulation technique (Suzuki et al., 1998 ). The sample was magnetized by an external magnetic field, H = 2 T, applied in the direction of the incident beam, and the helicity was changed from positive to negative at each energy point. In this way the spin-dependent absorption coefficient was obtained as the difference of the absorption coefficient, μ_c = (μ⁻ − μ⁺), for antiparallel, μ⁻, and parallel, μ⁺, orientation of the photon helicity and sample magnetization. For the sake of accuracy, the direction of the applied magnetic field was reversed to obtain the XMCD, now corresponding to μ_c = (μ⁺ − μ⁻), by switching the helicity. Subtraction of the XMCD spectra recorded for both field orientations cancels, if present, any spurious signal.

3. Results and discussion

Both RAl₂ and R_1−x $[R_{x}^{\,\prime}]$ Al₂ series of compounds crystallize in the cubic Laves C15 MgCu₂ structure. The diffraction patterns were Rietveld refined using the FULLPROF code (Rodriguez-Carvajal, 1993 ). All the samples were found to be single phase and the cell parameters were determined from the X-ray diffraction patterns (see Fig. 1). The cell parameters of both the RAl₂ and the Gd_1−xR_xAl₂ compounds are summarized in Table 1. As shown in Fig. 1, the cell volume of the pure RAl₂ compounds decreases as the atomic number increases, as expected because of the lanthanide contraction. In addition, the cell parameters of the Gd_1−xR_xAl₂ compounds follow a linear variation with the composition (x) between the end-members, in agreement with Vegard's law.

Table 1
Main structural and magnetic parameters of the RAl₂ and R_1−x $[R_{x}^{\,\prime}]$ Al₂ compounds: lattice constant (a), unit-cell volume (V), Curie temperature (T_C) and the magnetization measured at T = 4.2 K and H = 5 T (M_5T)

Compound	a (Å)	V (Å³)	T_C (K)	M_5T (μ_B/f.u.)
PrAl₂	8.028	517.3	33	2.94
NdAl₂	8.001	512.1	79	2.39
SmAl₂	7.942	501.0	64	0.24
GdAl₂	7.898	492.6	164	6.74
TbAl₂	7.863	486.1	109	8.90
DyAl₂	7.837	481.4	58	9.64
HoAl₂	7.812	476.8	29	9.20
ErAl₂	7.791	472.9	13	7.63
Gd_0.75Dy_0.25Al₂	7.880	489.3	145	8.37
Gd_0.50Dy_0.50Al₂	7.864	486.2	115	8.76
Gd_0.75Ho_0.25Al₂	7.874	488.2	141	8.46
Gd_0.50Ho_0.50Al₂	7.855	484.7	101	8.64
Gd_0.75Er_0.25Al₂	7.875	488.4	135	7.80
Gd_0.50Er_0.50Al₂	7.839	481.7	94	7.73
Gd_0.75Lu_0.25Al₂	7.856	484.8	128	5.26

Figure 1
(a) X-ray powder diffraction patterns of the RAl₂ series. (b) Variation of the lattice parameter through the RAl₂ series. (c) Dependence of the lattice parameter on the rare-earth substitution in the Gd_1−x $[R_{x}^{\,\prime}]$ Al₂ [R′ = Dy (filled circles), Ho (red, open circles), Er (blue, filled squares) and Lu (green, open squares)] series. This figure is in colour in the electronic version of this paper.

The temperature dependence of the magnetization through the RAl₂ series is shown in Fig. 2 together with the magnetization versus applied magnetic field curves recorded at 4.2 K. The RAl₂ compounds order ferromagnetically. The magnetic order temperature, T_C, of the series scales well with the de Gennes factor (g − 1)²J(J + 1) (de Gennes, 1966 ), in agreement with the predictions of the simple RKKY model. This result indicates that the magnetic order is mainly driven by the R sublattice, which differs from the isomorphous RFe₂ compounds where magnetic order is governed by the itinerant subsystem. The magnetic moments of these compounds are slightly smaller than the corresponding free rare-earth ion values, gJ, indicating some crystal field quenching (Purwins & Leson, 1990 ). The results summarized in Fig. 2 and Table 1 are in agreement with the numerous investigations that have been performed on RAl₂ compounds (Buschow, 1979 ; Purwins & Leson, 1990).

Figure 2
(a) Temperature dependence of the magnetization of the RAl₂ compounds measured under an applied magnetic field H = 0.1 T. (b) Magnetization versus applied magnetic field curves of the RAl₂ compounds recorded at T = 4.2 K. (c) Comparison of the magnetization of the RAl₂ at T = 4.2 K and H = 5 T (black, filled circles) and the free-ion μ_4f magnetic moments (red, open circles). (d) Comparison of the Curie temperatures of the RAl₂ compounds (red, open circles) and the J(J + 1)(g − 1)² dependence (black, filled circles) through the series. This figure is in colour in the electronic version of this paper.

Within the series, GdAl₂ exhibits the highest Curie temperature (T_C = 164 K). This fact, and the absence of any significant effect of crystal fields on the S state of the Gd³⁺ ion (Burd & Lee, 1977 ), makes GdAl₂ a good candidate for studying systematically the effect of replacing Gd by a different rare-earth. Hence, we have synthesized the Gd_1−xR_xAl₂ compounds in which Gd is replaced by Dy, Ho, Er and non-magnetic Lu. The dilution of Gd by Lu is expected to act as a simple magnetic dilution effect because Lu carries no magnetic moment and the magnetic state of Gd is thought to remain unaffected by the substitution. For a 25% Lu substitution, the magnetization decreases from 6.74 μ_B/f.u. in GdAl₂ to 5.26 μ_B/f.u. Hence, it is 78% of the magnetization of the parent compound, in agreement with the expected magnetic dilution effect. A similar reduction is found for the magnetic order temperature that decreases from 164 K in GdAl₂ to 128 K in Gd_0.75Lu_0.25Al₂ (see Fig. 3).

Figure 3
(a) Temperature dependence of the magnetization of the Gd_1−x $[R_{x}^{\,\prime}]$ Al₂ compounds measured under an applied magnetic field H = 0.1 T: R′ = Er (blue, filled down triangles), Ho (green, filled circles) and Dy (red, filled triangles); and x = 0.25 (solid symbols); x = 0.5 (open symbols). (b) Comparison of the magnetization versus applied magnetic field curves of the pure RAl₂ (solid symbols) and Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ (open symbols) compounds for R′ = Er (blue, open down triangles), Ho (green, open circles) and Dy (red, open triangles). This figure is in colour in the electronic version of this paper.

In the case of the substitution of Gd by a magnetic rare-earth, the ferromagnetic order is preserved although the substitution has different consequences regarding both the magnetization and the magnetic ordering temperature of the systems. The magnetization of Gd_1−xR_xAl₂ is reinforced with respect to what is expected from the addition of the magnetization of both RAl₂ and R′Al₂ pure compounds according to a two-sublattice model. Within this framework, it is assumed that the total magnetization of the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds corresponds to the weighted addition of the magnetization of the parent single compounds, M_Tot = 0.5M(GdAl₂) + 0.5M(R′Al₂). In the case of Gd_0.5Dy_0.5Al₂, this model yields M_Calc = 8.19 μ_B/f.u., while the measured magnetization at T = 4.2 K and H = 5 T is M_exp = 8.76 μ_B/f.u. The same trend is found for both Gd_0.5Ho_0.5Al₂, M_exp = 8.64 versus M_Calc 7.97 μ_B/f.u., and Gd_0.5Er_0.5Al₂, M_exp = 7.73 versus M_Calc 7.19 μ_B/f.u. Interestingly, a better agreement is found if the magnetization is calculated by using the 4f free-ion magnetic moments values: M_Calc = 8.5 μ_B/f.u. for Dy and Ho, and 8 μ_B/f.u. for Er. These results indicate that the rare-earth ions in the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds retain their magnetic properties upon dilution. However, the modification of the magnetic ordering temperature indicates that the exchange interaction is strongly modified with respect to that of the RAl₂ compounds.

This situation represents the best starting point to study the relationship between the rare-earth L_2,3-edge XMCD signals and the magnetic properties of the materials. In principle, if the amplitude of the XMCD signal was proportional to the magnetic moment of the absorbing atom or to the magnetization of the compound, no significant variation of the amplitude of the XMCD signal recorded at the Gd L_2,3-edges through the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ series would be expected. The total magnetization of the systems increases after the Gd substitution. Therefore, the amplitude of the XMCD signals should be increased through the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ series. By contrast, if the amplitude of the XMCD signals was determined by the exchange interaction, a strong modification of the XMCD amplitude should be expected. In this respect, we show in Fig. 4 the XMCD spectra recorded at the Gd L₂-edge in the investigated Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds. The Gd L₂-edge XMCD spectrum shows in all cases a main negative peak at the edge. This spectral profile is similar for all the compounds and only the amplitude of the signal is modified upon substitution of Gd by another lanthanide. Similar results are found at the Gd L₃-edge. In this case, the XMCD is positive and its intensity is one half of the L₂ one. Moreover, the intensity of the main peak of the XMCD spectrum and the integral of the signal over all the experimental range scale perfectly at both the L₂- and L₃-edges. Therefore, the modification of the amplitude of the XMCD spectra will be referred hereafter to the intensity values.

Figure 4
(a) Comparison of the XMCD spectra recorded at T = 50 K at the Gd L₂-edge in the case of GdAl₂ (black, filled circles), the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds with R′ = Er (blue, open squares), Ho (green, filled squares), Dy (red, open circles), and in Gd_0.75Lu_0.25Al₂ (dark green, open triangles). (b) Comparison of the XMCD spectra recorded at T = 50 K at the Gd L₂-edge in the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds after subtracting the XMCD of the GdAl₂ one: R′ = Er (blue, open squares), Ho (green, filled squares), Dy (red, open circles), and in Gd_0.75Lu_0.25Al₂ (black, filled circles). This figure is in colour in the electronic version of this paper.

As shown in Fig. 4, the intensity of the Gd L₂-edge XMCD in Gd_0.75Lu_0.25Al₂ is ∼90% of that in GdAl₂. However, the intensity of the XMCD signal markedly decreases through the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ series. Compared with that of GdAl₂, its amplitude is ∼80%, 50% and 25% for Dy, Ho and Er, respectively. Such a variation is not expected in terms of the diminution of the Gd magnetic moment. Similarly, this behaviour is not expected on the basis of the modification of the total magnetization, which increases after substitution. It might be argued that the magnetization at the working temperatures departs from the relation found at T = 4.2 K and H = 5 T. However, this is not the case. We have recorded the magnetization under the same experimental conditions as for the XMCD measurements, i.e. T = 50 K and H = 2 T, verifying that a similar relation holds. Under these conditions the magnetization of GdAl₂, Gd_0.5Dy_0.5Al₂, Gd_0.5Ho_0.5Al₂ and Gd_0.75Lu_0.25Al₂ is ∼86% of that at T = 4.2 K and H = 5 T, while it is only ∼60% in the case of Gd_0.5Er_0.5Al₂. Finally, it should also be noted that the variation of the XMCD intensity through the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ series does not follow that of the magnetic ordering temperature. Indeed, as shown in Table 1, the maximum variation should be expected for the Gd_0.5Er_0.5Al₂ compound for which T_C/T_C(GdAl₂) ≃ 0.6. By contrast, the ratio of the XMCD amplitude for this compound, XMCD/XMCD(GdAl₂) = 0.25, is significantly smaller than the ratio of the magnetic ordering temperatures.

Atempting to gain a deeper insight into this peculiar behaviour, we have considered our previous findings in the case of RT₂ compounds in which T is a 3d transition metal such as Fe or Co. In these cases we have demonstrated that the transition metal contributes to the XMCD signals recorded at the rare-earth L_2,3-edges (Laguna-Marco et al., 2005b, 2007a, 2008a,b), and, moreover, that this contribution is related to the molecular field owing to the transition metal acting at the rare-earth sites (Chaboy et al., 2007b). Then, we have checked the possibility that the rare-earth substituting Gd in the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds could also contribute to the XMCD of the Gd L-edges. The existence of such a contribution can be highlighted by subtracting the XMCD spectra of GdAl₂ from those of the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds. The result of the substraction is reported in Fig. 4 for the case of the L₂-edge (similar results are found at the L₃-edge). In all cases, with the exception of Lu, the extracted signal shows a sharp positive peak at the edge. While its shape is the same for all of the compounds, the intensity shows marked differences as a function of the rare-earth (Dy, Ho, Er) that substitutes for Gd. While in the case of Lu this difference can be associated with a simple dilution effect, the magnitude of the differences found for the cases in which R is a magnetic rare-earth does not show a direct relationship with the magnetic moments. The maximum difference signal is found for the case of Er, its intensity being ∼1.5 and 4 times greater than those of Ho and Dy, respectively. As commented above, these differences cannot be easily accounted for in terms of the different magnetic moments of the rare-earths substituting Gd, i.e. μ_R′ = 10 μ_B for Dy and Ho, and 9 μ_B for Er.

We have studied whether this contribution can be regarded as being due to the hybridization of the 5d states of both Gd and R′ ions. In this way, the Gd 5d states will be polarized by the interatomic 4f–5d exchange but, in addition, the R′ ions should also contribute to the polarization of the 5d band through the action of the interatomic molecular field. It should be noted that the sign of the XMCD spectra indicates the orientation of the magnetic moment of the states probed in the photoabsorption process with respect to the magnetization of the system. However, the XMCD signals recorded at the L_2,3-edges of the rare-earths yield an erroneous sign (Schütz et al., 1988). Indeed, if one considers that the XMCD spectrum reflects the difference in the density of empty states with different spin moment, this model yields that the 5d spin would be antiparallel to the 4f spin, which is in contradiction with the current knowledge (Campbell, 1972; Yamada et al., 1984; Yamada & Shimizu, 1985). This paradox has been solved by taking into account the spin dependence of the matrix elements previously neglected (Wang et al., 1993). It should be noted that the L_2,3 XMCD returns the correct sign when the rare-earth does not exhibit a 4f magnetic moment and the 5d spin is induced by a transition metal or by another rare-earth showing a localized 4f moment. This is the case for the Lu L_2,3 XMCD in LuFe₂ and Gd_0.75Lu_0.25Al₂ compounds (Chaboy et al., 2007c ). In a similar way, the results reported in Fig. 4 indicate that the polarization of the 5d states associated with the R′ atoms agrees with the ferromagnetic coupling of the Gd and R′ magnetic moments in the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds. In order to explore the relationship between the R′ contribution to the Gd L_2,3 XMCD signals and the molecular field owing to the R′ ions acting on the Gd sites, we have calculated B_mol(R′ → Gd) within a mean-field approach (Buschow, 1988 ). In this model, the intersublattice molecular field coefficient describing the interaction between the two rare-earth sublattices is given by

$[N_{RR'}=\left({|T_C-T_R|\,|T_C-T_{R'}|}\over{C_R\,C_{R'}}\right)^{1/2},\eqno(1)]$

where C_R = N_Rg_J²J(J + 1)μ_B²/3k_BT, and T_R and T_R′ are the Curie temperatures of the RAl₂ and R′Al₂ compounds, respectively. The corresponding values of N_RR′ and B_mol, obtained as B_mol(R′ → Gd) = N_GdR′μ_R′, are listed in Table 2.

Table 2
Intersublattice molecular coefficient and molecular field that the R′ atoms exerts on the Gd sites

Compound	N_RR′ (10⁻⁵ T m A⁻¹)	B_mol (R′ → Gd) (T)
Gd_0.5Dy_0.5Al₂	3.7	7.1
Gd_0.5Ho_0.5Al₂	4.7	8.9
Gd_0.5Er_0.5Al₂	5.8	10.0

As we can see in Table 2, the molecular field coefficient N_RR′ increases from Dy to Er as the maximum intensity of the subtracted Gd L₂ XMCD signal does. The N_RR′ increase reflects the variation of T_C observed along the Gd_1−x $[R_{x}^{\,\prime}]$ Al₂ series. In the case of Er, T_C increases from 13 K in ErAl₂ to 94 K in Gd_0.5Er_0.5Al₂, that is ΔT_C = 81 K, which corresponds to a ∼623% increase. In the Ho series, T_C increases from 29 K in HoAl₂ to 101 K in Gd_0.5Ho_0.5Al₂, or equivalently, ΔT_C = 72 K, which corresponds to an increase of ∼248%, whereas in the case of Dy this increase is only ∼98% as T_C increases from 58 K in DyAl₂ to 115 K in Gd_0.5Dy_0.5Al₂. That is, the values of T_C indicate that the exchange interaction between Gd and R′ increases from Dy to Er. Finally, the obtained values of B_mol(R′ → Gd) have been compared in Fig. 5 with the intensity of the subtracted Gd L₂ XMCD signals. The good agreement shown in this figure gives support to our hypothesis regarding the relationship between the XMCD and the molecular field acting on the absorbing sites.

Figure 5
Top: comparison of the maximum intensity of the difference XMCD spectra (black, filled circles) and the intersublattice molecular field (blue, open triangles) through the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ series (see text for details). Bottom: comparison of the relative maximum intensity of the difference XMCD spectra prior (black, filled circles) and after applying the magnetization correction (red, open circles) (see text for details) and the relative variation of the intersublattice molecular field (blue, open triangles) through the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ series. This figure is in colour in the electronic version of this paper.

The magnitude of the subtracted Gd L₂ XMCD signals deserves a final comment, being of the same order of magnitude as those previously found in the RFe₂ systems (Laguna-Marco et al., 2008a). In this respect, it should be noted that when applying the procedure above we have subtracted the same Gd L₂ XMCD signal of GdAl₂ recorded at T = 50 K as those of the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds recorded under the same conditions. However, this temperature (T = 50 K) is not so far from the magnetic ordering temperatures of the substituted Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds and, consequently, this approach might no longer be valid. Indeed, the magnetization measured at T = 50 K and H = 5 T is 6.09 μ_B/f.u. and 7.95 μ_B/f.u. for GdAl₂ and Gd_0.5Dy_0.5Al₂, respectively, yielding a M_5T(50 K)/M_5T(4.2 K) ratio of 0.9. This ratio decreases to 0.8 for Gd_0.5Ho_0.5Al₂ [M_5T(50 K) = 6.83 μ_B/f.u.] and to 0.7 in the case of Gd_0.5Er_0.5Al₂ [M_5T(50 K) = 5.32 μ_B/f.u.]. These results suggest that subtracting the XMCD signal of GdAl₂ from the XMCD signals of the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds is appropriate for the Dy case, but probably not for the Ho and Er cases. Consequently, we have modified the subtraction procedure by taking into account these factors. In this way, the GdAl₂ signal has been factorized by 0.8/0.9 and 0.7/0.9 prior to subtracting it from the XMCD spectra of the Ho and Er compounds, respectively. The result of such a procedure is incorporated in the bottom panel of Fig. 5. As shown in the figure, while the magnitude of the extracted signal is reduced, the trend of the intensity variation through the substituted series does not vary. As a consequence, a comparison of the intensity of the extracted XMCD signals and the value of the intersublattice molecular field also shows a remarkable agreement.

After applying this correction we found that the intensity of the extracted XMCD signals in the Gd_0.5 $[R_{0.5}^{\,\prime}]$ Al₂ compounds is about a half of that found in the RFe₂ series, while the intersublattice molecular field is about five times smaller (applying the same procedure as discussed above yields B_mol = 45.4 T for GdFe₂). These differences are presumably due to the different hybridization mechanism occurring in both R_0.5 $[R_{0.5}^{\,\prime}]$ Al₂, R(5d)–R′(5d), and RFe₂, R(5d)–Fe(3d), systems. The present results suggest that, while the magnitude of the discussed effect on the XMCD spectra is determined by the details of the interplay of the hybridization and the spin polarization of the R(5d) states, the relative variation through the same series is mainly determined by the molecular field acting on the rare-earth absorbing sites.

4. Summary and conclusions

We have presented here an XMCD study performed at the rare-earth L_2,3-edges in the case of R_x $[R_{1-x}^{\,\,\prime}]$ Al₂ compounds. It is shown that both R and R′ atoms contribute to the XMCD recorded at the L-edges of the selected rare-earth. In the case of the Gd_x $[R_{1-x}^{\,\,\prime}]$ Al₂ compounds, we have extracted the contribution of R′ to the Gd L_2,3-edges XMCD spectra. We have shown that the variation of the intensity of this contribution through the series is determined by the molecular field owing to the R′ atoms acting on the Gd sites. These results close a longstanding study on the origin and the interpretation of the L_2,3-edge XMCD spectra of the rare-earths in the case of multi-component magnetic systems.

Acknowledgements

This work was partially supported by a Spanish CICYT-MAT2008-06542-C04-01 grant. MALM and RB acknowledge the Ministerio de Eduación y Ciencia of Spain for a Postdoctoral and a PhD grant, respectively. This study was performed with the approval of Japan Synchrotron Radiation Research Institute (JASRI) (Proposals No. 1999A0388 and 2001A0062).

References

Boada, R., Laguna-Marco, M. Á. & Chaboy, J. (2009). J. Synchrotron Rad. 16, 38–42. Web of Science CrossRef CAS IUCr Journals Google Scholar
Boada, R., Piquer, C., Laguna-Marco, M. A., Kawamura, N., Suzuki, M. & Chaboy, J. (2009). Phys. Rev. B. Submitted. Google Scholar
Burd, J. & Lee, E. W. (1977). J. Phys. C, 10, 4581–4586. CrossRef CAS Web of Science Google Scholar
Buschow, K. H. J. (1979). Rep. Prog. Phys. 42, 1374–1477. CrossRef Web of Science Google Scholar
Buschow, K. H. J. (1988). In Handbook of Magnetic Materials, Vol. 4, edited by K. H. J. Buschow, ch. 1. Amsterdam: Elsevier Science. Google Scholar
Campbell, I. A. (1972). J. Phys. F, 2, L47–L50. CrossRef CAS Web of Science Google Scholar
Carra, P., Harmon, B. N., Thole, B. T., Altarelli, M. & Sawatzky, G. A. (1991). Phys. Rev. Lett. 66, 2495–2498. CrossRef PubMed CAS Web of Science Google Scholar
Carra, P., Thole, B. T., Altarelli, M. & Wang, X. (1993). Phys. Rev. Lett. 70, 694–697. CrossRef PubMed CAS Web of Science Google Scholar
Chaboy, J., Bartolomé, F., García, L. M. & Cibin, G. (1998a). Phys. Rev. B, 57, R5598–R5601. Web of Science CrossRef CAS Google Scholar
Chaboy, J., García, L. M., Bartolomé, F., Maruyama, H., Marcelli, A. & Bozukov, L. (1998b). Phys. Rev. B, 57, 13386–13389. Web of Science CrossRef CAS Google Scholar
Chaboy, J., Laguna-Marco, M. A., Maruyama, H., Ishimatsu, N., Isohama, Y. & Kawamura, N. (2007a). Phys. Rev. B, 75, 144405. Web of Science CrossRef Google Scholar
Chaboy, J., Laguna-Marco, M. Á., Piquer, C., Boada, R., Maruyama, H. & Kawamura, N. (2008). J. Synchrotron Rad. 15, 440–448. Web of Science CrossRef CAS IUCr Journals Google Scholar
Chaboy, J., Laguna-Marco, M. A., Piquer, C., Maruyama, H. & Kawamura, N. (2007b). J. Phys. Condens. Matter, 19, 436225. Web of Science CrossRef Google Scholar
Chaboy, J., Laguna-Marco, M. A., Piquer, C., Maruyama, H., Kawamura, N., Ishimatsu, N., Suzuki, M. & Takagaki, M. (2007c). Phys. Rev. B, 75, 064410. Web of Science CrossRef Google Scholar
Chaboy, J., Laguna-Marco, M. A., Sánchez, M. C., Maruyama, H., Kawamura, N. & Suzuki, M. (2004). Phys. Rev. B, 69, 134421. Web of Science CrossRef Google Scholar
Chaboy, J., Maruyama, H., García, L. M., Bartolomé, J., Kobayashi, K., Kawamura, N., Marcelli, A. & Bozukov, L. (1996). Phys. Rev. B, 54, R15637–R15640. CrossRef CAS Google Scholar
Chaboy, J., Piquer, C., Plugaru, N., Artigas, M., Maruyama, H., Kawamura, N. & Suzuki, M. (2003). J. Appl. Phys. 93, 475–478. Web of Science CrossRef CAS Google Scholar
Chaboy, J., Piquer, C., Plugaru, N., Bartolomé, F., Laguna-Marco, M. A. & Plazaola, F. (2007d). Phys. Rev. B, 76, 134408. Web of Science CrossRef Google Scholar
Chen, C. T., Idzerda, Y. U., Lin, H.-J., Meigs, G., Chaiken, A., Prinz, G. A. & Ho, G. H. (1993). Phys. Rev. B, 48, 642–645. CrossRef CAS Web of Science Google Scholar
Crocombettey, J. P., Thole, B. T. & Jollet, F. (1996). J. Phys. Condens. Matter, 8, 4095–4105. Google Scholar
Funk, T., Deb, A., George, S. J., Wang, H. & Cramer, S. P. (2005). Coord. Chem. Rev. 249, 3–30. Web of Science CrossRef CAS Google Scholar
Gennes, P. G. de (1966). C. R. Acad. Sci. (Paris), 247, 1836–1838. Google Scholar
Giorgetti, C., Dartyge, E., Baudelet, F. & Galéra, R.-M. (2004). Phys. Rev. B, 70, 035105. Web of Science CrossRef Google Scholar
Goering, E. (2005). Philos. Mag. B, 85, 2895–2911. CAS Google Scholar
Igarashi, J. & Hirai, K. (1994). Phys. Rev. B, 50, 17820–17829. CrossRef CAS Web of Science Google Scholar
Igarashi, J. & Hirai, K. (1996). Phys. Rev. B, 53, 6442–6450. CrossRef CAS Web of Science Google Scholar
Ishimatsu, N., Miyamoto, S., Maruyama, H., Chaboy, J., Laguna-Marco, M. A. & Kawamura, N. (2007). Phys. Rev. B, 75, 180402. Web of Science CrossRef Google Scholar
Kortright, J. B., Awschalom, D. D., Stöhr, J., Bader, S. D., Idzerda, Y. U., Parkin, S. S. P., Schuller, I. K. & Siegmann, H.-C. (1999). J. Magn. Magn. Mater. 207, 7–44. Web of Science CrossRef CAS Google Scholar
Laguna-Marco, M. A. (2007). Editor. A New Insight into the Interpretation of the T K-edge and R L_2,3-Edges XMCD Spectra in R–T Intermetallics. Zaragoza: Prensas Universitarias de Zaragoza. Google Scholar
Laguna-Marco, M. A., Chaboy, J. & Maruyama, H. (2005a). Phys. Rev. B, 72, 094408. Web of Science CrossRef Google Scholar
Laguna-Marco, M. A., Chaboy, J. & Piquer, C. (2008a). Phys. Rev. B, 77, 125132. Web of Science CrossRef Google Scholar
Laguna-Marco, M. A., Chaboy, J. & Piquer, C. (2008b). J. Appl. Phys. 103, 07E141. Web of Science CrossRef Google Scholar
Laguna-Marco, M. A., Chaboy, J., Piquer, C., Maruyama, H., Ishimatsu, N. & Kawamura, N. (2007a). AIP Conf. Proc. 882, 484–486. CrossRef CAS Google Scholar
Laguna-Marco, M. A., Chaboy, J., Piquer, C., Maruyama, H., Ishimatsu, N., Kawamura, N., Takagaki, M. & Suzuki, M. (2005b). Phys. Rev. B, 72, 052412. Web of Science CrossRef Google Scholar
Laguna-Marco, M. A., Chaboy, J., Piquer, C., Maruyama, H., Kawamura, N. & Takagaki, M. (2007b). J. Magn. Magn. Mater. 316, e425–e427. Web of Science CrossRef CAS Google Scholar
Laguna-Marco, M. A., Piquer, C. & Chaboy, J. (2009). Phys. Rev. B. Submitted. Google Scholar
Lang, J. C., Kycia, S. W., Wang, X. D., Harmon, B. N., Goldman, A. I., Branagan, D. J., McCallum, R. W. & Finkelstein, K. D. (1992). Phys. Rev. B, 46, 5298–5302. CrossRef CAS Web of Science Google Scholar
Lang, J. C., Srajer, G., Detlefs, C., Goldman, A. I., König, H., Wang, X., Harmon, B. N. & McCallum, R. W. (1995). Phys. Rev. Lett. 74, 4935–4938. CrossRef PubMed CAS Web of Science Google Scholar
Lang, J. C., Wang, X., Harmon, B. N., Goldman, A. I., Dennis, K. W., McCallum, R. W. & Finkelstein, K. D. (1994). Phys. Rev. B, 50, 13805–13808. CrossRef CAS Web of Science Google Scholar
Lovesey, S. W. & Collins, S. P. (1996). Editors. X-ray Scattering and Absorption by Magnetic Materials. London: Clarendon. Google Scholar
Maruyama, H. (2001). J. Synchrotron Rad. 8, 125–128. Web of Science CrossRef CAS IUCr Journals Google Scholar
Purwins, H. G. & Leson, A. (1990). Adv. Phys. 39, 309–405. CrossRef CAS Web of Science Google Scholar
Rodriguez-Carvajal, J. (1993). Physica B, 192, 55–69. CrossRef CAS Web of Science Google Scholar
Rueff, J. P., Galéra, R. M., Giorgetti, C., Dartyge, E., Brouder, C. & Alouani, M. (1998). Phys. Rev. B, 58, 12271–12281. Web of Science CrossRef CAS Google Scholar
Scherz, A., Wende, H. & Baberschke, K. (2004). Appl. Phys. A, 78, 843–846. Web of Science CrossRef CAS Google Scholar
Schütz, G., Frahm, R., Wienke, R., Wilhelm, W., Wagner, W. & Kienle, P. (1989). Rev. Sci. Instrum. 60, 1661–1665. CrossRef Google Scholar
Schütz, G., Wagner, W., Wilhelm, W., Kienle, P., Zeller, R., Frahm, R. & Materlik, G. (1987). Phys. Rev. Lett. 58, 737–740. CrossRef PubMed Web of Science Google Scholar
Schütz, G. & Wienke, H. (1989). Hyperfine Interact. 50, 457–476. Google Scholar
Schütz, G., Wienke, R., Knülle, M., Wilhelm, W., Wagner, W., Kienle, P. & Frahm, R. (1988). Z. Phys. B, 73, 67–75. Google Scholar
Stähler, S., Schütz, G. & Ebert, H. (1993). Phys. Rev. B, 47, 818–826. CrossRef Web of Science Google Scholar
Stöhr, J. (1999). J. Magn. Magn. Mater. 200, 470–497. Web of Science CrossRef CAS Google Scholar
Suzuki, M., Kawamura, N., Mizumaki, M., Urata, A., Maruyama, H., Goto, S. & Ishikawa, T. (1998). Jpn. J. Appl. Phys. 37, L1488–L1490. Web of Science CrossRef CAS Google Scholar
Thole, B. T., Carra, P., Sette, F. & van der Laan, G. (1992). Phys. Rev. Lett. 68, 1943–1946. CrossRef PubMed CAS Web of Science Google Scholar
Wang, X., Leung, T. C., Harmon, B. N. & Carra, P. (1993). Phys. Rev. B, 47, 9087–9090. CrossRef CAS Web of Science Google Scholar
Yamada, H., Inoue, J., Terao, K., Kanda, S. & Shimizu, M. (1984). J. Phys. F, 14, 1943–1960. CrossRef CAS Web of Science Google Scholar
Yamada, H. & Shimizu, M. (1985). J. Phys. F, 15, L175–L180. CrossRef CAS Web of Science Google Scholar

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Volume 16| Part 3| May 2009| Pages 405-412

doi:10.1107/S0909049509009807

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