Temperature dependence of the Ho L₂-edge XMCD spectra of Ho₆Fe₂₃

An X-ray magnetic circular dichroism (XMCD) study performed at the Ho L_2,3-edges in Ho₆Fe₂₃ as a function of temperature is presented. It is demonstrated that the anomalous temperature dependence of the Ho L₂-edge XMCD signal is due to the magnetic contribution of Fe atoms. By contrast, the Ho L₃-edge XMCD directly reflects the temperature dependence of the Ho magnetic moment. By combining the XMCD at both Ho L₂- and L₃-edges, the possibility of determining the temperature dependence of the Fe magnetic moment is demonstrated. Then, both μ_Ho(T) and μ_Fe(T) have been determined by tuning only the absorption L-edges of Ho. This result opens new possibilities of applying XMCD at these absorption edges to obtain quantitative element-specific magnetic information that is not directly obtained by other experimental tools.

1. Introduction

X-ray magnetic circular dichroism (XMCD) has become in recent years a standard tool for studying the localized magnetism in many magnetic systems (Lovesey & Collins, 1996; Stöhr, 1999; Funk et al., 2005). By incorporating element specificity, analysis of the XMCD signals in the soft X-ray range provides quantitative estimates of the magnetic moments, including the disentangling of spin and orbital contributions, in the case of localized states carrying a magnetic moment. However, the contribution of XMCD to the study of the conduction band magnetism is not so straightforward. This is the case of the XMCD at the L_2,3-edges of the rare-earths and at the K-edge of 3d transition metals in which delocalized states (5d and 4p, respectively) are probed in the absorption process.

The XMCD at the rare-earth L_2,3-edges has been a matter of study for years, especially regarding the non-negligible role of quadrupolar transitions (Lang et al., 1994, 1995; Chaboy, Bartolomé et al., 1998), the spin-dependence of the radial matrix elements of the dipolar transition (Wang et al., 1993) and the importance of the 5d–4f exchange interaction (Jo & Imada, 1993). All these ingredients acting at the L_2,3 XMCD spectra avoid establishing a direct relationship between the XMCD and the magnetic state of the 5d states. Beyond the interest in fundamental physics, this scenario casts doubts regarding whether the XMCD at these absorption edges can provide useful and quantitative information not directly attained by other experimental tools.

In this respect we have performed a longstanding study of the rare-earth L_2,3- and transition-metal K-edges in rare-earth transition-metal intermetallic compounds (Chaboy et al., 1996, 2004; Chaboy, García et al., 1998; Laguna-Marco, Chaboy, Piquer et al., 2005; Chaboy, Laguna-Marco, Maruyama et al., 2007; Chaboy, Piquer et al., 2007; Ishimatsu et al., 2007; Laguna-Marco, 2007). The results of this research indicate that the study of the conduction band at these absorption edges is further complicated in these multi-component magnetic systems as both atomic species, R and T, influence the XMCD spectra recorded at the K-edge of the transition metal and at the L-edges of the rare-earth, respectively. These studies have also shown the relationship between the XMCD and the molecular field (Chaboy, Laguna-Marco et al., 2007) as well as a way of experimentally determining the R(5d)–T(3d) hybridization (Laguna-Marco et al., 2008) in these R–T compounds. Moreover, it has been recently shown that the correct interpretation of the R L_2,3- and T K-edge XMCD signals opens the possibility of disentangling the magnetic contribution of different atomic species within the same material by using a single X-ray absorption edge (Chaboy et al., 2008).

To date, most of these experiments have been performed on RT₂ Laves phase compounds in which the total magnetization of the system is dominated by the rare-earth. The question posed is to verify whether the above results are common to all R–T intermetallics independently of their stoichiometry. To this end we have performed an analysis of the temperature dependence of the XMCD signal recorded at the L_2,3-edges of Ho in Ho₆Fe₂₃. The suitability of this material to the present study resides in the fact that owing to the ferrimagnetic coupling of the Fe and Ho moments, and to the 6:23 stoichiometry, the overall magnetization of the system is determined either by the Fe sublattice or the Ho sublattice depending on the temperature range. A previous work on this system (Laguna-Marco, Chaboy & Maruyama, 2005) allows us to identify the contribution of the Fe atoms to the XMCD recorded at the L₂-edge of Ho yielding an anomalous temperature dependence. However, detailed quantitative information on this contribution such as its relationship with the Fe magnetic moment was missed. On the basis of the results recently published (Chaboy et al., 2008), we have re-investigated such anomalous behavior aiming to verify the possibility of extracting quantitative magnetic information of the different atoms (Fe and Ho) present in the material by tuning the absorption edge of a single atom (Ho). Our results show that by tuning the X-ray absorption at the L_2,3-edges of the rare-earth it is possible to determine the temperature dependence of the magnetic moments of both Ho, μ_Ho(T), and Fe, μ_Fe(T). These results open the possibility of obtaining a quantitative magnetic characterization of complex magnetic systems by using XMCD in the hard X-ray region, including element-specific magnetometry, by tuning the X-ray absorption of a single atomic species.

2. Experimental

The R₆Fe₂₃ samples (with R = Y and Ho) were prepared following standard procedures (Herbst & Croat, 1984). X-ray diffraction analysis showed that all the samples were single phase (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 the transmission mode at the Ho L_2,3-edges by using the helicity-modulation technique (Suzuki et al., 1998). They were recorded under the action of a 0.6 T magnetic field applied at 45° away from the incident beam direction at different fixed temperatures from room temperature down to 80 K. The sample was magnetized by an external magnetic field applied in the direction of the incident beam and the helicity was changed from positive to negative at 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. 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 onto an adhesive tape. 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.

3. Results and discussion

The ferrimagnetic Ho₆Fe₂₃ compound exhibits a magnetization compensation phenomenon as a function of temperature which originates from the different temperature dependence of both the iron, μ_Fe, and Ho, μ_Ho, magnetic moments. In a first approach the magnetization of the compound can be described as corresponding to the addition of the magnetization of each magnetic, Fe and Ho, sublattice. At room temperature the Fe sublattice dominates the overall magnetization of the system. On cooling from room temperature, the magnetization continuously decreases up to T_Comp ≃ 192 K and then it increases for further cooling up to 4.2 K. This temperature dependence is due to the fact that the Ho magnetic moment, being ferrimagnetically coupled to that of Fe, increases faster than μ_Fe as the temperature decreases. Therefore the total magnetization decreases until it vanishes at T_Comp. On further cooling below T_Comp, the magnetization of the Ho sublattice prevails and the total magnetization of the system shows a continuous increase (Laguna-Marco, Chaboy & Maruyama, 2005). The Ho magnetic moment can be extracted from the magnetization measurements by assuming that the temperature dependence of the Fe sublattice in Ho₆Fe₂₃ corresponds to that of Y₆Fe₂₃ (Herbst & Croat, 1984). In this way it has been determined that μ_Ho increases from 4.70μ_B at room temperature to 9.26μ_B at T = 5 K. While the relative modification of μ_Ho between ambient and low temperature is ∼97%, it is only ∼17% for μ_Fe (from 1.61μ_B to 1.87μ_B).

The XMCD spectra recorded at both the L_2,3-edges of Ho are reported in Fig. 1. It should be noted that the XMCD spectra show a sign reversal below the compensation temperature, reflecting the change of the magnetic sublattice governing the sign of the total magnetization above (Fe) and below (Ho) T_Comp. For the sake of clarity, all the spectra are displayed with the same sign as the low-temperature ones, i.e. when Ho dominates the overall magnetization of the system. In the case of the Ho L₃-edge the XMCD spectra exhibit two main features of opposite sign located, respectively, at −5 eV (A) and 3 eV (B) above the edge. This spectral shape is not modified when the temperature varies and only the amplitude of the overall signal is concerned. In this way the integration of L₃-edge XMCD spectra yields a temperature dependence that fits well the variation of the Ho magnetic moment derived from magnetization data. This comparison is shown in Fig. 1(c) in which the variation of both XMCD integral and μ_Ho are plotted in relation to their room-temperature values. The same criterion will be followed hereafter to evaluate the relative variation of the signals. By contrast with the L₃ case, the spectral shape of the Ho L₂-edge XMCD is modified as a function of temperature. At room temperature the main structures of the L₂-edge XMCD spectrum are a positive peak (C) at 1 eV and a negative one (D) at ∼3 eV above the edge. As the temperature decreases, the amplitude of the signal increases as expected from the enhancement of the Ho magnetic moment. However, the intensity of peak C shows the contrary trend and this peak is progressively depleted. As previously discussed (Laguna-Marco, Chaboy & Maruyama, 2005), this anomalous behaviour is due to the influence of the Fe sublattice magnetization even when the Ho L₂-edge is tuned.¹ As a consequence, the integral of the XMCD signal shows a temperature dependence with a relative variation one order of magnitude greater than that expected for μ_Ho.

Figure 1 (a) and (b) Temperature dependence of the XMCD spectra of Ho at the L3- (a) and L2-edge (b) in Ho6Fe23: T = 80 K (black, filled circles), T = 150 K (red, open circles), T = 225 K (green, filled squares), T = 250 K (blue, open squares) and T = 300 K (purple, filled triangles). For the sake of comparison, the Ho L2 XMCD spectrum of HoAl2 recorded at T = 5 K and H = 5 T is also shown (dark green, dashed line) in (b). The same is done for L3 in (a) but for the HoAl2 signal scaled to match the amplitude of Ho6Fe23 at T = 80 K. (c) and (d) Comparison of the temperature dependence, relative to the room-temperature values, of the Ho magnetic moment, derived from magnetization data (red, open circles) and the integrated XMCD signals (black, filled circles) of the Ho L3 (c) and L2 (d) absorption edges.

This anomalous behaviour stems from the competition of both Ho and Fe sublattice magnetization to the L₂ XMCD signal (Laguna-Marco, Chaboy & Maruyama, 2005). Indeed, peak C is absent in the case of HoAl₂, i.e. in a system in which the only magnetic contribution comes from Ho atoms. Then, our main aim is to disentangle both Fe and Ho contributions from the Ho L₂-edge XMCD spectra as a function of temperature in order to determine both μ_Fe(T) and μ_Ho(T) from the same absorption spectra.

To this end we have considered the XMCD signals recorded at the Ho L_2,3-edges in HoAl₂ at T = 4.2 K and under the action of an applied magnetic field H = 5 T. Under these experimental conditions the magnetic moment of Ho is close to its free-ion value and, consequently, one can assume that these signals would reflect the Ho contribution to the Ho₆Fe₂₃ L-edges spectra in the absence of any Fe contribution. However, one has to consider that, at T = 80 K, μ_Ho does not correspond to the free-ion value. Therefore, we have scaled the Ho L₃ XMCD of HoAl₂ to match that of Ho₆Fe₂₃ at T = 80 K, and this scaling factor has been further applied to the L₂ spectrum (see Fig. 1). By subtracting now the scaled HoAl₂ signal from the L₂ spectra of Ho₆Fe₂₃ the Ho contribution is cancelled and the remaining signal would correspond to the Fe contribution. The result of applying this procedure is shown in Fig. 2. The difference signal is characterized by an intense positive peak at the edge whose intensity should be proportional to the Fe magnetization. However, this procedure would only be valid at T = 80 K. Indeed, despite the fact that the shape of the extracted signal does not vary with temperature, the intensity of the extracted Fe contribution increases with temperature, while μ_Fe is expected to decrease. The reason for this discrepancy is that, as the temperature increases, μ_Ho decreases faster than μ_Fe. Therefore the Ho contribution has to be subtracted from Ho₆Fe₂₃ by taking into account the temperature dependence, that should be different from that of Fe. Then, we have assumed that the amplitude of the Ho L₃ XMCD signal is directly related to μ_Ho and, consequently, μ_Ho(T) is given by the temperature dependence of the XMCD amplitude at this absorption edge. In this way we considered that the Ho L₂-edge XMCD signal can be decomposed as the addition of two contributions, XMCD_Tot(T) = XMCD_Ho(T) + XMCD_Fe(T), where the Ho contribution XMCD_Ho(T) = f(T) × XMCD_HoAl2(80 K) and the proportionality factor is derived from the intensity ratio, f(T) = XMCD_L3(T)/XMCD_L3(T = 80 K), of the Ho L₃ XMCD spectra. After applying this procedure the intensity of the obtained signal, the Fe contribution, decreases as the temperature increases, in agreement with the expected variation of μ_Fe(T).

Figure 2 (a) Comparison of the signal obtained after subtracting from the Ho L2 XMCD Ho6Fe23 signals the XMCD spectrum of HoAl2 after scaling to T = 80 K: T = 80 K (black, filled circles), T = 150 K (red, open circles), T = 225 K (green, filled squares), T = 250 K (blue, open squares) and T = 300 K (purple, filled triangles). (b) Same comparison as above after weighting the HoAl2 signal with the temperature dependence observed at the Ho L3-edge (see text for details).

The final step here is to determine how reliable the obtained μ_Ho(T) and μ_Fe(T) temperature dependences are. At T = 80 K the magnetic moments of Ho and Fe are, respectively, μ_Ho = 8.15μ_B and μ_Fe = 1.77μ_B, as derived from magnetization data (Laguna-Marco, Chaboy & Maruyama, 2005). By considering these values and the temperature dependence of the Ho L_2,3-edges XMCD spectra we obtain the quantitative determination for both μ_Ho(T) and μ_Fe(T) shown in Fig. 3. These results agree with the faster decrease of the Ho magnetic moment than that of Fe as the temperature increases. Moreover, we have compared in Fig. 3(b) the magnetization of the Ho₆Fe₂₃ compound measured by conventional magnetometry methods and built from the μ_Ho(T) and μ_Fe(T) values determined from the XMCD data. The obtained agreement supports the success of disentangling the magnetic contribution of both Fe and Ho by using only the Ho X-ray absorption edges.

Figure 3 (a) Comparison of the temperature dependence of the magnetic moment of Ho (blue, filled circles) and Fe (black, open circles) extracted, respectively, from the L3 and L2 XMCD spectra of Ho6Fe23. (b) Comparison of the temperature dependence of the magnetization of Ho6Fe23 measured at SQUID (red, open triangles) and obtained (green, filled triangles) by using the magnetization of the Ho and Fe sublattices derived from the Ho L2,3-edges XMCD spectra.

4. Summary and conclusions

We have presented a systematic study of the temperature dependence of the XMCD signals recorded at the Ho L_2,3-edges in Ho₆Fe₂₃. While the amplitude of the Ho L₃-edge XMCD spectra follows the variation of the Ho magnetic moment with temperature, the behaviour of the Ho L₂-edge XMCD signal is neither proportional to the Ho magnetic moment nor to the magnetization of the system. This anomalous behaviour has been accounted for in terms of the contribution of the Fe sublattice magnetization to the Ho L₂-edge XMCD signal. On the basis of the results recently published (Chaboy et al., 2008) we have re-investigated such anomalous behavior aiming to verify the possibility of extracting quantitative magnetic information of the different atoms (Fe and Ho) present in the material by tuning the absorption of a single atom (Ho).

Our results show that by tuning the X-ray absorption at the L_2,3-edges of the rare-earth as a function of temperature it is possible to determine the temperature dependence of the magnetic moments of both Ho, μ_Ho(T), and Fe, μ_Fe(T). These results open the possibility of obtaining a quantitative magnetic characterization of complex magnetic systems by using XMCD in the hard X-ray region, including element-specific magnetometry, by tuning the X-ray absorption of a single atomic species.

Footnotes

¹This contribution is not detected at the L₃-edge XMCD. See Chaboy, Laguna-Marco, Piquer et al. (2007) for a detailed discussion.