Alloys, compounds and superlattices - Handbook on the Physics and

Up to this point we have concerned ourselves solely with X-ray scattering from the lanthanide elements. In this section we shall review key results that have been gathered on composite systems containing lanthanides including alloys, compounds and artificial structures, such as superlattices and thin films. The aim here is not to give an exhaustive list, but rather to choose examples that illustrate how the unique characteristics of the X-ray scattering cross-section can be exploited to illuminate particular features of the system under investigation. As we shall see, the chosen examples encompass many disparate fields, and this reflects the wide ranging applicability of the technique.

5.1. Lanthanide alloys

In a general context, the study o f random alloys has helped to advance our understanding of the magnetic interactions in the lanthanides (Jensen and Mackintosh 1991). From an X-ray scattering point of view the appeal in studying these systems is to apply resonant

62 D.E M c M O R R O W et al.

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scattering techniques. By tuning the X-ray energy to the L edge of one the constituents it is possible to selectively enhance its contribution to the total magnetic scattering. This species-sensitive magnetic diffraction is a unique feature of X-ray resonant scattering, and several experiments have now been performed to exploit it in a variety of ways.

5.1.1. H o - E r

As has been outlined in previous sections, Ho and Er each exhibit spin-slip structures at low temperatures, and the expectation is that alloys of these two elements should also display some interesting and related features. Indeed a neutron scattering study of a Ho0.sEr0.5 alloy by Howard and Bohr (1991) revealed three distinct temperature intervals.

(1) 47.5 K~< T ~< 104K. The alloy orders at a temperature close to the weighted average of the bulk transition temperatures, but unusually the moments form a c-axis modulated spiral in which the Ho and Er moments adopt different tilt angles with respect to the basal plane. (2) 35 K ~< T ~< 47.5 K. The Ho and Er moments collapse into the basal plane to form a flat helix. (3) T ~< 35 K. The Ho and Er moments lift out of the basal plane to form a cone.

Pengra et al. (1994) studied a single crystal of Ho0.sEr0.5 using resonant scattering.

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Fig. 40. The temperature dependence of the modulation wave vector q in a Ho0.sEr0. 5 alloy. The X-ray data were taken at the (0,0,4+q) satellite at the Ho LII 1 resonance (solid circle, 8069 eV) and at the Er L m resonance (*, 8358 eV). Also shown are neutron measurements (open circles) taken at the (0,0,2-q) satellite. (From Pengra

et al. 1994.)

64 D.E McMORROW et al.

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Fig. 41. Ho0.sEr05 alloy. Integrated intensity of the resonant satellites from the same data series as in fig. 40:

Ha edge X-ray data (solid circles), Er edge data (*), and neutron data (open circles). The vertical lines mark the boundaries o f the three magnetic phases. (From Pengra et al. 1994.)

from neutron and X-ray scattering experiments, where dhe X-ray data were obtained with the energy tuned to the Lm edges of Ho and Er. These results establish that in the alloy the individual Ho and Er moments order with the same wave vector, so as to produce a structure described by a single wave vector. A similar comparison for the temperature dependence of the intensity of the magnetic scattering is given in fig. 41. Here it can be seen that whereas the neutron data has an increase in intensity in the intermediate phase, the X-ray data has a dip. This was shown by Pengra et al. to arise from differences in the geometric selection rules for neutron and X-ray resonant magnetic scattering. The former is sensitive to the component of the moment perpendicular to Q, while for dipolar transitions the latter is most sensitive to the component of the moment along the scattered wave vector (Hill and McMorrow 1996). Thus, for Q along [00g], as the moments collapse into a basal plane spiral the former increases and the latter decreases. The study by Pengra et al. also highlights how X-ray and neutron scattering can be combined to good effect to tackle a complex structural problem.

5.1.2. Dy-Lu

Everitt et al. (1995) also exploited the species-sensitivity of the resonant cross-section in their study of Dy alloyed with non-magnetic Lu. (Lu is the last element in the lanthanide series, and as such has a full complement of fourteen 4f electrons and no net 4f moment.) The novel aspect of this experiment was that the X-ray scattering displayed a resonant peak not only at the Dy Lm edge, but also a much weaker peak at the Lm edge of Lu (fig. 42). From the selection rules governing the polarization dependence of magnetic scattering, it was shown that the latter peak was magnetic in origin. As expected, it was found that the Lu scattering peaked at the same wave-vector in reciprocal space, and

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Fig. 42. Q-integrated intensity of the (0,0,2+%) magnetic peak vs energy through the Lu Lnl edge in a Dy0.6Luo. 4 alloy. The residual intensity is at- tributed to the non-resonant scattering from the Dy moments. Inset: The same, measured through the Dy L m edge.

An MgO (420) analyzer was used for both measurements. Lorentzian- squared curves with a FWHM of 7 eV have been fitted to both data sets.

(From Everitt et al. 1995.)

66 D.E McMORROW et al.

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Fig. 43. Dy0.6Lu0. 4 alloy. Temperature dependence of the (0,0,2+~'m) magnetic peak. Squares, Lu-edge data taken in the a - ;c geometry; circles, Dy-edge data taken in high-resolution mode. Inset: neutron diffraction data for

the same sample. (From Everitt et al. 1995.)

followed the same temperature dependence (see fig. 43), as the scattering at the Lm edge of Dy. I f we recall that a dipole transition at the Lm edge of the lanthanides couples a 2p3/2 core state to a 5d level, and that in the lanthanides the 5d electrons form part of the conduction band, then it is apparent that the scattering at the Lu Lm edge is sensitive to the magnetization of the 5d band induced at the Lu sites. By comparing the intensity of the scattering at the two Lm edges, the amplitude of the 5d polarization was estimated to be about 0.2/~B per atom, within a factor of two of its mean-field value.

5.1.3. H o - P r

A recent related study to the work on H o - E r involves a combined X-ray and neutron scattering characterization of the structure and magnetism of a series of H o - P r alloys (Goff et al. 1998, Vigliante et al. 1998). In contrast to Ho, Pr has a dhcp chemical lattice and a non-magnetic singlet ground state which does not exhibit magnetic ordering above T = 0.05 K. The combined results show that the alloys exhibit three distinct lattice and magnetic structures versus Pr concentration, c. In the Pr-rich phase (c(Pr) > 60%), the alloy chemical lattice has dhcp symmetry and does not exhibit magnetic ordering down to 0.1 K, just as in bulk. For Pr concentrations between 40 and 60%, the alloys have a Sm lattice and magnetic structure. In the Ho-rich phase (c(Pr)< 40%), the chemical lattice has hcp symmetry and supports a spiral magnetic structure, as in bulk Ho. Each of the magnetic alloys exhibited a concentration-dependent N6el temperature and lock- in transitions to simply commensurate wave vectors at low temperatures (see fig. 44).

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In the Sm-like phase, the magnetic wave vectors remained locked to rm = ½ at all temperatures, while in the spiral phase they locked to rm = 2, the latter is reminiscent of Ho thin films. X-ray resonant magnetic scattering was also used to show that a small static spin-density-wave is induced in the alloy 5d bands, propagating at both Ho and Pr sites of the spiral and Sm-like magnetic structures. To within the available statistics, it was found that the induced Pr 5d moment/atom was independent of concentration.

Among the most intriguing results of these studies was the observation of asymmetric LIzI/LrI branching ratios, just as previously observed in the pure elements (Gibbs et al.

1991, Hill et al. 1995a, D. Watson et al. 1995). Specifically, it was found that LIII/Ljt (Ho) ~ 10 and Lm/LH (Pr) ~ 0 . 1 . In the simplest theories (Harmon et al. 1988), these branching ratios are predicted to be of order unity. Resolving these discrepancies will be required before induced moment amplitudes can be reliably extracted from the resonant intensities. Moreover, their existence in both the heavy and light elements implies that

68 D.E McMORROW et al.

the standard picture of the lanthanide electronic structure used in the calculations of the resonant cross-section is not adequate (van Veenendaal et al. 1997).

5.2. Compounds

5.2.1. Magnetism and superconductioity in RNi2B2C

The RNi2BzC (R = lanthanide) family of compounds are of interest because the ground state may either be superconducting or magnetic, or even both at the same time. The study of the interaction between these two ground states has benefited greatly from the use of X-ray magnetic scattering techniques, with perhaps the study of HoNizBzC being the prime example (Hill et al. 1996).

HoNi2BzC adopts a tetragonal crystal structure (space group I4/mmm) and is a type- II superconductor for temperatures below Tc = 8 K. Approximately 1 K lower the Ho 4f moments order with an incommensurable modulation, and at the same temperature there is a large reduction in the upper critical field He2. (Currently, a clear picture of the role of the smaller Ni moments is not available.) Below 5 K, the 4f moments are confined to the a-b plane and are antiferromagnetically coupled along the c axis. The main contributions of X-ray scattering experiments in the study of this material has been to show that the magnetic structure of the incommensurable phase is more elaborate than had been deduced from neutron diffraction. These latter measurements had indicated that the incommensurable phase was characterized by two wave vectors, qc = 0.915c* and qa = 0.585a*. Utilising the higher Q resolution of X-ray scattering and the resonant enhancement of the magnetic scattering at the Lm edge of Ho, Hill et al. (1996) were able to show that the c-axis modulation was in fact comprised of two components with wave vectors of ql = 0.906c* and q2 ⁼ 0.919c*, as shown in fig. 45. At the lowest temperatures studied in the antiferromagnetic phase a scan along the [00g] direction revealed a sharp peak at the (0,0,3) position, confirming the simple antiferromagnetic stacking of the moments. For temperatures above 5 K this peak broadened and decreased rapidly in intensity, and two new peaks appeared near (0,0,2.906) and (0,0,2.919). The interaction between complex incommensurate order and the superconducting ground state revealed in this study has yet to be explained and, as Hill et al. (1996) point out, it provides a good test case for theories of antiferromagnetic superconductors.

Although not a superconductor, the X-ray study of GdNi2BzC by Detlefs et al. (1996) is also worth mentioning in this section, as it represents the first attempt to solve a magnetic structure by combining resonant and non-resonant techniques. Due to the very large neutron absorption cross-section of naturally occurring Gd, GdNi2B2C is unsuitable for study with neutron diffraction, and so prior to the study of Detlefs et al. (1996) all that was known about its magnetic structure had been gleaned from bulk probes, such as magnetization experiments. These had established that the Gd 4f moments order below TN = 20 K, and indicated the existence of a possible spin reorientation below TR = 14 K.

The X-ray scattering experiments of Detlefs et al. (1996) were performed with the sample mounted in the (h0£) zone, and with the a axis bisecting the incident and

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Dalam dokumen Handbook on the Physics and (Halaman 72-80)