Zuckermann, Transport properties (electrical resistivity, thermoelectric power and thermal conductivity) of intermetallic rare earth compounds 117. Rogl, Phase equilibria in ternary and higher order systems with rare earth elements and silicon 52.
E McMORROW
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 3 virtually all of the knowledge we possess today concerning magnetic structures was
The polarization dependence of the magnetic cross-section provides a natural technique for quantitative determinations of magnetic structures. In this way, the energy and polarization dependence of the magnetic scattering explores the fine structure of magnetic states.
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 5 The lanthanide metals have played a special role in these developments. The striking
- The X-ray scattering cross-section
3 we describe the results of X-ray scattering studies of the lanthanide metal Ho, while results of the rest of the lanthanide metals are considered in sect. For a free electron, the ratio of the magnetic dipole reradiation to electric dipole reradiation (hoo/mec2) is 2, which is of order 10 4 for photons with energy h e ) = 10keV.
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 7
Here we follow the notation of Blume and Gibbs (1988) and use double primes on the polarization vector .4" to avoid confusion with .4, the vector potential of the photon field. We choose the linear components of the photon polarization to be parallel or perpendicular to the diffraction plane (spanned of the vectors k and fc').The Or component of the polarization is defined to be perpendicular to the diffraction plane and the Jr component to lie within the diffraction plane (see Fig. 2).
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 9 predominantly a-polarized, while in a horizontal scattering geometry it is predominantly
- Dipolar transitions (El)
- Quadrupolar transitions (E2)
For such a transition, the scattering amplitude can be written as are linear combinations of the FLM factors given in Eq. For example, at the Lm edge of Ho, the cross section for the 2p3/2 -+ 4f processes at the first harmonic is approximately one quarter of the dipole (Gibbs et al. 1988).
If we now assume that the incident beam is essentially plane polarized in the orbital plane of the synchrotron, then the density matrix simplifies to. It has been demonstrated that the Jr component is dominant, consistent with the large orbital moment in Ho, and that the Q dependence of the orbital and spin forms.
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 17 factors was qualitatively in agreement with theoretical calculations. Further experiments
- The magnetic structure of holmium
The one spin-slip phase. at low temperatures there were fifth and seventh harmonics in the diffraction pattern, indicating that the moments about the nearest easy axis are bundled in the basal plane, as in fig. These and later neutron scattering studies by Felcher et al. 1976), and Pechan and Stassis (1984) determined that there were additional features in the diffraction patterns that could not be explained by a simple bundle spiral, but a unified model that could explain all the features was not forthcoming .
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 19
Temperature dependence of the Ho modulation wave vector r obtained with both synchrotron X-ray (open circles) and neutron (solid circles) scattering. When the magnetic peak reaches Tm = ~7 c*, the radial width of the charge scattering narrows and grows in intensity.
RAY SCATTERING STU~)IES OF LANTHANIDE MAGNETISM 25 inhomogeneous structures composed of commensurable regions separated by domain
We thus interpret this second peak as arising from the distortions of the lattice due to the spin slips. More generally, we can calculate the spin-slip wave vector Ts for any compensable phase as.
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 27
Magnetic, sample 1
Temperature (Kelvin)
The different orientations of the magnetic moments relative to the crystal field give rise to local differences in the magnetostriction. Support for the results of the detailed modeling of the spindle lip structures by Cowley and Bates (1988) was produced by self-consistent mean-field calculations (Jensen and Mackintosh 1991).
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 35
Open circles show the degree of linear polarization P~ of the charge distribution for chemical and (006) reflections. The solid line is calculated assuming that R = [(L'.. The crazy dashed dotted lines are calculated assuming that R = 4 and 2, respectively.) At small Q this provides an adequate description of the data, but at high Q there is a considerable deviation from the expected shape.
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 37
Furthermore, the :r-polarized component of the scattering acts asymmetrically with a long tail to lower the energy. It is then natural to associate the spread observed above the inflection point of the absorption in fig.
- The lanthanide elements
Half width at half maximum (HWHM) of the wide and narrow components for scans within the basal plane. 25 a summary of the temperature dependence of the wave vector of all additional peaks is given.
Scans of the a-polarized (top) and x-polarized (bottom) components of the beam scattered by Er taken along the [00g] direction at 40 K for two energies near and below the absorption edge L m (8358eV) o f Er. In addition to elucidating the resonant cross-sectional shape, the study by Sanyal et al. 1994) also produced some intriguing results.
1 - Cone
Note the separation on the y-axis between the Er and Tm curves.) The solid lines are guides to the eye. Also, the exponents for Er and Tm are the same and are close to the mean field value o f ½. 36, where it can be seen that at least for Er and Tm it was possible to measure up to the fourth-order satellite.
This is due to the fact that the other light lanthanides are either difficult to prepare as single crystals (Ce, Eu and Pm), or have a very low ordering temperature (Pr). Compared to the heavy lanthanides, the light lanthanides are more chemically reactive, exhibit more complex chemical structures, and two of the series (Pr and Nd) exhibit multi-q magnetic structures.
- Neodymium
Alloys, compounds and superlattices
In a general context, the study of random alloys has helped advance our understanding of the magnetic interactions in the lanthanides (Jensen and Mackintosh 1991). A similar equation for the temperature dependence of the intensity of the magnetic scattering is shown in fig. The most important contribution of X-ray scattering experiments in the study of this material was to show that the magnetic structure of the immeasurable phase is more extended than that deduced from neutron diffraction.
Taking advantage of 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. At the lowest temperatures studied in the antiferromagnetic phase, a scan in the [00g] direction revealed a sharp peak at the (0,0,3) position, confirming the simple antiferromagnetic stacking of the moments.
The temperature dependence of the X-ray scattering from Ho20/Er20 for scans of the wave vector transmission along [00g]. The temperature dependence of the Gaussian width of the main magnetic peak from a Hoz0/Er2o superlattice. One of the Er films was grown on a Y substrate (resulting in an in-plane expansion and an out-of-plane compression of the film), while the other was grown on a Lu substrate (resulting in an in-plane compression and an out-plane expansion).
It can be seen from the figure that the main differences between the films and the bulk include multiphase coexistence, pronounced hysteresis, and suppression of the 2 ~ cone structure at low temperature. Summary of materials investigated using X-ray resonance magnetic scattering techniques, where estimates of the intensity branching ratio I(L./Lz11) are given (after D. Watson et al. 1996).
RAY SCATTERING STUDIES OF LANTHANIDE MAGNETISM 81 lanthanide series seems well accounted for. The same arguments apply to the variation of
- Summary
- Introduction
- Effect of static pressure on the phase transition to a magnetically ordered state
- Influence o f static pressure on the magnetic phase diagrams and magnetic o r d e r - o r d e r phase transitions
- T h e e f f e c t o f statie p r e s s u r e o n t h e s p i n s t r u e t u r e s o f t h e l a n t h a n i d e m e t a l s Neutron diffraction measurements under hydrostatic pressure were made on Tb, Ho and
- Sound attenuation and internal friction 1. Introduction
- Elastic properties 1. lntroduction
The dependence of F on the interatomic distance was considered in the framework of the modified RKKY model proposed by Robinson et al. In this case, the transition of the f electrons to the conduction band under pressure is possible. Longitudinal sound waves propagating along the c-axis (and also along the a-axis in Gd) were found to show an attenuation maximum near the temperature corresponding to the magnetic ordering.
The magnetic field dependence of the attenuation coefficient of longitudinal acoustic waves propagating along the c -axis (H aligned in the basal plane) was analyzed for the spiral state of Dy by Isci and Palmer (1978) . The total thermodynamic potential of the system in a magnetic field H was written in the form The size of the helical domains in the helical state was found to be highly sensitive to sample purity.
Magnetic field dependence of the elastic constant c33 at different temperatures in Dy (field along the a-axis).
H (kOe)
Southem and Goodings (1973) considered theoretically the field dependence of the elastic constants c~j in the ferromagnetic state in lanthanide metals with a hexagonal crystal structure. In the case of a magnetic field aligned parallel to the c axis, the variation of the elastic constant C44 has the form All investigators observed anomalies in the elastic constants of gadolinium near the Curie temperature (see Scott 1978).
Experimental measurements of the field behavior of c33 in the region of spin reorientation were performed by Long et al. Temperature dependences of the elastic constant c33 of gadoiinium in various magnetic fields. a) Field in the basal plane; (b) field along the c-axis.
Temperature (K)
Conclusion
The origin of the magnetic deviations from the elastic properties (mainly pure metals) is taken into account. The magnetic phase diagrams for metals and alloys obtained by measurements of the elastic constants are discussed. In this chapter, the focus is on the IEM of the Co sublattice in different R-Co systems.
The published experimental information on the electronic and magnetic properties of the RCo2 compounds is also reviewed. The magnetic properties of the systems consisting of both itinerant electrons and localized spins are formulated based on the s-d model.
Theoretical approaches to itinerant electron metamagnetism (IEM) 1. Itinerant electron system
Schematic diagrams of the dependence of the density of states on the energy N(~) near ~ = e F for the cases of (a) negative curvature and (b-d) positive curvature N(e) for (left) B = 0 and (right) B > 0. Hence we can see that the sensitivity of a traveling paramagnet can increase as the field is strengthened. In Stoner's model at 0 K, the total energy in the presence of a magnetic field is written as the sum of the electronic (Fd) and elastic (Flat) parts.
Here, the reference volume V0 was chosen to obtain the minimum total energy at this volume in the paramagnetic state. If the d-electrons are considered in the tight-binding approximation, the volume dependence of the bandwidth is given by W = W0 exp(-qf2), where q is of the order of 1 to 5_3 for 3d electrons (Slater and Koster 1954).
