The advantages of these methods are high resolution, strict symmetry selection rules, small sample sizes, and rare earth isotope independence. Zuckermann, Transport Properties (Electrical Resistivity, Thermoelectric Power, and Thermal Conductivity) of Rare Earth Intermetallic Compounds 117 .
Chapter 93
BALCAR
- Introduction
- Scientific background
- Summary
- Forward scattering cross-sections
- The dipole approximation
- General theory of scattering
- Experimental aspects of neutron scattering
- Spin-orbit transitions
The non-relativistic formulation allows the decoupling of the angular components from the radial components in the 4f wavefunctions. In the second half of the sequence, where J = L + S, the dipole transitions from the ground state correspond to J' = J - 1.
Section 4.3 deals with measurements on anomalous lanthanide systems, where significant departures from the normal systems are encountered
Neodymium
The spin-orbit splitting of the Sm 2+ ion is the smallest of all lanthanide ground state configurations. The temperature dependence of the cross-section is also consistent with the RPA model (Mook et al. 1978).
Coulomb transitions
- Samarium
The neutron results provide direct evidence of the persistence of strong intraatomic correlations, eg, in the heavy fermion compound UPt 3. The lowest-energy Coulomb transitions are found in the f2 configuration of the Pr 3+ ion.
Theory
- Tensor operators
- Many-electron matrix elements
- Orbital interactions
- Spin interactions
- NMR spectra
The main effort in calculating a many-electron matrix element is to obtain a value for the reduced matrix elements of the Racah tensors W (~'k~ and W (~'~x). An important step in the calculation of the spin contribution to magnetic interaction, Eq. .
GdAI2
Microscopic information about the macroscopic properties of magnetically ordered intermetallic compounds
As examples here we arbitrarily select information on the temperature dependence of the spontaneous magnetization (Sect. 2.1) and on the direction of easy magnetization ('easy direction') (Sect. This variation should not be compared with the temperature dependence To discuss possible differences in the variations of V~es(r )h%s(0K), h ( r ) = Hhf(T)/, so only a careful N M R analysis is worthwhile.
The temperature dependence of the NMR frequencies for GdA12 agrees with Bloch's T 3/2 law up to 0.5Tc, while that for DyA12 has been explained in terms of molecular fields (MF) and crystal electric fields (CEF).]. They were able to follow the temperature dependence up to T = 0.94 To, using the temperature variation instead of the frequency variation to record the NMR lines. NMR IN INTERMETALLIC COMPOUNDS 75 dependence of the normalized hyperfine coupling constant contains a T 5/2 term in the lowest order:.
An interesting piece of information for understanding the wall type can be obtained in this way, but it apparently does not reveal the easy direction of the magnetization.
NMR information about the electronic structure of intermetallic compounds with non-magnetic partners
- Analysis of the conduction electron spin polarization 1. Uniform polarization model
- Correlation of magnetic ordering temperatures and transferred hyperfine fields
- Anisotropy of the transferred magnetic hyperfine interaction
- Crystal-field effects for lanthanides in paramagnetic compounds
- Crystal-field splitting, magnetic order and the hyperfine interaction
The observed Knight shift in the paramagnetic intermetallic compound, depending on temperature, is correlated with the paramagnetic part of the total susceptibility:. Modifications of the simple RKKY model were also used, see e.g. Oppel et al. The shoulder on the main line indicates the influence of the second and third nearest neighbors (N 2 = N 3 = 12).
This neighbor was identified via the dipole part of the anisotropy of the hyperfine interaction- see fig. If the contributions of the conduction electrons to the magnetic order and hyperfine field at the rare-earth site, as discussed in sect. In addition to the magnetic dipole and electric quadrupole, an octupolar contribution (w) from the hyperfine interaction at the lanthanide site must also be taken into account.
The orbital effects in the RA12 series are present, but relatively weak - at most 30% of the spin polarization field.
Intermetallic compounds with 3d transition metals
The influence of the lanthanide moments on the iron sublattice is generally relatively weak. Satellites of the Y and Gd NMR lines were also observed by Vasil'kovskii et al. Many results of NMR studies of the R-Co series of intermetallic compounds were discussed by Figiel (1983) (in Polish).
They analyzed the Co hyperfine field as a superposition of the contribution of the 'own' momentum of the Co ion and the contributions of the Co- and R-neighbors. Hirosawa and Nakamura (1982a) also used Tbl_xYxCo 2 to derive the R contribution to the Co hyperfine field and observed well-separated satellites. Its magnitude indicated the important role of the orbital moment on the magnetism of YCo 2 (Hirosawa and Nakamura 1982a).
The different behavior of the Mn moment may be related to the atomic spacing of Mn in these systems.
Intermetallic compounds with special properties
Weaver and Schirber (1976a) (see Schirber and Weaver 1979) analyzed the pressure dependence 0(ln K)/Op and the temperature dependence of the NMR shifts in compounds such as PrP, PrAs or TmP (and others) with the NMR of 14 ~pr , 169Tm and the nuclei of the non-magnetic partners. This was interpreted as indicating strong 3D mixing in the wavefunction at the Fermi surface and d-spin contribution to sensitivity. Kumagai et al., on the other hand. 1979) found via 11B NMR only a small polarization of the conduction electrons at the B-site in the magnetically ordered compounds RRh4B 4 (R = Tb, Dy, Ho and Er).
They reported that T 1 increases exponentially with lowering the temperature due to the energy gap. They pointed to the fact that a universal thermal dependence of the f-electron fluctuation rate 1/%ff is observed. Here the NMR spectrum was characteristic of the paramagnetic phase, and quadrupolar splitting was observed at 77K (Kawakami et al. 1981).
For the intermediate valence compound YbCuAI, MacLaughlin et al. 1979) only observed a linear relationship between 27K and X for temperatures above the bulk sensitivity maximum.
Concluding remarks
DORMANN
General remarks
The disadvantage of light scattering being limited to small excitation wave vectors is negligible in the case of localized electronic excitations. Difficulties due to the small depth of light penetration can be overcome by careful surface preparation techniques, such as cracking or fracturing under an inert gas atmosphere. These problems arise due to the inadequacy of conventional band structure calculation methods for dealing with multi-electron bound states.
Their experimental determination not only serves as a spectroscopic test of microscopic theories, but is an indispensable prerequisite for any understanding of the fascinating and numerous macroscopic properties of these compounds. Schematic diagram of the energy levels of the interconfigurational fluctuation (ICF) model describing the valence fluctuations between two 4f configurations (4f", 4f"-1) characterized by a Jmultiplet level structure. The basic parameters of the ICF model E x and Tf characterize the interconfigurational excitation energy and the interconfigurational mixing width, respectively.
In this subsection, we discuss electronic Raman scattering from the 4f spin-orbit-split level in Sml_xRxSe and Sml_zRxS solid solutions near the transition of the 4f configuration from the stable valence to the intermediate valence (IV) state.
There is currently no answer to this apparent discrepancy, which may indicate a drastic decrease in the electronic Raman scattering cross section of Sml_xYxS induced by valence mixing near the configurational junction. In addition, Eu-based compounds serve as model systems due to the fairly simple ground states of the two 4f configurations involved in the valence fluctuation process: Eu 2+ (4f 7) has only the J = S = 7 pure spin configuration without CEF splittings and Eu 3÷ (4f 6) has a J = 0 ground state. The J = 1 Eu 3+ state lies about 550 K (De Shazer and Dieke 1963) above the J = 0 ground state and can be thermally populated, offering the possibility of strong modification of the valence fluctuation process by temperature variations.
Moreover, for Eu-based group IV compounds, the investigation of the valence and its temperature dependence is easily feasible by M6ssbauer and Lm edge absorption spectroscopy. The top of the figure shows the levels of J-multiplets observed by electron Raman scattering in SmSe (Gfintherodt et al. 1981a). This is expected since the J levels for Eu 3+ should be the same as for Sm 2÷ 4f 6 (configuration 7Fj).
This broadening develops into a well-pronounced split at 145 K, best seen at the J = 2, 3, and 4.
Frequency Shift (cm-1)
Temperature dependence of (a) the interconfigurational excitation energy (Ex) and (b) the upper limit of the fluctuation temperature Tf of EuPd2Si 2 as directly revealed in the Raman spectra of Figs. Temperature dependence of (a) the interconfigurational excitation energy E x and (b) an upper limit on the fluctuation temperature Tf for EuCu2Si 2 as directly revealed in the Raman spectra of Figs. These excitations are interpreted as electronic transitions from the ground state of the J = 152 configuration to the four doublets of the J = 7 configuration.
However, Zirngiebl and co-workers derived this information from the anomalous shift of the 372 cm -1 peak in Fig. Symmetric analysis of the transition Fs-~ CEF and Raman-active phonons CeB 6 at 77 K. 12, which so far provides the simplest interpretation of the measured thermal, elastic and magnetic data (Zirngiebl et al. 1984).
Excitation at 24 meV was not observed in the neutron scattering due to the small transition matrix element F(s2) ~ F 6.
NdBB I
Phonon Raman scattering 1. Introduction
The primary interest in investigating mixed-valence materials using Raman scattering arose from the estimate (Varma 1976) that the inverse time scale of the 4f charge fluctuations that induce volume changes of up to 15% can be of the order of the phonon frequencies . Therefore, early Raman scattering experiments in materials of intermediate valence by G/intherodt et al. concerned with the study of phonon anomalies and their relation to the electron-phonon interaction. In particular, polarized Raman scattering (G/intherodt et al.. 1981b, c, Kress et al. 1981) has provided an experimental test of the relative importance of the different charge deformabilities introduced in the lattice dynamical model calculations (G/intherodt et al. ah 1981b, Kress et al. 1981, Bilz et al. 1979).
The mode frequency behavior in alloys of stable divalent and trivalent R ions as found for example in Gd~_xEUxB 6 by Ishii et al. Based on this result, the phonon mode frequencies of the IV compound are expected to lie between those of the reference divalent and trivalent compounds according to the valence mixing ratio. However, Fc should soften the phonon compared to the stable valence reference compounds because the charge fluctuation rate can easily follow the movement of the ions and thereby soften the lattice.
It has been emphasized (Mock et al. 1986) that, in addition to a systematic understanding of the presence or absence of elastic and phonon anomalies in different IV compounds, the concept introduced above allows a first experimental estimation of charge fluctuation rates .
We will discuss the behavior of acoustic and optical phonon mode frequencies hw in IV compounds according to the following classification regimes: h~o >>. In the following, we review Raman and Brillouin scattering from phonons in different IV compounds and their stable valence reference compounds, highlighting the resulting estimate of the charge fluctuation rate in the IV compound under investigation. A compilation of the different crystal structures and corresponding vibrational mode symmetries of various types of valence fluctuating materials is given in table 1.
The stable trivalent RB 6 shows a linear variation of the mode frequencies with a 0 as indicated by the solid lines. The reference lines for the stable divalent RB 6 (dotted lines) are defined by E u B 6 and are drawn parallel to the solid lines. The frequencies of the A~g, Eg, and T2g modes of IV StuB 6 appear between the stable divalent and trivalent reference lines, depending on the valence mixing ratio.
On the other hand, the Tau mode of SmB 6 shows a softening with respect to the coincident stable valence reference lines.
