Machida concludes this volume with a review of rare-earth and actinide half-sandwich tetrapyrrole complexes. Chabot, Crystal structures and crystal chemistry of ternary rare earth transition metal borides, silicides and homologues 113.
Introduction
As is tradition, research into the giant magnetostrictive thin films has also been based on the lanthanide iron alloys. In the case of thin films, which are the subject of this review, magnetostriction research is also concentrated on the lanthanide transition metal materials.
Magnetoelastic phenomena
Problems in determining the magnetostriction coefficients of thin layers are presented in the chapter. This results in not only a change in the magnetocrystalline anisotropy, but also a deformation of the crystal lattice.
Magnetism in amorphous lanthanide-transition metal alloys
Magnetic and magnetostrictive properties of the RCo2 compounds: Curie temperature (Tc), saturation magnetic magnetization (Ms), easy magnetization direction (EMD),)~o0 and )q H at 4.2 K. At T > 0 K, next to the average of the spatial projection (identified with angle brackets), one must also take into account the thermal average of the magnetic moment (identified by an overline).
Giant magnetostrictive thin film materials
The values of the magnetostriction in the deposited TbFe thin films collected from different sources are summarized in Fig. A comparison of the magnetostriction of Sm-Co and Tb-Co systems is shown in Fig.
Summary and recent developments
Practically, the effect of Zr and Mo additions on crystallization and magnetic properties was studied by Winzek et al. It is clearly seen that this magnetostrictive sensitivity is comparable to magnetostrictive multilayers. Experimentally, the R-T molecular field can be enhanced near the strongly magnetic FeCo layer.
In this case, layers must be sufficiently thin, then a noticeable volume of the R-T layer can be subjected to the large molecular field. Ludwig and Quandt (2000) reported the possibility to control the orientation of the magnetic easy axis by magnetic annealing and thus could improve the magnetostriction in the desired direction. In particular, for magnetostrictive multilayers the nature of the interfaces is critical; their contributions to the magnetic and magnetostrictive properties must be taken into account.
In this context, a general review of magnetoelasticity in heterogeneous magnetic materials (including nanoscale thin films, multilayers, superlattices, nanocrystalline magnetic alloys, and magnetic grain films) may be useful. The fundamental difference between 4f and 5f magnetism is the possibility of significant delocalization of the 5f wave function in the light actinides.
The pSR technique
High magnetic fields
Electromagnets cannot be easily configured for longitudinal geometry, as they require a bore in at least one of the pole shoes to transfer the beam to the field region. The application of high pressure reduces the separation of neighboring atoms and thus causes changes in the overlap of their outer electronic orbitals. It is clear that this is an important parameter in magnetism in general and in 5f magnetism in particular, where overlap strongly affects the localization of the electrons responsible for magnetic properties.
High-pressure measurements have been pursued with vigor in almost every area of experimental condensed matter physics. Furthermore, it is important that hydrostatic conditions prevail, as internal stress in the sample will produce lattice defects, which can trap muons and can also cause broad distributions in internal fields, which then cause rapid attenuation of the gSR signal (see Section 3.2). This has been used to study the volume dependence of the local field in the transition metals Fe and Ni (Butz et al. 1980).
All high pressure components are mounted inside the isolated area which is only accessible if the high pressure is released (via an electro-pneumatic valve). The pressure limit was 0.9 GPa, i.e. less than the design limit of the gas pressure system.
Time 0xsec)
In the standard semiclassical formulation, the magnetic influence of the material on the muon is represented by an effective field B~ which acts on the spin S~ of the muon at its interstitial site. It should be emphasized that the muon sees only one resulting fieM independent of its sources. Bint is produced by the fields of (i) magnetic dipole moments on (paramagnetic) atoms in the magnet, (ii) nuclear dipoles, and (iii) by conduction electron spin polarization at the muon site.
The Boon term is called the Fermi contact field and is produced by the net spin density of conduction electrons in contact with the muon. The spin polarization of the conduction electrons is in turn induced by the dipole moments on lattice sites. In addition, the positive charge of the muon increases the conduction electron charge density around its site.
Even then, it is not trivial to relate the Boon to the magnitude of the atomic dipole moments present. The field created by a magnetic dipole/7 at vector distance r from the muon site is given by. 13) The total dipolar field Bdip sensed by the muon can then in principle be calculated by performing the appropriate lattice sum ~ j Bj(rj) over the entire crystal.
Sample
Lorentz Sphere
The crucial point in the Lorentz construction is how to choose the size of the Lorentz sphere. With B~ we denote in the following the average field observed by the muon ensemble (for clarity we no longer use the notation (B~)). In addition to obtaining information about the size of Bg and its distribution, a main goal of ~tSR in magnetic materials is the measurement of the muon spin relaxation function which can then be related to the dynamics of the spin ensemble in the sample material .
That being said, this does not necessarily mean that the field is directed perpendicular to the muon beam. Upon detection of a transverse field, the muon spin will precess in a plane perpendicular to the field axis, generating an asymmetric spectrum. In the case of a dense system of randomly oriented moments, we can assume that the field distribution has a Gaussian shape.
Cross-field p.SR spectra showing the limiting cases of (a) static (Gaussian) and (b) full dynamic (exponential) depolarization. limit situations of static and dynamic damping with the two spectra shown in fig. 21) measurements of the transverse field in principle allow the separation of the width of the static field (oc a) from the rate of oscillation (l / r) in the intermediate case. In the static limit (v --+ oc) we can extract the second moment of the field distribution (see equation 20).
Elemental metals
- Anisotropic spin fluctuations
Grebinnik et al. performed the first b~SR measurements on a series of metals (Pr, Nd, Sm Eu, Tb, Dy, Ho, Er). SR STUDIES OF RARE EARTH AND ACTINIDE MAGNETIC MATERIALS 125. detectable in the relaxation rates of the above equations. Later studies included more detailed investigations of the dynamic critical behavior in the paramagnetic state (see next section).
The data from the two studies are quite similar in the AFM regime, but near Tc the results of Schreier et al. The stopping point of the muon is not known, but calculations of the dipolar fields are. 34 (left) we show the result of Barsov et al. 1986c) expressed in terms of the relaxation fictions G H and G± as introduced in Sect.
Right: temperature dependence of the two spontaneous precession frequencies (bottom) and their attenuation rates (top) in the FM state. The pressure dependence of the spontaneous spin precession frequencies in the two metals was determined at different temperatures in their magnetically ordered states.
Intermetallics
In this section, it will be assumed that the magnetic orbital remains localized around its specific core when the ion is embedded in a crystal, and the rest of the crystal can be treated as external to it (no hybridization). When there are also magnetic interactions between the lanthanide ions in a specific material, the importance of the CEF depends on its relative strength. If the magnetic ordering temperature is close to or greater than the extent of splitting of the CEF levels that would occur in the absence of magnetism (as it is in the elemental lanthanides), then the CEF effects are relatively small.
On the other hand, for non-cubic lanthanide sites and low magnetic ordering (or freezing) temperatures, CEF effects may need to be outlined before we can begin to understand the magnetic interactions. CEF parameter values can be deduced from data from many probes (and ~tSR is usually not one of them). Therefore, the Gd member of the isostructural series will be free of the CEF anisotropy of the other members of the series.
Because the CEF varies with position around the center of the ion site, and because vibrations move around the ion charge cloud, the CEF couples to phonons. The root causes for the unusual ~tSR spectra are the influences of the muon on the CEF interaction, as will be discussed below.
PrNis
Laves-phase compounds
- MAI2
TN is rather sample dependent, typically ranging from 3.4 to 3.9 K. The low transition temperature allowed Hartmann et al. 1989) to determine the muon stopping site from the angular dependence of the depolarization rate using a single crystal sample. Left: Inhomogeneous transition region in the AFM state as seen in the ~tSR data of Hartmann et al. Top: Temperature dependence of the amplitudes of the oscillatory (A 0 ) and non-oscillatory (Az) signals.
In contrast, Shapiro et al. 1979) pointed out that the magnetic structure must be described by a multiple-k arrangement. The main features of this study were:. i) The signal from muons stopped in the sample disappears below Tc. ii) Above Tc the spectra are characterized by a temperature (and field) dependent depolarization rate which shows a divergent rise towards Tc starting at temperatures well above the critical temperature. iii). In the fast fluctuation limit, the rates 1/T1 (measured in ZF) and 1/T2 (measured in TF and corrected for inhomogeneous line broadening) must be equal (Hayano et al. 1979).
In summary, the work of Hartmann et al. 1986) formed the basis for the treatment of ~tSR data in R intermetallics. DyA12 has also been studied in ZF and LF by Gradwohl et al. 1986) using a single crystal.
