Bernard R. Cooper

Magnetic Properties of Rare Earth Metals

Publisher Summary This chapter discusses the theory of the magnetic behavior of the lattice of localized moments corresponding to the unfilled 4 f shells, and to a description of the relevant experimental information. It begins by describing the equilibrium magnetic arrangements, the basic model for magnetic behavior of the heavy rate earth metals, and the way in which one obtains transitions between various equilibrium magnetic arrangements within this model. The emphasis is on the theory for the excited magnetic states—that is, spin-wave-like states, and the experimental manifestations of these excited magnetic states. These topics are treated in this chapter. It discusses the theory of spin wave behavior when the equilibrium magnetic arrangement is ferromagnetic. That Part includes a discussion of the temperature dependence, as well as discussion of applied field and magnetoelastic effects. The excited magnetic state behavior for periodic moment arrangements is discussed here.

Anisotropic Magnetization of TmSb

We report the experimental observation, with pulsed field, of the anisotropy in magnetization theoretically predicted for single crystals of TmSb. Agreement with crystal‐field‐only theory is excellent at 1.5°K. At 20.4°K, agreement between isothermal theory and experiment is poorer. This discrepancy can be explained if spin‐lattice relaxation effects cause the observed magnetization to be a mixture of isothermal and adiabatic effects.

Orbital effects in rare earth magnetism

Abstract Rare earth materials show a fascinating variety of magnetic behavior. This is true for the elemental metals, their alloys, and compounds. These lectures will emphasize those aspects of rare earth magnetic behavior in which the crystallattice acting through the large orbital contribution to the rare earth moments significantly affects the nature of the magnetic behavior. In addition to the rare earth elemental metals, certain rare earth intermetallic compounds where the cry s t al-ele c t ric-field profoundly alters the magnetic behavior will be discussed.

High‐Field Destruction of the Nonmagnetic Ground State in TmN

The octahedral cubic symmetry at a Tm site in TmN gives a singlet (nonmagnetic) level as the ground state of the Tm3+ ion in the crystal field. We have used pulsed magnetic fields up to 265 kOe to counteract the crystal‐field effects and induce large ionic moments. Magnetizations measured at 4.2°, 20.4°, and 77°K show an approach to saturation at the highest fields used. For 4.2°K, the moment at 265 kOe is 4.5 μB per molecule as compared to the saturation value of 7 μB. The experimental results for the magnetization and susceptibility are compared to the theoretical results for crystal‐field calculations. This comparison enables us to discuss the way in which exchange forces enter the magnetization process at high magnetic fields as the ground state becomes polarized. The fourth‐ and sixth‐order crystal‐field parameters have been evaluated by observing paramagnetic resonance at 9.35 Gc/sec for the Γ5(2) excited triplet.

Phenomenological Theory of Magnetic Ordering: Importance of Interactions with the Crystal Lattice

The diverse, and sometimes exotic, magnetic behavior of the rare earth elements and their alloys as observed in the past fifteen or so years is basically understood in terms of a very simple physical picture. The key element of this picture is that one makes a sharp distinction between localized, magnetic, 4f electrons and outer-shell conduction electrons; and one takes the magnetic system for these metals as a lattice of localized tripositive rare earth ions (divalent for Eu) with moments corresponding to the unfilled 4f shells. (The ionic moment is quite well given by the application of Hund’s rules so that in general, J, the total spin plus orbital angular momentum, is treated as a good quantum number for the magnetic system of tripositive ions.) This lattice of localized ions, with their corresponding localized moments, is then immersed in a sea of conduction electrons to which each rare-earth atom contributes its three outer electrons. This picture is excellent for the heavy rare earth metals(1, 2) (gadolinium through thulium), and is reasonably good for most of the light rare earths. (The most complex behavior in the rare earth series, requiring concepts beyond those of this simple picture, is found for the end members, cerium and ytterbium.)

Magnetic Properties and Collective Excitations of Systems with Singlet Crystal‐Field Ground State

We discuss the magnetic behavior of rare‐earth systems where the crystal‐field‐only ground state of the rare‐earth ion is a singlet. For such materials there is a threshold value for the ratio of exchange to crystal‐field interaction necessary for magnetic ordering even at zero temperature. The magnetization process for singlet ground‐state systems is first discussed from the effective field point of view. We then treat the theory of the collective excitations and the relationship of their behavior to the magnetic ordering process. A discussion is given of the present experimental situation and of a variety of promising possibilities for future experiments to increase understanding of such systems. The techniques discussed are neutron diffraction and scattering, susceptibility, high‐field magnetization, nuclear magnetic resonance, specific heat, and paramagnetic resonance experiments. The discussion of the experimental situation emphasizes the role of the rare‐earth—Group V compounds. The system TbxY1−xSb...

Phase Shift Parametrization: Band Structure of Silver

We discuss a band parametrization scheme (within the KKR framework) specifying the phase shifts n0, n1, and n2 as functions of energy. Such an approach is particularly useful for the noble and transition metals where both d-band and free-electron-like effects are important. The nl(E) for a family of elements are expected to have characteristic energy dependences, with each nl(E) being specified over a substantial energy range by a few parameters. First, we show the existence of such characteristic behavior for the noble metals. We then use our phase shift parametrization scheme in a semi-empirical way to find the band structure of Ag. To do this, we use a first principles calculation as a guide, and adjust the parameters specifying the nl(E) to fit available Fermi surface, optical and photoemission data.

Characterization of energy bands in metals by scattering phase shifts

Abstract We discuss an electron energy band parameterization scheme specifying the phase shifts η 0 , η 1 and η 2 as functions of energy. The use of this scheme has been investigated for Cu, Ag and Al.