In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

A new magneto-optical sum rule is derived for circular magnetic dichroism in the x-ray region (CMXD). The integral of the CMXD signal over a given edge allows one to determine the ground-state expectation value of the orbital angular momentum. Applications are discussed to transition-metal and rare-earth magnetic systems.

X-ray circular-dichroism as a probe of orbital magnetization

Gold is an element whose unique properties are strongly influenced by relativistic effects. A large body of appropriate calculations now exists and its main conclusions are summarized in this critical review. The present paper completes the recent reviews by Pyykko (2004, 2005) (529 references).

Theoretical chemistry of gold. III

In this work a simple concept was used for a systematic search for materials with high spin polarization It is based on two semiempirical models First, the Slater-Pauling rule was used for estimation of the magnetic moment This model is well supported by electronic structure calculations The second model was found particularly for ${\mathrm{Co}}_{2}$ based Heusler compounds when comparing their magnetic properties It turned out that these compounds exhibit seemingly a linear dependence of the Curie temperature as function of the magnetic moment Stimulated by these models, ${\mathrm{Co}}_{2}\mathrm{FeSi}$ was revisited The compound was investigated in detail concerning its geometrical and magnetic structure by means of x-ray diffraction, x-ray absorption, and M\"ossbauer spectroscopies as well as high and low temperature magnetometry The measurements revealed that it is, currently, the material with the highest magnetic moment $(6{\ensuremath{\mu}}_{B})$ and Curie temperature (1100 K) in the classes of Heusler compounds as well as half-metallic ferromagnets The experimental findings are supported by detailed electronic structure calculations

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Geometric, electronic, and magnetic structure of Co2FeSi: Curie temperature and magnetic moment measurements and calculations

X-ray absorption and dichroism of transition metals and their compounds

Energy-band calculations have been performed for Ce, Pr, and Nd. The normal local-spin-density approximation to exchange and correlation for the potential is used but spin-orbit coupling and a newly developed additional contribution to the 4f eigenvalue splittings arising from orbital polarization of the 4f electrons are also included. This procedure represents the application of all three Hund's rules in the solid state. The observed volume collapses of the light rare-earth metals are correctly described by theory.

Orbital polarization in narrow-band systems: Application to volume collapses in light lanthanides.

The spin and orbital contributions to the magnetic moments of Fe, Co, and Ni are calculated from first principles, using the linear muffin-tin orbitals method with the spin-orbit coupling treated at each variational step. In these calculations the spin and orbital moments agree with previously reported results obtained from spin-polarized Dirac calculations. When Hund's second rule is accounted for in the band Hamiltonian by adding an additional term for orbital polarization, the orbital moments agree better with experiment and the trends in the experimental orbital moments across the series can be explained. Specifically, the maximum orbital moment for Co is shown to occur because of its hcp equilibrium crystal structure.

Orbital magnetism in Fe, Co, and Ni.

The magnetic moments of the RFe2 (R=Gd-Yb) Laves phase compounds have been calculated. Agreement with published measured values for single crystals is excellent. The R 4f magnetic moments were obtained from the standard Russell-Saunders scheme but the radial 4f spin density was otherwise part of the self-consistent density functional calculation. The influence of the localized 4f magnetism upon the conduction band magnetism is examined in detail and exchange interactions extracted. The site- and angular-momentum-resolved contributions to the total conduction bands magnetic moments are calculated and shown to obey an approximate sum rule which conserves the total conduction band moment, despite the change of 4f moment, across the series.

https://iopscience.iop.org/article/10.1088/0953-8984/3/14/015/pdf

3d-5d band magnetism in rare earth-transition metal intermetallics: total and partial magnetic moments of the RFe2 (R=Gd-Yb) Laves phase compounds

We explain the anomaly in the lattice constants of the series Ce${\mathrm{Fe}}_{2}$-Ce${\mathrm{Ni}}_{2}$ quantitatively in terms of $3d\ensuremath{-}4f$ hybridization rather than a valence change. Ce${\mathrm{Fe}}_{2}$ is calculated to be magnetic and is the first Ce compound for which self-consistent energy-band calculations yield the correct total moment (${2.4}_{\mathrm{\ensuremath{\mu}}\mathrm{B}}$/formula unit) including a contribution of ${\ensuremath{-}0.4}_{\mathrm{\ensuremath{\mu}}\mathrm{B}}$ from the $4f$ electrons. The calculated magnetization density and spin-resolved density of states, which are unique to itinerant-electron theory, may be verified in detail by magnetic form-factor and spin-polarized photoemission measurements.

4f-band magnetism in CeFe2.

We have calculated ab initio the direct interband electric dipole transitions of the carbides, nitrides, and oxides of Ti, Zr, and Hf in the rocksalt structure using the full-potential linear muffin-tin orbital method. The dipole matrix elements are calculated explicitly. Our results are in extraordinarily good agreement with experiment. The optical spectra are analyzed and we explain the origin of the different structures in the spectra in terms of the calculated electronic structure. We also discuss the trends in the optical properties as the metal and nonmetal atom types are changed and how these trends relate to general concepts such as band filling, nuclear charge, and bandwidth. \textcopyright{} 1996 The American Physical Society.

M. S. S. Brooks

Papers

Orbital polarization in narrow-band systems: Application to volume collapses in light lanthanides.

Orbital magnetism in Fe, Co, and Ni.

3d-5d band magnetism in rare earth-transition metal intermetallics: total and partial magnetic moments of the RFe2 (R=Gd-Yb) Laves phase compounds

4f-band magnetism in CeFe2.

Optical properties of the group-IVB refractory metal compounds