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

Spintronics is a multidisciplinary field involving physics, chemistry, and engineering, and is a new research area for solid-state scientists. A variety of new materials must be found to satisfy different demands. The search for ferromagnetic semiconductors and stable half-metallic ferromagnets with Curie temperatures higher than room temperature remains a priority for solid-state chemistry. A general understanding of structure-property relationships is a necessary prerequisite for the design of new materials. In this Review, the most important developments in the field of spintronics are described from the point of view of materials science.

Spintronics: a challenge for materials science and solid-state chemistry.

Magnetic flux can penetrate a type-II superconductor in the form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux phi 0=h/2e. These tiny vortices of supercurrent tend to arrange themselves in a triangular flux-line lattice (FLL), which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-Tc superconductors (HTSCs) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSCs the FLL is very soft mainly because of the large magnetic penetration depth lambda . The shear modulus of the FLL is c66~1/ lambda 2, and the tilt modulus c44(k)~(1+k2 lambda 2)-1 is dispersive and becomes very small for short distortion wavelengths 2 pi /k<< lambda . This softness is enhanced further by the pronounced anisotropy and layered structure of HTSCs, which strongly increases the penetration depth for currents along the c axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may `melt` the FLL and cause thermally activated depinning of the flux lines or ofthe two-dimensional `pancake vortices` in the layers. Various phase transitions are predicted for the FLL in layered HTSCs. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSCs as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

https://iopscience.iop.org/article/10.1088/0034-4885/58/11/003/pdf

The flux-line lattice in superconductors

Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices. These tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-$T_c$ supercon- ductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth: The shear modulus of the FLL is thus small and the tilt modulus is dispersive and becomes very small for short distortion wavelength. This softness of the FLL is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these uniaxial crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause thermally activated depinning of the flux lines or of the 2D pancake vortices in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to interesting effects which strongly depend on the geometry of the experiment.

The Flux-Line Lattice in Superconductors

We review experimental studies of the time decay of the nonequilibrium magnetization in high-temperature superconductors, a phenomenon known as magnetic relaxation. This effect has its origin in motion of flux lines out of their pinning sites due to thermal activation or quantum tunneling. The combination of relatively weak flux pinning and high temperatures leads to rich properties that are unconventional in the context of low temperature superconductivity and that have been the subject to intense studies. The results are assessed from a purely experimental perspective and discussed in the context of present phenomenological theories. [S0034-6861(96)00403-5]

Magnetic relaxation in high-temperature superconductors

Taking the pseudobinary C15 Laves phase compound $\mathrm{Ce}({\mathrm{Fe}}_{0.96}{\mathrm{Al}}_{0.04}{)}_{2}$ as a paradigm for studying a ferromagnetic to antiferromagnetic phase transition, we present interesting thermomagnetic history effects in magnetotransport as well as magnetization measurements across this phase transition. A comparison is made with history effects observed across the ferromagnetic to antiferromagnetic transition in ${R}_{0.5}{\mathrm{Sr}}_{0.5}{\mathrm{MnO}}_{3}$ crystals.

https://arxiv.org/pdf/cond-mat/0012472.pdf

First-order transition from antiferromagnetism to ferromagnetism in C e ( F e 0.96 Al 0.04 ) 2

Evidence of a magnetic glass state in the magnetocaloric material Gd 5 Ge 4

High-${T}_{c}$ superconductors have critical current densities ${J}_{c}$ that decay sharply with increasing magnetic fields. We solve Bean's model for ${J}_{c}$ decaying exponentially with H and obtain virgin magnetization curves and hysteresis loops. We show that the shape of the hysteresis loop can be altered significantly if the maximum field applied is not large enough, and we explain discrepancies between various magnetization data reported in the literature.

Extension of Bean’s model for high- T c superconductors

Experimental results of magnetization measurements of first-order ferromagnetic-antiferromagnetic transitions in Ce(Fe 0 . 9 6 Ru 0 . 0 4 ) 2 alloy are presented. The metastability of states in the transition region gives rise to large relaxation and lack of end-point-memory effect in the magnetization. Traditional phenomenological asymmetry between the extent of supercooling and superheating is observed in the temperature and magnetic field variation of the magnetization and is also confirmed in relaxation results. Nonuniform variation of the relaxation rate with magnetic field gives a clear picture of the nucleation and growth of phases.

Metastability and giant relaxation across the ferromagnetic to antiferromagnetic transition in Ce (Fe 0.96 Ru 0.04 ) 2

Results of isothermal magnetization and magnetic relaxation measurements are presented probing the nature of the magnetic-field-induced magnetostructural transition in the intermetallic compound ${\mathrm{Gd}}_{5}{\mathrm{Ge}}_{4}$. This transition shows the characteristics of a disorder-influenced first order transition including distinct metastable behavior. Below approximately $21\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the transition from the magnetic-field-induced ferromagnetic state back to the antiferromagnetic state shows additional interesting features. Similarities with other classes of magnetic systems exhibiting magnetostructural transitions are pointed out.

P. Chaddah

Papers

First-order transition from antiferromagnetism to ferromagnetism in C e ( F e 0.96 Al 0.04 ) 2

Evidence of a magnetic glass state in the magnetocaloric material Gd 5 Ge 4

Extension of Bean’s model for high- T c superconductors

Metastability and giant relaxation across the ferromagnetic to antiferromagnetic transition in Ce (Fe 0.96 Ru 0.04 ) 2

Metastable magnetic response across the antiferromagnetic to ferromagnetic transition in Gd 5 Ge 4