Magnetic Ordering in Systems of Identical Particles with an Arbitrary Spin

E V Orlenko ,Fedor E Orlenko

doi:10.3390/chemosensors7040054

Abstract

The Wigner–Eckart theorem is used for considering the collective effects related to ordering spins in systems of identical particles in ferro- and antiferromagnetic electronic systems, as well as magnetic effects that occur in high spin systems. The Hamiltonian, written in the spin representation in the form obtained by Heisenberg, Dirac, and van Vleck used to describe spin ordering in systems of particles with spin ½, is not appropriate for a description of particle systems with a spin different from ½. “High” spin particles in the spin representation need other forms of the Hamiltonian of the exchange interaction in the spin representation. The Hamiltonian for high-spin particles has been developed from the first principles, and the effects of magnetic ordering in systems of identical particles with arbitrary spin are considered in this review. An effect of giant negative magnetoresistance in the Indium antimonide has been interpreted from the exchange contribution of a high spin heavy holes point of view.

Highlights

The Wigner–Eckhart theorem [1,2] is widely used when considering the collective effects related to ordering spins in systems of identical particles with their own mechanical moments of arbitrary magnitude
The Wigner–Eckart theorem is used for considering the collective effects related to ordering spins in systems of identical particles in ferro- and antiferromagnetic electronic systems, as well as magnetic effects that occur in high spin systems
The Hamiltonian, written in the spin representation in the form obtained by Heisenberg, Dirac, and van Vleck used to describe spin ordering in systems of particles with spin 1/2, is not appropriate for a description of particle systems with a spin different from 1/2

Summary

Introduction

The Wigner–Eckhart theorem [1,2] is widely used when considering the collective effects related to ordering spins in systems of identical particles with their own mechanical moments of arbitrary magnitude. Particle systems with spins other than 1/2, or the so-called “high” spins, have been intensively studied since the beginning of the 1990s and form a large set of theoretical works in the field of quantum gases and statistical physics. These systems have a number of properties that are fundamentally different from the properties of arranged systems of localized spins 1/2. The existence of giant negative magnetoresistance in the millikelvin range of temperature gives rise to the creation of advanced cryogenic devices, such as thermometers, bolometers, and selective sensors for millimeter and radio-frequency wavelength [17]

Prerequisites from the Quantum Theory of Angular Momentum

Spin Hamiltonian of Identical Particles System with Arbitrary Spins

A Giant Negative Magnetoresistance in a Nonmagnetic Crystal

Results and Discussions