Magnetoelectric effects theory by Heisenberg method based on permutation group symmetry of nanoparticles

Abstract

The Heisenberg theory of ferromagnetism is widened to include external electric field action. The material relations are derived by means of differentiation of logarithm of partition function with respect to the magnetic and electric fields. The mean energy coefficients as the exchange integrals combinations are expressed via characters of irreducible representations of corresponding permutation groups by the Heitler method. The thermodynamic equations of state for polarization and magnetization, as functions of the electric and magnetic fields, are derived and illustrated by figures. The magnetization and hysteresis curves in magnetization -magnetic field components plane are built. The theory is applied to nanoparticles, the particle partition function is modeled as the product of the surface and bulk parts. The statistical sum is constructed having explicit expressions for the mean energy in terms of exchange integrals and number of closest neighbors for surface and bulk atoms. The relative contribution of the surface and bulk terms is evaluated.

Ferromagnetic Hysteresis by Heisenberg Partition Function and Its Processing Methods in Nanoparticle Magnetization Modeling

“…Below we give a lot of examples of the case. The condition (18) is equated in the critical temperature point T = θ and β here gets the assignation β θ . It brings us to the quadratic equation: The previously mentioned expression with square root 1 − 8 z figures further in computations by the Heisenberg theory (inclusively for the exchange integral J evaluation) as the consequence of a quadratic equation solution way via the discriminant.…”

“…A further development of the Heisenberg theory implies explicit account of a space symmetry [14], that would allow to introduce anisotropy parameters within the partition function. Some basic observations and modeling outline for nanoscale objects are presented in [14,18]. Note, that at huge values of the spin, the problem may be considered as the quasiclassical approximation as it does in the transition to the continuous description (e.g.…”