Antiferromagnetic state: spectrum, wave functions and thermodynamic properties.


Serge N. Zagoulaev

Quantum Mechanics Dept., Saint-Petersburg State University


Abstract

A new method to describe the electronic structure and physical properties
of antiferromagnets (AF) is proposed. The main feature and the novelty of
 our method is the use of spin-nonpolarized pure spin states which form a
subspace of a degenerate ground state of AF crystals with the zero total
spin z-projection M=0. From the statistical physics analysis of AF experimental
properties, some constraints on the energy spectrum in the vicinity of
the ground state were obtained. For the many-electron many-determinant
wave functions of the ground and low lying excited states, a new ansatz
is proposed with taking into account these constraints.

The model operator H(x_1,...,x_N) corresponding to required spectrum was obtained.
It is the abelian restriction of exact many-electron Hamiltonian with the
relativistic correction to the spin dipole-dipole interaction on the subspace
of AF ground state wave functions.

Using the constructed N-electron functions, an analytical calculation of
characteristic physical properties of antiferromagnets was performed.
Namely, the explicit expression of antiferromagnetic crystall
interference function was obtained for the angular dependence of the differential
cross section during the elastic magnetic neutron scattering by antiferromagnetic
target.

 Taking into account the (N/2+1)^2 lowest states of the spectrum, we have
managed  to reproduce the typical thermodynamic properties of AF: the typical
antiferromagnetic temperature dependence of the spin susceptibility and
the spin contribution to the specific heat temperature dependence. In contrast to
the Neel model, for the zero total spin z-projection, these state give the zero
local magnetization M(R)=0 at any point R.