Unified Molecular Field Theory for Collinear and Noncollinear Heisenberg Antiferromagnets

TL;DR

This paper introduces a unified molecular field theory applicable to both collinear and noncollinear Heisenberg antiferromagnets, enabling comprehensive calculations of magnetic properties without relying on magnetic sublattices.

Contribution

The formulation allows for calculations of magnetic susceptibility and other properties directly from exchange interactions and structure, applicable to various AF structures including noncollinear arrangements.

Findings

Predicts isotropic susceptibility for noncollinear 120° structures on triangular lattices.

Provides laws of corresponding states for magnetic and thermal properties.

Constructs phase diagrams for high-field magnetization and heat capacity.

Abstract

A unified molecular field theory (MFT) is presented that applies to both collinear and planar noncollinear Heisenberg antiferromagnets (AFs) on the same footing. The spins in the system are assumed to be identical and crystallographically equivalent. This formulation allows calculations of the anisotropic magnetic susceptibility chi versus temperature T below the AF ordering temperature TN to be carried out for arbitrary Heisenberg exchange interactions J{ij} between arbitrary neighbors j of a given spin i without recourse to magnetic sublattices. The Weiss temperature theta_p in the Curie-Weiss law is written in terms of the J{ij} values and TN in terms of the J{ij} values and an assumed AF structure. Other magnetic and thermal properties are then expressed in terms of quantities easily accessible from experiment as laws of corresponding states for a given spin S. For collinear ordering these properties are the reduced temperature t = T/TN, the ratio f = theta_p/TN and S. For planar noncollinear helical or cycloidal ordering, an additional parameter is the wavevector of the helix or cycloid. The MFT is also applicable to AFs with other AF structures. The MFT predicts that chi(T <= TN) of noncollinear 120 degree spin structures on triangular lattices is isotropic and independent of S and T and thus clarifies the origin of this universally observed behavior. The high-field magnetization and heat capacity for fields applied perpendicular to the ordering axis (collinear AFs) and ordering plane (planar noncollinear AFs) are also calculated and expressed for both types of AF structures as laws of corresponding states for a given S, and the reduced perpendicular field versus reduced temperature phase diagram is constructed.