Unified molecular field theory for collinear and noncollinear Heisenberg antiferromagnets

David C. Johnston
Phys. Rev. B 91, 064427 – Published 27 February 2015

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 χ versus temperature T below the AF ordering temperature TN to be carried out for arbitrary Heisenberg exchange interactions Jij between arbitrary neighbors j of a given spin i without recourse to magnetic sublattices. The Weiss temperature θp in the Curie-Weiss law is written in terms of the Jij values and TN in terms of the Jij 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=θp/TN, and S. For planar noncollinear helical or cycloidal ordering, an additional parameter is the wave vector of the helix or cycloid. The MFT is also applicable to AFs with other AF structures. The MFT predicts that χ(TTN) of noncollinear 120 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.

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  • Received 23 July 2014
  • Revised 27 January 2015

DOI:https://doi.org/10.1103/PhysRevB.91.064427

©2015 American Physical Society

Authors & Affiliations

David C. Johnston

  • Department of Physics and Astronomy and Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA

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Issue

Vol. 91, Iss. 6 — 1 February 2015

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