Frustrated Heisenberg Antiferromagnets on Cubic Lattices: Magnetic Structures, Exchange Gaps, and Non-Conventional Critical Behaviour

TL;DR

This study investigates frustrated Heisenberg antiferromagnets on cubic lattices, analyzing magnetic structures, exchange gaps, and critical behavior, revealing class-dependent critical indices and fluctuation effects near the Neel temperature.

Contribution

It classifies antiferromagnets into seven classes based on lattice and magnetic structure, and computes class-specific critical indices considering fluctuation corrections.

Findings

Degeneracy is lifted below $T_N$, favoring collinear structures.

Exchange gaps open at certain wave vectors and close near $T_N$.

Critical indices $ u$ and $eta$ differ between classes A and B.

Abstract

We have studied the Heisenberg antiferromagnets characterized by the magnetic structures with the periods being two times larger than the lattice period. We have considered all the types of the Bravais lattices (simple cubic, bcc and fcc) and divided all these antiferromagnets into 7 classes i.e. 3 plus 4 classes denoted with symbols A and B correspondingly. The order parameter characterizing the degeneracies of the magnetic structures is an ordinary Neel vector for A classes and so-called 4-complex for B classes. We have taken into account the fluctuation corrections for these states within the spin-wave and large-N expansions ($N$ is the number of spin components). Below the Neel temperature $T_{\rm{N}}$ quantum and thermal fluctuations lift the degeneracy making simple one-wave vector collinear structure preferable for all the classes. A satellite of this effect is opening of the exchange gaps at certain wave vectors in the spin wave spectrum (there is an analogous effect for the nonuniform static transverse susceptibility). However, as the temperature approaches $T_{\rm{N}}$, the exchange gaps are closing. We have calculated the critical indices $\eta$ and $\nu$ to order of $1/N$ and found that they differ for A and B classes.