Heisenberg magnet with modulated exchange

TL;DR

This paper investigates how weak lattice distortions modulate exchange interactions in Heisenberg magnets, leading to incommensurate spin structures, new magnetic Bragg peaks, and potential stabilization of spiral phases through Umklapp interactions.

Contribution

It introduces a model for exchange modulation due to lattice distortion, revealing effects on spin structures and stability of incommensurate phases in Heisenberg magnets.

Findings

Lattice distortion causes exchange modulation and new Bragg peaks.

Incommensurate spiral phases can be stabilized by exchange modulation.

Umklapp terms can lock spin structures to lattice modulation vectors.

Abstract

A modification of the ground state of the classical-spin Heisenberg Hamiltonian in the presence of a weak superstructural distortion of an otherwise Bravais lattice is examined. It is shown that a slight modulation of the crystal lattice with wavevector $\bQ_c$ results in a corresponding modulation of the exchange interaction which, in the leading order, is parametrized by no more than two constants per bond, and perturbs the spin Hamiltonian by adding the ``Umklapp'' terms $\sim S^\alpha_{\bq} S^\alpha_{\bq \pm \bQ_c}$. As a result, for a general spin-spiral ground state of the non-perturbed exchange Hamiltonian, an incommensurate shift of the propagation vector, $\bQ$, and additional new magnetic Bragg peaks, at $\bQ \pm n\bQ_c$, $n = 1,2,...$, appear, and its energy is lowered as it adapts to the exchange modulation. Consequently, the lattice distortion may open a region of stability of the incommensurate spiral phase which otherwise does not win the competition with the collinear N\'{e}el state. Such is the case for the frustrated square-lattice antiferromagnet. In addition, the ``Umklapp'' terms provide a commensuration mechanism, which may lock the spin structure to the lattice modulation vector $\bQ_c$, if there is sufficient easy-axis anisotropy, or a magnetic field in an easy plane.