Generalized Helimagnets Between Two and Four Dimensions

TL;DR

This paper investigates phase transitions in generalized helimagnets with specific symmetry breaking patterns across different dimensions, revealing complex fixed point structures and phase behaviors relevant to real magnetic materials.

Contribution

It provides a combined renormalization group and mean-field analysis of helimagnets, identifying fixed points and phase transitions in various dimensions, especially near two and four dimensions.

Findings

Discovery of a nematic-like phase near two dimensions.

Identification of an XY-like transition in the physical case.

First-order transition line replacing the principal chiral fixed point in three dimensions.

Abstract

We study the phase transitions of N-components generalized helimagnets that obey the symmetry breaking pattern O(N) x O(N-1) -> O(N-1)_diag . In the neighborhood of two dimensions, a D=2+epsilon renormalization group study reveals a rich fixed point structure as well as a nematic-like phase with partial spin ordering. In the physical case O(3) x O(2) -> O(2)_diag , relevant to real magnets with noncollinear ordering, we show that this implies an XY-like transition between the ordered phase and the nematic-like phase. A non-Abelian mean-field calculation qualitatively valid above four dimensions is shown to lead to the same picture but then the principal chiral fixed point, which had been proposed earlier as the relevant fixed point for D=3 helimagnets, plays no role due to the appearance of a first-order line.