Spiral order from orientationally correlated random bonds in classical XY models

TL;DR

This paper investigates how impurity bonds in three-dimensional XY ferromagnets induce spiral order, demonstrating that disorder can lead to a stable spiral state through analytical and simulation methods.

Contribution

It introduces a novel mechanism where randomly distributed impurity bonds cause spiral order in XY ferromagnets, supported by rigorous analysis and Monte Carlo simulations.

Findings

Impurity bonds induce a transition to spiral order at a critical frustration threshold.

Spiral order emerges with a wave vector proportional to impurity concentration.

Analytical results are validated by Monte Carlo simulations.

Abstract

We discuss the stability of ferromagnetic long-range order in three-dimensional classical XY ferromagnets upon substitution of a small subset of equally oriented bonds by impurity bonds, on which the ferromagnetic exchange J_perp > 0 is replaced by a strong antiferromagnetic coupling J_imp < 0. In the presence of a single impurity bond, once the absolute value of the frustrating coupling J_imp < 0 exceeds a threshold J_c > 0, the ground state becomes two-fold degenerate, corresponding to either clockwise or anticlockwise canting of the spins in the vicinity of the impurity bond. In the presence of a small concentration of impurity bonds, the effective low-energy Hamiltonian is that of Ising variables encoding the sense of rotation of the local canting around the impurities. Those degrees of freedom interact through a dipolar interaction mediated by spin waves. A ferromagnetic Ising ground state indicates the instability of the XY ferromagnet towards a spiral state with a wave vector proportional to the concentration of impurity bonds. To analyze under which circumstances such a ground state arises, we study first impurities forming superlattices. For a subclass of those, we can rigorously establish the existence of spiral order. For another class of superlattices, the Ising variables order ferromagnetically in planes perpendicular to the orientation of impurity bonds, but antiferromagnetically parallel to it, which results in a fan-like XY ground state. Second, we consider the case when the impurity bonds are randomly distributed on the three-dimensional host lattice according to a Poisson process. We show the phenomenon of spiral order by disorder with an ordering wave vector proportional to the impurity concentration. The analytical predictions are confirmed by Monte Carlo simulations and are relevant for magnetic materials such as YBaCuFeO_5.