Frustration induced highly anisotropic magnetic patterns in classical $XY$ model on kagome lattice

TL;DR

This paper predicts and observes highly anisotropic magnetic patterns in a frustrated classical XY model on a kagome lattice, revealing a phase transition and unique scaling behavior at a critical frustration level.

Contribution

It introduces the discovery of novel anisotropic magnetic patterns and a specific scaling law in the frustrated XY kagome model, linked to a double-degenerate ground state.

Findings

Observation of highly anisotropic magnetic patterns.

Scaling of magnetization as N^{-1/4} in the frustrated regime.

Identification of a phase transition at f=3/4.

Abstract

We predict and observed novel highly anisotropic magnetic patterns obtained in the model of frustrated planar interacting magnetic moments (the classical $X-Y$ model) on the regular kagome lattice. The frustration is provided by the presence of both ferromagnetic and anti-ferromagnetic interactions between adjacent magnetic moments defined on the lattice nodes. At the critical value of the frustration $f=f_{cr}=3/4$ such a systems displays the phase transition from the ordered ferromagnetic state to the disordered frustration regime characterized by the highly-degenerated ground state. In the frustrated regime, $f_{cr}< f \leq 1$, unexpected scaling of spatially averaged magnetization $\langle \vec{M} \rangle $ on the total number of nodes,$N$, i.e. $\langle \vec{M} \rangle \simeq N^{-1/4}$, has been obtained. Such scaling is provided by highly anisotropic magnetic patterns displaying the ferromagnetic ordering along the $y$-direction, and short-range correlations of magnetic moments along the $x$-direction. We conjecture that all these intriguing features are explained by the presence of the double-degenerated ground state in the basic cell, i.e. single triangle, of the kagome lattice accompanying a large amount of intrinsic constraints. We anticipate the implementation of the phase transition and anisotropic magnetic patterns in various systems, e.g. natural magnetic molecular clusters, artificially prepared Josephson junctions networks, trapped-ions and/or photonic crystals.