How do frustrations without disorder result in the spin-glass-like behavior of the kagom\'{e} antiferromagnet?

TL;DR

This paper investigates how frustration in the classical Heisenberg kagome antiferromagnet leads to spin-glass-like behavior without disorder, focusing on domain formation, correlations, and differences between field-cooled and zero-field-cooled regimes.

Contribution

It introduces a domain-based framework to understand spin-glass-like freezing in a disorder-free frustrated magnet, highlighting the role of coplanar states and domain hierarchies.

Findings

Negligible statistical weight of ${f q} =0$ domains.

Formation of $ ext{sqrt}(3) imes ext{sqrt}(3)$ domains with three spin orientations.

Emergence of a hierarchical domain structure in the FC regime.

Abstract

Freezing of the classical spin liquid of the Heisenberg kagom\'{e} antiferromagnet is studied. At low temperature, the coplanar spin configurations are known to dominate among all possible three-dimensional low-energy states because of the fluctuation interaction. It is shown that the statistical weight of ${\bf q} =0$ domains is negligible. This allows one to describe coplanar states in terms of $\sqrt{3}\times \sqrt{3}$ domains with three possible spin orientations. The domain walls are mapped onto closed self-avoiding loops on the hexagonal lattice. The probability of domain formation is evaluated. It is shown that in FC (field cooled) regime a telescopic hierarchy of domains appears. The spatial and temporal behavior of the spin correlation function is estimated. The difference between FC and ZFC behavior is discussed.