Chiral order emergence driven by quenched disorder

TL;DR

The study analyzes the classical $J_1$-$J_3$ HK Heisenberg model on the kagome lattice with site dilution ($p$) to demonstrate that quenched disorder can induce a new chiral order in an $O(3)$ spin system, distinct from the clean ground state. Parallel tempering Monte Carlo with disorder averaging maps the phase diagram in the $T$–$p$ plane and analyzes $C_V^{\max}$ and the susceptibilities of the $K_4$ order parameter $\Sigma$ and the chirality $\chi$, confirming the emergence of a chiral phase for finite dilution. In the clean case ($p=0$) the transition belongs to the four-state Potts universality class with exponents $\alpha/\nu=1$, $\gamma/\nu=7/4$, $1/\nu=3/2$, while for $p>0$ a chiral Ising transition appears with $\alpha/\nu=0$, $\gamma/\nu=7/4$, $1/\nu=1$, and the $K_4$ order is destroyed by the Imry-Ma mechanism in $d=2$. The results show a robust chiral phase for small $p$, with $\chi\neq 0$ and a finite-temperature Ising transition up to $p\lesssim 0.1$, supporting the order-by-quenched-disorder mechanism and suggesting this chirality could generalize to other frustrated lattices with multiple sublattices.

Abstract

Quenched disorder can destroy magnetic order, for example when a random field is applied in a 2-dimensional Ising model. Even when an order exists in the presence of quenched disorder, it is usually only the survival of the order of the clean model. We present here a surprising phenomenon where an order emerges, driven by quenched disorder. This order has nothing in common with the order present in the clean model. This type of \textit{order by disorder} differs from the usual thermal or quantum one. The classical $J_1-J_3$ Heisenberg model on the kagome lattice is studied by parallel tempering Monte Carlo simulations, with site dilution. After analyzing the effect of a few vacancies on the ground state, favoring non-coplanar configurations, we show the emergence of a low-temperature chiral phase and the progressive destruction of the collinear $q=4$ Potts order, the only order present in the absence of vacancies.

Figures (6)

• Figure 1: Phase diagram of the $J_1J_3$HK model with $J_1 = -1$ and $J_3 = 1$. $p$ denotes the dilution rate and $T$ the temperature. The blue region indicates a phase with non-zero scalar chirality $\chi\neq 0$, while the green region corresponds to non-zero $K_4$ order parameter $\sigma\neq 0$. Blue and red dots indicate phase transitions, while green crosses correspond to a crossover.
• Figure 2: Left: First ($J_1$) and third-neighbor ($J_3$) interactions in the $J_1J_3$HK model. Right: spin orientations of the collinear $K_4$ order, characterized by a four-site unit cell (dashed outline). Sites with the same spin orientation form hexagons (light green) and triangle (light blue).
• Figure 3: Spin structure in the 3subAF phase on the kagome lattice. Circles denote the three sublattices $A$, $B$, and $C$, connected via third-neighbor $J_3$ couplings (colored links). Each sublattice independently exhibits Néel order with two opposing spin orientations (light/dark arrows, of the color of the sublattice). The collinear limit of this structure corresponds to the $K_4$ order shown in Fig. \ref{['fig:neighbor_kagome']}.
• Figure 4: Ground state spin-spin correlation $\mathbf S_i\cdot \mathbf S_0$ between sites of the $A$ and $C$ sublattices and the central site $0$ belonging to the $B$ sublattice, for a periodic $24\times24\times3$ lattice. The exchanges of the $J_1$ and $J_3$ links emanating from site $0$ tend to zero. Correlations between $B$ sites are not shown (they are strongly antiferromagnetic and near $\pm1$), and the diameter of circles saturate for absolute values above 0.04
• Figure 5: (left) Maxima of heat capacity $C_V^{\rm max}$ versus the linear lattice size $L$ and (right) $T_c^{C_V}(L)$ versus $L^{-3/2}$, for several dilution rates $p$.