Destruction of long-range order in noncollinear two-dimensional antiferromagnets by random-bond disorder

We consider frustrated Heisenberg antiferromagnets, whose clean-limit ground state is characterized by noncollinear long-range order with nonzero vector chirality, and study the effects of quenched bond disorder, i.e., random exchange couplings. A single bond defect is known to induce a dipolar texture in the spin background independent of microscopic details. Using general analytical arguments as well as large-scale simulations for the classical triangular-lattice Heisenberg model, we show that any finite concentration of such defects destroys long-range order for spatial dimension $d\le 2$, in favor of a glassy state whose correlation length in $d=2$ is exponentially large for small randomness. Our results are relevant for a wide range of layered frustrated magnets.

Figure 1

Schematic ground-state phase diagram of chiral noncollinear magnets with quenched bond disorder in space dimension $1<d\le 2$, with $\mathrm{\Delta }/J$ parametrizing the disorder strength. (a) Classical limit $\left(S\to \infty \right)$: The LRO of the clean system is destroyed for infinitesimal disorder in favor of a spin glass. (b) Quantum case (conjectured): The spin glass turns into a random-singlet (or valence-bond) state at a critical level of disorder (whose value depends on microscopic details).

Figure 2

Single bond defect in a triangular-lattice Heisenberg antiferromagnet. (a) Spin configuration near the defect bond (shaded) for $\delta J=-J_1$ (2) and $J_2=0$; the unperturbed ${120}^{\circ }$ order is shown in gray. (b) Defect-induced spin rotation angles $\delta \mathrm{\Theta }$ as a function of distance $r$ from the defect, for $\delta J=-J_1/10$ and different $\alpha \equiv J_2/J_1$. The dashed lines are fits to $1/r$ behavior for $2<r<20$; deviations at large $r$ arise from finite sample size and periodic boundary conditions, $L=300$.

Figure 3

Magnetic correlation length $\xi$ for the triangular-lattice Heisenberg model with Gaussian bond disorder. (a) Finite-size scaling of $1/\xi$ as function of linear system size $L$ for $\alpha =0.05,T=0$, and different disorder strength $\mathrm{\Delta }$. (b) Comparison of $\xi$ obtained from finite-$T$ MC simulation and $T=0$ energy minimization (EM), for $\alpha =0.05$ and $L=36$. (c) $ln\xi$ plotted as a function of $1/{\mathrm{\Delta }}^2$, illustrating the scaling from Eq. (6). (d) Test of stiffness dependence: ${[ln(\xi /{\xi }_{\infty })]}^{1/2}\mathrm{\Delta }$ and single-defect $1/\left[r\delta \mathrm{\Theta }\right(r\left)\right]$ for different $\alpha$, plotted as functions of spin stiffness. The solid line corresponds to the RG result for $\xi$. Dashed lines are linear fits.