The phase diagram of a frustrated Heisenberg model: from disorder to order and back again

TL;DR

This study investigates how disorder affects phase transitions in a frustrated Heisenberg model, revealing that impurities destroy the ordered phase and induce a complex nematic glass state with non-trivial magnetic responses.

Contribution

We demonstrate that any finite disorder destroys the Ising-like transition in the frustrated $J_1$-$J_2$ model and identify the resulting nematic glass phase with unique magnetic properties.

Findings

Disorder destroys the finite-temperature Ising transition.

The resulting phase is a nematic glass with non-trivial magnetic response.

Disorder induces non-collinear spin-vortex-crystal order and random fields.

Abstract

We study the effects of bond and site disorder in the classical $J_{1}$-$J_{2}$ Heisenberg model on a square lattice in the order-by-disorder frustrated regime $2J_{2}>\left|J_{1}\right|$. Combining symmetry arguments, numerical energy minimization and large scale Monte Carlo simulations, we establish that the finite temperature Ising-like transition of the clean system is destroyed in the presence of any finite concentration of impurities. We explain this finding via a random-field mechanism which generically emerges in systems where disorder locally breaks the same real-space symmetry spontaneously globally broken by the associated order parameter. We also determine that the phase replacing the clean one is a paramagnet polarized in the nematic glass order with non-trivial magnetic response. This is because disorder also induces non-collinear spin-vortex-crystal order and produces a conjugated transverse dipolar random field. As a result of these many competing effects, the associated magnetic susceptibilities are non-monotonic functions of the temperature. As a further application of our methods, we show the generation of random axes in other frustrated magnets with broken SU(2) symmetry. We also discuss the generality of our findings and their relevance to experiments.