Quantum versus thermal fluctuations in the fcc antiferromagnet: Alternative routes to order by disorder

In frustrated magnetic systems with competing interactions fluctuations can lift the residual accidental degeneracy. We argue that the state selection may have different outcomes for quantum and thermal order by disorder. As an example, we consider the semiclassical Heisenberg fcc antiferromagnet with only the nearest-neighbor interactions. Zero-point oscillations select the type 3 collinear antiferromagnetic state at $T=0$. Thermal fluctuations favor instead the type 1 antiferromagnetic structure. The opposite tendencies result in a finite-temperature transition between the two collinear states. Competition between effects of quantum and thermal order by disorder is a general phenomenon and is also realized in the $J_1\text{−}{J}_2$ square-lattice antiferromagnet at the critical point $J_2=\frac{1}{2}{J}_1$.

Figure 1

Type 1 (left) and type 3 (right) antiferromagnetic structures on an fcc lattice.

Figure 2

Color intensity map for the magnon dispersion in two collinear antiferromagnetic states with fixed $k_y=2\pi /a$: AF1 (top panel) and AF3, lower branch (bottom panel).

Figure 3

Main panel: temperature dependence of the free energy in the AF1 and AF3 states. Inset: the quantum correction $\mathrm{\Delta }E$ to the ground-state energy for the degenerate classical spirals vs pitch $q$ (full line). $\mathrm{\Delta }E$ for the AF3 state is marked with a cross.