The Finite-Temperature Behavior of a Triangular Heisenberg Antiferromagnet

Abstract

We investigate the classical antiferromagnetic Heisenberg model on the triangular lattice with up to third-nearest neighbor exchange couplings using the Nematic Bond Theory. This approach allows us to compute the free energy and the neutron scattering static structure factor at finite temperatures. We map out the phase diagram with a particular emphasis on finite-temperature phase transitions that break lattice-rotational symmetries, spiral spin liquids and the broad specific heat hump that is ubiquitous in the antiferromagnetic 120 degree phase. We identify this specific heat hump as signaling the onset of an exponentially increasing correlation length. Further, we map out the temperature of the specific heat hump and the transition temperatures of the symmetry-breaking transitions throughout the exchange-coupling space. Along the line $J_3 = J_2/2$, the Fourier-transformed exchange coupling exhibits a degenerate ring-like minimum, giving rise to spiral spin liquid behavior at intermediate temperatures. We investigate the structure factor of the spiral spin liquid as function of $J_2$ and identify the corresponding low-temperature order, which coincides with the single-$\vec{q}$ spiral states of maximum spin-wave entropy along the degenerate ring.