Color ice states, weathervane modes, and fluctuation-driven phase transition in a pyrochlore Heisenberg antiferromagnet

We expose a new example of fluctuation-driven phase transition in the pyrochlore bilinear-biquadratic Heisenberg antiferromagnet, $H = \sum_{\langle ij\rangle}J\mathbf{S}_i\cdot\mathbf{S}_j+B(\mathbf{S}_i\cdot\mathbf{S}_j)^2$, with positive biquadratic exchange interaction ($B>0$), in the semi-classical limit ($S\gg 1$, $BS^2/J \sim O(1)$). We will show that this model possesses remarkable properties. First of all, the ground state manifold contains an extensively large family of non-coplanar spin states known as ``color ice states'', which are generalization of the familiar Ising spin ice states. Furthermore, the color ice states support two-dimensional analog of the weathervane modes in the classical kagome Heisenberg antiferromagnet. Finally, even though the bilinear and the biquadratic interactions admit a common ground state manifold, they produce different quantum fluctuations. As a result, the quantum order-by-disorder mechanism selects different states as $BS^2/J$ changes, resulting in a phase transition purely driven by fluctuations. The talk is based on arXiv:1607.02185.