Beller Lectureship: Magnetic field tuning of order by disorder in frustrated Ising pyrochlores*

We demonstrate the appearance of thermal order by disorder in Ising pyrochlores with staggered antiferromagnetic order frustrated by an applied magnetic field. We use a mean-field cluster variational method, a low-temperature expansion, and Monte Carlo simulations to characterize the order-by-disorder transition. By direct evaluation of the density of states, we quantitatively show how a symmetry-broken state is selected by thermal excitations. We discuss the relevance of our results to experiments in 2D and 3D samples and evaluate how anomalous finite-size effects could be exploited to detect this phenomenon experimentally in two-dimensional artificial systems, or in antiferromagnetic all-in–all-out pyrochlores like Nd₂Hf₂O₇ or Nd₂Zr₂O₇ , for the first time.