Thermodynamics and fractal dynamics of a nematic spin ice: A doubly frustrated pyrochlore Ising magnet

The Ising antiferromagnets on the triangular and on the pyrochlore lattices are two of the most iconic examples of magnetic frustration, paradigmatically illustrating many exotic properties such as emergent gauge fields, fractionalization, and topological order. In this paper, we show that the two instances of frustration can, remarkably, be combined in a single system, where they coexist without inducing conventional long-range ordering. Our results indicate that the system undergoes a first-order phase transition upon lowering the temperature, into a yet different frustrated phase that we characterize to exhibit nematic order. We argue that an extensive degeneracy survives down to zero temperature, at odds with a customary Pauling estimate. Dynamically, we find evidence of anomalous noise in the power spectral density, arising from an effectively fractal anisotropic motion of monopoles at low temperature.