Entropy Induced Two-dimensionality Magnetic Monopole Gases

The discovery of magnetic-monopole-quasiparticles in R₂Ti₂O₇ (R = Ho, Dy) spin ice has attracted a lot of attentions. However, in bulk spin ice the numbers of monopoles and antimonopoles are always equal, leading to inactive magnetic charge degree of freedom and monopole-insulating behaviors. Recently, we proposed a metallic monopole gas with a net magnetic charge, confined at R₂Ir₂O₇/R₂Ti₂O₇ (spin ice/antiferromagnetic) interfaces. However, the two-dimensionality of the monopole gas is yet to be understood, as the monopole gas is not energetically trapped near the interface. Here, we provide an understanding that the two-dimensionality is driven by entropy instead of energy. The latter induces two-dimensionality in the electron gas counterparts. We demonstrate this picture in a toy model where we maximized the total entropy of magnetic monopoles and the spin ice layer they live in. We compared the results from this toy model with those from our Monte Carlo spin simulations which contained all the lattice and interaction information and both methods show very similar magnetic monopole distribution in the heterostructure, which is confined at R₂Ir₂O₇/R₂Ti₂O₇ interfaces by a couple of unit cells. We further use both methods to demonstrate that magnetic field and temperature are effective tuning knobs to further tailor the dimensionality of the monopole gas. Our results reveal the exotic entropic nature of the monopole gas, providing an alternative two-dimensional platform for future device applications.