Magnetic field dependent thermodynamic properties of square and quadrupolar artificial spin ice

Applied magnetic fields are an important tuning parameter for artificial spin ice (ASI) systems, as they can drive phase transitions between different magnetic ground states or tune through regimes with high populations of emergent magnetic excitations (e.g., monopole-like quasiparticles). Here, using simulations supported by experiments, we investigate the thermodynamic properties and magnetic phases of square and quadrupolar ASI as a function of applied in-plane magnetic fields. Monte Carlo simulations are used to generate field-dependent maps of the magnetization, the magnetic specific heat, the thermodynamic magnetization fluctuations, and the magnetic order parameters, all under equilibrium conditions. These maps reveal the diversity of magnetic orderings and the phase transitions that occur in different regions of the phase diagrams of these ASIs, and are experimentally supported by magnetooptical measurements of the equilibrium "magnetization noise" in thermally active ASIs.