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). In this work, using both simulations and experiments, we thoroughly investigate the thermodynamic properties and magnetic phases of square and quadrupolar ASI as a function of applied in-plane magnetic fields. Monte Carlo (MC) simulations are used to generate field-dependent maps of the magnetization, the magnetic specific heat, and the thermodynamic magnetization fluctuations, 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. Furthermore, the MC calculations allow us to probe the stability of different phases as a function of applied field and temperature. Those calculations are experimentally supported by magneto-optical measurements of the equilibrium "magnetization noise" in thermally-active ASIs. Our results provide a window into a rich landscape of collective magnetic behavior associated with the application of magnetic field to ASI systems.