Thermodynamics and entropic inference of nanoscale magnetic structures in Gd

A bulk gadolinium (Gd) single crystal exhibits virtually zero remnant magnetization, a common trait among soft uniaxial ferromagnets. This characteristic is reflected in our magnetometry data showing virtually hysteresis free isothermal magnetization loops with large saturation magnetization. The absence of hysteresis allows to model the measured easy axis magnetization as a function of temperature and applied magnetic field, rather than a relation, which permits the application of Maxwell relations from equilibrium thermodynamics. Demagnetization effects broaden the isothermal first-order transition from negative to positive magnetization. By analyzing magnetization data within the coexistence regime, we deduce the isothermal entropy change and the field-induced heat capacity change. Comparing the numerically inferred heat capacity with relaxation calorimetric data confirms the applicability of the Maxwell relation. Analysis of the entropy in the mixed phase region suggests the presence of hitherto unresolved nanoscale magnetic structures in the demagnetized state of Gd. To support this prediction, Monte Carlo simulations of a 3D Ising model with dipolar interactions are performed. Analyzing the cluster size statistics and magnetization from the model provides strong qualitative support of our analytic approach.