Monte Carlo simulations of the thermodynamic behavior of exchange graded ferromagnets

In this work, we investigate the thermodynamic behavior of exchange graded ferromagnetic films using Monte Carlo simulations. The systems are modeled by using a classical Heisenberg Hamiltonian, considering only nearest neighbor exchange interactions and a linear depth-dependent effective magnetic exchange coupling strength profile. Our quantitative assessment of the local physical quantities shows that each layer exhibits rather isolated thermodynamic behavior, since both layerwise magnetization and susceptibility data indicate layer-specific "local" Curie temperatures as a consequence of the depth-dependent change in the exchange coupling strength. We also propose and evaluate a predictive formulation for such profiles of "local" Curie temperatures, whose only input is the pre-selected exchange coupling profile. Having this very precise predictive tool, we show how it can be used to obtain the temperature-dependent ferromagnetic state including its depth-dependent magnetization profile at any given temperature. Thus, it is possible to predict which exchange profile will produce a desired thermodynamic behavior and associated functionality, without the need to perform complex experiments or time-consuming computations. With this study, we furthermore demonstrate that nonlocal aspects of the thermodynamic state formation in graded magnetic materials are relevant only over very short length scales, which is in outstanding qualitative agreement with prior numerical and experimental work.