Magnetic properties of body-centred cubic ferromagnetic thin films described by the fourth order perturbed Heisenberg Hamiltonian

TLAB simulations, we created 3-D and 2-D graphs to analyse energy in relation to the spin exchange interaction and azimuthal angle. Our results show that the total magnetic energy can vary significantly, reaching orders of 10¹⁷ when the fourth-order anisotropy constant in the bottom spin layer is minimized. In contrast, when the middle spin layer has lower anisotropy, the total magnetic energy decreases to the order of 10¹³, indicating that it becomes easier for the magnetic moments to rotate. We also found that the angle between consecutive magnetic easy and hard directions is not always 90 degrees, and interchanging layers leads to slight changes in energy maxima and minima. Importantly, the total magnetic energy is significantly higher in configurations with two spin layers, ranging from 10⁴² to 10⁴³, compared to those with three layers. These results underscore the sensitivity of bcc ferromagnetic thin films to variations in magnetic anisotropy and provide important insights for future applications in magnetic storage, sensors, and spintronic technologies.