Magnetic instability criterion for spin–lattice systems

Abstract

It is of vital importance to determine the critical magnetic and/or mechanical conditions under which the magnetic spin order becomes unstable in order to understand the microscopic nature of magnetic instabilities in ferromagnetic materials, often in conjunction with structural lattice instabilities, e.g., magnetic phase transitions and domain switching, as the source of diverse functionalities or the cause of critical failure of magnetic devices. Here, we propose an analytical method based on state-of-the-art spin–lattice modeling of ferromagnets to enable rigorous descriptions of magnetic instabilities in arbitrary atomic systems under a finite magnetic field and/or mechanical loading. The present theory yields, as an instability criterion, the condition that the minimum eigenvalue of the Hessian matrix of potential energy with respect to atomic coordinate and magnetic moment must be zero. In addition, the corresponding eigenvector represents the magnetic behavior of the spin moment at the instability, which is successfully validated by applying the criterion to magnetization switching in ferromagnetic Fe under an external magnetic field. Our approach thus provides a novel insight into the cause of magnetic instabilities and allows us to address complicated magnetic instability issues in practical situations.