Stable solitons in a nearly [formula omitted]-symmetric ferromagnet with spin-transfer torque

Abstract

We consider the Landau–Lifshitz equation for the spin torque oscillator — a uniaxial ferromagnet in an external magnetic field with polarised spin current driven through it. In the absence of the Gilbert damping, the equation turns out to be PT-symmetric. We interpret the PT-symmetry as a balance between gain and loss — and identify the gaining and losing modes. In the vicinity of the bifurcation point of a uniform static state of magnetisation, the PT-symmetric Landau–Lifshitz equation with a small dissipative perturbation reduces to a nonlinear Schrödinger equation with a quadratic nonlinearity. The analysis of the Schrödinger dynamics demonstrates that the spin torque oscillator supports stable magnetic solitons. The PT near-symmetry is crucial for the soliton stability: the addition of a finite dissipative term to the Landau–Lifshitz equation destabilises all solitons that we have found.