Stable solitons in a nearly $\mathcal{PT}$-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 $\mathcal{PT}$-symmetric. We interpret the $\mathcal{PT}$-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 $\mathcal{PT}$-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 $\mathcal{PT}$ 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.

Publication
Physica D: Nonlinear Phenomena