Stable solitons in a nearly PT-symmetric ferromagnet with spin-transfer torque

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 Schr\"odinger equation with a quadratic nonlinearity. The analysis of the Schr\"odinger 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.