Publisher's Note: Breathers and rogue waves excited by all-magnonic spin-transfer torque [Phys. Rev. E 94, 042220 (2016)].

This corrects the article DOI: 10.1103/PhysRevE.94.042220.

Breathers and rogue waves excited by all-magnonic spin-transfer torque.

In terms of Darboux transformation we investigate the dynamic process of spin wave passing through a magnetic soliton. It causes nonlinear excitations, such as Akhmediev breathers solution and Kuznetsov-Ma soliton. The former case demonstrates a spatial periodic process of a magnetic soliton forming the petal with four pieces. The spatial separation of adjacent magnetic petals increases rapidly, while one valley splits into two and the amplitude of valley increases gradually with the increasing amplitude of spin wave. The other case shows a localized process of the spin-wave background. In the limit case, we get rogue waves and clarify its formation mechanism.

Screw-pitch effect and velocity oscillation of a domain wall in a ferromagnetic nanowire driven by spin-polarized current.

We investigate the dynamics of a domain wall in a ferromagnetic nanowire with spin-transfer torque. The critical current condition is obtained analytically. Below the critical current, we get the static domain wall solution, which shows that the spin-polarized current cannot drive a domain wall moving continuously. In this case, the spin-transfer torque plays both the anti-precession and anti-damping roles, which counteracts not only the spin precession driven by the effective field but also Gilbert damping of the moment. Above the critical value, the dynamics of the domain wall exhibits the novel screw-pitch effect characterized by the temporal oscillation of domain wall velocity and width, respectively. Both the theoretical analysis and numerical simulation demonstrate that this novel phenomenon arises from the conjunctive action of Gilbert damping and spin-transfer torque. We also find that the roles of spin-transfer torque are completely opposite for the cases below and above the critical current.

Soliton solution for the spin current in a ferromagnetic nanowire.

We investigate the interaction of a periodic solution and a one-soliton solution for the spin-polarized current in a uniaxial ferromagnetic nanowire. The amplitude and wave number of the periodic solution for the spin current give different contributions to the width, velocity, and amplitude of the soliton. Moreover, we found that the soliton can be trapped only in space with proper conditions. Finally, we analyze the modulation instability and discuss dark solitary wave propagation for a spin current on the background of a periodic solution. In some special cases, the solution can be expressed as the linear combination of the periodic and soliton solutions.

Soliton solution of continuum magnetization equation in a conducting ferromagnet with a spin-polarized current.

Exact soliton solutions of a modified Landau-Lifshitz equation for the magnetization of conducting ferromagnet in the presence of a spin-polarized current are obtained by means of inverse scattering transformation. From the analytical solution the effects of spin current on the frequency, wave number, and dispersion law of spin wave are investigated. The one-soliton solution indicates obviously current-driven precession and periodic shape variation as well. The inelastic collision of solitons, by which we mean the shape change before and after collision, appears due to the spin current. We, moreover, show that complete inelastic collisions can be achieved by adjusting spectrum and current parameters. This may lead to an potential technique for shape control of spin wave.

Exact soliton solution and inelastic two-soliton collision in a spin chain driven by a time-dependent magnetic field.

We investigate dynamics of exact N-soliton trains in a spin chain driven by a time-dependent magnetic field by means of an inverse scattering transformation. The one-soliton solution indicates obviously the spin precession around the magnetic field and periodic shape variation induced by the time-varying field as well. In terms of the general soliton solutions, N-soliton interaction and particularly various two-soliton collisions are analyzed. The inelastic collision by which we mean the soliton shape change before and after collision appears is generally due to the time-varying field. We, moreover, show that complete inelastic collisions can be achieved by adjusting spectrum and field parameters. This may lead to a potential technique of shape control of soliton.