Inverse scattering method for square matrix nonlinear Schr\"odinger equation under nonvanishing boundary conditions

Matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schr\"odinger equation with nonvanishing boundary conditions. It is shown that the initial value problem can be solved exactly. The multi-soliton solution is obtained from the Gel'fand--Levitan--Marchenko equation.Comment: 25 pages, 2 figures; (v2) title changed, typos in equations corrected, sec.3.1 modified and extende

Effects of mechanical rotation on spin currents

We study the Pauli--Schr\"odinger equation in a uniformly rotating frame of reference to describe a coupling of spins and mechanical rotations. The explicit form of the spin-orbit interaction (SOI) with the inertial effects due to the mechanical rotation is presented. We derive equations of motion for a wavepacket of electrons in two-dimensional planes subject to the SOI. The solution is a superposition of two cyclotron motions with different frequencies and a circular spin current is created by the mechanical rotation.Comment: 4 pages, 2 figure

Spin-dependent inertial force and spin current in accelerating systems

The spin-dependent inertial force in an accelerating system under the presence of electromagnetic fields is derived from the generally covariant Dirac equation. Spin currents are evaluated by the force up to the lowest order of the spin-orbit coupling in both ballistic and diffusive regimes. We give an interpretation of the inertial effect of linear acceleration on an electron as an effective electric field and show that mechanical vibration in a high frequency resonator can create a spin current via the spin-orbit interaction augmented by the linear acceleration.Comment: 11 pages,4 figure

Spin–Orbit-Induced Ising Ferromagnetism at a van der Waals Interface:Nano Letters

Magnetocrystalline anisotropy, a key ingredient for establishing long-range order in a magnetic material down to the two-dimensional (2D) limit, is generally associated with spin–orbit interaction (SOI) involving a finite orbital angular momentum. Here we report strong out-of-plane magnetic anisotropy without orbital angular momentum, emerging at the interface between two different van der Waals (vdW) materials, an archetypal metallic vdW material NbSe2 possessing Zeeman-type SOI and an isotropic vdW ferromagnet V5Se8. We found that the Zeeman SOI in NbSe2 induces robust out-of-plane magnetic anisotropy in V5Se8 down to the 2D limit with a more than 2-fold enhancement of the transition temperature. We propose a simple model that takes into account the energy gain in NbSe2 in contact with a ferromagnet, which naturally explains our observations. Our results demonstrate a conceptually new magnetic proximity effect at the vdW interface, expanding the horizons of emergent phenomena achievable in vdW heterostructures