Spin-Motive Forces and Current-Induced Torques in Ferromagnets

In metallic ferromagnets, the spin-transfer torque and spin-motive force are known to exhibit a reciprocal relationship. Recent experiments on ferromagnets with strong spin-orbit coupling have revealed a rich complexity in the interaction between itinerant charge carriers and magnetization, but a full understanding of this coupled dynamics is lacking. Here, we develop a general phenomenology of the two reciprocal processes of charge pumping by spin-motive forces and current-driven magnetization dynamics. The formalism is valid for spin-orbit coupling of any strength and presents a systematic scheme for deriving all possible torque and charge-pumping terms that obey the symmetry requirements imposed by the point group of the system. We demonstrate how the different charge pumping and torque contributions are connected via the Onsager reciprocal relations. The formalism is applied to two important classes of systems: isotropic ferromagnets with non-uniform magnetization and homogeneous ferromagnets described by the point group $C_{2v}$.Comment: Final version accepted by Physical Review

Twists in Ferromagnetic Monolayers With Trigonal Prismatic Symmetry

Two-dimensional materials such as graphene or hexagonal boron nitride are indispensable in industry. The recently discovered 2D ferromagnetic materials also promise to be vital for applications. In this work, we develop a phenomenological description of non-centrosymmetric 2D ferromagnets with trigonal prismatic crystal structure. We chose to study this special symmetry group since these materials do break inversion symmetry and therefore, in principle, allow for chiral spin structures such as magnetic helices and skyrmions. However, unlike all non-centrosymmetric magnets known so far, we show that the symmetry of magnetic trigonal prismatic monolayers neither allow for an internal relativistic Dzyaloshinskii-Moriya interaction (DMI) nor a reactive spin-orbit torque. We demonstrate that the DMI only becomes important at the boundaries, where it modifies the boundary conditions of the magnetization and leads to a helical equilibrium state with a helical wavevector that is inherently linked to the internal spin orientation. Furthermore, we find that the helical wavevector can be electrically manipulated via dissipative spin-torque mechanisms. Our results reveal that 2D magnets offer a large potential for unexplored magnetic effects.Comment: 5 pages, 3 figure

Nonlocal Damping of Helimagnets in One-Dimensional Interacting Electron Systems

We investigate the magnetization relaxation of a one-dimensional helimagnetic system coupled to interacting itinerant electrons. The relaxation is assumed to result from the emission of plasmons, the elementary excitations of the one-dimensional interacting electron system, caused by slow changes of the magnetization profile. This dissipation mechanism leads to a highly nonlocal form of magnetization damping that is strongly dependent on the electron-electron interaction. Forward scattering processes lead to a spatially constant damping kernel, while backscattering processes produce a spatially oscillating contribution. Due to the nonlocal damping, the thermal fluctuations become spatially correlated over the entire system. We estimate the characteristic magnetization relaxation times for magnetic quantum wires and nuclear helimagnets.Comment: Final version accepted by Physical Review

The Administration of the Counseling Program in the Junior High Schools of Yakima, Washington

It was the purpose of this study to (1) establish the need for a sound counseling program in the junior high school; (2) indicate difficulties found when the counseling program serves the administrator rather than the students; and (3) offer positive recommendations for administration of a counseling program of specific value to junior high school students in Yakima, Washington

Composite Topological Excitations in Ferromagnet-Superconductor Heterostructures

We investigate the formation of a new type of composite topological excitation -- the skyrmion-vortex pair (SVP) -- in hybrid systems consisting of coupled ferromagnetic and superconducting layers. Spin-orbit interaction in the superconductor mediates a magnetoelectric coupling between the vortex and the skyrmion, with a sign (attractive or repulsive) that depends on the topological indices of the constituents. We determine the conditions under which a bound SVP is formed, and characterize the range and depth of the effective binding potential through analytical estimates and numerical simulations. Furthermore, we develop a semiclassical description of the coupled skyrmion-vortex dynamics and discuss how SVPs can be controlled by applied spin currents.Comment: Final version accepted by Physical Review Letters; 9 pages, 5 figure