Theory of Current-Driven Domain Wall Motion: A Poorman's Approach

A self-contained theory of the domain wall dynamics in ferromagnets under finite electric current is presented. The current is shown to have two effects; one is momentum transfer, which is proportional to the charge current and wall resistivity (\rhow), and the other is spin transfer, proportional to spin current. For thick walls, as in metallic wires, the latter dominates and the threshold current for wall motion is determined by the hard-axis magnetic anisotropy, except for the case of very strong pinning. For thin walls, as in nanocontacts and magnetic semiconductors, the momentum-transfer effect dominates, and the threshold current is proportional to \Vz/\rhow, \Vz being the pinning potential

Current-induced domain wall motion in Rashba spin-orbit system

Current-induced magnetic domain wall motion, induced by transfer of spin transfer effect due to exchange interaction, is expected to be useful for next generation high-density storages. We here show that efficient domain wall manipulation can be achieved by introduction of Rashba spin-orbit interaction, which induces spin precession of conduction electron and acts as an effective magnetic field. Its effect on domain wall motion depends on the wall configuration. We found that the effect is significant for Bloch wall with the hard axis along the current, since the effective field works as $\beta$ or field-like term and removes the threshold current if in extrinsic pinning is absent. For N\'eel wall and Bloch wall with easy axis perpendicular to Rashba plane, the effective field induces a step motion of wall corresponding to a rotation of wall plane by the angle of approximately $\pi$ at current lower than intrinsic threshold. Rashba interaction would therefore be useful to assist efficient motion of domain walls at low current

Diffusive versus local spin currents in dynamic spin pumping systems

Using microscopic theory, we investigate the properties of a spin current driven by magnetization dynamics. In the limit of smooth magnetization texture, the dominant spin current induced by the spin pumping effect is shown to be the diffusive spin current, i.e., the one arising from only a diffusion associated with spin accumulation. That is to say, there is no effective field that locally drives the spin current. We also investigate the conversion mechanism of the pumped spin current into a charge current by spin-orbit interactions, specifically the inverse spin Hall effect. We show that the spin-charge conversion does not always occur and that it depends strongly on the type of spin-orbit interaction. In a Rashba spin-orbit system, the local part of the charge current is proportional to the spin relaxation torque, and the local spin current, which does not arise from the spin accumulation, does not play any role in the conversion. In contrast, the diffusive spin current contributes to the diffusive charge current. Alternatively, for spin-orbit interactions arising from random impurities, the local charge current is proportional to the local spin current that constitutes only a small fraction of the total spin current. Clearly, the dominant spin current (diffusive spin current) is not converted into a charge current. Therefore, the nature of the spin current is fundamentally different depending on its origin and thus the spin transport and the spin-charge conversion behavior need to be discussed together along with spin current generation

Gauge Field Formulation of Adiabatic Spin Torques

Previous calculation of spin torques for small-amplitude magnetization dynamics around a uniformly magnetized state [J. Phys. Soc. Jpn. {\bf 75} (2006) 113706] is extended here to the case of finite-amplitude dynamics. This is achieved by introducing an `` adiabatic'' spin frame for conduction electrons, and the associated SU(2) gauge field. In particular, the Gilbert damping is shown to arise from the time variation of the spin-relaxation source terms in this new frame, giving a new physical picture of the damping. The present method will allow a `` first-principle'' derivation of spin torques without any assumptions such as rotational symmetry in spin space.Comment: 4 pages, 3 figure

Existence of vertical spin stiffness in Landau-Lifshitz-Gilbert equation in ferromagnetic semiconductors

We calculate the magnetization torque due to the spin polarization of the itinerant electrons by deriving the kinetic spin Bloch equations based on the $s$-$d$ model. We find that the first-order gradient of the magnetization inhomogeneity gives rise to the current-induced torques, which are consistent to the previous works. At the second-order gradient, we find an effective magnetic field perpendicular to the spin stiffness filed. This field is proportional to the nonadiabatic parameter $\beta$. We show that this vertical spin stiffness term can significantly modify the domain-wall structure in ferromagnetic semiconductors and hence should be included in the Landau-Lifshitz-Gilbert equation in studying the magnetization dynamics.Comment: 7 pages, 4 figure

Cross -cultural Comparisons of Science Education Reform:Japan and the United States

The results of this study comparing teacher perceptions and observed teacher behaviors for teachers from Japan and the U.S. are attributed to cultural differences, difficulty in interpretation of the practices, or differing degrees of confidence in implementing constructivist practices, or a combination of factors remains to be seen. But, this investigation is but a beginning in terms of successes and failures with science education reform initiatives around the world. Looking at these problems globally may be important to assure that current reforms are successful for all and will stimulate continuous progress

A Quantum Analogue of the Jarzynski Equality

A quantum analogue of the Jarzynski equality is constructed. This equality connects an ensemble average of exponentiated work with the Helmholtz free-energy difference in a nonequilibrium switching process subject to a thermal heat bath. To confirm its validity in a practical situation, we also investigate an open quantum system that is a spin 1/2 system with a scanning magnetic field interacting with a thermal heat bath. As a result, we find that the quantum analogue functions well.Comment: 7 pages, 1 figure; to appear in J. Phys. Soc. Jpn. 69 (2000

Controlled release of neurotrophin-3 and platelet-derived growth factor from fibrin scaffolds containing neural progenitor cells enhances survival and differentiation into neurons in a subacute model of SCI

A consistent problem with stem/neural progenitor cell transplantation following spinal cord injury (SCI) is poor cell survival and uncontrolled differentiation following transplantation. The current study evaluated the feasibility of enhancing embryonic stem cell-derived neural progenitor cell (ESNPC) viability and directing their differentiation into neurons and oligodendrocytes by embedding the ESNPCs in fibrin scaffolds containing growth factors (GF) and a heparin-binding delivery system (HBDS) in a subacute rat model of SCI. Mouse ESNPCs were generated from mouse embryonic stem cells (ESCs) using a 4-/4+ retinoic acid (RA) induction protocol. The ESNPCs were then transplanted as embryoid bodies (EBs, 70% neural progenitor cells), into the subacute model of SCI. ESNPCs (10 EBs per animal) were implanted directly into the SCI lesion, encapsulated in fibrin scaffolds, encapsulated in fibrin scaffolds containing the HBDS, neurotrophin-3 (NT-3) and platelet derived growth factor (PDGF), or encapsulated in fibrin scaffolds with NT-3 and PDGF with no HBDS. We report here that the combination of the NT-3, PDGF and fibrin scaffold (with or without HBDS) enhanced the total number of ESNPCs present in the spinal cord lesion 2 weeks after injury. In addition, the inclusion of the HBDS with growth factor resulted in an increase in the number of ESNPC-derived NeuN positive neurons. These results demonstrate the ability of fibrin scaffolds and the controlled release of growth factors to enhance the survival and differentiation of neural progenitor cells following transplantation into a SCI model

Cross -cultural Comparisons of Science Education Reform:Japan and the United States

The results of this study comparing teacher perceptions and observed teacher behaviors for teachers from Japan and the U.S. are attributed to cultural differences, difficulty in interpretation of the practices, or differing degrees of confidence in implementing constructivist practices, or a combination of factors remains to be seen. But, this investigation is but a beginning in terms of successes and failures with science education reform initiatives around the world. Looking at these problems globally may be important to assure that current reforms are successful for all and will stimulate continuous progress

Macroscopic Quantum Dynamics of a Free Domain Wall in a Ferromagnet

We study macroscopic quantum dynamics of a free domain wall in a quasi-one-dimensional ferromagnet by use of the spin-coherent-state path integral in {\it discrete-time} formalism. Transition amplitudes between typical states are quantitatively discussed by use of {\it stationary-action approximation} with respect to collective degrees of freedom representing the center position and the chirality of the domain wall. It is shown that the chirality may be loosely said to be canonically conjugate to the center position; the latter moves with a speed depending on the former. It is clarified under what condition the center position can be regarded as an effective free-particle position, which exhibits the phenomenon of wave-packet spreading. We demonstrate, however, that in some case the non-linear character of the spin leads to such a dramatic phenomenon of a non-spreading wave packet as to completely invalidate the free-particle analogy. In the course of the discussion, we also point out various difficulties associated with the continuous-time formalism.Comment: 23 pages, REVTEX, 4 figures, submitted to Phys. Rev.