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

Effects of Domain Wall on Electronic Transport Properties in Mesoscopic Wire of Metallic Ferromagnets

We study the effect of the domain wall on electronic transport properties in wire of ferromagnetic 3$d$ transition metals based on the linear response theory. We considered the exchange interaction between the conduction electron and the magnetization, taking into account the scattering by impurities as well. The effective electron-wall interaction is derived by use of a local gauge transformation in the spin space. This interaction is treated perturbatively to the second order. The conductivity contribution within the classical (Boltzmann) transport theory turns out to be negligiblly small in bulk magnets, due to a large thickness of the wall compared with the fermi wavelength. It can be, however, significant in ballistic nanocontacts, as indicated in recent experiments. We also discuss the quantum correction in disordered case where the quantum coherence among electrons becomes important. In such case of weak localization the wall can contribute to a decrease of resistivity by causing dephasing. At lower temperature this effect grows and can win over the classical contribution, in particular in wire of diameter $L_{\perp}\lesssim \ell_{\phi}$, $\ell_{\phi}$ being the inelastic diffusion length. Conductance change of the quantum origin caused by the motion of the wall is also discussed.Comment: 30 pages, 4 figures. Detailed paper of Phys. Rev. Lett. 78, 3773 (1997). Submitted to J. Phys. Soc. Jp

Domain Wall Resistance based on Landauer's Formula

The scattering of the electron by a domain wall in a nano-wire is calculated perturbatively to the lowest order. The resistance is calculated by use of Landauer's formula. The result is shown to agree with the result of the linear response theory if the equilibrium is assumed in the four-terminal case

Geometrically constrained magnetic wall

The structure and properties of a geometrically constrained magnetic wall in a constriction separating two wider regions are investigated theoretically. They are shown to differconsiderably from those of an unconstrained wall, so that the geometrically constrained magnetic wall truly constitutes a new kind of magnetic wall, besides the well known Bloch and Neel walls. In particular, the width of a constrained wall cann become very small if the characteristic length of the constriction is small, as is actually the case in an atomic point contact. This provides a simple, natural explanation for the large magnetoresistance observed in ferromagnetic atomic point contacts.Comment: RevTeX, 4 pages, 4 eps figures; v2: revised version; v3: ref. adde

Permanent current from non-commutative spin algebra

We show that a spontaneous electric current is induced in a nano-scale conducting ring just by putting three ferromagnets. The current is a direct consequence of the non-commutativity of the spin algebra, and is proportional to the non-coplanarity (chirality) of the magnetization vectors. The spontaneous current gives a natural explanation to the chirality-driven anomalous Hall effect.Comment: 7 pages, 4 figures on separate pag

Effect of a Domain Wall on the Conductance Quantization in a Ferromagnetic Nanowire

The effect of the domain wall (DW) on the conductance in a ballistic ferromagnetic nanowire (FMNW) is revisited by exploiting a specific perturbation theory which is effective for a thin DW; the thinness is often the case in currently interested conductance measurements on FMNWs. Including the Hund coupling between carrier spins and local spins in a DW, the conductance of a FMNW in the presence of a very thin DW is calculated within the Landauer-B\"{u}ttiker formalism. It is revealed that the conductance plateaus are modified significantly, and the switching of the quantization unit from $e^2/h$ to ``about $2e^2/h$'' is produced in a FMNW by the introduction of a thin DW. This accounts well for recent observations in a FMNW.Comment: 5 pages, 2 figures, Corrected typos and added reference

Resistivity due to a Domain Wall in Ferromagnetic Metal

The resistivity due to a domain wall in ferromagnetic metallic wire is calculated based on the linear response theory. The interaction between conduction electrons and the wall is expressed in terms of a classical gauge field which is introduced by the local gauge transformation in the electron spin space. It is shown that the wall contributes to the decoherence of electrons and that this quantum correction can dominate over the Boltzmann resisitivity, leading to a decrease of resisitivity by nucleation of a wall. The conductance fluctuation due to the motion of the wall is also investigated. The results are compared with recent experiments.Comment: 9 pages, 3 figure

Dephasing Effects by Ferromagnetic Boundary on Resistivity in Disordered Metallic Layer

The resistivity of disordered metallic layer sandwiched by two ferromagnetic layers at low-temperature is investigated theoretically. It is shown that the magnetic field acting at the interface does not affect the classical Boltzmann resistivity but causes a dephasing among electrons in the presence of the spin-orbit interaction, suppressing the anti-localization due to the spin-orbit interaction. The dephasing turns out to be stronger in the case where the magnetization of the two layers is parallel, contributing to a positive magnetoresistance close to a switching field at low temperature.Comment: 11 pages, 3 figures. Title modified in journal versio