Gen Tatara

Theory of current-driven domain wall motion: spin transfer versus momentum transfer.

We formulate the problem of domain wall dynamics in the presence of electric current, and explore some new features such as current-induced depinning of the wall. We start from a microscopic Hamiltonian with an exchange interaction between conduction electrons and spins of a domain wall With a key observation that the position X and polarization φ0 of the wall are the proper collective coordinates to describe its dynamics, it follows straightforwardly that the electric current affects the wall motion in two different ways, in agreement with Berger’s observation[2]. The first is as a force on X, or momentum transfer, due to the reflection of conduction electrons. This effect is proportional to the charge current and wall resistance, and hence negligible except for very thin walls. The other is as a spin torque (a force on φ0), arising when an electron passes through the wall. Nowadays it is also called as spin transfer [3] between electrons and wall magnetization. This effect is the dominant one for thick walls where the spin of the electron follows the magnetization adiabatically. The motion of a domain wall under a steady current is studied in two limiting cases. In the adiabatic case, we show that even without a pinning force, there is a threshold spin current, j s , below which the wall does not move. This threshold is proportional to K⊥, the hard-axis magnetic anisotropy. Underlying this is that the angular momentum transferred from the electron can be carried by both translational motion (X) and polarization (φ0) of the wall, and the latter can completely absorb the spin transfer if the spin current is small, js < j cr s . The pinning potential V0 for the wall position (X) affects j cr s only if it is very strong, V0 > K⊥/α, where α is the damping parameter in the Landau-Lifshits-Gilbert equation. In most real systems with small α, the threshold would thus be determined by K⊥. Therefore, the critical current for the adiabatic wall will be controllable by the sample shape and, in particular, by the thickness of the film, and does not suffer very much from pinning arising from sample irregularities. This would be a great advantage in application. The wall velocity after depinning is found to be 〈Ẋ〉 ∝ √ (js/j s ) 2 − 1. In the case of thin wall, the wall is driven by the momentum transfer, which is proportional to the charge current j and wall resistivity ρw. The critical current density in this case is given by j ∝ V0/ρw.

Current-induced resonance and mass determination of a single magnetic domain wall.

A magnetic domain wall (DW) is a spatially localized change of magnetization configuration in a magnet. This topological object has been predicted to behave at low energy as a composite particle with finite mass. This particle will couple directly with electric currents as well as magnetic fields, and its manipulation using electric currents is of particular interest with regard to the development of high-density magnetic memories. The DW mass sets the ultimate operation speed of these devices, but has yet to be determined experimentally. Here we report the direct observation of the dynamics of a single DW in a ferromagnetic nanowire, which demonstrates that such a topological particle has a very small but finite mass of 6.6 × 10-23u2009kg. This measurement was realized by preparing a tunable DW potential in the nanowire, and detecting the resonance motion of the DW induced by an oscillating current. The resonance also allows low-current operation, which is crucial in device applications; a DW displacement of 10u2009µm was induced by a current density of 1010u2009Au2009m-2.

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.

Chirality-Driven Anomalous Hall Effect in Weak Coupling Regime

Anomalous Hall effect arising from non-trivial spin configuration (chirality) is studied treating perturbatively the exchange coupling to localized spins. Scattering by normal impurities is included. Chirality is shown to drive locally Hall current and leads to overall Hall effect if there is a finite uniform chirality. This contribution is independent of the conventional spin–orbit contribution and shows distinct low-temperature behavior. In mesoscopic spin glasses, the chirality-induced anomalous Hall effect is expected below the spin–glass transition temperature. Measurement of the Hall coefficient would be useful in experimentally confirming the chirality ordering.

Ballistic and diffuse transport through a ferromagnetic domain wall

We study transport through ballistic and diffuse ferromagnetic domain walls in a two-band Stoner model with a rotating magnetization direction. For a ballistic domain wall, the change in the conductance due to the domain wall scattering is obtained from an adiabatic approximation valid when the length of the domain wall is much longer than the Fermi wavelength. In diffuse systems, the change in the resistivity is calculated using a diagrammatic technique to the lowest order in the domain-wall scattering and taking into account spin dependent scattering lifetimes and screening of the domain-wall potential.

Magnetic relaxation in Ni wires

Abstract The magnetic relaxation in Ni wires has been investigated using a SQUID magnetometer. The magnetization M exhibited logarithmic dependence on time. The distribution of energy barriers was estimated from the temperature dependence of magnetic viscosity S = d M /d(log t ). Thermal excitation explains the field dependence of S - T curves except below 20 K. Below 20 K, macroscopic quantum tunneling and/or the interaction between Ni wires must be considered.

Anomalous Hall Effect and Skyrmion Number in Real and Momentum Spaces

We study the anomalous Hall effect (AHE) for the double exchange model with the exchange coupling | J H | being smaller than the bandwidth | t | for the purpose of clarifying the following unresolv...

Permanent current from noncommutative spin algebra

We show that a spontaneous electric current is induced in a nanoscale conducting ring just by attaching three ferromagnets. The current is a direct consequence of the noncommutativity of the spin algebra, and is proportional to the noncoplanarity (chirality) of the magnetization vectors. The spontaneous current gives a natural explanation to the chirality-driven anomalous Hall effect.

DOMAIN WALL RESISTIVITY BASED ON A LINEAR RESPONSE THEORY

The resistivity due to a domain wall in a ferromagnetic metal is calculated based on a linear response theory. The scattering by impurities is taken into account. The electron-wall interaction is derived from the exchange interaction between the conduction electron and the magnetization by use of a local gauge transformation in the spin space. This interaction is treated perturbatively to the second order. The classical (Boltzmann) contribution from the wall scattering turns out to be negligiblly small if the wall is thick compared with the fermi wavelength. In small contacts a large classical domain wall resistance is expected due to a thin wall trapped in the constriction. In the dirty case, where quantum coherence among electrons becomes important at low temperature, spin flip scattering caused by the wall results in dephasing and hence suppresses weak localization. Thus the quantum correction due to the wall can lead to a decrease of resistivity. This effect grows rapidly at low temperature where the ...We study the effect of the domain wall on electronic transport properties in wire of ferromagnetic 3

From ballistic to non-ballistic magnetoresistance in nanocontacts: theory and experiments

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