The issue of whether a thermal gradient acts like a magnetic field or an electric current in the domain wall (DW) dynamics is investigated. Broadly speaking, magnetization control knobs can be classified as energy-driving or angular-momentum driving forces. DW propagation driven by a static magnetic field is the best known example of the former in which the DW speed is proportional to the energy dissipation rate, and the current-driven DW motion is an example of the latter. Here we show that DW propagation speed driven by a thermal gradient can be fully explained as the angular momentum transfer between thermally generated spin current and DW. We found DWplane rotation speed increases as DW width decreases. Both DW propagation speed along the wire and DW-plane rotation speed around the wire decrease with the Gilbert damping. These facts are consistent with the angular momentum transfer mechanism, but are distinct from the energy dissipation mechanism. We further show that magnonic spin-transfer torque (STT) generated by a thermal gradient has both damping-like and field-like components. By analyzing DW propagation speed and DW-plane rotational speed, the coefficient (β) of the field-like STT arising from the nonadiabatic process, is obtained. It is found that β does not depend on the thermal gradient; increases with uniaxial anisotropy K (thinner DW); and decreases with the damping, in agreement with the physical picture that a larger damping or a thicker DW leads to a better alignment between the spin-current polarization and the local magnetization, or a better adiabaticity.
The localization properties are investigated within a transfer matrix formulation. We find that there may exist one extended eigenstate when the rank of the transfer matrix is odd. An edge state in a quantum Hall system is such an example. It is a chiral state that can always carry a current. [5] used this method to study the one-dimensional localization problem. Shapiro generalized the formulation into a high dimensional system [6]. In the Anderson localization model, an electron in a channel can move in two opposite directions due to the time reversal symmetry. The rank of an m-channel transfer matrix is 2m, an even number, because there are two modes on each channel. The transfer matrix method is also used to investigate transport properties of a two-dimensional electron gas under a strong magnetic field, a quantum Hall (QH) system in which the time reversal symmetry is broken. According to a semiclassical model, an electronic state in a strong magnetic field and a smooth potential can be decomposed into a rapid cyclotron motion and a slow drifting motion of its guiding centre. The direction of the drifting motion is unidirectional, i.e., electrons are in chiral states [7]. One can use a so-called Chalker-Coddington (CC) network model to investigate a QH system [8]. In this model, electrons on each link can move in only one direction. Thus there is only one mode on each channel. Consequently, the rank of the transfer matrix in the CC model, which is the number of independent modes, may be odd because there is no restriction on the channel number. This is different from the transfer matrix in the Anderson localization model, whose
The observation of magnetoresistance (MR) varying with the rotation of magnetization in the plane perpendicular to the electric current is an important discovery in spintronics in recent years. The famous conventional anisotropic MR (AMR) says that the resistance of a polycrystalline magnetic material must depend on magnetization component along the current direction only, thus cannot account for this newly observed unusual AMR (UAMR). This UAMR leads to the notion of the spin-Hall MR (SMR) in the famous SMR theory. However, the SMR theory may only explain UAMR observed in heavy-metal/magnetic-insulator bilayers, not other types of bilayers. Here, we present a two-vector theory that can explain not only all existing experiments on the unusual angular dependence of longitudinal and transverse resistivity when the magnetization rotates in three mutually perpendicular planes, but also how three amplitudes of MR angular oscillation are related to each other. The theory is very general and its correctness depends only on the assumption that the magnetization and interfacial field are the only vectors affecting electron transport besides of other scalar variables such as the temperatures and impurities. Experiments that can test this theory against the SMR theory are also proposed.
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