We derive a continuum equation for the magnetization of a conducting ferromagnet in the presence of a spin-polarized current. Current effects enter in the form of a topological term in the Landau-Lifshitz equation . In the stationary situation the problem maps onto the motion of a classical charged particle in the field of a magnetic monopole. The spatial dependence of the magnetization is calculated for a one-dimensional geometry and suggestions for experimental observation are made. We also consider time-dependent solutions and predict a spin-wave instability for large currents.Phenomena associated with spin-polarized currents in layered materials and in Mn-oxides have attracted high interest recently. Efforts are strongly concentrated on theoretical and experimental investigation of large magnetoresistance, which is of great value for future applications. Examples of the effect are GMR in layered materials (see review [1]), spin valve effect for a particular case of a three-layer sandwich and CMR in the manganese oxides (see review [2]).The dependence of resistivity on magnetic field is explained conceptually in two steps: first the magnetic field changes the magnetic configuration of the material and that in turn influences the current. Of course, as for any interaction there must be a back-action of the current on the magnetic structure. The existence of such backaction was explored in [3,4]. Several current-controlled micro-devices utilizing this principle were proposed [3]. In both papers layered structures with magnetization being constant throughout the magnetic layers were considered. In the present paper we derive the equations for a continuously changing magnetization in the presence of a spin-polarized current. This equation takes the form of a Landau-Lifshitz equation with an additional topological term, and admits a useful analogy with a mechanical system. We discuss several solutions in one-dimensional geometries. Our equations also can be viewed as a continuum generalization of [3,4] for layer thickness going to zero.Consider a current propagating through a conducting ferromagnet. Conducting electrons are viewed as free electrons interacting only with local magnetization M. The motion of each individual electron is governed by the Schroedinger equation with a term J H σM, where J H is the value of the Hund's rule coupling or in general of the local exchange. Since spin-up electrons have lower energy a nonzero average spin of conducting electrons (1/2) σ develops. An angular momentum density (h/2) σ is then carried with the electron current so we have a flux of angular momentum. This leads to a nonzero average torque acting on the magnetization which can deflect it from the original direction (see figure 1). metal S x y z j n(0) ν θ φ Magnet Normal FIG. 1. Experimental setting: spin-polarized current enters a half-infinite magnet from the left. Originally the magnetization is aligned along the easy-axis ν z. However if the incoming electrons are spin-polarized in a different direction, their inter...
The superconducting critical temperature (T(c)) of ferromagnet-superconductor-ferromagnet systems has been predicted to exhibit a dependence on the magnetization orientation of the ferromagnetic layers such that T(AP)(c)>T(P)(c) for parallel (P) and antiparallel (AP) configurations of the two ferromagnetic layers. We have grown CuNi/Nb/CuNi films via magnetron sputtering and confirmed the theoretical prediction by measuring the resistance of the system as a function of temperature and magnetic field. We find an approximately 25% resistance drop occurs near T(c) in Cu0.47Ni0.53(5 nm)/Nb(18)/CuNi(5) when the two CuNi layers change their magnetization directions from parallel to antiparallel, whereas there is no corresponding resistance change in the normal state.
We calculate the effect of a Dirac point ͑a conical singularity in the band structure͒ on the transmission of monochromatic radiation through a photonic crystal. The transmission as a function of frequency has an extremum near the Dirac point, depending on the transparencies of the interfaces with free space. The extremal transmission T 0 = ⌫ 0 W / L is inversely proportional to the longitudinal dimension L of the crystal ͑for L larger than the lattice constant and smaller than the transverse dimension W͒. The interface transparencies affect the proportionality constant ⌫ 0 , and they determine whether the extremum is a minimum or a maximum, but they do not affect the "pseudodiffusive" 1 / L dependence of T 0 .
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