Modification of the Landau-Lifshitz equation in the presence of a spin-polarized current in colossal- and giant-magnetoresistive materials

Abstract

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...

Reversal-mechanism of perpendicular switching induced by an in-plane current

“…All of these results indicate that this type of switching behavior is caused by current-induced domain nucleation and subsequent DW motion and is not resulting from coherent switching [3][4][5] . Because the domain nucleation in these structures can be assisted by other effects [11][12][13][14] , the spin Hall angle calculated from I c by using coherent switching model may be overestimated 4,5 .…”

“…In a normal FM, the currentinduced magnetization instability arises from conventional STTs [11][12][13][14] , but in HM/FM/MO structures, SHT and DMI must also be involved in the domain nucleation process. The investigation of the detailed domain nucleation mechanism in these HM/FM/MO structures is beyond the scope of this paper.…”

“…Therefore, we tend to believe that the spin torques dominate the domain nucleation process. Early STT theories have shown that a large current always induces the instability of a uniform magnetization, and the instability will trigger reversal domain nucleation [11][12][13][14] .…”

“…For the first condition, as shown below, we experimentally demonstrate that, without any external fields, a large current can break a uniform magnetization state by forming 50% ↑ and ↓ domains in HM/FM structures. Generally, the current-induced domain nucleation can be caused by Joule heating and current-induced spin torques [11][12][13][14] . However, by monitoring the sample resistance change during the applied current pulses, we show that the current-induced temperature rise is only several K, which cannot dominate the domain nucleation process.…”

Microwave oscillations of a nanomagnet driven by a spin-polarized current

“…1b include a lead resistance of ~ 6 Ω from high-frequency (50 GHz) probes and a topcontact resistance of ~ 9 Ω. 3 We measure the spectra of microwave power that result from magnetic motions by using a heterodyne mixer circuit 19 (Fig. 1a).…”