# Electrical and mechanical magnetization torques

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## Abstract

Only charge degree of freedom is utilized in most electronic devices. The use of the spin degree of freedom is relatively recent. The discovery of the Giant Magnetoresistance (GMR) effect initiated the development of magnetoelectronics - the field that studies effects on electron transport involving the spin degree of freedom. GMR is a very large change in electrical resistance observed in ferromagnet/nonmagnet multilayer structures when the relative orientations of the magnetizations in ferromagnetic layers change as a function of applied field. The development of magnetoelectronics was very rapid leading to useful applications already within several years. For example, the GMR effect is presently routinely used to sense magnetic fields of data in read heads of magnetic hard disk drives. Whereas in GMR the relative direction of the magnetizations defines the current flowing through the system, an opposite effect of current on the magnetizations is also possible. Slonczewski predicted this effect - the spin transfer torque. In a ferromagnet/normal metal/ferromagnet structure with one magnetization free and the other fixed, the magnetization dynamics of the free layer can be driven by a current through the system as a result of spin-transfer torques. The magnetization dynamics in small magnetic clusters and films is a basic problem of condensed matter physics and is also important for applications: the spin-transfer effect may find applications in the so-called magnetic random access memories in which the direction of the magnetization is used to store the data and the rewriting process can be done by spin-transfer torques. Magnetoelectronics is a rapidly developing field at the moment and this thesis deals with some aspects of it related to magnetization dynamics and torques. The main subject of the thesis is torque, i.e. a change of angular momentum in time. We deal with torques that arise in spin valves and small magnetic cantilevers; spin-transfer torques in the former and magnetomechanical torques in the latter case. In order to describe spin-transfer torques we develop an approach based on the diffusion equation with quantum mechanical boundary conditions. With some simplifications this leads to magnetoelectronic circuit theory. This allows us to treat arbitrary diffuse spin valves and other devices. Magnetomechanical torques arise in small magnetic cantilevers. An example is a cantilever with one end fixed and the other covered with a magnetic film. It is important that the magnetic film has strong crystal or shape magnetic anisotropy, which provides coupling between vibrations and the magnetization dynamics. The anisotropy in the film leads to magnetomechanical torques that affect both the magnetization dynamics and the mechanical motion of the cantilever. This can open new possibilities for Magnetic Resonance Force Microscopy in imaging and sensor applications. In Chapter 1 of this thesis we introduce the basic concepts of magnetoelectronics such as the spin-polarized current, the GMR effect, the spin-transfer torque and the magnetization dynamics. We introduce also magnetomechanical torques and analyze an example of a nanomechanical system that can be used for detecting magnetomechanical torques. We introduce magnetoelectronic circuit theory that can be used to describe spin-transfer torques. Furthermore, we give a short account of the derivation of the Landau-Lifshitz-Gilbert equation. In generalized form this equation allows us to describe the magnetization dynamics as a result of magnetic fields and/or spin-transfer torques. Finally, applications of the magnetomechanical torques in Magnetic Resonance Force Microscopy is mentioned, and a design for a novel "spin-transfer motor" is proposed. In Chapter 2, we apply the diffusion equation to electronic transport in disordered ferromagnet (F) - normal metal (N) spin valves and show its equivalence to the magnetoelectronic circuit theory. The spin-transfer torque appears naturally in the diffusion approach from the boundary conditions at N-F interfaces; spin currents polarized perpendicular to the magnetization are absorbed at the interface of the ferromagnet. We obtain analytical expressions for the spin transfer torque and the angular magnetoresistance in asymmetric F1-N-F2 spin valves. The effect of spin-flip processes in the normal metal and ferromagnet constituents are obtained analytically as well. In an N1-F1-N2-F2-N3 system, spin-flip in the center metal N2 reduces the spin-transfer, whereas spin-flip in the outer normal metals N1 and N3 can increase it by effectively enhancing the spin polarization of the device. In Chapter 3, magnetoelectronic circuit theory is employed to analyze perpendicular spin valves with ultra-thin ferromagnetic layers. We consider two finite size effects in transport through magnetic multilayers. The first effect arises when the magnetic layer thickness in spin valves becomes of the order or smaller than the spin-flip diffusion length. In this case the spin valve can become effectively asymmetric, which affects the transport properties and spin-transfer torques. The second effect arises in magnetic layers with thickness approaching the magnetic coherence length. In this case spin currents polarized perpendicular to the magnetization can pass through the thin ferromagnetic layer (the coherence length in transition metals is of the order of several atomic layers; much smaller than the spin-diffusion length and mean-free path). We investigate both effects on the angular magnetoresistance (aMR) and spin transfer torque. The spin-flip diffusion length in the ferromagnet as well as the interface spin-mixing conductance are determined by a fit to recent aMR experiments. At the end, we propose a three terminal device to measure the ferromagnetic coherence length. In Chapter 4, we study a small magnetic cantilever (e.g. a Si cantilever covered by a magnetic film or an entirely ferromagnetic cantilever). Such cantilevers can serve for observation of magnetomechanical torques, which, for example, leads to hybrid magnetovibrational ({}``polaritonic{}'') modes and line splittings in ferromagnetic resonance spectra. Magnetomechanical torques can even cause a complete magnetization reversal. It is still very difficult to make nanoelectromechanical systems working at microwave frequencies, but many new possibilities arise. We propose to build nanoelectromechanical systems propelled by spin-transfer and magnetomechanical torques. Such systems can extend the limits of detecting and exciting motion at the nanoscale and can serve as electric transducers of nanomechanical motion.