Electrons have a charge and a spin, but until recently these were considered separately. In classical electronics, charges are moved by electric fields to transmit information and are stored in a capacitor to save it. In magnetic recording, magnetic fields have been used to read or write the information stored on the magnetization, which 'measures' the local orientation of spins in ferromagnets. The picture started to change in 1988, when the discovery of giant magnetoresistance opened the way to efficient control of charge transport through magnetization. The recent expansion of hard-disk recording owes much to this development. We are starting to see a new paradigm where magnetization dynamics and charge currents act on each other in nanostructured artificial materials. Ultimately, 'spin currents' could even replace charge currents for the transfer and treatment of information, allowing faster, low-energy operations: spin electronics is on its way.

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The emergence of spin electronics in data storage

The recent discovery that a spin-polarized electrical current can apply a large torque to a ferromagnet, through direct transfer of spin angular momentum, offers the possibility of manipulating magnetic-device elements without applying cumbersome magnetic fields. However, a central question remains unresolved: what type of magnetic motions can be generated by this torque? Theory predicts that spin transfer may be able to drive a nanomagnet into types of oscillatory magnetic modes not attainable with magnetic fields alone, but existing measurement techniques have provided only indirect evidence for dynamical states. The nature of the possible motions has not been determined. Here we demonstrate a technique that allows direct electrical measurements of microwave-frequency dynamics in individual nanomagnets, propelled by a d.c. spin-polarized current. We show that spin transfer can produce several different types of magnetic excitation. Although there is no mechanical motion, a simple magnetic-multilayer structure acts like a nanoscale motor; it converts energy from a d.c. electrical current into high-frequency magnetic rotations that might be applied in new devices including microwave sources and resonators.

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

http://files.janapv.webnode.cz/200000097-8a03f8afdf/ex_bias_nano.pdf

Exchange bias in nanostructures

https://ralphgroup.lassp.cornell.edu/papers/JMMM-320-1190-2008.pdf

Spin transfer torques

The mutual dependence of spin-dependent conduction and magnetization dynamics of ferromagnets provides the key mechanisms in various spin-dependent phenomena. We compute the response of the conduction electron spins in a spatial and time varying magnetization M(r,t) in the time-dependent semiclassical transport theory. We show that the induced nonequilibrium conduction spin density in turn generates four spin torques acting on the magnetization-with each torque playing a different role in magnetization dynamics. By comparing with recent theoretical models, we find that one of these torques which has not been previously identified is crucial to consistently interpreting experimental data on domain wall motion.

Roles of nonequilibrium conduction electrons on the magnetization dynamics of ferromagnets.

We propose a generalized stochastic Landau-Lifshitz equation and its corresponding Fokker-Planck equation for the magnetization dynamics in the presence of spin-transfer torques. Since the spin-transfer torque can pump a magnetic energy into the magnetic system, the equilibrium temperature of the magnetic system is ill defined. We introduce an effective temperature based on a stationary solution of the Fokker-Planck equation. In the limit of high-energy barriers, the law of thermal agitation is derived. We find that the N\'eel-Brown relaxation formula remains valid as long as we replace the temperature by an effective one that is linearly dependent on the spin torque. We carry out the numerical integration of the stochastic Landau-Lifshitz equation to support our theory. Our results agree with existing experimental data.

Thermally assisted magnetization reversal in the presence of a spin-transfer torque

The magnetization reversal and dynamics of a spin valve pillar, whose lateral size is $64\ifmmode\times\else\texttimes\fi{}64{\mathrm{nm}}^{2},$ are studied by using micromagnetic simulation in the presence of spin-transfer torque. Spin torques display both characteristics of magnetic damping (or antidamping) and of an effective magnetic field. For a steady-state current, both $M\ensuremath{-}I$ and $M\ensuremath{-}H$ hysteresis loops show unique features, including multiple jumps, unusual plateaus, and precessional states. These states originate from the competition between the energy dissipation due to Gilbert damping and the energy accumulation due to the spin torque supplied by the spin current. The magnetic energy oscillates as a function of time even for a steady-state current. For a pulsed current, the minimum width and amplitude of the spin torque for achieving current-driven magnetization reversal are quantitatively determined. The spin torque also shows very interesting thermal activation that is fundamentally different from an ordinary damping effect.

Magnetization dynamics with a spin-transfer torque

In a first approximation, known as the adiabatic process, the direction of the spin polarization of currents is parallel to the local magnetization vector in a domain wall. Thus the spatial variation of the direction of the spin current inside the domain wall results in an adiabatic spin-transfer torque on the magnetization. We show that domain-wall motion driven by this spin torque has many unique features that do not exist in the conventional wall motion driven by a magnetic field. By analytically and numerically solving the Landau-Lifshitz-Gilbert equation along with the adiabatic spin torque in magnetic nanowires, we find that the domain wall has its maximum velocity at the initial application of the current but the velocity decreases to zero as the domain wall begins to deform during its motion. We have computed domain-wall displacement and domain-wall deformation of nanowires, and concluded that the spin torque based on the adiabatic propagation of the spin current in the domain wall is unable to maintain wall movement. We also introduce the concept of domain-wall inductance to characterize the capacity of the spin-torque-induced magnetic energy stored in a domain wall. In the presence of domain-wall pinning centers, we construct a phase diagram for the domain-wall depinning by the combined action of the magnetic field and the spin current.

Domain-wall dynamics driven by adiabatic spin-transfer torques

Current-driven vortex wall dynamics is studied by means of a two-dimensional analytical model and micromagnetic simulation. By constructing a trial function for the vortex wall in the magnetic wire, we analytically solve for domain wall velocity and deformation in the presence of the current-induced spin torque. A critical current for the domain wall transformation from the vortex wall to the transverse wall is calculated. A comparison between the field- and current-driven wall dynamics is carried out. Micromagnetic simulations are performed to verify our analytical results.

Current-driven vortex domain wall dynamics by micromagnetic simulations

We present analytical and numerical calculations of dynamic magnetization states of a spin valve in the presence of dc and ac currents. Three distinct dynamic phases, synchronization, modification, and chaos, are identified within the experimental parameter space. A particularly interesting result is the appearance of the synchronization-chaos boundaries. In the region of synchronization, our results agree with experiments. In the modification and chaos regions, we predict experimentally observable power spectra.

Z. Li

Papers

Thermally assisted magnetization reversal in the presence of a spin-transfer torque

Magnetization dynamics with a spin-transfer torque

Domain-wall dynamics driven by adiabatic spin-transfer torques

Current-driven vortex domain wall dynamics by micromagnetic simulations

Dynamic magnetization states of a spin valve in the presence of dc and ac currents : Synchronization, modification, and chaos