Session Y15: Focus Session: Spins in Metals: Spin Torque Theory, Spin Dependent Transport

Newtonian reciprocality between spinmotive forces (SMF) and spin-torque-transfer (STT)

An SMF and the STT effect are reflected in definitions $$ \vec p = m\vec v + e\vec A_s \ \ \ \ \ {\rm and } \ \ \ \ \ H = H_0+e\Phi_s + eA_{0s}, $$ valid beyond the adiabatic approximation, where the momentum $m\vec v$ is mechanical, while $\vec p$ is that conjugate to the position $\vec r$, $H$ is the full Hamiltonian while $H_0$ is that for uniform magnet. Here $(\vec A_s, A_{0s})$ is the four vector which reflects the {\it linear\/} momentum of the magnetic system. The spin magnetic and electric fields $$ B_i = - \frac{im^2}{\hbar}\epsilon_{ijk}[v_j,v_k]\ \ \ \ {\rm and} \ \ \ \ E_i = - \frac{im^2}{\hbar} [v_i,v_0]; \ \ \ \ i = \{x,y,z\} $$ where $i\partial_t = mv_0 + e A_0$, and involve commutators. The Landau-Lfttshitz equations are an {\it emergent}. They correspond to $$ [S_z, (H_0+ e\Phi_s + eA_{0s})] = 0 $$ as required to separate the {\it slow\/} magnetic and {\it fast\/} electronic degrees of freedom. E.g. $ L = (enA \dot z - \dot q)\frac{\hbar}{e} \phi + g \mu_B B nAx - q{\mathcal E} $ is the Lagrangian for simple domain wall connected to a battery emf ${\mathcal E}$. SMF-SST reciprocality reflects Newtonian third law and {\it not\/} an Onsager relationship between transport coefficients. Experiment for spin-valves and MTJs will be reviewed.   

Theoretical investigation of the dynamics of a magnetic bilayer in the presence of spin transfer torque

Magentoelectronic nanodevices, such as magnetic memory cells and spin torque nano-oscillators, generally utilize at least two magnetic layers, the ``reference'' and the ``free'' layer. While most previous studies focused only on the behaviors of the ``free'' layer, the dynamics of the ``reference'' layer can also be important due to the coupling between the layers. We utilize Landau-Lifshitz-Slonczewski equations in the macrospin approximation to analyze the dynamics of a magnetic bilayer driven by a dc current. We show that even in the absence of magnetic or RKKY interactions, coupling between the layers is efficiently mediated by the spin transfer torque. We use an axially symmetric approximation to derive an analytical stability condition for the bilayer. The stability is determined by the physical characteristics of the bilayer and two control parameters - the dc current and the external time-independent magnetic field. Additionally, we use an averaging technique to find synchronized precessional motions of the two nanomagnets. Finally, we show that for some conditions, the dynamics of the bilayer becomes chaotic. Such chaotic dynamics is prohibited for a single macrospin due to the limitations imposed by the dimensionality of the system.   

Interplay between conduction electron spin current and magnon spin current

Spin current is a flow of angular momentum that can be carried by conduction electrons as well as magnons. In conducting ferromagnets, both electron spin currents and magnon currents are present. By using a semiclassical description for conduction electrons and magnons, we evaluate the distribution functions of the non-equilibrium electrons and magnons in the presence of electron-magnon interactions. In some interesting limiting cases, we have derived novel diffusion equations for both electrons and magnons. We then apply our formalisms to study the spin currents for various bilayer and trilayer systems. In particular, we predict how an electron spin current in a metallic layer can be converted into a pure magnon current in a ferromagnetic insulator layer at interface. We also discuss possible experimental realizations for non-equilibrium magnon currents. \newline   

A Unified Quantum Theory of Spin Transfer Torque and Electron Transport in Magnetic Nanostructures

Dynamical control of nanoscale magnetization by spin-polarized current has attracted intensive studies due to its vast potential applications in spintronics. The magnetization dynamics driven by spin transfer torque is usually described by the semiclassical theory, where the quantum nature of the magnet is neglected. Here, we present a unified theory which describes the magnetization and the spin-polarized electrons at the full quantum level. The quantum state of the magnetization is given by the coherent state in angular momentum space, and is driven by the continuous scatterings with the electrons in the stochastic nature. Based on this picture, the Monte Carlo simulation is applied to get the mean trajectory and fluctuations of the magnetization, and also the electric current and the current shot noise. We also analyze the different sources which contribute to the magnetization noise and current noise, and show that the quantum noise due to the scattering can be comparable to the thermal noise at low temperature. An analytic theory is also formulated in terms of the density matrix technique. We obtain the master equation of the density matrix of the magnet driven by spin transfer torque, and find that it becomes a Fock-Planck equation in the coherent representation. Solutions from this approach is highly consistent with the results from the Monte Carlo method. We forsee that our theory will play an important role when the quantum nature of the nanomaget emerges in the spintronics devices. For references, see [1] Yong Wang and L.J. Sham, Quantum Dynamics of a Nanomagnet driven by Spin-Polarized Current, arxiv : 1106.2359. [2] Yong Wang and L.J. Sham, A Quantum Theory of Spin Transfer Torque, to be submitted.   

Spin-population inversion in magnetic point contacts under non-equilibrium conditions

The creation of a novel type of spin-based electronics is one of the most intensively researched topics in current solid-state physics. The unifying characteristics in this advancing field is that the spin degree of freedom of the electron rather than its charge is exploited to achieve a specific device functionality. Recently, theoretical predictions suggest that spin-inversion in metallic point contacts under strong non-equilibrium conditions may enable the design of novel types of radiation sources. These radiation sources are highly tunable and of giant intensity compared to cutting-edge semiconductor devices, due to the much larger electron density in metals. Moreover, the accessible frequency range covers both, microwave (GHz) and THz radiation. Especially the later one is of great interest, since up to date there is no miniaturized, high intensity THz source available. Therefore, the experimental demonstration of this lasing effect in metallic systems is an important breakthrough in solid state physics. Presently the concept of spin-flip lasing in magnetic point contacts rests on theoretical predictions and first proof of principle studies. Herein we present detailed investigations on the magneto-transport properties of magnetic herterostructures and -point contacts. In particular, we study the complex interplay between magnetization, current density and the influence of high frequency (GHz and THz) fields on the magneto-transport properties of magnetic point contacts. The results illustrate that a successful spin-population inversion can be detected via transport spectroscopy.   

Two-channel resonant tunneling in the presence of spin-orbit coupling

We study resonant tunneling through a pair of localized states independently coupled to two-dimensional electron gas (2DEG) in the leads. The shape of tunneling conductance is determined by the coherent coupling of localized states via electron continuum in the leads. We show that spin-orbit coupling (Rashba and Dresselhaus) in 2DEG leads to a splitting of the narrow (subtunneling) peak by the amount proportional to spin-orbit coupling constant. The conductance lineshape is highly sensitive to the magnitude and orientation of in-plane magnetic field.   

Non-equilibrium coherent potential approximation for electron transport

Treatment of disorder in extended systems presents essential difficulties because the disorder breaks the periodicity of the system. The coherent potential approximation (CPA) solves this problem by replacing the disordered medium with a periodic effective medium [1]. However, calculating the electron current within CPA requires summing scattering diagrams to infinite order, the so called vertex corrections. In this work we reformulate CPA for non-equilibrium electron transport (NE-CPA). This approach, based on the non-equilibrium Green function formalism, provides an efficient and precise way to solve the transport problems in the presence of disorder. We demonstrate that the NE-CPA current is equivalent to the CPA current with vertex corrections to infinite order. [1] B. Velicky, Phys. Rev. 184, 614 (1969).   

Semiclassical dynamics of Bloch electrons to second order in electromagnetic fields

Berry curvature appears in the semi-classical theory of Bloch electrons already to first order in electromagnetic fields, resulting in profound modification of the carrier velocity and phase space density of states. Here we derive the equations of motion for the physical position and crystal momentum to second order in the fields. The dynamics still has a Hamiltonian structure, albeit with noncanonical Poisson brackets between the physical variables. We are able to expand both the carrier energy and the Poisson brackets to second order in the fields with terms of clear physical meaning. To demonstrate the utility of our theory, we obtain with much ease the electromagnetic response and orbital magnetic susceptibility.   

Zero bias STS Kondo anomalies of Co impurities on Cu surfaces: do ab initio calculations work?

Transition metal atoms such as Co on Cu (111), (100), and (110) surfaces produce STS I-V spectra showing different zero bias Kondo anomalies [1] but these differences have been neither quantitatively predicted nor fully explained theoretically. We apply to this problem the DFT+NRG scheme of Lucignano et al [2], where one solves by NRG an Anderson model built from ab initio phase shifts provided by DFT. For Co/Cu(100) and Co/Cu(110) our calculations describe correctly the experimental trend of Kondo temperatures, and fairly the lineshapes too. By contrast, they fail to describe Co/Cu(111) where in particular the anti-lorentzian lineshape found in experiment remains unexplained. This failure underscores the role of surface states, probably relevant for Co/Cu(111) [3] but not correctly described by our thin slab calculations. Future efforts to quantitatively include Kondo screening by surface states are therefore called for. 1. N. Knorr et al PRL 88, 096804 (2002); M. Ternes et al 2009 J. Phys.: Cond. Matt. 21, 053001 (2009); A. Gumbsch et al PRB81, 165420 (2010). 2. P. Lucignano et al Nature Mat. 8, 563 (2009); P.P. Baruselli et al, Physica E, doi:10.1016/j.physe.2011.05.005. 3. C. Lin et al. PRB 71, 035417 (2005).   

Linear magnetoresistance as a Berry phase effect

Conventional theory of charge carrier dynamics in metals and semiconductors predicts a quadratic field dependence in the magnetoresistance (MR) in the weak field limit. A linear dependence is usually explained as a quantum effect known as weak localization. However, in systems with time reversal symmetry breaking, a linear dependence can be observed even above room temperature, where quantum coherence is absent. Here we show that linear MR can arise from the Berry curvature modified semiclassical dynamics of the charge carriers, and evaluate its magnitude in several model systems and make preliminary comparisons with experimental results.   

Theory of conducting electrons in textured antiferromagnets

The dynamics of conducting electrons in antiferromagnetic texture is shown to exhibit an SU(2) geometric phase in the iso-spin that characterizes a locked spin-sublattice degree of freedom. The iso-spin rotation is purely geometrical and can be expressed in terms of the flux of a novel Berry curvature jointing the real and momentum space, a crucial quantity that has been overlooked in conventional transport theory. We provide an example of one dimensional domain wall, where the iso-spin rotation is topologically quantized. Scattering by skyrmion centers in two dimensions are also discussed, where a Mott like scattering of the iso-spins is predicted.   

Exchange field induced large magnetoresistance in the correlated insulator phase of ultrathin Beryllium films

We present a detailed study of low-temperature magnetotransport properties of ultrathin, amorphous Be films in the EuS/Be bilayers. Significant magnetoresistance (MR) of pure insulating Be films can only be observed in fairly high magnetic field ( $> \quad \sim $5 tesla ), but by depositing insulating ferromagnetic EuS on top of Be film, one can obtain the same value of MR at low magnetic field ($\sim $ 0.2 tesla). We argue that this shift of MR from high field to low field may be caused by the exchange field in the Be component of Be/EuS bilayers.