Spin-Torque Driven Magnetization Dynamics: Micromagnetic Modelling

In this paper we present an overview of recent progress made in the understanding of the spin-torque induced magnetization dynamics in nanodevices using mesoscopic micromagnetic simulations. We first specify how a spin-torque term may be added to the usual Landau-Lifshitz-Gilbert equation of magnetization motion and detail its physical meaning. After a brief description of spin-torque driven dynamics in the macrospin approximation, we discuss the validity of this approximation for various experimentally relevant geometries. Next, we perform a detailed comparison between accurate experimental data obtained from nanopillar devices and corresponding numerical modelling. We show that, on the one hand, many qualitatively important features of the observed magnetization dynamics (e.g., non-linear frequency shift and frequency jumps with increasing current) can be satisfactory explained by sophisticated micromagnetic models, but on the other hand, understanding of these experiments is still far from being complete. We proceed with the numerical analysis of point-contact experiments, where an even more complicated magnetization dynamics is observed. Simulations reveal that such a rich behaviour is due to the formation of several strongly non-linear oscillation modes. In the last part of the paper we emphasize the importance of sample characterization and conclude with some important remarks concerning the relation between micromagnetic modelling and real experiments.Comment: Submitted to "Current Perspectives" on spin-transfer torque phenomena (edited by Dan Ralph and Mark Stiles), to be published in Journal of Magnetism and Magnetic Material

'Hole-digging' in ensembles of tunneling Molecular Magnets

The nuclear spin-mediated quantum relaxation of ensembles of tunneling magnetic molecules causes a 'hole' to appear in the distribution of internal fields in the system. The form of this hole, and its time evolution, are studied using Monte Carlo simulations. It is shown that the line-shape of the tunneling hole in a weakly polarised sample must have a Lorentzian lineshape- the short-time half-width $\xi_o$ in all experiments done so far should be $\sim E_0$, the half-width of the nuclear spin multiplet. After a time $\tau_o$, the single molecule tunneling relaxation time, the hole width begins to increase rapidly. In initially polarised samples the disintegration of resonant tunneling surfaces is found to be very fast.Comment: 4 pages, 5 figure

Magnonic Metamaterials

A large proportion of the recent growth of the volume of electromagnetics research has been associated with the emergence of so called electromagnetic metamaterials1 and the discovered ability to design their unusual properties by tweaking the geometry and structure of the constituent “meta-atoms”. For example, negative permittivity and negative permeability can be achieved, leading to negative refractive index metamaterials. The negative permeability could be obtained via geometrical control of high frequency currents, e.g. in arrays of split ring resonators, or alternatively one could rely on spin resonances in natural magnetic materials, as was suggested by Veselago. The age of nanotechnology therefore sets an intriguing quest for additional benefits to be gained by structuring natural magnetic materials into so called magnonic metamaterials, in which the frequency and strength of resonances based on spin waves (magnons) are determined by the geometry and magnetization configuration of meta-atoms. Spin waves can have frequencies of up to hundreds of GHz (in the exchange dominated regime) and have already been shown to play an important role in the high frequency magnetic response of composites. Moreover, in view of the rapid advances in the field of magnonics, which in particular promises devices employing propagating spin waves, the appropriate design of magnonic metamaterials with properties defined with respect to propagating spin waves rather than electromagnetic waves acquires an independent and significant importance

Calculation of high-frequency permeability of magnonic metamaterials beyond the macrospin approximation

We present a method of calculation of the effective magnetic permeability of magnonic metamaterials containing arrays of magnetic inclusions of arbitrary shapes. The method fully takes into account the spectrum of spin waves confined in the inclusions. We evaluate the method by considering a particular case of a metamaterial formed by a stack of identical two-dimensional (2D) periodic hexagonal arrays of disk-shaped magnetic inclusions in a nonmagnetic matrix. Two versions of the method are considered. The first approach is based on a simple semianalytical theory that uses the numerically calculated susceptibility tensor of an isolated inclusion as input data for an analytical calculation in which the magnetodipole interaction between inclusions within each 2D array is taken into account. In the second approach, we employ micromagnetic packages with periodic boundary conditions to calculate the susceptibility of the whole 2D periodic array of such inclusions. The comparison of the two approaches reveals the necessity of retaining higher-order terms in the analytical calculation of the magnetodipole interaction via the multipole expansion. Models limited to the dipolar term can lead to remarkable underestimation of the effect of the magnetodipole interaction, in particular, for modes localized near the edge regions of inclusions. To calculate the susceptibility tensor of an isolated inclusion, we have implemented two different methods: (a) a method based on micromagnetic simulations, in which we have compared three different micromagnetic packages: the finite-element package nmag and the two finite differences packages oommf and micromagus; and (b) the modified dynamical matrix method (DMM). The comparison of the different micromagnetic packages and the DMM (based on the calculation of the susceptibility tensor of an isolated inclusion) demonstrate that their results agree to within 3%. Frequency regions in which the metamaterial is characterized by the negative permeability are identified. We speculate that the proposed methodology could be generalized to more complex arrangements of magnetic inclusions, e.g., to those with multiple periods or fractal arrangements, as well as to arrays of inclusions with a distribution of properties

Asymmetric Domain Walls of Small Angle in Soft Ferromagnetic Films

45 pages, 6 figuresInternational audienceWe focus on a special type of domain walls appearing in the Landau-Lifshitz theory for soft ferromagnetic films. These domain walls are divergence-free $S^2$-valued transition layers that connect two directions in $S^2$ (differing by an angle $2\theta$) and minimize the Dirichlet energy. Our main result is the rigorous derivation of the asymptotic structure and energy of such "asymmetric" domain walls in the limit $\theta \to 0$. As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model

Front propagation in anisotropic magnetic media

75.30.Gw Magnetic anisotropy, 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.), 83.60.Uv Wave propagation, fracture, and crack healing, 05.45.Yv Solitons,