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Register a new userMagnetization Dynamics in Holographic Ferromagnets: Landau-Lifshitz Equation from Yang-Mills Fields
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We introduce a new approach to understand magnetization dynamics in ferromagnets based on the holographic realization of ferromagnets. A Landau-Lifshitz equation describing the magnetization dynamics is derived from a Yang-Mills equation in the dual gravitational theory, and temperature dependences of the spin-wave stiffness and spin transfer torque appearing in the holographic Landau-Lifshitz equation are investigated by the holographic approach. The results are consistent with the known properties of magnetization dynamics in ferromagnets with conduction electrons.
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A holographic realization for ferromagnetic systems has been constructed. Owing to the holographic dictionary proposed on the basis of this realization, we obtained relevant thermodynamic quantities such as magnetization, magnetic susceptibility, and free energy. This holographic model reproduces the behavior of the mean field theory near the critical temperature. At low temperatures, the results automatically incorporate the contributions from spin wave excitations and conduction electrons.
We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the stochastic generalization of the Landau-Lifshitz-Gilbert equation proposed by Brown, with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this stochastic equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized equation ensures the conservation of the magnetization modulus and the approach to the Gibbs-Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward.
We investigate in details the inertial dynamics of a uniform magnetization in the ferromagnetic resonance (FMR) context. Analytical predictions and numerical simulations of the complete equations within the Inertial Landau-Lifshitz-Gilbert (ILLG) model are presented. In addition to the usual precession resonance, the inertial model gives a second resonance peak associated to the nutation dynamics provided that the damping is not too large. The analytical resolution of the equations of motion yields both the precession and nutation angular frequencies. They are function of the inertial dynamics characteristic time $tau$, the dimensionless damping $alpha$ and the static magnetic field $H$. A scaling function with respect to $alphataugamma H$ is found for the nutation angular frequency, also valid for the precession angular frequency when $alphataugamma Hgg 1$. Beyond the direct measurement of the nutation resonance peak, we show that the inertial dynamics of the magnetization has measurable effects on both the width and the angular frequency of the precession resonance peak when varying the applied static field. These predictions could be used to experimentally identify the inertial dynamics of the magnetization proposed in the ILLG model.
We study the response of a (2+1)-dimensional gauge theory to an external rotating electric field. In the strong coupling regime such system is formulated holographically in a top-down model constructed by intersecting D3- and D5-branes along 2+1 dimensions, in the quenched approximation, in which the D5-brane is a probe in the AdS_5 x S^5 geometry. The system has a non-equilibrium phase diagram with conductive and insulator phases. The external driving induces a rotating current due to vacuum polarization (in the insulator phase) and to Schwinger effect (in the conductive phase). For some particular values of the driving frequency the external field resonates with the vector mesons of the model and a rotating current can be produced even in the limit of vanishing driving field. These features are in common with the (3+1) dimensional setup based on the D3-D7 brane model and hint on some interesting universality. We also compute the conductivities paying special attention to the photovoltaic induced Hall effect, which is only present for massive charged carriers. In the vicinity of the Floquet condensate the optical Hall coefficient persists at zero driving field, signalling time reversal symmetry breaking.
A theoretical model based on the Landau-Lifshitz-Bloch equation is developed to study the spin-torque effect in ferrimagnets. Experimental findings, such as the temperature dependence, the peak in spin torque, and the angular-momentum compensation, can be well captured. In contrast to the ferromagnet system, the switching trajectory in ferrimagnets is found to be precession free. The two sublattices are not always collinear, which produces large exchange field affecting the magnetization dynamics. The study of material composition shows the existence of an oscillation region at intermediate current density, induced by the nondeterministic switching. Compared to the Landau-Lifshitz-Gilbert model, our developed model based on the Landau-Lifshitz-Bloch equation enables the systematic study of spin-torque effect and the evaluation of ferrimagnet-based devices.
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