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Register a new userDispersion relation of nutation surface spin waves in ferromagnets
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Added by
Mikhail Cherkasskii
Publication date
2021
fields
Physics
and research's language is
English
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Inertia effects in magnetization dynamics are theoretically shown to result in a different type of spin waves, i.e. nutation surface spin waves, which propagate at terahertz frequencies in in-plane magnetized ferromagnetic thin films. Considering the magnetostatic limit, i.e. neglecting exchange coupling, we calculate dispersion relation and group velocity, which we find to be slower than the velocity of conventional (precession) spin waves. In addition, we find that the nutation surface spin waves are backward spin waves. Furthermore, we show that inertia causes a decrease of the frequency of the precession spin waves, namely magnetostatic surface spin waves and backward volume magnetostatic spin waves. The magnitude of the decrease depends on the magnetic properties of the film and its geometry.
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The inertial dynamics of magnetization in a ferromagnet is investigated theoretically. The analytically derived dynamic response upon microwave excitation shows two peaks: ferromagnetic and nutation resonances. The exact analytical expressions of frequency and linewidth of the magnetic nutation resonance are deduced from the frequency dependent susceptibility determined by the inertial Landau-Lifshitz-Gilbert equation. The study shows that the dependence of nutation linewidth on the Gilbert precession damping has a minimum, which becomes more expressive with increase of the applied magnetic field.
The dipolar (magnetostatic) interaction dominates the behavior of spin waves in magnetic films in the long-wavelength regime. In an in-plane magnetized film, volume modes exist with a negative group velocity (backward volume magnetostatic spin waves), in addition to the forward surface-localized mode (Damon-Eshbach). Inside the film of finite thickness $L$, the volume modes have a nontrivial spatial dependence, and their two-dimensional dispersion relations $omega(mathbf{k})$ can be calculated only numerically. We present explicit perturbative expressions for the profiles and frequencies of the volume modes, taking into account an in-plane applied field and uniaxial anisotropy, for the regimes $lVert mathbf{k}L rVert gg 1$ and $lVert mathbf{k}L rVert ll 1$, which together provide a good indication of the behavior of the modes for arbitrary wavevector $mathbf{k}$. Moreover, we derive a very accurate semianalytical expression for the dispersion relation $omega(mathbf{k})$ of the lowest-frequency mode that is straightforward to evaluate using standard numerical routines. Our results are useful to quickly interpret and control the excitation and propagation of spin waves in (opto-)magnetic experiments.
A continuum model of frustrated ferromagnets is analyzed in detail in the regime of low applied magnetic field, $H_0<1/4$, where the ground state is a spatially varying conical spiral. By changing variables to a corotating spin field, the model is reformulated as a gauged sigma model in a fixed background gauge, allowing the construction of stable isolated Skyrmions, and stable multi-Skyrmion clusters, which approach the conical ground state at spatial infinity. Owing to the spatial anisotropy induced by the ground state, these Skyrmions exhibit only discrete symmetries, and are of neither Neel nor Bloch type. These Skyrmions are continuously connected to the more familar solutions in the high field regime ($H_0>1/4$), acquiring axial symmetry in the limit $H_0rightarrow 1/4$. The propagation of small amplitude spin waves through the conical ground state is also analyzed and is found to depend strongly on both $H_0$ and propagation direction relative to the ground state. In contrast to spin waves in the high field regime ($H_0>1/4$) there is no spectral gap: waves may propagate with any angular frequency.
First principles calculations show that electric fields applied to ferromagnets generate spin currents flowing perpendicularly to the electric field. Reduced symmetry in these ferromagnets enables a wide variety of such spin currents. However, the total spin current is approximately the sum of a magnetization-independent spin Hall current and an anisotropic spin anomalous Hall current. Intrinsic spin currents are not subject to dephasing, enabling their spin polarizations to be misaligned with the magnetization, which enables the magnetization-independent spin Hall effect. The spin Hall conductivity and spin anomalous Hall conductivities of transition metal ferromagnets are comparable to those found in heavy metals, opening new avenues for efficient spin current generation in spintronic devices.
We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its perimeter. Using a spatio-temporal optical measurement, we report the full dispersion relation of azimuthal waves propagating along the inner and outer torus borders, highlighting several branches modeled as varicose, sinuous and sloshing modes. Standing azimuthal waves are also studied leading to polygon-like patterns arising on the two torus borders with a number of sides different when a tunable decoupling of the two interfaces occurs. The quantized nature of the dispersion relation is also evidenced.
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