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Register a new userMagnetization Dynamics, Gyromagnetic Relation, and Inertial Effects
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The gyromagnetic relation - i.e. the proportionality between the angular momentum $vec L$ (defined by an inertial tensor) and the magnetization $vec M$ - is evidence of the intimate connections between the magnetic properties and the inertial properties of ferromagnetic bodies. However, inertia is absent from the dynamics of a magnetic dipole (the Landau-Lifshitz equation, the Gilbert equation and the Bloch equation contain only the first derivative of the magnetization with respect to time). In order to investigate this paradoxical situation, the lagrangian approach (proposed originally by T. H. Gilbert) is revisited keeping an arbitrary nonzero inertial tensor. A dynamic equation generalized to the inertial regime is obtained. It is shown how both the usual gyromagnetic relation and the well-known Landau-Lifshitz-Gilbert equation are recovered at the kinetic limit, i.e. for time scales above the relaxation time $tau$ of the angular momentum.
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The dynamical equation of the magnetization has been reconsidered with enlarging the phase space of the ferromagnetic degrees of freedom to the angular momentum. The generalized Landau-Lifshitz-Gilbert equation that includes inertial terms, and the corresponding Fokker-Planck equation, are then derived in the framework of mesoscopic non-equilibrium thermodynamics theory. A typical relaxation time $tau$ is introduced describing the relaxation of the magnetization acceleration from the inertial regime towards the precession regime defined by a constant Larmor frequency. For time scales larger than $tau$, the usual Gilbert equation is recovered. For time scales below $tau$, nutation and related inertial effects are predicted. The inertial regime offers new opportunities for the implementation of ultrafast magnetization switching in magnetic devices.
We have numerically solved the Landau-Lifshitz-Gilbert (LLG) equation in its standard and inertial forms to study the magnetization switching dynamics in a $3d$ thin film ferromagnet. The dynamics is triggered by ultrashort magnetic field pulses of varying width and amplitude in the picosecond and Tesla range. We have compared the solutions of the two equations in terms of switching characteristic, speed and energy analysis. Both equations return qualitatively similar switching dynamics, characterized by regions of slower precessional behavior and faster ballistic motion. In case of inertial dynamics, ballistic switching is found in a 25 % wider region in the parameter space given by the magnetic field amplitude and width. The energy analysis of the dynamics is qualitatively different for the standard and inertial LLG equations. In the latter case, an extra energy channel, interpreted as the kinetic energy of the system, is available. Such extra channel is responsible for a resonant energy absorption at THz frequencies, consistent with the occurence of spin nutation.
Spin vortices in magnetic nanopillars are used as GHz oscillators, with frequency however essentially fixed in fabrication. We demonstrate a model system of a two-vortex nanopillar, in which the resonance frequency can be changed by an order of magnitude, without using high dc magnetic fields. The effect is due to switching between the two stable states of the vortex pair, which we show can be done with low-amplitude fields of sub-ns duration. We detail the relevant vortex-core dynamics and explain how field anharmonicity and phase control can be used to enhance the performance.
We extend a microscopic theory of polarization and magnetization to include the spin degree of freedom of the electrons. We include a general spin orbit coupling and Zeeman interaction term to account for the modifications to the dynamics upon treating the electrons as spinful particles. We find a contribution to the magnetization due to the intrinsic angular momentum of the electrons. Additionally, the charge current gains a component transverse to both this intrinsic magnetization and the electric field of the crystal lattice. The microscopic polarization and magnetization fields are introduced throughout an extended system using a set of orthogonal orbitals associated with each site. As well free charge and current density fields are introduced associated with charge movement from site to site. The sites act as natural expansion points for the microscopic fields allowing for the evaluation of multipole moments associated with the polarization and magnetization fields. Associated with the dipole moments are the respective macroscopic polarization and magnetization fields, from which we can extract various response tensors. We focus on topologically trivial insulators in the limit of uniform fields to recover the magnetoelectric polarizability (MP) tensor, which contains the accepted expression for the orbital magnetoelectric polarizability (OMP) tensor as well as an added explicitly spin dependent contribution. This general framework can then be extended to finite frequency responses.
The understanding of how spins move at pico- and femtosecond time scales is the goal of much of modern research in condensed matter physics, with implications for ultrafast and more energy-efficient data storage. However, the limited comprehension of the physics behind this phenomenon has hampered the possibility of realising a commercial technology based on it. Recently, it has been suggested that inertial effects should be considered in the full description of the spin dynamics at these ultrafast time scales, but a clear observation of such effects in ferromagnets is still lacking. Here, we report the first direct experimental evidence of inertial spin dynamics in ferromagnetic thin films in the form of a nutation of the magnetisation at a frequency of approximately 0.6 THz. This allows us to evince that the angular momentum relaxation time in ferromagnets is on the order of 10 ps.
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