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We used a toy model mimicking a ferromagnet-topological-insulator interface to illustrate the various effects, and we predicted an anisotropic gyromagnetic ratio and the dynamical stability for an in-plane magnetization.


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Our formalism can also be applied to the slow dynamics of other order parameters in crystalline solids. The arrows indicate the directions of magnetization motion.

Dynamics, numerical analysis and some geometry – Christian Lubich – ICM2018

B 98 , — Published 18 July Abstract To give a general description of the influences of electric fields or currents on magnetization dynamics, we developed a semiclassical theory for the magnetization implicitly coupled to electronic degrees of freedom. Research Areas. Magnetism Magnetoelectric effect Magnetotransport.

Physical Systems. Ferromagnets Topological insulators.

Computational Signaling Protein Dynamics and Geometric Mass Relations in Biomolecular Diffusion.

Boltzmann theory Landau-Lifschitz-Gilbert equation. See general information about how to correct material in RePEc. For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ionascu Costel. If you have authored this item and are not yet registered with RePEc, we encourage you to do it here.

Phys. Rev. B 98, () - Electronic contribution to the geometric dynamics of magnetization

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30 - 31 October 2015

Weinstein , both inspired by the work of Smale Symmetry of a Hamiltonian or Lagrangian system gives rise to conserved quantities, by Noether's theorem , and these conserved quantities are the components of the momentum map J. One of the important developments arising from the geometric approach to mechanics is the incorporation of the geometry into numerical methods.

In particular symplectic and variational integrators are proving particularly accurate for long-term integration of Hamiltonian and Lagrangian systems.


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As a modern subject, geometric mechanics has its roots in four works written in the s. Arnold's fundamental work showed that Euler's equations for the free rigid body are the equations for geodesic flow on the rotation group SO 3 and carried this geometric insight over to the dynamics of ideal fluids, where the rotation group is replaced by the group of volume preserving diffeomorphisms. Smale's paper on Topology and Mechanics investigates the conserved quantities arising from Noether's theorem when a Lie group of symmetries acts on a mechanical system, and defines what is now called the momentum map which Smale calls angular momentum , and he raises questions about the topology of the energy-momentum level surfaces and the effect on the dynamics.

In his book, Souriau also considers the conserved quantities arising from the action of a group of symmetries, but he concentrates more on the geometric structures involved for example the equivariance properties of this momentum for a wide class of symmetries , and less on questions of dynamics.


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