Project title: Spin-lattice Coupling in Magnetic Materials
Supervisor: Dr. Andrew Horsfield, Prof. Matthew Foulkes, Prof. Sergei Dudarev
The objective of this PhD project is to develop an electronic structure model capable of simulating the Einstein-de Haas (EdH) experiment. In the EdH experiment a cylinder of iron is suspended by a string, which allows it to freely rotate. Changes in external magnetic field cause the cylinder to gain a classical angular momentum as a response to the change of the orientations of the electron spins in order to conserve angular momentum . To describe the transfer of angular momentum from electron spin to the lattice we need to evolve the electron wavefunctions in time, with spin-orbit interactions included, and in the presence of a time-dependent external magnetic field.
Such an electronic structure model will be of practical use to scientists in the Culham Centre for Fusion Energy (CCFE), who will be able to use it to calculate heat transfer coefficients, and hence better predict heat flow and the effects of radiation damage in iron .
In the MSc project preceding the PhD it was shown that including the spin-orbit coupling term with the Pauli equation was sufficient to capture all of the physics needed from the fully-relativistic Dirac equation, although the accuracy of the approximation was shown to decrease with increasing atomic number. Building on the MSc project, the aim is to create a tight-binding model with spin-orbit coupling, and with forces on the nuclei calculated using the Hellman-Feynman theorem. This will be made time dependent to allow simulation of a gradual variation in the magnetic field, and thus reproduce the EdH effect.
 A. Einstein, W. J. de Haas, Experimental proof of the existence of Ampère's molecular currents (in English), Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings, 18 I, pp. 696–711
 Spin-lattice-electron dynamics simulations of magnetic materials, Pui-Wai Ma, S. L. Dudarev, and C. H. Woo Phys. Rev. B 85, 18430