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New relativistic Hamiltonian: the Angular MagnetoElectric coupling
Univ Paris Saclay, Lab SPMS, CNRS, UMR8580,CentraleSupelec, Chatenay Malabry, France.;Univ Arkansas, Dept Phys, Fayetteville, AR 72701 USA..
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
Univ Paris Saclay, Lab SPMS, CNRS, UMR8580,CentraleSupelec, Chatenay Malabry, France..
Show others and affiliations
2016 (English)In: Spintronics IX, 2016, UNSP 99312EConference paper, Published paper (Refereed)
Abstract [en]

Spin-Orbit Coupling (SOC) is a ubiquitous phenomenon in the spintronics area, as it plays a major role in allowing or enhancing many well-known phenomena, such as the Dzyaloshinskii-Moriya interaction, magnetocrystalline anisotropy, the Rashba effect, etc. However, the usual expression of the SOC interaction h/4 m(2)c(2) [E x p] . sigma (1) where p is the momentum operator, E the electric field, sigma the vector of Pauli matrices, breaks the gauge invariance required by the electronic Hamiltonian. On the other hand, very recently, a new phenomenological interaction, coupling the angular momentum of light and magnetic moments, has been proposed based on symmetry arguments: -xi/2[r x (E x B)] . M, (2) with M the magnetization, r the position, and xi the interaction strength constant. This interaction has been demonstrated to contribute and/or give rise, in a straightforward way, to various magnetoelectric phenomena, such as the anomalous Hall effect (AHE), the anisotropic magnetoresistance (AMR), the planar Hall effect and Rashba-like effects, or the spin -current model in multiferroics. This last model is known to be the origin of the cycloidal spin arrangement in bismuth ferrite for instance. However, the coupling of the angular momentum of light with magnetic moments lacked a fundamental theoretical basis. Starting from the Dirac equation, we derive a relativistic interaction Hamiltonian which linearly couples the angular momentum density of the electromagnetic (EM) field and the electrons spin ?. We name this coupling the Angular MagnetoElectric (AME) coupling. We show that in the limit of uniform magnetic field, the AME coupling yields an interaction exactly of the form of Eq. (2), thereby giving a firm theoretical basis to earlier works. The AME coupling can be expressed as: xi[E x A] . sigma-, (3) with A being the vector potential. Interestingly, the AME coupling was shown to be complementary to the traditional SOC, and together they restore the gauge invariance of the Hamiltonian. As an illustration of the AME coupling, we straightforwardly derived a relativistic correction to the so-called Inverse Faraday Effect (IFE), which is the emergence of an effective magnetic field under illumination by a circularly polarized light.

Place, publisher, year, edition, pages
2016. UNSP 99312E
Series
Proceedings of SPIE, ISSN 0277-786X ; 9931
Keyword [en]
Spin-Orbit, Angular MagnetoElectric coupling, Inverse Faraday Effect
National Category
Atom and Molecular Physics and Optics
Identifiers
URN: urn:nbn:se:uu:diva-316240DOI: 10.1117/12.2238196ISI: 000391482500023ISBN: 9781510602540 (print)OAI: oai:DiVA.org:uu-316240DiVA: diva2:1077293
Conference
9th Spintronics Symposium / SPIE Conference, AUG 28-SEP 01, 2016, San Diego, CA
Available from: 2017-02-27 Created: 2017-02-27 Last updated: 2017-09-11Bibliographically approved
In thesis
1. Relativistic theory of laser-induced magnetization dynamics
Open this publication in new window or tab >>Relativistic theory of laser-induced magnetization dynamics
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Ultrafast dynamical processes in magnetic systems have become the subject of intense research during the last two decades, initiated by the pioneering discovery of femtosecond laser-induced demagnetization in nickel. In this thesis, we develop theory for fast and ultrafast magnetization dynamics. In particular, we build relativistic theory to explain the magnetization dynamics observed at short timescales in pump-probe magneto-optical experiments and compute from first-principles the coherent laser-induced magnetization.

In the developed relativistic theory, we start from the fundamental Dirac-Kohn-Sham equation that includes all relativistic effects related to spin and orbital magnetism as well as the magnetic exchange interaction and any external electromagnetic field. As it describes both particle and antiparticle, a separation between them is sought because we focus on low-energy excitations within the particle system. Doing so, we derive the extended Pauli Hamiltonian that captures all relativistic contributions in first order; the most significant one is the full spin-orbit interaction (gauge invariant and Hermitian). Noteworthy, we find that this relativistic framework explains a wide range of dynamical magnetic phenomena. To mention, (i) we show that the phenomenological Landau-Lifshitz-Gilbert equation of spin dynamics can be rigorously obtained from the Dirac-Kohn-Sham equation and we derive an exact expression for the tensorial Gilbert damping. (ii) We derive, from the gauge-invariant part of the spin-orbit interaction, the existence of a relativistic interaction that linearly couples the angular momentum of the electromagnetic field and the electron spin. We show this spin-photon interaction to provide the previously unknown origin of the angular magneto-electric coupling, to explain coherent ultrafast magnetism, and to lead to a new torque, the optical spin-orbit torque. (iii) We derive a definite description of magnetic inertia (spin nutation) in ultrafast magnetization dynamics and show that it is a higher-order spin-orbit effect. (iv) We develop a unified theory of magnetization dynamics that includes spin currents and show that the nonrelativistic spin currents naturally lead to the current-induced spin-transfer torques, whereas the relativistic spin currents lead to spin-orbit torques. (v) Using the relativistic framework together with ab initio magneto-optical calculations we show that relativistic laser-induced spin-flip transitions do not explain the measured large laser-induced demagnetization.

Employing the ab initio relativistic framework, we calculate the amount of magnetization that can be imparted in a material by means of circularly polarized light – the so-called inverse Faraday effect. We show the existence of both spin and orbital induced magnetizations, which surprisingly reveal a different behavior. We establish that the laser-induced magnetization is antisymmetric in the light’s helicity for nonmagnets, antiferromagnets and paramagnets; however, it is only asymmetric for ferromagnets. 

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2017. 115 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1558
Keyword
Relativistic quantum electrodynamics, magneto-optics, spin-orbit coupling, ultrafast demagnetization, inverse Faraday effect, magnetic inertia, Gilbert damping
National Category
Condensed Matter Physics Atom and Molecular Physics and Optics
Research subject
Physics
Identifiers
urn:nbn:se:uu:diva-315247 (URN)978-91-513-0070-2 (ISBN)
Public defence
2017-10-27, Polhemsalen, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2017-10-03 Created: 2017-09-11 Last updated: 2017-10-18

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Mondal, RitwikBerritta, MarcoOppeneer, Peter M.

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