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Relativistic theory of laser-induced magnetization dynamics
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory.
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. , p. 115
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1558
Keywords [en]
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: urn:nbn:se:uu:diva-315247ISBN: 978-91-513-0070-2 (print)OAI: oai:DiVA.org:uu-315247DiVA, id: diva2:1139943
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
List of papers
1. Ab initio investigation of light-induced relativistic spin-flip effects in magneto-optics
Open this publication in new window or tab >>Ab initio investigation of light-induced relativistic spin-flip effects in magneto-optics
2015 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 91, no 17, article id 174415Article in journal (Refereed) Published
Abstract [en]

Excitation of a metallic ferromagnet such as Ni with an intensive femtosecond laser pulse causes an ultrafast demagnetization within approximately 300 fs. It was proposed that the ultrafast demagnetization measured in femtosecond magneto-optical experiments could be due to relativistic light-induced processes. We perform an ab initio investigation of the influence of relativistic effects on the magneto-optical response of Ni. To this end, first, we develop a response theory formulation of the additional appearing ultrarelativistic terms in the Foldy-Wouthuysen transformed Dirac Hamiltonian due to the electromagnetic field, and second, we compute the influence of relativistic light-induced spin-flip transitions on the magneto-optics. Our ab initio calculations of relativistic spin-flip optical excitations predict that these can give only a very small contribution (<= 0.1%) to the laser-induced magnetization change in Ni.

National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-256238 (URN)10.1103/PhysRevB.91.174415 (DOI)000354555300004 ()
Funder
Swedish Research Council
Available from: 2015-06-24 Created: 2015-06-22 Last updated: 2017-12-04Bibliographically approved
2. Relativistic interaction Hamiltonian coupling the angular momentum of light and the electron spin
Open this publication in new window or tab >>Relativistic interaction Hamiltonian coupling the angular momentum of light and the electron spin
Show others...
2015 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 92, no 10, article id 100402Article in journal (Refereed) Published
Abstract [en]

On the basis of the Dirac equation, a relativistic interaction Hamiltonian is derived which linearly couples the angular momentum density j of the electromagnetic (EM) field and the electron's spin sigma. The expectation value of this novel Hamiltonian is demonstrated to be precisely the recently proposed energy coupling the EM angular momentum density and magnetic moments [A. Raeliarijaona et al., Phys. Rev. Lett. 110, 137205 (2013)]. This previously overlooked Hamiltonian is also found to naturally result in the exact analytical form of the interaction energy inherent to the inverse Faraday effect, therefore demonstrating its relevance and easy use for the derivation of other complex magneto-optical and magnetoelectric effects originating from electron spin-light angular momentum couplings.

National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-264044 (URN)10.1103/PhysRevB.92.100402 (DOI)000361037200001 ()
Funder
EU, FP7, Seventh Framework Programme, 281043
Available from: 2015-10-06 Created: 2015-10-05 Last updated: 2017-12-01Bibliographically approved
3. New relativistic Hamiltonian: the Angular MagnetoElectric coupling
Open this publication in new window or tab >>New relativistic Hamiltonian: the Angular MagnetoElectric coupling
Show others...
2016 (English)In: Spintronics IX, 2016, article id 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.

Series
Proceedings of SPIE, ISSN 0277-786X ; 9931
Keywords
Spin-Orbit, Angular MagnetoElectric coupling, Inverse Faraday Effect
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:uu:diva-316240 (URN)10.1117/12.2238196 (DOI)000391482500023 ()9781510602540 (ISBN)
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
4. Relativistic theory of spin relaxation mechanisms in the Landau-Lifshitz-Gilbert equation of spin dynamics
Open this publication in new window or tab >>Relativistic theory of spin relaxation mechanisms in the Landau-Lifshitz-Gilbert equation of spin dynamics
2016 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 94, no 14, article id 144419Article in journal (Refereed) Published
Abstract [en]

Starting from the Dirac-Kohn-Sham equation, we derive the relativistic equation of motion of spin angular momentum in a magnetic solid under an external electromagnetic field. This equation of motion can be rewritten in the form of the well-known Landau-Lifshitz-Gilbert equation for a harmonic external magnetic field and leads to a more general magnetization dynamics equation for a general time-dependent magnetic field. In both cases there is an electronic spin-relaxation term which stems from the spin-orbit interaction. We thus rigorously derive, from fundamental principles, a general expression for the anisotropic damping tensor which is shown to contain an isotropic Gilbert contribution as well as an anisotropic Ising-like and a chiral, Dzyaloshinskii-Moriya-like contribution. The expression for the spin relaxation tensor comprises furthermore both electronic interband and intraband transitions. We also show that when the externally applied electromagnetic field possesses spin angular momentum, this will lead to an optical spin torque exerted on the spin moment.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-308648 (URN)10.1103/PhysRevB.94.144419 (DOI)000386093100004 ()
Funder
EU, FP7, Seventh Framework Programme, 281043Swedish Research CouncilKnut and Alice Wallenberg Foundation, 2015.0060Swedish National Infrastructure for Computing (SNIC)
Available from: 2016-11-30 Created: 2016-11-29 Last updated: 2017-11-29Bibliographically approved
5. Ab Initio Theory of Coherent Laser-Induced Magnetization in Metals
Open this publication in new window or tab >>Ab Initio Theory of Coherent Laser-Induced Magnetization in Metals
2016 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 117, no 13Article in journal (Refereed) Published
Abstract [en]

We present the first materials specific ab initio theory of the magnetization induced by circularly polarized laser light in metals. Our calculations are based on nonlinear density matrix theory and include the effect of absorption. We show that the induced magnetization, commonly referred to as inverse Faraday effect, is strongly materials and frequency dependent, and demonstrate the existence of both spin and orbital induced magnetizations which exhibit a surprisingly different behavior. We show that for nonmagnetic metals (such as Cu, Au, Pd, Pt) and antiferromagnetic metals the induced magnetization is antisymmetric in the light's helicity, whereas for ferromagnetic metals (Fe, Co, Ni, FePt) the imparted magnetization is only asymmetric in the helicity. We compute effective optomagnetic fields that correspond to the induced magnetizations and provide guidelines for achieving all-optical helicity-dependent switching.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-305334 (URN)10.1103/PhysRevLett.117.137203 (DOI)000383851000020 ()
Funder
EU, FP7, Seventh Framework Programme, 281043Swedish Research CouncilKnut and Alice Wallenberg FoundationSwedish National Infrastructure for Computing (SNIC)
Available from: 2016-10-14 Created: 2016-10-14 Last updated: 2017-11-29Bibliographically approved
6. Signatures of relativistic spin-light coupling in magneto-optical pump-probe experiments
Open this publication in new window or tab >>Signatures of relativistic spin-light coupling in magneto-optical pump-probe experiments
2017 (English)In: Journal of Physics: Condensed Matter, ISSN 0953-8984, E-ISSN 1361-648X, Vol. 29, no 19, article id 194002Article in journal (Refereed) Published
Abstract [en]

Femtosecond magneto-optical pump-probe measurements of ultrafast demagnetization show an intriguing difference in the first 100 fs of the magneto-optical Kerr response depending on whether the polarization of the pump and probe beams are in parallel or perpendicular configuration (Bigot et al 2009 Nat. Phys. 5 515). Starting from a most general relativistic Hamiltonian we focus on the ultra-relativistic light-spin interaction and show that this coupling term leads to different light-induced opto-magnetic fields when pump and probe polarization are parallel and perpendicular to each other, providing thus an explanation for the measurements. We also analyze other pump-probe configurations where the pump laser is circularly polarized and the employed probe contains only linearly polarized light and show that similar opto-magnetic effects can be anticipated.

Place, publisher, year, edition, pages
IOP PUBLISHING LTD, 2017
Keywords
ultrafast magnetism, pump-probe experiments, relativistic AME coupling, opto-magnetic field
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-321781 (URN)10.1088/1361-648X/aa68ea (DOI)000399254200002 ()28337969 (PubMedID)
Funder
Swedish Research CouncilKnut and Alice Wallenberg Foundation, 2015.0060Swedish National Infrastructure for Computing (SNIC)
Available from: 2017-05-11 Created: 2017-05-11 Last updated: 2017-09-11Bibliographically approved
7. Relativistic theory of magnetic inertia in ultrafast spin dynamics
Open this publication in new window or tab >>Relativistic theory of magnetic inertia in ultrafast spin dynamics
2017 (English)In: Physical review B: covering condensed matter and materials physics, ISSN 2469-9950, Vol. 96, no 2, article id 024425Article in journal (Refereed) Published
Abstract [en]

The influence of possible magnetic inertia effects has recently drawn attention in ultrafast magnetization dynamics and switching. Here we derive rigorously a description of inertia in the Landau-Lifshitz-Gilbert equation on the basis of the Dirac-Kohn-Sham framework. Using the Foldy-Wouthuysen transformation up to the order of 1/c(4) gives the intrinsic inertia of a pure system through the second order time derivative of magnetization in the dynamical equation of motion. Thus, the inertial damping I is a higher order spin-orbit coupling effect, similar to 1/c(4), as compared to the Gilbert damping Gamma that is of order 1/c(2). Inertia is therefore expected to play a role only on ultrashort timescales (subpicoseconds). We also show that the Gilbert damping and inertial damping are related to one another through the imaginary and real parts of the magnetic susceptibility tensor, respectively.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-328075 (URN)10.1103/PhysRevB.96.024425 (DOI)000405698000004 ()
Funder
Swedish Research CouncilEU, Horizon 2020, 737709Knut and Alice Wallenberg Foundation, 2015.0060Swedish National Infrastructure for Computing (SNIC)
Available from: 2017-08-16 Created: 2017-08-16 Last updated: 2017-10-18Bibliographically approved
8. Unified relativistic theory of magnetization dynamics with spin-current tensors
Open this publication in new window or tab >>Unified relativistic theory of magnetization dynamics with spin-current tensors
(English)Manuscript (preprint) (Other academic)
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-328349 (URN)
Available from: 2017-08-22 Created: 2017-08-22 Last updated: 2017-09-11

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