DOCSLIB.ORG

Spin-Orbit Coupling Effects

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Spin-Orbit Coupling Effects Gemeinschaft - Mitglied der Helmholtz der Mitglied Spin-Orbit Coupling Effects and their modeling with the FLEUR code 24. September 2019| Gustav Bihlmayer Peter Grünberg Institut and Institute for Advanced Simulation Forschungszentrum Jülich, Germany Overview Ø basics • the Dirac equation • Pauli equation and spin-orbit coupling Ø relativistic effects in non-magnetic solids • bulk: Rashba and Dresselhaus effect • topological insulators OeNB Ø magnetic systems • Dzyaloshinskii-Moriya interaction • magnetic anisotropy images: Wikipedia/ images: 24. September 2019 Folie 2 Schrödinger type DFT Hamiltonian classical Hamiltonian image: OeNB image: continuity equation quantum mechanical Hamiltionian and interpretation of wavefunction spin enters (ad-hoc) as quantum number 24. September 2019 Folie 3 Non-collinear DFT calculation Noncollinear magnetism:120exampleo Néel state obtained from Schrödinger-type Hamiltonian: struct. energy moment (a) 5.4 meV 0 �9 (b) 5.4 meV 0 �9 (c) 0.0 meV 0.0042 � 9 (a) (b) (c) (d) (d) < 1.3 meV 0.0039 �9 Sandratskii & Kübler, PRL 76, 4963 (1996) Mn Sn 3 These configurations are indistighuishable without SOC! 24. September 2019 Folie 4 9. October 2008 NanoFerronics-2008 – p. 5 Relativistic extension by P.A.M.Dirac classical Hamiltonian Dirac’s Ansatz: image: Wikipedia image: 24. September 2019 Folie 5 2D- and 3D- Dirac equation 2D solution with Pauli spin matrices: Hˆ = c~ p~ + mc2σ · z 0 ~ 3D solution with 4x4 mat.: ~↵ = ~ 0 ✓ ◆ 2 Hˆ = βmc ~c~↵ p~ − · Bi (Z=83) bi-spinor wavefunction: In the FLEUR code we consider both components in the construction of the density. 24. September 2019 Folie 6 3D- Dirac equation Dirac equation with scalar (V) and vector potential (A): bi-spinor wavefunction: non-relativistic limit: 24. September 2019 Folie 7 Schrödinger and Pauli equation Usually, we ignore the vector potential in the Schrödinger equation: but: approximation to Dirac equation keeping terms up to 1/c2: mass- velocity term direct implementation in DarwinDFT Hamiltonian possiblespin (approximate-orbit (E+eVmagnetic)2 term ), SOC & magnetic field termterm couple the two spin channelscoupling field int. 24. September 2019 Folie 8 scalar relativistic calculations: block-diagonal equation in spin: 2 p~ e~ E + eV (~r) Bz(~r)σz + − 2m − 2mc 1 2 e~ (E + eV (~r)) + i E~ (~r) p~ =0 2mc2 (2mc)2 · ◆ with spin-dependent wave-function: 24. September 2019 Folie 9 relativistic effects in Ag and Au density of states (DOS): from www.oenb.at 24. September 2019 Folie 10 Spin-orbit coupling interaction with an (internal) magnetic field: similar to: with Thomas factor in a central potential (atom): note that the spin and the orbital momentum (L) couple antiparallel! 24. September 2019 Folie 11 Spin-orbit coupling effects in non-magnetic solids 24. September 2019 Folie 12 A typical semiconductor: Ge without SOC (l_soc=F) with SOC (l_soc=T) empty band heavy-hole band light-hole band split-off band 24. September 2019 Folie 13 Some symmetry considerations: Ge, Γ-point: Ø three p-orbitals, one split-off by SOC (atomic behavior) Ø all bands are doubly (spin) degenerate (Kramers pairs) Time reversal (TR) symmetry: ✏(~k, )=✏( ~k, ) " − # Inversion (I) symmetry: ✏(~k)=✏( ~k) − TR + I symmetry: ✏(~k, )=✏(~k, ) " # inversion center 24. September 2019 Folie 14 Broken I symmetry: Dresselhaus effect in presence of SOC: ✏ ( ~ k, ) = ✏ ( ~k, ) i.e. k-dependent spin splitting (here: α k3) " 6 # Dresselhaus Hamiltonian (kp-theory, e.g. in (111) direction): zincblende structure 24. September 2019 Folie 15 Broken I symmetry at a crystal surface Free electron gas in electric field: Suppose � = � �⃗ > and momentum confined in (x,y) plane: this describes electrons at a surface or an interface (e.g. doped layer between two semiconductors) 24. September 2019 Folie 16 Example: coinage metal surfaces (111) surface states www.almaden.ibm.cpm from from DFT calculations and SP-ARPES agree very well [experiment: Reinert et al., PRB 63, 115415 (2001)] 24. September 2019 Folie 17 Spin orientation in the Rashba effect good comparison between calculated and measured αR spin-dependent splittings require careful k-point sampling (±k) ! 24. September 2019 Folie 18 Sb2Te3 (0001) surface surface without SOC and with SOC: new states surface state with Rashba splitting 24. September 2019 Folie 19 The quantum spin Hall effect (QSHE) properties: Ø valence- and conduction band connected by edge states Ø spin-polarization of states is Rashba-like Ø one conduction channel per spin in the gap Kane & Mele, PRL 95, 226801 (2005) Ø topologically protected edge transport 24. September 2019 Folie 20 Band inversion in graphene (25μeV) Bandstructure around K (K’): mass inversion between K and K’: spin split edge state connecting K and K’ DFT calculation with SOC 24. September 2019 Folie 21 Band inversion II-VI semiconductors focus on Γ6 and Γ8: gap inv. gap responsible for band-inversion: Darwin-term of Pauli-equation 24. September 2019 Folie 22 . Spin-orbit effects in magnetic systems 24. September 2019 Folie 23 Magnetic interactions Interactions between two spins: on-site inter-site scalar traceless sym. scalar traceless sym. antisymmetric Stoner magnetic Heisenberg (pseudo)-dipolar Dzyaloshinskii magnet. anisotropy interaction interaction Moriya int. non-relativistic effects [T. Moriya, Phys. Rev. 120, 91 (1960)] 24. September 2019 Folie 24 Ansiotropic exchange ferromagnets: exchange >> Rashba splitting here: exchange interaction ≈ spin-orbit strength, e.g. two magnetic adatoms (SA,SB) on a heavy substrate with conduction electron σ: D. A. Smith, J. Magn. Magn. Mater. 1, 214 (1976) 24. September 2019 Folie 25 Ansiotropic exchange: E.g. 2 magnetic adatoms (Fe) on a heavy substrate (W) RKKY-type interaction: A. Fert and P. M. Levy, Phys. Rev. Lett. 44, 1538 (1980). Dzyaloshinskii-Moriya (DM) term, anisotropic exchange interaction. 24. September 2019 Folie 26 Dzyaloshinskii-Moriya interaction: distinguish clockwise – counterclockwise rotations without SOC with SOC 24. September 2019 Folie 27 Simple 1D example: two domain walls topological index, winding number 24. September 2019 Folie 28 Simple 1D example: two domain walls topologically trivial structure 24. September 2019 Folie 29 Domain walls in 2 Fe / W(110) Due to the Dzyaloshinskii- This domain wall Moriya interaction this (Neél- does not exist! type) domain-wall is stabilized Theory: M. Heide, G. Bihlmayer and S. Blügel, Phys. Rev. B, 140403(R) (2008) 24. September 2019 Folie 30 Exchange interactions: 2-spin terms: ~ ~ H = SiJ ijSj i<j X relativistic on-site terms: i=j: trace(J)=Stoner I effects symmetric, traceless part: magnetic anisotropy intersite terms: trace(J)=Heisenberg-type exchange symmetric, traceless part: quasi-dipolar exchange antisymmetric part: Dzyaloshinskii-Moriya interaction H = J S~ S~ + D~ S~ S~ + S~T S~ ij i · j ij · i ⇥ j i Ki i i<j i X h ⇣ ⌘i X specify magnetization direction giving polar angles in the input! <soc theta=“0.00” phi=“0.00” l_soc=T ….> 24. September 2019 Folie 31 Magnetic Anisotropy: magnetization direction dependence of free energy of a cubic crystal: K F (Mˆ )=K + 1 (3 4 cos 2✓ + cos 4✓)(1 cos 4φ) + 8(1 cos 4✓) + K 0 64 { − − − } 2 4 Uniaxial system: F (Mˆ )=K0 + K1 sin ✓ + K2sin ✓ 24. September 2019 Folie 32 Effect of SOC on Fe band structure 1 2 2 dx -y dxy 0 dyz/dzx (eV) F 2 -1 dz E - dxy -2 dyz/dzx 10 k z d 2 2 H3 x -y N1 -3 R 8 Γ Γ H3 H H3 H F2 F1 6 Different band gaps open in formerly equivalent directions P (eV) F (dependingF on 4 the magnetization direction) D E - 2 G H k E. Młyńczak et al., Phys. Rev. X 6, 041048 (2016) N y k x 0 -2 24. September 2019 Folie 33 -4 H N P N Magneto-crystalline anisotropy (MCA): 2nd order perturbation theory: for a specific direction, �@, the matrix elements are: Hˆ L~ S~ ' L~ eˆ ' i| SOC| j / i| · | j / i| · | j D E D E D E Le < zx | < yz | < xy | < x2-y2 | < 3z2-r2 | | zx > 0 -iez iex -iey i√3ey | yz > iez 0 -iey -iex -i√3ex | xy > -iex iey 0 2iez 0 2 2 | x -y > iey iex -2iez 0 0 2 2 | 3z -r > -i√3ey i√3ex 0 0 0 24. September 2019 Folie 34 MCA of a molecular magnet: dimer model: HOMO level determines easy axis ΔL = Lz-Lr = 0.19 μB ΔE = Ez-Er = -13.7 meV N. Atodiresei et al., Phys. Rev. Lett. 100, 117207 (2008) 24. September 2019 Folie 35 A solid example: Magnetite Early compass: images: Wikipedia images: 24. September 2019 Folie 36 Magnetite: larger MCA with Co doping 2+ 2- 3+ 2- 4 -3 Fe3O4: (Fe O )(Fe2 O3 ) K1= -210 (J/m ) 2+ 2- 3+ 2- 6 -3 CoFe2O4: (Co O )(Fe2 O3 ) K1≈10 (J/m ) "e g " eg m= 2 1 d 0 -1 t2g -2 "t 2g " atomic spin-orbit splitting spherical cubic trigonal Co2+ Co2+ Co2+ 24. September 2019 Folie 37 Single ion anisotropy: 5 4 -3 2 1 7 Gd: K1= -1.210 K2= +8.010 (J/m ) conf: 6s 5d 4f 7 6 -3 2 1 8 Tb: K1= -5.710 K2= -4.610 (J/m ) conf: 6s 5d 4f 24. September 2019 Folie 38 Other relativistic effects in magnetism: Ø spin – other orbit coupling: H = C S~ L~ i,j i · j i,j X Ø spin – spin coupling (magnetic dipolar interaction between spin moments at the same ion) Ø quadrupole – quadrupole interaction (electrostatic interaction between electron clouds) Breit correction: captures relativistic 2-particle effects (dipole-dipole int.) e2 e2 (~↵ ~r )(~↵ ~r ) E + Hˆ + Hˆ + = ~↵ ~↵ + 1 · 1 2 · 2 1 2 r 2r 1 · 2 r2 ✓ 12 ◆ 12 12 not captured in our DFT formalism! 24. September 2019 Folie 39 Summary: relativistic effects: Ø single particle Dirac equation (can be studied with l_soc=“t”) Ø scalar relativistic effects (d-band position Au, Ag) Ø spin-orbit effects Ø T & S inversion symmetry (p1/2-p3/2 splitting) Ø T inversion symmetry (Rashba & Dresselhaus effect) Ø no T inversion symmetry (magneto-crystalline anisotropy) Ø no T & S (anisotropic exchange, Dzyaloshinskii-Moryia interaction) Ø topological effects Ø k-space: topological insulators Ø real space: magnetic skyrmions Ø two particle effects (Breit correction, dipole-dipole interaction) 24.
Load more

Recommended publications
  • Rashba Spin-Orbit Coupling in the Oxide 2D Structures: the Ktao (001) Surface
    Rashba spin-orbit coupling in the oxide 2D structures: The KTaO3 (001) Surface Sashi Satpathy Department of Physics" University of Missouri, Columbia, USA E Ref: K. V. Shanavas and S. Satpathy, Phys. Rev. Letts. 112, 086802 (2014) ; Also: Supplementary section Correlated Oxides 2014, Minneapolis May 3, 2014 Gate control of the Rashba SOI in LaAlO3/SrTiO3 interface Measure Rashba coefficient from spin relaxation rates 2DEG Ben Shalom et al, PRL (2010) Caviglia, Gabay, et al., PRL (2010) 2 E Free-electron result : α R = 2m2c2 2 Ohtomo and Hwang, Nature (2004) βξ TB result : α R = , β ≈ E Popovic, SS, Martin, PRL (2008) ε ΔSO ΔE = 2α R k Looked for Rashba: Found small The Rashba Effect Momentum-dependent splitting of the spin bands in 2D systems (surfaces, interfaces, heterostructures) Rashba Hamiltonian: H R = α R (σ × k) · zˆ = α R (σ x ky − σ ykx ) Emmanuel I. Rashba (1927- ) E k kx y Spin degenerate Zeeman splitting B Rashba splitting E Ref: Rashba, Sov. Phys. Solid State (1960) Manifestation of the Rashba effect Theory: band structure Experiment Can drive a wide range of novel phenomena Spin tunneling, Spintronics, spin relaxation rates Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state in superconductors Topological p-wave superconductors Cold atoms Rashba splitting 2 α R | k | k 2 E↑↓ = ak ± α R | k | Expt: spin relaxation rates in STO/LAO: Caviglia et al., PRL (2010) Rashba effect: naïve derivation within the free electron model 1. Apply Electric field E = E zˆ 2. Electron sees the magne4c field in its rest frame: B = (v × E) / c2 3.
    [Show full text]
  • Spin Dynamics in Anisotropic Systems in the Presence of Spin-Orbit Coupling
    UNIVERSITÁ DEGLI STUDI ROMA TRE Doctorate in Physics – XXXI cycle Doctor of Philosophy dissertation Spin dynamics in anisotropic systems in the presence of spin-orbit coupling Candidate Supervisor Iryna Miatka Prof. Roberto Raimondi Doctorate courses 2015-2018 "You’ve got to jump off cliffs and build your wings on the way down." - Ray Bradbury Summary Chapter1 The first chapter smoothly prepares the reader for the next stages by familiar- izing with the main background of the study. The reader will understand the main goal of spintronics and why usage of spin-current has more advantages than the charge current. Chapter2 In Chapter 2 the reader can discover the mechanisms of spin-orbit in solid state systems, starting from the Dirac equation and from the energy band interaction in the Kane model. Chapter3 In this chapter, we enter in quasi-classical formalism in order to treat the transport problems at a quantum level. It will be derived the Eilenberger equation which is the background for understanding the result of the thesis. Chapter4 In this chapter we present our contribution - the result of the interplay of spin-orbit couplings onto the inverse spin-galvanic effect, one of the most relevant phenomena in spintronics that leads to charge-spin tunability. This chapter contains the main study of this work, satisfying the aim presented in the introduction. Chapter5 Here we describe how to generate synthetically spin-orbit coupling in a model that is free of disorder but is charge-neutral - ultracold atoms. Chapter6 We present the analytical time-dependent exact and approximate solutions to the anisotropic model of cold atoms with spin-orbit coupling and external perturbations.
    [Show full text]
  • Rashba Spin-Orbit Interaction in Semiconductor Nanostructures (Review)
    Asian Journal of Physical and Chemical Sciences 8(2): 32-44, 2020; Article no.AJOPACS.57016 ISSN: 2456-7779 Rashba Spin-orbit Interaction in Semiconductor Nanostructures (Review) Ibragimov Behbud Guseyn1* 1Institute of Physics, Azerbaijan National Academy of Sciences, Azerbaijan State Oil and Industry University, Azerbaijan. Author’s contribution The sole author designed, analysed, interpreted and prepared the manuscript. Article Information DOI: 10.9734/AJOPACS/2020/v8i230115 Editor(s): (1) Dr. Thomas F. George, University of Missouri - St. Louis One University Boulevard St. Louis, USA. (2) Dr. Shridhar N. Mathad, KLE Institute of Technology, India. Reviewers: (1) Kruchinin Sergei, Ukraine. (2) Subramaniam Jahanadan, Malaysia. (3) M. Abu-Shady, Menoufia University, Egypt. (4) Vinod Prasad, India. (5) Ricardo Luís Lima Vitória, Universidade Federal do Pará, Brazil. Complete Peer review History: http://www.sdiarticle4.com/review-history/57016 Received 25 March 2020 Accepted 01 June 2020 Review Article Published 09 June 2020 ABSTRACT In this work I review of the theoretical and experimental issue related to the Rashba Spin-Orbit interaction in semiconductor nanostructures. The Rashba spin-orbit interaction has been a promising candidate for controlling the spin of electrons in the field of semiconductor spintronics. In this work, I focus study of the electrons spin and holes in isolated semiconductor quantum dots and rings in the presence of magnetic fields. Spin-dependent thermodynamic properties with strong spin- orbit coupling inside their band structure in systems are investigated in this work. Additionally, specific heat and magnetization in two dimensional, one-dimensional quantum ring and dot nanostructures with Spin Orbit Interaction are discussed. Keywords: Spin-orbit interaction; Rashba effect; two dimension electron gas; one-dimensional ring; quantum wire; quantum dot; semiconductor nanostructures.
    [Show full text]
  • Dedigama Ou 0169D 10205.Pdf
    UNIVERSITY OF OKLAHOMA GRADUATE COLLEGE SPIN-ORBIT COUPLING EFFECTS IN InSb QUANTUM WELL STRUCTURES A DISSERTATION SUBMITTED TO THE GRADUATE FACULTY in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY By ARUNA RUWAN DEDIGAMA Norman, Oklahoma 2009 SPIN-ORBIT COUPLING EFFECTS IN InSb QUANTUM WELL STRUCTURES A DISSERTATION APPROVED FOR THE HOMER L. DODGE DEPARTMENT OF PHYSICS AND ASTRONOMY BY _______________________ Dr. Sheena Murphy (Chair) _______________________ Dr. Matthew B. Johnson _______________________ Dr. Michael B. Santos _______________________ Dr. Kieran Mullen _______________________ Dr. Zhisheng Shi 2 © Copyright by ARUNA RUWAN DEDIGAMA, 2009 All Rights Reserved. 3 To my parents 4 ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my thesis advisor Prof. Sheena Q. Murphy for her guidance, support and encouragement during my research work. Her expertise, patience and understanding have been remarkably helpful to me throughout my graduate studies at The University of Oklahoma. I am very grateful to my graduate committee members Prof. Matthew B. Johnson, Prof. Michael B. Santos, Prof. Kieran Mullen and Prof. Zhisheng Shi for their support and guidance in completing this work. I would like to acknowledge Prof. Matthew B. Johnson for providing invaluable guidance in nanofabrication instrumentation and Prof. Michael B. Santos for providing high quality InSb quantum well structures. Special thanks to Prof. Kieran Mullen for useful discussions and theoretical simulations, also I would like to thank him for his help in my admission process to the University of Oklahoma. I would like to thank all the faculty and staff members of the department of Physics and Astronomy for their valuable support during my graduate studies.
    [Show full text]
  • Reversible Spin Texture in Ferroelectric Hfo2 L
    Reversible spin texture in ferroelectric HfO2 L. L. Tao,* Tula R. Paudel, Alexey A. Kovalev, and Evgeny Y. Tsymbal† Department of Physics and Astronomy & Nebraska Center for Materials and Nanoscience University of Nebraska, Lincoln, Nebraska 68588, USA Spin-orbit coupling effects occurring in non-centrosymmetric materials are known to be responsible for non-trivial spin configurations and a number of emergent physical phenomena. Ferroelectric materials may be especially interesting in this regard due to reversible spontaneous polarization making possible for a non-volatile electrical control of the spin degrees of freedom. Here, we explore a technologically relevant oxide material, HfO2, which has been shown to exhibit robust ferroelectricity in a non-centrosymmetric orthorhombic phase. Using theoretical modelling based on density-functional theory, we investigate the spin-dependent electronic structure of the ferroelectric HfO2 and demonstrate the appearance of chiral spin textures driven by spin-orbit coupling. We analyze these spin configurations in terms of the Rashba and Dresselhaus effects within the kp Hamiltonian model and find that the Rashba-type spin texture dominates around the valence band maximum, while the Dresselhaus-type spin texture prevails around the conduction band minimum. The latter is characterized by a very large Dresselhaus constant αD = 0.578 eV Å, which allows using this material as a tunnel barrier to produce tunneling anomalous and spin Hall effects that are reversible by ferroelectric polarization. I. INTRODUCTION The linear SOC can be written in terms of an effective k- dependent field Ω(k) affecting the spin σ : 22 Crystalline materials lacking space inversion symmetry exhibit electronic energy bands that are split by spin-orbit coupling HSO Ω()k σ , (1) (SOC).
    [Show full text]
  • Band Splitting with Vanishing Spin Polarizations in Noncentrosymmetric Crystals
    ARTICLE https://doi.org/10.1038/s41467-019-13197-z OPEN Band splitting with vanishing spin polarizations in noncentrosymmetric crystals Kai Liu1,2, Wei Luo1,2, Junyi Ji1,2, Paolo Barone 3, Silvia Picozzi3* & Hongjun Xiang 1,2* The Dresselhaus and Rashba effects are well-known phenomena in solid-state physics, in which spin–orbit coupling splits spin-up and spin-down energy bands of nonmagnetic non- centrosymmetric crystals. Here, we discuss a phenomenon we dub band splitting with 1234567890():,; vanishing spin polarizations (BSVSP), in which, as usual, spin-orbit coupling splits the energy bands in nonmagnetic non-centrosymmetric systems. Surprisingly, however, both split bands show no net spin polarization along certain high-symmetry lines in the Brillouin zone. In order to rationalize this phenomenon, we propose a classification of point groups into pseudo-polar and non-pseudo-polar groups. By means of first-principles simulations, we demonstrate that BSVSP can take place in both symmorphic (e.g., bulk GaAs) and non-symmorphic systems (e.g., two dimensional ferroelectric SnTe). Furthermore, we identify a linear magnetoelectric coupling in reciprocal space, which could be employed to tune the spin polarization with an external electric field. The BSVSP effect and its manipulation could therefore form the basis for future spintronic devices. 1 Key Laboratory of Computational Physical Sciences (Ministry of Education), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, China. 2 Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China. 3 Consiglio Nazionale delle Ricerche CNR-SPIN Via dei Vestini 31, 66100 Chieti, Italy. *email: [email protected]; [email protected] NATURE COMMUNICATIONS | (2019) 10:5144 | https://doi.org/10.1038/s41467-019-13197-z | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-019-13197-z he study of a relativistic interaction, i.e., the spin-orbit effects.
    [Show full text]
  • Band Splitting with Vanishing Spin Polarizations In
    Band splitting with vanishing spin polarizations in noncentrosymmetric crystals Kai Liu1,2, Wei Luo1,2, Junyi Ji1,2, Paolo Barone3, Silvia Picozzi3*, Hongjun Xiang1,2* 1Key Laboratory of Computational Physical Sciences (Ministry of Education), State Key Laboratory of Surface Physics, and Department of Physics, Fudan University, Shanghai 200433, P. R. China 2Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, P. R. China 3Consiglio Nazionale delle Ricerche CNR-SPIN Via dei Vestini 31, Chieti 66100, Italy E-mail: [email protected], [email protected] Abstract: The Dresselhaus and Rashba effects are well-known phenomena in solid- state physics, in which spin–orbit coupling (SOC) splits spin-up and spin-down energy bands of nonmagnetic non-centrosymmetric crystals. Here, we discover a new phenomenon, dubbed as band splitting with vanishing spin polarizations (BSVSP), in which, as usual, SOC splits the energy bands in nonmagnetic non-centrosymmetric systems; surprisingly, however, both split bands show no net spin polarization along certain high-symmetry lines in the Brillouin zone. In order to rationalize this phenomenon, we propose a new classification of point groups into pseudo-polar and non-pseudo-polar groups. By means of first-principles simulations, we demonstrate that BSVSP can take place in both symmorphic (e.g., bulk GaAs) and non-symmorphic systems (e.g., two dimensional ferroelectric SnTe). Furthermore, we propose a novel linear magnetoelectric coupling in reciprocal space, which could be employed to tune the spin polarization with an external electric field. The BSVSP effect and its manipulation could therefore pave a new way to novel spintronic devices.
    [Show full text]
  • Hidden Spin Polarization in Inversion-‐Symmetric Bulk Crystals
    Hidden spin polarization in inversion-symmetric bulk crystals Xiuwen Zhang1,2,3,*, Qihang Liu1,4,*, Jun-Wei Luo3,#, Arthur. J. Freeman4 and Alex Zunger1,# 1University of Colorado, Boulder, CO 80309, USA 2Colorado School of Mines, Golden, CO 80401, USA 3National Renewable Energy Laboratory, Golden, CO 80401, USA 4Deprtment of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA *These authors contributed equally to this work. #E-mail: [email protected]; [email protected] 1 Spin-orbit coupling (SOC) can induce spin polarization in nonmagnetic 3D crystals when the inversion symmetry is broken, as manifested by the bulk Rashba (R-1) and Dresselhaus (D-1) effects. We determine that these spin polarization effects originate fundamentally from specific atomic site asymmetries, rather than from the generally accepted asymmetry of the crystal space-group. This understanding leads to the recognition that a previously overlooked hidden form of spin polarization should exist in centrosymmetric materials. Although all energy bands must be doubly degenerate in centrosymmetric materials, we find that the two components of such doubly degenerate bands could have opposite polarizations each spatially localized on one of the two separate sectors forming the inversion partners. We demonstrate such hidden spin polarizations in centrosymmetric crystals (denoted as R-2 and D-2) by first-principles calculations. This new understanding could considerably broaden the range of currently useful spintronic materials and enable control of spin polarization via operations on atomic scale. 2 Much of the recent interest in spintronics1, 2 has been prompted by the fact that when spin-orbit coupling (SOC) occurs in systems with sufficiently low crystalline symmetry, an effective magnetic field BVeff =λ[()]∇rp × emerges [where V(r) denotes the crystal potential and p the momentum])3 that leads to spin splitting and spin polarization even in nonmagnetic materials.
    [Show full text]
  • THÈSE DE DOCTORAT Mme. Mai Chung NGUYEN
    NNT: 2016SACLS460 THÈSE DE DOCTORAT DE L’UNIVERSITÉ PARIS-SACLAY PRÉPARÉE À L’UNIVERSITÉ PARIS-SUD ÉCOLE DOCTORALE 575 EOBE Electrical, optical, bio-physics and engineering Spécialité de doctorat: Physique Par Mme. Mai Chung NGUYEN Etude théorique de nanodispositifs électroniques et thermoélectriques à base de jonctions contraintes de graphène Thèse présentée et soutenue à Orsay, le 2 Décembre 2016: Composition du Jury: M. Henri HAPPY Université de Lille 1, IEMN Président Mme. Mireille MOUIS CNRS, IMEP-LAHC, Grenoble Rapporteur M. Nicolas CAVASSILAS Université d'Aix-Marseille, IM2NP Rapporteur M. Viet Hung NGUYEN IMCN, Université Catholique de Louvain Examinateur M. Huy-Viet NGUYEN Institute of Physics Hanoi Co-directeur de thèse M. Philippe DOLLFUS CNRS, C2N, Orsay Directeur de thèse Acknowledgements Firstly, I would like to express my sincere gratitude to my supervisors, Dr. Philippe DOLLFUS and Dr. HuyViet NGUYEN for their support, patience, motivation, and immense knowledge in all the time of study and writing of this thesis. I also express my deepest thanks to Dr. Vi- etHung NGUYEN, who has ever kept a post-doc position in our group (COMICS), for his training, helping and sharing in research. To be hon- est, I am really very lucky to work with them. Without their guidance and encouragement, this work would have taken a longer time to complete. Besides my advisors, I would like to take this opportunity to thank all my colleagues in COMICS group (Prof. Arnaud Bournel, Dr. Jerome Saint-Martin, Dr. Damien Querlioz, Dr. Michele Amato, Mr. Christophe Chassat, Dr. Tran Van Truong, Dr. Jerome Larroque, Dr. Thanayut Kaewmaraya, Mr.
    [Show full text]
  • Rashba and Dresselhaus Couplin
    Rashba and Dresselhaus Couplings in Halide Perovskites: Accomplishments and Opportunities for Spintronics and Spin-Orbitronics Mikael Kepenekian, Jacky Even To cite this version: Mikael Kepenekian, Jacky Even. Rashba and Dresselhaus Couplings in Halide Perovskites: Accom- plishments and Opportunities for Spintronics and Spin-Orbitronics. Journal of Physical Chemistry Letters, American Chemical Society, 2017, 8 (14), pp.3362-3370. 10.1021/acs.jpclett.7b01015. hal- 01551094 HAL Id: hal-01551094 https://hal.archives-ouvertes.fr/hal-01551094 Submitted on 5 Dec 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Page 1 of 29 1 2 3 4 5 6 7 8 Rashba and Dresselhaus Couplings in Halide 9 10 11 12 Perovskites: Accomplishments and Opportunities 13 14 15 for Spintronics and Spin-orbitronics 16 17 18 ,† ,‡ 19 Mikaël Kepenekian⇤ and Jacky Even⇤ 20 21 22 Institut des Sciences Chimiques de Rennes, UMR 6226, CNRS - Université de Rennes 1, France, 23 24 and Fonctions Optiques pour les Technologies de l’Information (FOTON), INSA de Rennes, 25 26 CNRS, UMR 6082, France
    [Show full text]