Superfluidity and spin superfluidity (in spinor Bose gases and - PowerPoint PPT Presentation

Superfluidity and spin superfluidity (in spinor Bose gases and magnetic insulators) Rembert Duine Institute for Theoretical Physics, Utrecht University Department of Applied Physics, Eindhoven University of Technology Nature Physics 11, 1022–1026 (2015), Phys. Rev. Lett. 116, 117201 (2016), arXiv:1603.01996 [cond-mat.quant-gas], arXiv:1604.03706 [cond-mat.mes-hall]

Collaborators Utrecht: Benedetta Flebus Kevin Peters Gerrit Bauer (also Delft/Sendai) Other: Jogundas Armaitis (Vilnius) Ludo Cornelissen, J. Liu, Bart van Wees (Groningen) Yaroslav Tserkovnyak, Scott Bender (UCLA->UU) J. Ben Youssef (Brest), Arne Brataas (NTNU)

Long-term motivation lead lead I=V/R with superconductor R independent of L below room T L lead lead ? spin superfluid above room T? L

Outline • Introduction superfluidity and spin superfluidity • Spinor gases: combining superfluidity and spin superfluidity (theory) • Spin transport through magnetic insulators (theory and experiment)

Superfluid (mass) transport c e    i = Superfluid U(1) order parameter: Im         v J m c c Re         j v supercurrent: carried by c c c   c j + condensate     c t     t chemical potential  Wave-like excitations:            J k 2 J k If zero then c c s (ballistic transport)  g  stiffness interactions c

Halperin/Hohenberg (1969) (ballistic) spin transport       H J S S Magnetic insulator xc i j (exchange only) i j ,         dS  Landau-Lifschitz        2 i   J S S J S S j xc i j xc equation: dt    j neigbours i          spin current: j J S S ; x y z , ,   xc   2 J k particle-like excitations: spin waves/magnons xc

Halperin/Hohenberg (1969); review: Sonin (2010) Spin superfluidity (I) Easy-plane magnetic insulator [SO(3) -> U(1)]           2       z z H J S S S K S B S   xc i i 1 i 1 i i i i i exchange anisotropy field    2 3  T k J 1 B K BEC B xc     Holstein- ˆ 2 Re a   Primakoff      trafo: S ~ 2 Im a ˆ      † ˆ ˆ a a 1   Review: Giamarchi (2008)

Halperin/Hohenberg (1969); Koenig et al. (2001); review: Sonin (2010) Spin superfluidity (II) Zero T dynamics governed by Landau-Lifshitz equation:    dS         2 z ˆ ˆ J S S KS z Bz   xc dt   Write:  2 n cos   c     S ~ 2 n sin c        n n 1        2 c c J n j  xc c s t Same as equations       for mass superfluid!   B K Kn  c   t J Kn k xc c

Spin superfluidity (III)     j J n ; polarization in -direction z  s , xc c

Halperin/Hohenberg (1969); review: Sonin (2010) Mass vs. spin superfluidity • mass current j c • spin current j s • phase of superfluid • in-plane angle of order parameter  magnetization  • superfluid stiffness J s • exchange interactions J xc • interparticle interactions g • easy-plane anisotropy K c e     i

Outline • Introduction superfluidity and spin superfluidity • Spinor gases: combining superfluidity and spin superfluidity (theory) • Spin transport through magnetic insulators (theory and experiment)

Related work • Our work: hydrodynamic description treating spin and mass superfluidity on equal footing • Spin currents in spinor gases: - K. Kudo and Y. Kawaguchi, Physical Review A 84 , 043607 (2011). - H. Flayac, et al ., Physical Review B 88 , 184503 (2013). - Q. Zhu, Q.-f. Sun, and B. Wu, Phys. Rev. A 91 , 023633 (2015). • Stability of spirals: - R. W. Cherng, et al ., Phys. Rev. Lett. 100 , 180404 (2008). • Magnon condensation: - Fang, et al ., Phys. Rev. Lett. 116 , 095301 (2016) – tonight’s evening talk (?). • Reviews: - Y. Kawaguchi and M. Ueda, Physics Reports 520 , 253 (2012). - D. M. Stamper-Kurn and M. Ueda, Rev. Mod. Phys. 85 , 1191 (2013).

Questions • Which system is both a mass and spin superfluid? • What is the interaction between mass and spin superfluidity in such a system? NB: a ferromagnetic mass superfluid  spin superfluid

Ferromagnetic spinor Bose with quadratic Zeeman effect leads to Bose easy-plane g 1 <0, leads to field We have condensation anisotropy ferromagnetism hamiltonian:       2 2        2 2 2             ˆ † z z † † ˆ ˆ ˆ ˆ ˆ ˆ H dx  BF K F  g g F 0 1   2 m Deep in ferromagnetic regime, zero T linearized mean-field equations reduce to equations for uncoupled mass and spin superfluid with:    Superfluid and spin stiffness: J J m s xc     Collective modes: K K B     k      c g g mk spin m mass 0 1 Armaitis and RD, arXiv (2016)

Collective (Goldstone) modes T T FM quadratic spin modes ferromagnet T BEC superfluid ferromagnet linear density + quadratic spin modes T magnon BEC linear density & spin modes superfluid & spin superfluid

Coupling between spin and mass superfluid Occurs via hydrodynamic derivative:                 v with v n   z t t m Influence of spin polarized mass current on magnetization Current driven by dynamics: “spin transfer” magnetic texture Armaitis and RD, arXiv (2016)

Stationary solutions   n K Stationary solutions     z   ' '  possible if:   2 J ' s Armaitis and RD, arXiv (2016)

Discussion • Dipolar interactions (lower critical current) • Upper critical current • Quasi-equilbrium magnon condensation • Magnon kinetics • Coupling to nematic/antiferromagnetic order

Outline • Introduction superfluidity and spin superfluidity • Spinor gases: combining superfluidity and spin superfluidity (theory) • Spin transport through magnetic insulators (theory and experiment)

Long-term motivation lead lead I=V/R with superconductor R independent of L below room T L lead lead ? spin superfluid above room T? L

Experiment (I) - Pt strips on magnetic insulator Yttrium-Iron-Garnett (YIG) - Non-local (“drag”) resistance R D =V/I - Room T

Experiment (II) - Short distance: 1/distance Long distance: exponential decay (length scale 10  m) -

Idea Electron charge current Magnon spintronics: electical control over magnon spin currents Electron spin current Magnonic many-body Magnon spin current physics Electron spin current Route to spin currents with low dissipation Electron charge current Image courtesy Ludo Cornelissen and Bart van Wees

cos  Interfacial spin current * cos  = cos  2 R=V/I

Model       e  j  L / magnon diffusion s m m signal ~  & relaxation:    2  2 m 1 For spin superfluid this would be ~  1 C L Takei and Tserkovnyak (2014); Flebus, Bender, Tserkovnyak, RD (2016)

Take home messages • Spin superfluidity is not ferromagnetic superfluidity • Spinor Bose gas can be spin and/or mass superfluid • Recent developments of spintronics pave the way for integration electronic and magnonic (eventually superfluid) low-dissipation spin currents & bosonic many-body physics