Spin torque induced by triplet supercurrent

Transcription

1 Spin torque induced by triplet supercurrent and Supercurrent induced noncollinear order Rina Takashima Kyoto Univ. in collaboration with T. Yokoyama (Tokyo Institute of Technology ), S. Fujimoto (Osaka University) Y. Motome, Y. Kato (University of Tokyo), Y. Yanase (Kyoto University)

2 Outline of this talk 1 st part Spin-torque induced by spin-triplet supercurrent 1 R. Takashima, S. Fujimoto, T. Yokoyama, PRB 96, (R) (2017) 2 nd part Noncollinear magnetic order induced by supercurrent R. Takashima, Y. Kato, Y. Yanase, Y. Motome (to be submitted ) 2

3 Outline 1 st part Spin-torque induced by spin-triplet supercurrent R. Takashima, S. Fujimoto, T. Yokoyama, arxiv: (to appear in PRB(R) ) Motivation Result : general form of spin torque Application: Domain wall dynamics 3

4 Triplet Cooper pairs Spin-triplet proximity effect inside ferromagnet - triplet SC FM with Sr 2 RuO 4 - singlet SC noncollinear magnet FM Singlet-Triplet Conversion Interplay of spin-triplet pairing and magnetic moment? 4

5 Current-induced torque in normal magnet Electric current in magnet exerts spin-torque on localized moment Manipulation of spin Application in magnetic devices (spin-transfer torque) Spin angular momentum is transferred Racetrack memory using domain wall / Skyrmions Parkin et al Science (2008) RIKEN News Letter No.404 (2015) 5

6 Motivation of our work Question: How triplet-correlation changes spin transfer torque? We study spin-transfer torque induced by triplet supercurrent c.f.) early works for spin-torque in magnetic Josephson junction: Waintal& Brouwer PRB(2002), Y. Tserkovnyak &A. Brataas PRB (2002), etc keypoint : - Supercurrent-induced torque might realize energetically efficient devices - Triplet order parameter (=d vector) might give new type of torque? (spin susceptibility characterizes spin-transfer process) 6

7 Model metallic magnet (s-d model) with proximity induced triplet pairing model ferromagnet SC (source of triplet) (square lattice) supercurrent flow is given by the spatial gradient of SC phase 7

8 Calculation of spin torque conduction electron local spin torque : = local spin density of electrons under supercurrent localized moment we calculate spin density within linear response We assume Localized moment varies smoothly Exchange splitting is large we only take equal spin pairing ( (anti)parallel to n) 8

9 Result: supercurrent-induced torque Obtained torque : direct transfer of spin from neighboring sites (~ adiabatic torque ) : deviation from direct transfer (~ β term ) ~ spin polarization of electrons -originate in order parameter. - depend on the direction of n (spatial dependence) explicit form:

10 What causes β term? c.f. ) Normal system Zhang& Li (2004), Tatara et al. (2008), Tserkovnyak et al(2008) - β is qualitatively important - magnetic impurity scattering / mistracking β term With triplet-sc correlation anisotropy in spin susceptibility deviation from direct transfer β term can be controlled by triplet order parameters (d-vector). ( in normal metals, it depends on extrinsic scattering) 10

11 Application: Domain wall manipulation Domain wall texture in ferromagnetic metal Assume the d-vector is favored Apply a current (=phase gradient ) Domain wall moves EOM of collective coordinates (X: domain wall center) 11

12 (detail) Spatial dependence of β domain wall configuration has strong spatial dependence 12

13 velocity velocity Domain wall dynamics Under a constant supercurrent, Current dependence of velocity at t = Time dependence of velocity current density current density No threshold current density *without extrinsic pinning w/o β terms, threshold current exists * β terms arises from d-vector time No oscillatory motion Normal metal, oscillation occurs * β depends on space 13

14 Summary of 1 st part RT, Fujimoto, Yokoyama,PRB 96, (R) Spin-transfer torque by triplet supercurrent We obtain the spin-torque given by a new type of term : Interplay of d-vector and magnetic moment n triplet correlation changes spin susceptibility of electrons (~spin transfer process) domain wall manipulation - threshold current density is lowerd - No oscillatory motion 14

15 Outline 1 st part Spin-torque induced by spin-triplet supercurrent 1 R. Takashima, S. Fujimoto, T. Yokoyama, arxiv: (to appear in PRB(R) ) 2 nd part Noncollinear magnetic order controlled by R. Takashima, Y. Kato, Y. Yanase, Y. Motome (to be submitted ) 15

16 Noncollinear magnetism and SC proximity effect Noncollinear magnetic order : Spins are not in parallel/antiparallel Noncollinear magnetic order is important in physics of SC proximity effects Singlet-triplet pairing conversion Keizer et al, Nat. Lett. (2006) Robinson et al, Science (2010) Topological superconductor w/o spin-orbit coupling Klinovaja et al. (2013) Klinovaja et al. (2013) 16

17 Motivation of our work Question: Can we switch/control noncollinear magnetic order in the presence of SC proximity effect? can be used to switch /optimize the singlet-triplet conversion to externally control topological SC and Majorana zero modes etc In our work: We propose a new way to induce noncollinear magnetic order by a supercurrent 17

18 Model model metal singlet SC 2d Correlated metal attached to s-wave SC with a supercurrent repulsive Hubbard interaction mean field of spin density singlet supercurrent ( spatial gradient of SC phase ) 18

19 Magnetic instability bare spin susceptibility in the continuum model : suppression by singlet gap w/o current supercurrent increase Anderson&Suhl (1959) much smaller than g >0 and peak at q/k F ~2 Supercurrent leads to magnetic instability 19

20 Magnetic order in lattice system square lattice model : w/o current Instability : Variational ansatz ( : variational parameter) single-q double-q double-q order is stabilized 1 st order transition behavior supercurrent density T=0K fixed U current magnitude Supercurrent induces first-order transition to double-q state for double-q 20

21 Switch to single-q magnetic order We can switch magnetic state by the direction of supercurrent supercurrent fixed U, κa current angle 21

22 Phase diagram (T=0K) Critical U decreases as current increases switch of magnetic states magnitude of current current angle 22

23 Summary of 2 nd part We propose a new way to control noncollinear order by supercurrent Supercurrent induces 1 st order phase transition to double-q state Switch magnetic states by current direction (singlet) supercurrent Remark 1) First-order transition metastable state of magnetic order w/o supercurrent 2) Different lattices/pairing a wide range of magnetic states, e.g. skyrmion 3)Rashba Spin-orbit coupling 23

24 Rashba spin orbit coupling Rashba SOC at the interface (singlet) Energy functional 1 spin-spiral plane is locked 2Inverse-Edelstein effect in-plane magnetic field cf) w/o SOC Realized magnetic states would be modulated 24

25 1 st part Conclusion Background Model experiments on triplet-proximity effect in magnet metallic magnet + triplet pairing potential Spin-triplet supercurrent give a new type of spin-transfer-torque RT, Fujimoto, Yokoyama,PRB 96, (R) 2 nd part Background Model Rich physics arise from interplay of noncollinear order and SC 2d correlated metal + singlet pairing potential Supercurrent induce double-q/single-q magnetic order R. Takashima, Y. Kato, Y. Yanase, Y. Motome (to be submitted) 25