Institute for Theoretical Physics

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1 Spintronics i with cold atoms Rembert Duine Phys. Rev. Lett. 103, (2009) Phys. Rev. Lett. 104, (2010) Phys. Rev. Lett. 105, (2010) Institute for Theoretical Physics Utrecht University

2 Collaborators Ph. D. Students: Ties Lucassen, Aaron Swaving, Hedwig van Ak Acknowledgements: ld Driel, Erik van der Bijl, Martijn Mink, Jogundas Armaitis, Gerrit Bauer (Delft) Rakpong Kittinaradorn Hiroshi Kohno (Osaka) postdocs: Clement Wong, Alice Bezett Maxim Mostovoy (Groningen) i Profs. Cristiane de Morais, Peter van der Straten and Henk Stoof (Utrecht University) Allan MacDonald (UT Austin) Paul Haney (NIST) Alvaro Núñez (Valparaiso, Chile) Jairo Sinova (Texas A&M) Achim Rosch s group (Cologne) Christian Pfleiderers group (TU Munich) R. Lavrijsen.+TU/e team Giovanni Vignale (Missouri) Marco Polini (SNS Pisa)

3 Spintronics i with cold atoms Does it exist? What can we learn from it? What is it good for?

4 Lecture - outline Solid-state electronics and spintronics Cold atoms Spintronics with cold-atom systems

5 Electronic transport t (I) V A(rea) L(ength) V EL E E I j ea j e ee R R RA L esistivity) e : conductivity

6 Electronic transport t (II) V Drift velocity: nv t dk f kt, 3 2 Newton s equation of motion+dissipation: k m nm e dv nmev nee dt tr relaxation

7 Electronic transport (III) V nm e dv nmev nee E e dt e tr j nev ee m ne dv steady state: 0 e 2 dt tr Drude formula

8 Transport relaxation time ps (metals) tr tr 0 ep ee + + Elastic impurity scattering Electron-phonon scattering Electron-electron interactions

9 Electron-electron l t interactions ti (I) nf Fermi-Dirac distribution function kt/ B F 1 T 2 for T T 0 F ee / F Due to Pauli blocking Hallmark of a Fermi liquid

10 Electron-electron interactions (II) k q q 2 k1 + Interactions do not contribute to change in drift velocity and do not contribute to resistivity in translation invariant system need underlying lattice need underlying lattice k k 2 1 Galilean invariance: resistivity zero

11 Electro-chemical l potential ti Closed circuit: E j=0 L Voltage 0 EL L Current j E e e e Ex cst e j e 0 Need: Conservation of charge L vftr

12 Recap (I): Lecture - outline Solid-state electronics and spintronics electric current, resistivity/conductivity, y electro-chemical potential, hydrodynamics Cold atoms Spintronics with cold-atom systems

13 Mott What is spintronics? i Removing the factor of two for spin degeneracy j E j E Spin drag (Orenstein talk?) for now ignore (should go like T 2 ) (This ignores non-collinear magnetization dynamics and strong spin-orbit coupling, heat current...)

14 Silsbee/Johson, Valet/Fert, Bauer (next talk) magnet-normal metal interface ferromagnet Normal metal Charge conservation: j e j e 0 Spin accumulation s 2 s s 2 sf Spin-flip rel. length Spin accumulation at interface

15 Recap (II): Lecture - outline Solid-state electronics and spintronics electric current, resistivity/conductivity, y electro-chemical potential, hydrodynamics, everything spin-resolved, spin accumulation Cold atoms Spintronics with cold-atom systems

16 Spintronics i with cold atoms Does it exist? What can we learn from it? What is it good for?

17 First: introducting ti cold atoms

18 Introducing cold atoms (I) Electrons in metals charge e Spin S=1/2 fermion ionic lattice disorder phonons spin-orbit coupling long range e-e interactions Trapped cold atoms neutral, e.g., Rb-87, Li-6/7,... (hyperfine) spin F=... Bosons and/or fermions magnetic and/or optical trap disorder can be phonons engineered spin-orbit coupling short-range atomic interactions

19 Introducing cold atoms (II) Laser cooling, harmonic confining potential, evaporative cooling,absorption imaging

20 Hulet group 13:30) Introducing cold atoms (III) This experiment: few million atoms (Generally ranges from ) Lithium-7 (Boson -> Bose Condensation!) Lithium-6 (Fermion, T/T_F~0.1)

21 First Bose condensate (1995) C. Wieman, E. Cornell (Nobel prize, 2001)

22 Two interfering i Bose condensates Classical waves W. Ketterle (Nobel prize, 2001) matter waves

23 Rotation: ti quantum vortices NB: rotation acts like magnetic field!!

24 Introducing cold atoms (IV) + many more (mostly equilibrium) results...e.g: e happy Bose condensate

25 Collective modes (I) Dipole oscillation

26 Collective modes (II) Breathing mode

27 Spintronics i with cold atoms Does it exist? What can we learn from it? What is it good for?

28 Homogeneous cold-atom system (I) Two spin states n n n Spin-dependent forces: F F No condensate dv v v nm nm nf dt No disorder/phonons; Only interactions that dv v v nm nm nf lead to spin drag dt

29 Homogeneous cold-atom system (II) Two spin states n n n Spin-dependent forces: F F No condensate Spin-resolved particle current dv v v nm nm nf j nv dt dv v v F nm nm nf j dt j F

30 Homogeneous cold-atom system (III) Two spin states n n n Spin-dependent forces: F F No condensate dv v v nm nm nf dt dv v v nm nm nf dt j s n v v j n v v j 0 F F j s 0 F F s /2

31 Homogeneous cold-atom system (IV) Two spin states n n n Spin-dependent forces: F F No condensate j s n v v j n v v j 0 F F j 0 F F /2 s s n s m Spin conductivity determined by interactions (spin drag)

32 Trapped cold atom systems (I) Bulk transport: Size of clouds should be larger than mean free path Size of clouds :L~m-mm relaxation time: ms Both collisionless and hydrodynamic regimes possible 2 d x nm d x x 2 nm nm x 2 dt dt 2 d x nm d x x 2 nm nm x 2 dt dt

33 Trapped cold atom systems (II) /2 X x x x x x 2 d x nm d x x 2 nm nm x 2 dt dt 2 d x nm d x x 2 nm nm x 2 dt dt

34 Trapped cold atom systems (II) 2 d X 2 nm nm X 2 dt 2 d x 2nm dx 2 nm nm x 2 dt dt d Dipole-mode undamped (Kohn s theorem) i sd ni m Measure spin conductivity it from damping spin-dipole mode s

35 Talk by M. Zwierlein, 14:40 Experiments on cold fermions 1 temperature Experiments with bosons: P. van der Straten (Utrecht)

36 Recap (III): Lecture - outline Solid-state electronics and spintronics electric current, resistivity/conductivity, y electro-chemical potential, hydrodynamics, everything spin-resolved, spin accumulation Cold atoms spin currents, spin conductivity, determined from collective modes Spintronics with cold-atom systems

37 Spintronics i with cold atoms Does it exist? What can we learn from it? What is it good for?

38 Recap (III): Lecture - outline Solid-state electronics and spintronics electric current, resistivity/conductivity, y electro-chemical potential, hydrodynamics, everything spin-resolved, spin accumulation Cold atoms spin currents, spin conductivity, determined from collective modes Spintronics with cold-atom systems spin conductivity: bosons vs. fermions

39 Spin transport properties cold gases (I) Boltzmann equation leads to: i sd ni m Measure spin conductivity from damping spin-dipole mode s 1 ~ all momenta f f 2 f 3 f 4 a k f k f k f k f k f k f k 1 f k 1 f k +momentum/energy conservation Pauli blocking vs. Bose enhancement

40 Spin transport properties cold gases (II) s ~ T (fermions "blocking" in 3D) 10 m ~ 1 ~ (bosons "lasing" in quasi-1d) 10 m (use charge= ) s T e Enhancement of spin resistivity (reduction of spin conductivity) upon approaching critical temperature for Bose condensation!

41 Spintronics i with cold atoms Does it exist? What can we learn from it? Fundamentals of spin transport, different regimes w.r.t. electrons in solids (interactions vs. disorder/phonons) What is it good for?

42 More examples/teasers: Poster Erik van der Bijl P Cl W M ij Mi k Posters Clement Wong, Martijn Mink, Hedwig van Driel, Alice Bezett

43 Spintronics i with cold atoms Does it exist? What can we learn from it? Fundamentals of spin transport, different regimes w.r.t. electrons in solids (interactions vs. disorder/phonons) What is it good for?

44 Spintronics i with cold atoms Does it exist? What can we learn from it? Fundamentals of spin transport, different regimes w.r.t. electrons in solids (interactions vs. disorder/phonons) What is it good for? Understanding magnon transport/bose condensation magnons in magnetic insulators

45 Quasi-equilibrium ilib i magnons Magnons with nonzero chemical potential:

46 Magnon spin transportt Tserkovnyak/Bauer S i t t l t l Spin transport accross normal metal magnetic insulator interface

47 One more teaser: Electrically driving i magnon BEC: Yaroslav Tserkovnyak/Scott Bender

48 Spintronics i with cold atoms Does it exist? What can we learn from it? Fundamentals of spin transport, different regimes w.r.t. electrons in solids (interactions vs. disorder/phonons) What is it good for? Understanding magnon transport/bose condensation magnons in magnetic insulators