Spin Currents and Spin Caloritronics Sergio O. Valenzuela ICREA and - PDF document

Spin Currents and Spin Caloritronics Sergio O. Valenzuela ICREA and Institut Catala de Nanotenologia Barcelona, Spain Cargèse March 6 th 2013 Image credit: NPG European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Spin currents and spin caloritronics Outline Spin caloritronics: Thermoelectricity meets spintronics – Nonequilibrium phenomena involving charge, energy and spin transport. Usually in magnetic structures Area of research Topic Electronics Transport/manipulation of charge Spin elec tronics or Spintronics Transport/manipulation of charge and spin Calori metry Study and measure the heat of chemical reactions or physical changes Spin Caloritronics Transport/manipulation of charge, spin and heat M. Johnson and R. H. Silsbee, Phys. Rev. B 35 , 4959 (1987) Reviews : Bauer, MacDonald, Maekawa, Solid State Commun. (2010); Bauer in Spin Current (Oxford University Press, 2012) European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics

Spin currents and spin caloritronics Outline Spin caloritronics: Why is important? Reviews : Bauer, MacDonald, Maekawa, Solid State Commun. (2010); Bauer in Spin Current (Oxford University Press, 2012) European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Spin currents and spin caloritronics Outline ICT Consumption Forecast TWh 4%: 750 TWh 5000 2010 4500 4000 3500 3000 2500 15%: 4750 TWh 2000 2025 1500 1000 500 0 2010 2015 2020 2025 Goal: To find creative ways of using wasted heat European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics

Spin currents and spin caloritronics Outline Spin caloritronics: Why is important? TWh 5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 2010 2015 2020 2025 Reviews : Bauer, MacDonald, Maekawa, Solid State Commun. (2010); Bauer in Spin Current (Oxford University Press, 2012) European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Spin currents and spin caloritronics Outline Thermoelectricity, energy harvesting, cooling Peltier cooler Thermopile Marlow Industries European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics

Spin currents and spin caloritronics Outline Spin caloritronics – Thermoelectricity – Seebeck effect – Peltier effect – Onsager reciprocity relation – Spin Currents: independent electron, collective – Thermoelectricity + Spins – Observed spin caloritronic effects: spin-dependent Seebeck effect, spin Peltier effect, thermal GMR, thermal GMR, thermal torques, magnon drag, spin Seebeck effect. European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Spin currents and spin caloritronics Outline Spin caloritronics – Thermoelectricity – Seebeck effect – Peltier effect – Onsager reciprocity relation – Spin Currents: independent electron, collective – Thermoelectricity + Spins – Observed spin caloritronic effects: spin-dependent Seebeck effect, spin Peltier effect, thermal GMR, thermal GMR, thermal torques, magnon drag, spin Seebeck effect. European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics

Thermoelectricity Electrical vs thermal transport > V 1 V 2 J c   J Electrical Conductivity     c    V   T 0 > T 1 T 2   J J Q     Q Thermal Conductivity      T  J 0 c Wiedemann-Franz Law     2 2 k         8 - 2 LT B L 2 . 4 10 W K    3 e European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Thermoelectricity Electrical vs thermal transport > V 1 V 2   J c J Electrical Conductivity     c    V   T 0 > T 1 T 2   J J Q     Q Thermal Conductivity      T  J 0 c Wiedemann-Franz Law   2   2 k         8 - 2 B LT L 2 . 4 10 W K    3 e European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics

Thermoelectricity Seebeck effect Conversion of temperature differences directly into electricity > T 1 T 2    V    S    T  J 0 c  V Seebeck coefficient Thomas J. Seebeck Thermocouple (1770-1831)    T S A    2 V S ( T ) S ( T ) dT B A T T 2 (reference) T 1 1     V ( S S ) T S B B A European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Thermoelectricity Peltier effect Conversion of charge current into heat flow T T   J     J c Q     J c   T 0  V Seebeck coefficient Jean C. A. Peltier Heat pump: cooler / heater (1785-1845)  A J Q J Q     J ( ) J Q B A c J c  B European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics

Thermoelectricity Metal  '      S T    See, e.g., Ashcroft/Mermin (Ch13)   '     E E E F European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Thermoelectricity Heat and charge transport (electron like)  '      S T    See, e.g., Ashcroft/Mermin (Ch13)   '     E E E G. Bauer et al. Nat. Mater. (2012) F European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics

Thermoelectricity Heat and charge transport (electron like)  '      S T    See, e.g., Ashcroft/Mermin (Ch13)   '     E E E G. Bauer et al. Nat. Mater. (2012) F European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Thermoelectricity Onsager reciprocity The Nobel Prize in Chemistry 1968: “for the discovery of the reciprocal relations bearing his name, which are fundamental for the thermodynamics of irreversible processes” Generalized force F n Generalized current J n   J L F If Linear response i ij j j dS   and entropy change rate F j J j dt Lars Onsager j then L ij = L ji (1906-1976) First law of thermodynamics: identify F n , J n        J 1 S V         c F n :  V , -  T / T             J      / T Q then  = ST (Thomson relation) European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics

Spin currents and spin caloritronics Outline Spin caloritronics – Thermoelectricity – Seebeck effect – Peltier effect – Onsager reciprocity relation – Spin Currents: independent electron, collective – Thermoelectricity + Spins – Observed spin caloritronic effects: spin-dependent Seebeck effect, spin Peltier effect, thermal GMR, thermal GMR, thermal torques, magnon drag, spin Seebeck effect. European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Spin currents vs. charge currents Charge  dt q   e  q    Moving charge, kinetic energy e  d j r j v   and dissipation Spín   dt       s  d      Spin currents are even under j r j s v r  time reversal Electrons do not need to move Spins in motion (independent electron) Nonvolatile memory Possibility to reduce dissipation Spin dynamics (collective) J. Shi, et al. , Phys. Rev. Lett. 96 , 076604 (2006). European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics

Spin generation and spin injection • Two spin channel model (Mott 1930) – Metallic ferromagnets. Spin-up and spin-down are two independent families of carriers • Spin splitting – Different density of states at the Fermi level for spin up and down carriers – Different mobility for spin up and down carriers  N N  M m Minority Majority P -1 ≤ P ≤ 1  N N M m I.I. Mazin, PRL 83 , 1427-1430 (1999) European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics Spin currents and spin accumulation • Spin polarized current in a nonmagnetic metal • Spin accumulation decays exponentially • Characteristic length. Spin diffusion/relaxation length  sf     1             2 Johnson and Silsbee PRB 35 , 4959 (1987)  van Son et al., PRL 58 , 2271 (1987) sf European School on Magnetism 2013, Cargèse, Corsica Spin Currents and Spin Caloritronics