Spin(calori)tronics = spin+heat+electronics

Transcription

1 Heat = (ergy ー Work) pi(calori)troic = pi+heat+electroic errit Bauer errit.w. Bauer "CD orced Covectio Heat ik " by Iofil Lecture DC Magetoelectroic 2 AC Magetoelectroic 3 pi Caloritroic i. Theroelectric ii. Oager reciprocity iii. pi depedet theroelectric iv. pi theroelectric Thoa oha eebeck (770-83) Metal Theroelectric power V c V 2 T T 2 Wiedea-raz Law: Lorez uber: c V T 0 K T K li T 0 c 0 e 0 LT 2 2 k B L0 3 e V T T 2 T 0 V Therocouple: T 2 A T B V T B A c eebeck coefficiet

2 Peltier effect Heat traport i etal T c T 2 =T c T 0 Peltier coefficiet e k B T(x) Theroelectric heat pup: x h c A A B c f(,x) B Heat ad charge traport (electro like) Heat ad charge traport (hole like) e > h e < h k B T(x) k B T (x) x x h h g()f(,x) el0t g ( ) li 0 T 0 g ( ) g()f(,x) el0t g ( ) li 0 T 0 g ( ) Lar Oager Meorial at TU Trodhei obel Prize i Cheitry 968: for the dicovery of the reciprocal relatio bearig hi ae, which are fudaetal for the therodyaic of irreverible procee Oager yetry (93) i = {a, charge, eergy, volue, (agular) oetu, } geeralized force geeralized curret X i i LX If: X ii The: i L L ij ji liear repoe etropy creatio rate Oager relatio Whe tie reveral yetry i broke: L H, L, H ij ext i j ji ext Lar Oager eve (charge) i whe variable i odd (pi) 2

3 t Law of Therodyaic: du d dw T d d du = =2 d d T T T T 2 du du 2 du ; d d 2 d 2 =ev 2 du d U ; d d d 2 d U T T T T T T d T T T ; T2 T T : T U T T ix i 0 cojugate curret T i ad force idetified! Theroelectric V c L L2 T L2 L22 T L L 2 2 V R c K T Oager reciprocity = =2 T T+T V V +V R = / electrical reitace K theral coductace eebeck coefficiet = T Peltier coefficiet Oager-Thoo (Kelvi) relatio Cotet pi-accuulatio ad pi-curret d D f pi-depedet theroelectric d D f pi-flip diffuio legth diffuio cotat pi-flip relaxatio tie Theral pi-ijectio by etal Theral pi-ijectio by etal M 0 T V 0 T V T T K T T / T e / 2 c P T V V P PT V V 2 T PT LT 0 T / T P P P pi-depedet Peltier effect pi-depedet eebeck effect Mark oho ad R. H. ilbee (987) 3

4 pi-depedet eebeck effect pi eebeck effect! pi-depedet Peltier effect T lachter et al. (200) lipe et al. (202) Oager reciprocity hold betwee pi-depedet eebeck ad Peltier effect. pi teperature pi heat valve (with half etal) 0 T 0 V 0 0 T V T 0 KT 0 T / T 0 T 0 KT T / T Atiparallel cofiguratio: T T o-iteractig: K L0 T 0 D f D Hatai et al. (2007) Heikkilä et al. (200) trogly iteractig: K L0 T ; 0 2 iat violatio of Wiedea-raz Law! pi teperature ad heat accuulatio Cotet YI Dejee et al. (203) pi theroelectric 4

5 Curret-iduced pi-trafer torque pi torque ad pi pupig Oager reciprocal (Brataa et al., 20) pi curret caue agetizatio otio (pi trafer torque, loczewki, 996). Magetizatio otio caue pi curret (pi pupig, Terkovyak, 2002). T I g V V g V V I pi-ixig coductace pi accuulatio I 0 Berger (996) loczewki (996) LL equatio pi trafer torque M L L Heff L L V pi pupig pi coductace T L Μ L Μ pi ixig coductace g H eff M e V Collective effect i iulator agetic (electric) iulator M (Logitudial) pi eebeck effect pi-depedet eebeck effect! V [V] Uchida et al. (2000) oie-iduced pi curret oie-iduced pi curret M M Kajiwara et al. oro et al. (2005) Xiao et al. (2009) g T T pup - oie M e Xiao et al. (200) Adachi et al. (20) 5

6 Magetic iulator i parallel field T T pi Peltier effect (lipe et al., 204) YI (200 ) Pt (5 ) t haroic igal V P V M H eff pi eebeck effect M L L L z H eff L L L V L T / T L L heat coductace pi Peltier effect 200 Magetic iulator i parallel field T T Colliear pi cofiguratio pi coductace M H eff V M L L L z H eff L L L V L T / T L L heat coductace pi Peltier effect pi eebeck effect I I 0 pi curret coverio pi curret coverio I I 0 I I 0 6

7 all agle pi trafer olde rule iterface pi curret ago creatio by pi trafer ago aihilatio by pi pupig ago k k kt B e T ago (particle) accuulatio ago heat accuulatio pio k k kt B R e g j dd B B M k 0 BT kbt R Beder et al. (202), Duie et al. (205) Mago traport (differet fro Kajiwara et al. (200)) Corelie et al. (205) 7