Heattronics Thermomagnotronics Nanospinheat Calefactronics Fierytronics Coolspintronics Thermospintronics What

? Heattronics? Thermomagnotronics? Nanospinheat ? Calefactronics? Fierytronics? Coolspintronics? Thermospintronics? What I learned in kinder garden: Fire is cool What I learned in Leiden: Spin+Fire is cooler

Bauer’s slide

Spin caloritronics: a growing field? But still a fraction of heattronics!

The Nernst Lamp

Hall effect sensors Wikipedia: A Hall effect sensor is a transducer that varies its output voltage in response to changes in magnetic field. Hall sensors are used for proximity switching, positioning, speed detection, and current sensing applications. The magnetic piston (1) in this pneumatic cylinder will cause the Hall effect sensors (2 and 3) mounted on its outer wall to activate when it is fully retracted or extended

Ettingshausen Cooler ❆ Particle-hole symmetry required to prevent Vh from stopping heat transport by the majority carrier. ❆ Both carriers contribute to heat pumping. ❆ Thomson heat is zero (je·jq=0). ❆ No doping required so that semimetals ( no gap) are OK, and in fact best efficiency occurs when thermopower is zero (S=0)!!! ❆ Magnetoresistance reduces je · Ebatt and ups je. XEbatt. Slide from Albert Migliori

What about spin Hall caloritronics?

Pourret et al PRB 2007 Theory: normal heat current def. is wrong; 3 rd law violated

What we learned about today Heard a lot about anomalous Hall effect

Anomalous Hall transport: lots to think about AHE in complex spin textures SHE Wunderlich et al Intrinsic AHE (magnetic monopoles? ) Taguchi et al Inverse SHE Valenzuela et al SHE Fang et al Kato et al 15

Anomalous Hall effect Spin dependent “force” deflects like-spin particles _ __ FSO majority FSO I minority V Simple electrical measurement of magnetization In. Mn. As 16

Anomalous Hall effect (scaling with ρ) Co films Kotzler and Gil PRB 2005 Ga. Mn. As Strong SO coupled regime Dyck et al PRB 2005 Weak SO coupled regime Edmonds et al APL 2003 17

AHE contributions Two types of contributions: i) S. O. from band structure interacting with the field (external and internal) ii) Bloch electrons interacting with S. O. part of the disorder 18

Dephasing and Disorder effects in Quantum Spin Hall Effect X. C. Xie The topology feature of the QSHE Physics Today 61, 19 (2008)

Transport measurement: experiment M. Konig, et al. , Science 318, 766 (2007). Ø d<dc normal insulator Ø d>dc With small L and W, R 14, 23 is quantized, insensitive to W variations. With large L, R 14, 2 3 is no longer quantized. QSH signal is robust against temperature change.

Anderson impurity influence: current density (II) We only consider spin up parts W=0 me. V W=150 me. V W=60 me. V

Lorenz number study of dissipationless and dissipative anomalous Hall currents M Jq “Anomalous Thermal Hall effect” Heat current ÑT Yoshinori Onose University of Tokyo Collaborator: Y. Shiomi, Y. Tokura

Effect of scattering on anomalous Hall effect Region I: sxx>106 S/cm Skew scattering is dominant Regin II: 104<sxx<106 S/cm sxy is independent of rxx. “dissipationless” Miyasato, Asamitsu et al. Onoda and Nagaosa Region III: sxx<104 S/cm sxy µsxx. 1. 6

Skew scattering feature in Fe and its alloy Low temperature: Magnitude and sign depend on sample. Skew scattering High temperature: Intrinsic mechanism

Co-doped Si-doped Consistent with the skew scattering theory

sxy, kxy, Lxy in Co 3% doped Fe sxy, kxy, Lxy in Si 0. 3% doped Fe ～ ～

Berry Phase, Orbital Magnetization and Anomalous Transport Qian Niu Currents driven by statistical force Statistical forces such as ▽m, ▽T do not enter into the equation of motion, therefore there is no anomalous velocity term. How does a transverse current arise in this situation? • Einstein relation: The equivalence between the electric field and gradient of chemical potential. • Mott relation: The accompany of a heat current to a charge current. • Onsager relation: Symmetry between cross transport coefficients connecting thermoelectric Hall currents and forces.

Einstein & Mott relations Driving Force Intrinsic Contribution to Hall Current Cooper, Halperin, Ruzin, PRB 1997

Anomalous Nernst Effect Yong Pu, et al, PRL 2008: Ga. Mn. As

Calculation of Spin Seebeck effect Permalloy Unit of magnet 6 mm T=0 K T=100 K ISHE for observing Spin Seebeck Effect Pt Charge current Spin Current

Modelling MR in a metal with Fmn. C’s (spin impurities) F Approximation of static exchange fie F N S. Zhang - Appl Phys Lett 61, 1855 (1992) S. Zhang, P. Levy - J Appl Phys 73, 5315 (1993) F Classical macro-spin impurit Tsyplyatev & Fal'ko, Int J Mod Phys B 19, 2175 (2005) MR can be studied using perturbation theory methods after taking into account interplay between exchange and potential interaction of electron with nanocluster

Nature Materials 5, 730– 734 (2006) MTGV GMR Tsyplyatyev, Kashuba & Fal’ko Phys. Rev. B 74, 132403 (2006) J Appl Phys 101, 014324 (2007)

VERY speculative comments and questions

How can a “dissipationless” Hall current give rise to a heat current? • How to define heat current in magnetic systems when interactions are important? • Is it USEFUL? or use. LESS? • What about side-jump, etc. ? • Can it lead to any meaningful cooling?

High ZT is related to topological protected states Prediction: ZT will be MUCH larger in Hg. Te wells in the inverted regime

Spin Seebeck Effect: real or artifact?

Can ANY spin thermoelectric effects lead to effective cooling of switches?

AHE in Rashba 2 D system: “dirty” metal limit? 39

Where is the scaling? 40