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. transducervoltagemagnetic field 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 the thermopower is zero (S=0)!!! ❆ Magnetoresistance reduces je · E batt and ups je X E batt. 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

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

Anomalous Hall effect Simple electrical measurement of magnetization Spin dependent “force” deflects like-spin particles I _ F SO _ _ _ majority minority V InMnAs 16

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

18 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

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

Transport measurement: experiment M. Konig, et al., Science 318, 766 (2007).  d<dc normal insulator  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=0meV W=60meV W=150meV

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

Effect of scattering on anomalous Hall effect Region I:  xx >10 6 S/cm Skew scattering is dominant Regin II: 10 4 <  xx <10 6 S/cm  xy is independent of  xx. “dissipationless” Region III:  xx <10 4 S/cm  xy  xx. 1.6 Miyasato, Asamitsu et al. Onoda and Nagaosa

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

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

 xy,  xy, L xy in Co 3% doped Fe  xy,  xy, L xy in Si0.3% doped Fe ～ ～ ～ ～

Currents driven by statistical force 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. Statistical forces such as ▽ , ▽ 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? Berry Phase, Orbital Magnetization and Anomalous Transport Qian Niu

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

Anomalous Nernst Effect Yong Pu, et al, PRL 2008: GaMnAs

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

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

Nature Materials 5, 730–734 (2006) MTGV GMR Tsyplyatyev, Kashuba & Fal’ko Phys. Rev. B 74, (2006) J Appl Phys 101, (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 useLESS? 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 HgTe wells in the inverted regime

Spin Seebeck Effect: real or artifact?

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

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

Where is the scaling? 40