Spin-Seebeck Effect

Dongwook Go

Department of Physics, POSTECH

ReferencesReview article- Gerrit E. W. Bauer et al., Spin caloritronics, Nature Materials 11, 391 (2012).

Theory references

- J. Xiao et al., Theory of magnon-driven spin Seebeck effect, Phys. Rev. B 81, 214418 (2010).

- Hiroto Adachi et al., Theory of the spin Seebeck effect, Rep. Prog. Phys. 76, 036501 (2013).

Experiment references

- K. Uchida et al., Observation of the spin Seebeck effect, Nature, 455, 778 (2008).

- C. M. Jarowski et al., Observation of the spin-Seebeck effect in a ferromagnetic semiconductor, Nature Materials, 9, 898 (2010).

- K. Uchida et al., Spin Seebeck insulator, Nature Materials, 9, 894 (2010).

- K. Uchida et al., Observation of longitudinal spin-Seebeck effect in magnetic insulators, Appl. Phys. Lett. 97, 172205 (2010).

- Hiroto Adachi et al., Gigantic enhancement of spin Seebeck effect by phonon drag, Appl. Phys. Lett. 97, 252506 (2010).

- C. M. Jarowski et al., Spin-Seebeck Effect: A Phonon Driven Spin Distribution, Phys. Rev. Lett. 106, 186601 (2011).

- K. Uchida et al., Thermal spin pumping and magnon-phonon-mediated spin-Seebeck effect, J. Appl. Phys. 111, 103903 (2012).

Overview : spin Seebeck effect

K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

Measurement Mechanism: inverse spin Hall effect

S. Maekawa, Nature Materials 8, 777 (2009).

Spin Hall effect Inverse spin Hall effect

K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

Paramagnetic material used for the experiment should have large spin-orbit coupling, i.e. Pt, Ta…

Spin Seebeck Effect : sample configuration

K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

Spin dependent two-current model

Gerrit E. W. Bauer et al., Nature Materials 11, 391 (2012).

Breakdown ofconduction electron scenario

Length scale relevant to the experiment : ~ 1 mmTypical spin-flip diffusion length in metal : ~ 1-10 nm

Spin Seebeck coefficient does NOT depend on the conductance of the material.

Spin Seebeck effect is observed in magnetic insulator, i.e. YIG (YFeO), La-YIG (LaYFeO).

→ Magnon scenario

Spin current is not only carried by conduction electrons, but also by magnons.

Spin Current :

Conduction electron contribution

Magnon contribution

Gerrit E. W. Bauer et al., Nature Materials 11, 391 (2012).Hiroto Adachi et al., Rep. Prog. Phys. 76, 036501 (2013).

Local picture of thermal spin injection by magnons

Hiroto Adachi et al., Rep. Prog. Phys. 76, 036501 (2013).Gerrit E. W. Bauer and Yaraslav Tserkovnyak, Physics, 4, 40 (2011)

Conduction electron interacts with the magnon and changes its spin by 1. From the coupling between the magnon and conduction electron, spin current is pumped (spin pumping).

Local picture of thermal spin injection by magnons

Hiroto Adachi et al., Rep. Prog. Phys. 76, 036501 (2013).

F-side magnetization: Landau-Lifshitz-Gilbert (LLG) equation

,

N-side conduction electron : Bloch equation

,

Local picture of thermal spin injection by magnons

Hiroto Adachi et al., Rep. Prog. Phys. 76, 036501 (2013).

Perturbative calculation treating 𝐉𝐬𝐝 as small variable leads to

, where

Alternative expression :

(spin conservation)

Local picture of thermal spin injection by magnons

Hiroto Adachi et al., Rep. Prog. Phys. 76, 036501 (2013).K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

𝑇𝐹 = 𝑇𝑁 leads to 𝐼𝑠 = 0 (?)

Local temperature should be replaced by some effective temperature 𝑇∗

𝑇𝑁 = 𝑇𝑁∗ = 𝑇𝑙𝑜𝑐−𝑒𝑞 = 𝑇𝑜𝑝𝑡−𝑝ℎ

𝑇𝐹 = 𝑇𝐹∗ = 𝑇𝑚𝑎𝑔 or 𝑇𝑎𝑐𝑐−𝑝ℎ

Magnon-phonon-mediated thermal spin pumping and spin Seebeck effect

Hiroto Adachi et al., Rep. Prog. Phys. 76, 036501 (2013).

Detection of Longitudinal Spin-Seebeck Effectin Ferromagnetic Insulator, YIG (YFeO)

K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

Detection of Longitudinal Spin-Seebeck Effectin Ferromagnetic Insulator, YIG (YFeO)

K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

Strong evidence of phonon-drag mechanism!

1) Low temperature → Suppression of phonon unklapp process → increased phonon lifetime

2) Zero kelvin → signal vanishes (the third law of thermodynamics)3) Phonon-drag spin Seebeck effect must have a peak at low temperature.

Detection of Transverse Spin-Seebeck Effectin Ferromagnetic Insulator, La:YIG (LaYFeO)

K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

Detection of Transverse Spin-Seebeck Effectin Ferromagnetic Insulator, La:YIG (LaYFeO)

K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

Measuring the characteristic length via

Which gets larger as temperature decreases. This can be explained from the phonon-drag scenario.

Detection of Transverse Spin-Seebeck Effectin Ferromagnetic Semiconductor, GaMnAs: Scratch Experiment

C. M. Jarowski et al., Nature Materials, 9, 898 (2010).

This scratch experiment supports the phonon scenario!

Detection of Transverse Spin-Seebeck Effectin Ferromagnetic Metal, 𝑵𝒊𝟖𝟏𝑭𝒆𝟏𝟗

K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

Detection of Transverse Spin-Seebeck Effectin Ferromagnetic Metal, 𝑵𝒊𝟖𝟏𝑭𝒆𝟏𝟗: Acoustic spin Seebeck effect

K. Uchida et al., J. Appl. Phys. 111, 103903 (2012).

Magnon channel is blocked, and only phonon-mediated effect is observed.

Summary & Conclusion

The spin Seebeck effect generates a spin voltage as a result of a temperature gradient in ferromagnet.

In the paramagnet, the spin current is converted into an electric field due to the invserse spin Hall effect.

The spin Seebeck effect is not only observed in ferromagnetic metal, but also in ferromagnetic semiconductor and insulator.

Theoretical model is based on the thermal spin pumping mediated by magnon and phonon, which is supported by many experiments.

Summary & Conclusion