In the prototypical dilute ferromagnetic semiconductor Ga_{1-x}Mn_xAs, simultaneous measurements of the anomalous Hall and anomalous Nernst effects by Pu et al. [Phys. Rev. Lett. 101, 117208 (2008)] revealed, as a byproduct, a pronounced low-temperature peak in the longitudinal Seebeck coefficient Sxx(T)S_{xx}(T) that appears systematically in post-growth-annealed films but not in as-grown ones. The authors tentatively attributed this peak to enhanced phonon drag arising from the increased phonon mean free path after annealing removes Mn interstitials, but explicitly left its physical origin open. The open problem is to establish quantitatively which mechanisms — phonon drag, magnon drag, impurity/carrier scattering changes, or band-structure modifications — produce the peak, its magnitude, and its temperature position, and why it emerges upon annealing. A 2011 theoretical treatment of (Ga,Mn)As thermopower by Śliwa and Dietl acknowledges that drag terms should dominate at low temperature in annealed samples but defers, stating that a quantitative theory of phonon and magnon scattering in (Ga,Mn)As was still awaited; the origin of the peak remains an open question.

Background

Ga_{1-x}Mn_xAs is the canonical dilute ferromagnetic semiconductor: Mn substituting for Ga in GaAs provides both local magnetic moments and holes, and the material orders ferromagnetically below a Curie temperature of order 100 K. Its thermoelectric response is characterized by the Seebeck coefficient SxxS_{xx}, the open-circuit voltage per unit longitudinal temperature gradient, and, when a transverse voltage appears instead, by the Nernst coefficient; in a ferromagnet the transverse signal contains an anomalous Nernst effect (ANE), the thermoelectric counterpart of the anomalous Hall effect (AHE), proportional to the out-of-plane magnetization rather than to an applied field. The Mott relation, S∼(π2kB2T/3e) (∂ln⁡σ/∂E)EFS \sim (\pi^2 k_B^2 T / 3e)\,(\partial \ln \sigma / \partial E)_{E_F}, links the Seebeck coefficient to the energy derivative of the conductivity; Xiao, Yao, Fang, and Niu [Phys. Rev. Lett. 97, 026603 (2006)] proved it applies even to the dissipation-less anomalous transport driven by the Berry curvature — the momentum-space curvature of the carrier Bloch wave functions, which acts on carriers as an effective magnetic field. Pu, Chiba, Matsukura, Ohno, and Shi [Phys. Rev. Lett. 101, 117208 (2008)] used simultaneous zero-field measurements of ρxx\rho_{xx}, ρxy\rho_{xy}, SxxS_{xx}, and SyxS_{yx} in (Ga,Mn)As films with perpendicular magnetic anisotropy (magnetization oriented out of the film plane) to verify the Mott relation for the anomalous Hall and Nernst effects and to fix the exponent n≈2n \approx 2 in the anomalous-Hall scaling law ρxyAHE∝ρxxn\rho_{xy}^{AHE} \propto \rho_{xx}^{n} (resistivity to the power nn), which signals an intrinsic, scattering-independent mechanism; that part of the paper is complete. In the thermoelectric data, however, all three post-growth-annealed samples (x = 0.04–0.07, 50 nm films annealed at 250 °C in air for 60 minutes, a treatment known to remove Mn interstitials — Mn atoms on non-substitutional lattice sites that act as compensating centers and scattering sources — and thereby raise the Curie temperature and lower the resistivity) developed a pronounced low-temperature peak in Sxx(T)S_{xx}(T), reaching values of order a few hundred µV/K, whereas the as-grown sample showed none. Two standard contributions to thermopower must be distinguished: the diffusion term, set by the energy dependence of the carrier density of states and mobility, and the phonon-drag term, in which nonequilibrium acoustic phonons flowing down the temperature gradient impart momentum to carriers; in a ferromagnet a magnon-drag term (drag by spin-wave excitations) is also possible. Phonon drag grows with the phonon relaxation time and typically peaks at low temperature, so the annealing-induced peak is plausibly tied to the longer phonon mean free path expected once interstitial Mn scattering centers are removed — but this was a conjecture, not an established result.

Problem Statement

Establish the physical origin of the pronounced low-temperature peak in the longitudinal Seebeck coefficient Sxx(T)S_{xx}(T) of post-growth-annealed Ga_{1-x}Mn_xAs ferromagnetic semiconductor films, as observed by Pu et al. [Phys. Rev. Lett. 101, 117208 (2008)] in all annealed samples (x = 0.04–0.07) but absent in as-grown films. Specifically, determine quantitatively whether the peak is produced by enhanced phonon drag due to the increased phonon mean free path expected after annealing removes interstitial Mn scattering centers, by magnon drag, by changes in impurity and carrier scattering, or by band-structure modification, and account for the peak's magnitude, its temperature position, and its systematic appearance only in the annealed state. The target is a quantitative identification of the dominant mechanism(s) sufficient to reproduce the observed Sxx(T)S_{xx}(T) of both annealed and as-grown Ga_{1-x}Mn_xAs and to account for the difference between them.

References

  1. Yong Pu, Daichi Chiba, Fumihiro Matsukura, Hideo Ohno, Jing Shi, 'Mott Relation for Anomalous Hall and Nernst Effects in Ga_{1-x}Mn_xAs Ferromagnetic Semiconductors', Phys. Rev. Lett. 101, 117208 (2008). DOI: 10.1103/PhysRevLett.101.117208; arXiv:0807.4942; https://doi.org/10.1103/PhysRevLett.101.117208
  2. Cezary Śliwa, Tomasz Dietl, 'Thermodynamic and thermoelectric properties of (Ga,Mn)As and related compounds', Phys. Rev. B 83, 245210 (2011). DOI: 10.1103/PhysRevB.83.245210; arXiv:1103.0671; https://doi.org/10.1103/PhysRevB.83.245210
  3. Yong Pu, E. Johnston-Halperin, D. D. Awschalom, Jing Shi, 'Anisotropic Thermopower and Planar Nernst Effect in Ga_{1-x}Mn_xAs Ferromagnetic Semiconductors', Phys. Rev. Lett. 97, 036601 (2006). DOI: 10.1103/PhysRevLett.97.036601; https://doi.org/10.1103/PhysRevLett.97.036601
  4. Ts. Naydenova, P. Dürrenfeld, K. Tavakoli, N. Pégard, L. Ebel, K. Pappert, K. Brunner, C. Gould, L. W. Molenkamp, 'Diffusion Thermopower of (Ga,Mn)As/GaAs Tunnel Junctions', Phys. Rev. Lett. 107, 197201 (2011). DOI: 10.1103/PhysRevLett.107.197201; arXiv:1110.6339; https://doi.org/10.1103/PhysRevLett.107.197201
  5. I. V. Soldatov, N. Panarina, C. Hess, L. Schultz, R. Schäfer, 'Thermoelectric effects and magnetic anisotropy of Ga_{1-x}Mn_xAs thin films', Phys. Rev. B 90, 104423 (2014). DOI: 10.1103/PhysRevB.90.104423; https://doi.org/10.1103/PhysRevB.90.104423
  6. C. M. Jaworski, J. Yang, S. Mack, D. D. Awschalom, J. P. Heremans, R. C. Myers, 'Observation of the spin-Seebeck effect in a ferromagnetic semiconductor', Nature Materials 9, 898-903 (2010). DOI: 10.1038/nmat2860; https://doi.org/10.1038/nmat2860
  7. C. M. Jaworski, J. Yang, S. Mack, D. D. Awschalom, R. C. Myers, J. P. Heremans, 'Spin-Seebeck Effect: A Phonon Driven Spin Distribution', Phys. Rev. Lett. 106, 186601 (2011). DOI: 10.1103/PhysRevLett.106.186601; https://doi.org/10.1103/PhysRevLett.106.186601
  8. Kjetil M. D. Hals, Arne Brataas, Gerrit E. W. Bauer, 'Thermopower and thermally induced domain wall motion in (Ga, Mn)As', Solid State Communications 150, 461-465 (2010). DOI: 10.1016/j.ssc.2010.01.023; arXiv:0911.1758; https://doi.org/10.1016/j.ssc.2010.01.023
  9. M. A. Mayer, P. R. Stone, N. Miller, H. M. Smith, O. D. Dubon, E. E. Haller, K. M. Yu, W. Walukiewicz, X. Liu, J. K. Furdyna, 'Electronic structure of Ga_{1-x}Mn_xAs analyzed according to hole-concentration-dependent measurements', Phys. Rev. B 81, 045205 (2010). DOI: 10.1103/PhysRevB.81.045205; https://doi.org/10.1103/PhysRevB.81.045205
  10. Di Xiao, Yugui Yao, Zhong Fang, Qian Niu, 'Berry-Phase Effect in Anomalous Thermoelectric Transport', Phys. Rev. Lett. 97, 026603 (2006). DOI: 10.1103/PhysRevLett.97.026603; https://doi.org/10.1103/PhysRevLett.97.026603