- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Temperature gradient driven motion of magnetic domains in a magnetic metal multilayer by entropic forces

Lin Huang1,2,*, Joseph Barker1, Lekshmi Kailas1, Soumyarup Hait1, Simon D. Connell1, Gavin Burnell1, and Christopher H. Marrows1,†

  • *Present address: CORNERSTONE, Optoelectronics Research Centre, University of Southampton, Building 60, University Road, Southampton SO17 1BJ, United Kingdom.
  • †Contact author: c.h.marrows@leeds.ac.uk
PDF

Phys. Rev. B 113, 014428 – Published 20 January, 2026

DOI: https://doi.org/10.1103/152r-5wvt

Abstract

We studied the displacement of magnetic domains under temperature gradients in perpendicularly magnetized Ta/[Pt/Co68B32/Ir]×10/Pt multilayer tracks with microfabricated Pt heaters and thermometers by magnetic force microscopy. Subtracting out the effects of the Oersted field from the heating current reveals the pure temperature gradient driven motion, which is always toward the heater. The higher the thermal gradient along the track is (owing to the proximity to the heater or larger heater currents), the greater the observed displacements of the domains are, up to a velocity of around 1 nm/s in a temperature gradient of 20 K/µm. This velocity lies in the creep regime. Quantitative estimates of the strength of different driving mechanisms for the effect that have been proposed theoretically show that entropic forces dominate over those arising from the spin Seebeck and spin-dependent Seebeck effects in driving the domain motion.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (52)

  1. G. E. W. Bauer, E. Saitoh, and B. J. van Wees, Spin caloritronics, Nat. Mater. 11, 391 (2012).
  2. H. Adachi, K.-I. Uchida, E. Saitoh, and S. Maekawa, Theory of the spin Seebeck effect, Rep. Prog. Phys. 76, 036501 (2013).
  3. H. Yu, S. D. Brechet, and J.-P. Ansermet, Spin caloritronics, origin and outlook, Phys. Lett. A 381, 825 (2017).
  4. K.-I. Uchida, Transport phenomena in spin caloritronics, Proc. Jpn. Acad., Ser. B 97, 69 (2021).
  5. C. H. Marrows, Spin-polarised currents and magnetic domain walls, Adv. Phys. 54, 585 (2005).
  6. D. C. Ralph and M. D. Stiles, Spin transfer torques, J. Magn. Magn. Mater. 320, 1190 (2008).
  7. A. Thiaville, S. Rohart, E. Jué, V. Cros, and A. Fert, Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films, Europhys. Lett. 100, 57002 (2012).
  8. F. Jonietz, S. Mühlbauer, C. Pfleiderer, A. Neubauer, W. Münzer, A. Bauer, T. Adams, R. Georgii, P. Böni, R. A. Duine, K. Everschor, M. Garst, and A. Rosch, Spin transfer torques in MnSi at ultralow current densities, Science 330, 1648 (2010).
  9. W. Jiang, P. Upadhyaya, W. Zhang, G. Yu, M. B. Jungfleisch, F. Y. Fradin, J. E. Pearson, Y. Tserkovnyak, K. L. Wang, O. Heinonen, S. G. E. te Velthuis, and A. Hoffmann, Blowing magnetic skyrmion bubbles, Science 349, 283 (2015).
  10. S. Woo, K. Litzius, B. Krüger, M.-Y. Im, L. Caretta, K. Richter, M. Mann, A. Krone, R. M. Reeve, M. Weigand, P. Agrawal, I. Lemesh, M.-A. Mawass, P. Fischer, M. Kläui, and G. S. D. Beach, Observation of room-temperature magnetic skyrmions and their current-driven dynamics in ultrathin metallic ferromagnets, Nat. Mater. 15, 501 (2016).
  11. K. Zeissler, S. Finizio, C. Barton, A. J. Huxtable, J. Massey, J. Raabe, A. V. Sadovnikov, S. A. Nikitov, R. Brearton, T. Hesjedal, G. van der Laan, M. C. Rosamond, E. H. Linfield, G. Burnell, and C. H. Marrows, Diameter-independent skyrmion Hall angle observed in chiral magnetic multilayers, Nat. Commun. 11, 428 (2020).
  12. K. Uchida, J. Xiao, H. Adachi, J. Ohe, S. Takahashi, J. Ieda, T. Ota, Y. Kajiwara, H. Umezawa, H. Kawai, G. E. W. Bauer, S. Maekawa, and E. Saitoh, Spin Seebeck insulator, Nat. Mater. 9, 894 (2010).
  13. C. M. Jaworski, J. Yang, S. Mack, D. D. Awschalom, J. P. Heremans, and R. C. Myers, Observation of the spin-Seebeck effect in a ferromagnetic semiconductor, Nat. Mater. 9, 898 (2010).
  14. K. Uchida, M. Ishida, T. Kikkawa, A. Kirihara, T. Murakami, and E. Saitoh, Longitudinal spin Seebeck effect: From fundamentals to applications, J. Phys. Condens. Matter 26, 343202 (2014).
  15. A. A. Kovalev and Y. Tserkovnyak, Thermoelectric spin transfer in textured magnets, Phys. Rev. B 80, 100408(R) (2009).
  16. J. C. Slonczewski, Initiation of spin-transfer torque by thermal transport from magnons, Phys. Rev. B 82, 054403 (2010).
  17. D. Hinzke and U. Nowak, Domain wall motion by the magnonic spin Seebeck effect, Phys. Rev. Lett. 107, 027205 (2011).
  18. P. Yan, X. S. Wang, and X. R. Wang, All-magnonic spin-transfer torque and domain wall propagation, Phys. Rev. Lett. 107, 177207 (2011).
  19. X.-G. Wang, G.-H. Guo, Y.-Z. Nie, G.-F. Zhang, and Z.-X. Li, Domain wall motion induced by the magnonic spin current, Phys. Rev. B 86, 054445 (2012).
  20. A. A. Kovalev and Y. Tserkovnyak, Thermomagnonic spin transfer and Peltier effects in insulating magnets, Europhys. Lett. 97, 67002 (2012).
  21. P. Yan, Y. Cao, and J. Sinova, Thermodynamic magnon recoil for domain wall motion, Phys. Rev. B 92, 100408(R) (2015).
  22. M. A. S. Akanda, M. T. Islam, and X. R. Wang, Role of SSW on thermal-gradient induced domain-wall dynamics, J. Phys. Condens. Matter 35, 315701 (2023).
  23. K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, and E. Saitoh, Observation of the spin Seebeck effect, Nature (London) 455, 778 (2008).
  24. L. Yi, D. Yang, M. Liu, H. Fu, L. Ding, Y. Xu, B. Zhang, L. Pan, and J. Q. Xiao, Concepts of spin Seebeck effect in ferromagnetic metals, Adv. Funct. Mater. 30, 2004024 (2020).
  25. Y.-R. Wang, C. Yang, Z.-C. Wang, and G. Su, Domain-wall dynamics driven by thermal and electrical spin-transfer torque, Phys. Rev. B 106, 054432 (2022).
  26. F. Schlickeiser, U. Ritzmann, D. Hinzke, and U. Nowak, Role of entropy in domain wall motion in thermal gradients, Phys. Rev. Lett. 113, 097201 (2014).
  27. J. Chico, C. Etz, L. Bergqvist, O. Eriksson, J. Fransson, A. Delin, and A. Bergman, Thermally driven domain-wall motion in Fe on W(110), Phys. Rev. B 90, 014434 (2014).
  28. S. Moretti, V. Raposo, E. Martinez, and L. Lopez-Diaz, Domain wall motion by localized temperature gradients, Phys. Rev. B 95, 064419 (2017).
  29. H. Yu, S. Granville, D. P. Yu, and J.-P. Ansermet, Evidence for thermal spin-transfer torque, Phys. Rev. Lett. 104, 146601 (2010).
  30. P. Möhrke, J. Rhensius, J.-U. Thiele, L. Heyderman, and M. Kläui, Tailoring laser-induced domain wall pinning, Solid State Commun. 150, 489 (2010).
  31. J. P. Tetienne, T. Hingant, J.-V. Kim, L. H. Diez, J.-P. Adam, K. Garcia, J. F. Roch, S. Rohart, A. Thiaville, D. Ravelosona, and V. Jacques, Nanoscale imaging and control of domain-wall hopping with a nitrogen-vacancy center microscope, Science 344, 1366 (2014).
  32. A. J. Ramsay, P. E. Roy, J. A. Haigh, R. M. Otxoa, A. C. Irvine, T. Janda, R. P. Campion, B. L. Gallagher, and J. Wunderlich, Optical spin-transfer-torque-driven domain-wall motion in a ferromagnetic semiconductor, Phys. Rev. Lett. 114, 067202 (2015).
  33. W. Jiang, P. Upadhyaya, Y. Fan, J. Zhao, M. Wang, L.-T. Chang, M. Lang, K. L. Wong, M. Lewis, Y.-T. Lin, J. Tang, S. Cherepov, X. Zhou, Y. Tserkovnyak, R. N. Schwartz, and K. L. Wang, Direct imaging of thermally driven domain wall motion in magnetic insulators, Phys. Rev. Lett. 110, 177202 (2013).
  34. J. Torrejon, G. Malinowski, M. Pelloux, R. Weil, A. Thiaville, J. Curiale, D. Lacour, F. Montaigne, and M. Hehn, Unidirectional thermal effects in current-induced domain wall motion, Phys. Rev. Lett. 109, 106601 (2012).
  35. X. Yu, et al., Real-space observations of 60-nm skyrmion dynamics in an insulating magnet under low heat flow, Nat. Commun. 12, 5079 (2021).
  36. Z. Wang, et al., Thermal generation, manipulation and thermoelectric detection of skyrmions, Nat. Electron. 3, 672 (2020).
  37. E. Raimondo, E. Saugar, J. Barker, D. Rodrigues, A. Giordano, M. Carpentieri, W. Jiang, O. Chubykalo-Fesenko, R. Tomasello, and G. Finocchio, Temperature-gradient-driven magnetic skyrmion motion, Phys. Rev. Appl. 18, 024062 (2022).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/152r-5wvt for further details of the sample fabrication and characterisation as well as details of the data analysis.
  39. D. Nečas and P. Klapetek, Gwyddion: An open-source software for SPM data analysis, Cent. Eur. J. Phys. 10, 181 (2012).
  40. P. Kienzle, J. Krycka, N. Patel, and I. Sahin, bumps, version 0.9.2, https://pypi.org/project/bumps/.
  41. P. J. Metaxas, J. P. Jamet, A. Mougin, M. Cormier, J. Ferré, V. Baltz, B. Rodmacq, B. Dieny, and R. L. Stamps, Creep and flow regimes of magnetic domain-wall motion in ultrathin Pt/Co/Pt films with perpendicular anisotropy, Phys. Rev. Lett. 99, 217208 (2007).
  42. A. A. Thiele, Steady-state motion of magnetic domains, Phys. Rev. Lett. 30, 230 (1973).
  43. A. Thiaville, Y. Nakatani, J. Miltat, and Y. Suzuki, Micromagnetic understanding of current-driven domain wall motion in patterned nanowires, Europhys. Lett. 69, 990 (2005).
  44. L. J. Cornelissen, K. J. H. Peters, G. E. W. Bauer, R. A. Duine, and B. J. van Wees, Magnon spin transport driven by the magnon chemical potential in a magnetic insulator, Phys. Rev. B 94, 014412 (2016).
  45. J Bass and W. Pratt, Current-perpendicular (CPP) magnetoresistance in magnetic metallic multilayers, J. Magn. Magn. Mater. 200, 274 (1999).
  46. D. Yang, L. Yi, S. Fan, X. He, Y. Xu, M. Liu, L. Ding, L. Pan, and J. Q. Xiao, Spin Seebeck coefficients of Fe, Co, Ni, and Ni80Fe20 3d-metallic thin films, Mater. Res. Bull. 136, 111153 (2021).
  47. U. Atxitia, D. Hinzke, O. Chubykalo-Fesenko, U. Nowak, H. Kachkachi, O. N. Mryasov, R. F. Evans, and R. W. Chantrell, Multiscale modeling of magnetic materials: Temperature dependence of the exchange stiffness, Phys. Rev. B 82, 134440 (2010).
  48. C. Kittel, Quantum Theory of Solids (Wiley, New York, 1963).
  49. H. T. Nembach, J. M. Shaw, M. Weiler, E. Jué, and T. J. Silva, Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii–Moriya interaction in metal films, Nat. Phys. 11, 825 (2015).
  50. J. B. Mohammadi, B. Kardasz, G. Wolf, Y. Chen, M. Pinarbasi, and A. D. Kent, Reduced exchange interactions in magnetic tunnel junction free layers with insertion layers, ACS Appl. Electron. Mater. 1, 2025 (2019).
  51. K. Alshammari, E. Haltz, M. Alyami, M. Ali, P. S. Keatley, C. H. Marrows, J. Barker, and T. A. Moore, Scaling of Dzyaloshinskii-Moriya interaction with magnetization in Pt/Co(Fe)B/Ir multilayers, Phys. Rev. B 104, 224402 (2021).
  52. L. Huang, J. Barker, L. Kailas, S. D. Connell, G. Burnell, and C. H. Marrows, Data associated with “Temperature gradient driven motion of magnetic domains in a magnetic metal multilayer by entropic forces”, Research Data Leeds (2025), https://doi.org/10.5518/1796.

Outline

Information

Phys. Rev. B 113, 014428– Published 20 January, 2026
  • Received 18 June 2025
  • Revised 13 November 2025
  • Accepted 5 December 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation