In the ferromagnetic semiconductor (Ga,Mn)As, a gate electric field applied through a metal–insulator–semiconductor structure modulates the hole density and thereby the magnetic anisotropy that fixes the magnetization direction. Chiba, Sawicki, Nishitani, Nakatani, Matsukura and Ohno (Nature 455, 515–518, 2008) showed that the in-plane uniaxial anisotropy field is by far the most gate-sensitive anisotropy component, changing sign with the applied field and allowing the magnetization easy axis to be rotated electrically, while micromagnetic simulations predicted full magnetization switching. The paper left two linked issues open: the microscopic origin of the exceptionally strong carrier-density (gate-voltage) sensitivity of the uniaxial anisotropy, which the standard p–d Zener model does not predict, and the experimental realization of non-volatile, deterministic magnetization switching by electric fields alone. As of 2026 the literature shows substantial but incomplete progress: field-free electric-field-induced switching was demonstrated but only stochastically (2013), electric-field-assisted switching required an external magnetic field (2017), non-volatile ferroelectric gating was achieved for the ferromagnetism magnitude and magnetotransport anisotropy but not for deterministic switching of the magnetization direction, and the shear-strain account of the uniaxial anisotropy was experimentally disfavored (2020). No predictive microscopic theory of the uniaxial anisotropy's gate sensitivity and no deterministic non-volatile electric-field-only switching of the magnetization direction in (Ga,Mn)As are found in the literature, while the broader goal of non-volatile electrical control of magnetization has been realized in other, room-temperature material systems.

Background

(Ga,Mn)As is a dilute ferromagnetic semiconductor: a GaAs crystal in which a few percent of Ga atoms are replaced by Mn, and the localized Mn spins are coupled to itinerant valence-band holes through the p–d exchange interaction. Because the holes mediate the ferromagnetic order, essentially every magnetic property — including the Curie temperature, the temperature below which spontaneous magnetization appears — depends on the hole concentration. The p–d Zener model (Dietl, Ohno, Matsukura, Cibert and Ferrand, Science 287, 1019, 2000) describes this hole-mediated ferromagnetism; combined with the spin–orbit-split valence band it also predicts the magnetocrystalline anisotropy, the dependence of the magnetic free energy on the direction of the magnetization vector, which selects the easy axes along which the magnetization rests (Abolfath, Jungwirth, Brum and MacDonald, Phys. Rev. B 63, 054418, 2001). In epitaxial (Ga,Mn)As layers the in-plane anisotropy is conventionally decomposed into a cubic term with fourfold symmetry, characterized by the anisotropy field HCH_{\mathrm{C}} and inherited from the zinc-blende (cubic) crystal structure of GaAs, and a uniaxial term with twofold symmetry, characterized by the anisotropy field μ0HU\mu_{0}H_{\mathrm{U}} along the [110] or [11ˉ0][1\bar{1}0] crystal direction. These fields are measured experimentally by angle-dependent magnetotransport, for example the planar Hall effect, a transverse voltage that depends on the angle between the magnetization and the current. The uniaxial term is anomalous: the ideal zinc-blende symmetry contains no in-plane twofold axis, so the term must originate in symmetry breaking, its magnitude varies from sample to sample, and its easy axis rotates with hole density and temperature (Sawicki et al., Phys. Rev. B 71, 121302, 2005). Electric-field control of hole density in (Ga,Mn)As was first used to modulate the ferromagnetism itself through field-effect structures (Chiba, Matsukura and Ohno, Appl. Phys. Lett. 89, 162505, 2006). The source paper (Chiba, Sawicki, Nishitani, Nakatani, Matsukura and Ohno, Nature 455, 515–518, 2008) connected the two ideas: applying a voltage across a metal–insulator–semiconductor gate stack with a ZrO2_{2} insulator on (Ga,Mn)As accumulates or depletes holes near the semiconductor surface, and the measured anisotropy fields track this gate field. The central observation was that the in-plane uniaxial anisotropy field μ0HU\mu_{0}H_{\mathrm{U}} is extraordinarily sensitive to the gate-induced hole-density change, varying reversibly by a large fraction and reversing sign with the electric field, whereas the cubic term changes comparatively little; the easy axis of the magnetization can therefore be rotated by the gate voltage alone. The same paper reports micromagnetic simulations (numerical solution of the continuum Landau–Lifshitz–Gilbert equation for the magnetization dynamics) showing that when a set of conditions is met — one of them the observed sign change of μ0HU\mu_{0}H_{\mathrm{U}} with electric field — the magnetization would switch between stable directions, i.e. a permanent reversal of the magnetization state. Two issues were thereby left open and are taken up by the later literature. First, the p–d Zener and related k·p theories (k·p denoting the standard perturbative description of the spin–orbit-split valence band used for these semiconductors) reproduce the strain-related and cubic anisotropy terms but do not predict an in-plane uniaxial term with the observed strength and carrier-density dependence; in calculations it must be inserted phenomenologically, most commonly as an in-plane shear strain, so the microscopic origin of the gate sensitivity — interface-induced symmetry breaking, growth-related Mn correlations, local lattice distortions, or neglected band-structure terms — is unidentified. Second, the magnetization switching existed only in simulation: a non-volatile, deterministic, reproducible switching of the magnetization direction by electric fields alone, persisting after the gate voltage is removed, had not been demonstrated experimentally. Comprehensive reviews of (Ga,Mn)As physics and of the electrical manipulation of magnetism across material systems frame this as the state of the field (Jungwirth et al., Rev. Mod. Phys. 86, 855, 2014; Matsukura, Tokura and Ohno, Nat. Nanotechnol. 10, 209, 2015).

Problem Statement

The problem, as identified by the source paper, is to extend the demonstrated electric-field control of magnetic anisotropy in the ferromagnetic semiconductor (Ga,Mn)As to a predictive microscopic theory and to non-volatile device operation. It has two linked parts serving this single objective. (1) Microscopic origin and predictive theory: identify the physical mechanism responsible for the exceptionally strong sensitivity of the in-plane uniaxial magnetic anisotropy of (Ga,Mn)As — quantified by the uniaxial anisotropy field μ0HU\mu_{0}H_{\mathrm{U}} — to the hole density modulated by a gate electric field in a metal–insulator–semiconductor structure, including the observed reversal of the sign of μ0HU\mu_{0}H_{\mathrm{U}} with applied gate field, and construct a theory that goes beyond the standard p–d Zener/k·p description (k·p being the standard perturbative valence-band band-structure method; it accounts for the strain-dependent and cubic anisotropy terms but predicts no such uniaxial term without a phenomenological symmetry-breaking input, usually a shear strain) and quantitatively reproduces the measured anisotropy-field versus electric-field data of gated (Ga,Mn)As. (2) Non-volatile electric-field switching: realize experimentally, in gated (Ga,Mn)As structures, deterministic, reproducible and device-compatible switching of the magnetization direction by electric fields alone — a permanent change of the magnetization state between stable directions that persists after the gate voltage is removed, without sustained gate bias and without applied external magnetic fields — as anticipated by the micromagnetic simulations reported in the source paper.

References

  1. D. Chiba, M. Sawicki, Y. Nishitani, Y. Nakatani, F. Matsukura, H. Ohno, Magnetization vector manipulation by electric fields, Nature 455, 515–518 (2008), DOI 10.1038/nature07318, https://doi.org/10.1038/nature07318
  2. T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Zener model description of ferromagnetism in zinc-blende magnetic semiconductors, Science 287, 1019–1022 (2000), DOI 10.1126/science.287.5455.1019, https://doi.org/10.1126/science.287.5455.1019
  3. M. Abolfath, T. Jungwirth, J. Brum, A. H. MacDonald, Theory of magnetic anisotropy in III1−x_{1-x}Mnx_xV ferromagnets, Phys. Rev. B 63, 054418 (2001), DOI 10.1103/PhysRevB.63.054418, https://doi.org/10.1103/PhysRevB.63.054418
  4. M. Sawicki, K.-Y. Wang, K. W. Edmonds, R. P. Campion, C. R. Staddon, N. R. S. Farley, C. T. Foxon, E. Papis, E. Kamińska, A. Piotrowska, T. Dietl, B. L. Gallagher, In-plane uniaxial anisotropy rotations in (Ga,Mn)As thin films, Phys. Rev. B 71, 121302 (2005), DOI 10.1103/PhysRevB.71.121302, https://doi.org/10.1103/PhysRevB.71.121302
  5. D. Chiba, F. Matsukura, H. Ohno, Electric-field control of ferromagnetism in (Ga,Mn)As, Appl. Phys. Lett. 89, 162505 (2006), DOI 10.1063/1.2362971, https://doi.org/10.1063/1.2362971
  6. J. Zemen, J. Kučera, K. Olejník, T. Jungwirth, Magnetocrystalline anisotropies in (Ga,Mn)As: Systematic theoretical study and comparison with experiment, Phys. Rev. B 80, 155203 (2009), DOI 10.1103/PhysRevB.80.155203, https://doi.org/10.1103/PhysRevB.80.155203
  7. M. Glunk, J. Daeubler, L. Dreher, S. Schwaiger, W. Schoch, R. Sauer, W. Limmer, A. Brandlmaier, S. T. B. Goennenwein, C. Bihler, M. S. Brandt, Magnetic anisotropy in (Ga,Mn)As: Influence of epitaxial strain and hole concentration, Phys. Rev. B 79, 195206 (2009), DOI 10.1103/PhysRevB.79.195206, https://doi.org/10.1103/PhysRevB.79.195206
  8. S. J. Chung, H. C. Kim, S. Lee, X. Liu, J. K. Furdyna, The effect of carrier density on magnetic anisotropy of the ferromagnetic semiconductor (Ga, Mn)As, Solid State Communications 149, 1739–1742 (2009), DOI 10.1016/j.ssc.2009.07.024, https://doi.org/10.1016/j.ssc.2009.07.024
  9. D. Chiba, Y. Nakatani, F. Matsukura, H. Ohno, Simulation of magnetization switching by electric-field manipulation of magnetic anisotropy, Appl. Phys. Lett. 96, 192506 (2010), DOI 10.1063/1.3428959, https://doi.org/10.1063/1.3428959
  10. P. Balestriere, T. Devolder, J. Wunderlich, C. Chappert, Electric field induced anisotropy modification in (Ga,Mn)As: A strategy for the precessional switching of the magnetization, Appl. Phys. Lett. 96, 142504 (2010), DOI 10.1063/1.3379016, https://doi.org/10.1063/1.3379016
  11. I. Stolichnov, S. W. E. Riester, E. Mikheev, N. Setter, A. W. Rushforth, K. W. Edmonds, R. P. Campion, C. T. Foxon, B. L. Gallagher, T. Jungwirth, H. J. Trodahl, Ferroelectric polymer gates for non-volatile field effect control of ferromagnetism in (Ga, Mn)As layers, Nanotechnology 22, 254004 (2011), DOI 10.1088/0957-4484/22/25/254004, https://doi.org/10.1088/0957-4484/22/25/254004
  12. E. Mikheev, I. Stolichnov, Z. Huang, A. W. Rushforth, J. A. Haigh, R. P. Campion, K. W. Edmonds, B. L. Gallagher, N. Setter, Non-volatile ferroelectric gating of magnetotransport anisotropy in (Ga,Mn)(As,P), Appl. Phys. Lett. 100, 262906 (2012), DOI 10.1063/1.4731245, https://doi.org/10.1063/1.4731245
  13. T. Jungwirth, J. Wunderlich, V. Novák, K. Olejník, B. L. Gallagher, R. P. Campion, K. W. Edmonds, A. W. Rushforth, A. J. Ferguson, P. Němec, Spin-dependent phenomena and device concepts explored in (Ga,Mn)As, Rev. Mod. Phys. 86, 855–896 (2014), DOI 10.1103/RevModPhys.86.855, https://doi.org/10.1103/RevModPhys.86.855
  14. D. Chiba, T. Ono, F. Matsukura, H. Ohno, Electric field control of thermal stability and magnetization switching in (Ga,Mn)As, Appl. Phys. Lett. 103, 142418 (2013), DOI 10.1063/1.4821778, https://doi.org/10.1063/1.4821778
  15. H. Subramanian, J. E. Han, In-plane uniaxial magnetic anisotropy in (Ga, Mn)As due to local lattice distortions around Mn2+^{2+} ions, J. Phys.: Condens. Matter 25, 206005 (2013), DOI 10.1088/0953-8984/25/20/206005, https://doi.org/10.1088/0953-8984/25/20/206005
  16. M. Birowska, C. Śliwa, J. A. Majewski, T. Dietl, Origin of Bulk Uniaxial Anisotropy in Zinc-Blende Dilute Magnetic Semiconductors, Phys. Rev. Lett. 108, 237203 (2012), DOI 10.1103/PhysRevLett.108.237203, https://doi.org/10.1103/PhysRevLett.108.237203
  17. L. Chen, F. Matsukura, H. Ohno, Electric-Field Modulation of Damping Constant in a Ferromagnetic Semiconductor (Ga,Mn)As, Phys. Rev. Lett. 115, 057204 (2015), DOI 10.1103/PhysRevLett.115.057204, https://doi.org/10.1103/PhysRevLett.115.057204
  18. F. Matsukura, Y. Tokura, H. Ohno, Control of magnetism by electric fields, Nat. Nanotechnol. 10, 209–220 (2015), DOI 10.1038/nnano.2015.22, https://doi.org/10.1038/nnano.2015.22
  19. M. Sawicki, O. Proselkov, C. Śliwa, P. Aleshkevych, J. Z. Domagała, J. Sadowski, T. Dietl, Cubic anisotropy in (Ga,Mn)As layers: Experiment and theory, Phys. Rev. B 97, 184403 (2018), DOI 10.1103/PhysRevB.97.184403, https://doi.org/10.1103/PhysRevB.97.184403
  20. M. Birowska, C. Śliwa, J. A. Majewski, Energetic, electronic, and magnetic properties of Mn pairs on reconstructed (001) GaAs surfaces, Phys. Rev. B 95, 115311 (2017), DOI 10.1103/PhysRevB.95.115311, https://doi.org/10.1103/PhysRevB.95.115311
  21. H. Wang, J. Ma, X. Yu, Z. Yu, J. Zhao, Electric-field assisted switching of magnetization in perpendicularly magnetized (Ga,Mn)As films at high temperatures, J. Phys. D: Appl. Phys. 50, 025003 (2017), DOI 10.1088/1361-6463/50/2/025003, https://doi.org/10.1088/1361-6463/50/2/025003
  22. H. Wang, J. Ma, J. Zhao, Giant modulation of magnetism in (Ga,Mn)As ultrathin films via electric field, J. Semicond. 40, 092501 (2019), DOI 10.1088/1674-4926/40/9/092501, https://doi.org/10.1088/1674-4926/40/9/092501
  23. M. Kraimia, L. Largeau, K. Boujdaria, B. Croset, C. Mocuta, A. Lemaître, C. Gourdon, L. Thevenard, Exploring the shear strain contribution to the uniaxial magnetic anisotropy of (Ga,Mn)As, J. Appl. Phys. 127, 093901 (2020), DOI 10.1063/1.5140078, https://doi.org/10.1063/1.5140078
  24. M. Tian, T. Wang, Y. Su, J.-Q. Zhu, K. Liu, M.-J. Tang, Z.-W. Xie, Y. Yuan, M. Wang, Plotting philosophy picture of uniaxial magnetic anisotropy in arsenide and phosphide dilute ferromagnetic semiconductors, Results in Physics 60, 107687 (2024), DOI 10.1016/j.rinp.2024.107687, https://doi.org/10.1016/j.rinp.2024.107687
  25. A. Fert, R. Ramesh, V. Garcia, F. Casanova, M. Bibes, Electrical control of magnetism by electric field and current-induced torques, Rev. Mod. Phys. 96, 015005 (2024), DOI 10.1103/RevModPhys.96.015005, https://doi.org/10.1103/RevModPhys.96.015005