Spin-current in a Magnetic Semiconductor Tunnel Junction: Effect of External Bias Voltage
Author affiliations
DOI:
https://doi.org/10.15625/0868-3166/17046Keywords:
spin-orbit interaction, III-V semiconductor, magnetic tunnel junction, spin-current, multi-band transport, transfer matrix, k.p methodAbstract
This paper investigates spin-current transport in a GaMnAs/GaAs/GaMnAs magnetic semiconductor tunnel junctions under applied bias voltages. The 30-band k.p approach is used to describe the materials within the heterostructure, incorporating both spin-orbit and exchange interactions. We use the transfer-matrix formalism to derive numerical solutions for the wave functions. At specific bias values, we calculate the polarization of the spin-current component along the z direction of the structure. We show oscillations of the two spin-current components perpendicular to the magnetization with equal polarization amplitude and characteristic period. The polarization amplitude varies around 10%, reflecting the typical polarization in such type of material. The oscillation period - which relates to the Larmor frequency for spin precession - increases with the bias voltage values.
Downloads
Metrics
References
J. C. Slonczewski, Current-driven excitation of magnetic multilayers, J. Magn. Magn. Mater. 159 (1996) L1-L7. DOI: https://doi.org/10.1016/0304-8853(96)00062-5
L. Berger, Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B 54 (13) (1996) 9353. DOI: https://doi.org/10.1103/PhysRevB.54.9353
M. Elsen, O. Boulle, J. -M. George, H. Jaffres, R. Mattana, V. Cros, A. Fert, A. Lemaitre, R. Giraud and G. Faini, Spin transfer experiments on (Ga, Mn) As / (In, Ga) As / (Ga, Mn) As tunnel junctions, Phys. Rev. B 73 (2006) 035303. DOI: https://doi.org/10.1103/PhysRevB.73.035303
I. M. Miron, G. Gaudin, S. Auffret, B. Rodmacq, A. Schuhl, S. Pizzini, J. Vogel and P. Gambardella, Current-driven spin torque induced by the Rashba effect in a ferromagnetic metal layer, Nat. Mater. 9 (2010) 230. DOI: https://doi.org/10.1038/nmat2613
Y. Wang, D. Zhu, Y. Wu, Y. Yang, J. Yu, R. Ramaswamy, R. Mishra, S. Shi, M. Elyasi, K. -L. Teo, Y. Wu and H. Yang, Room temperature magnetization switching in topological insulator-ferromagnet heterostructures by spin-orbit torques, Nat. Commun. 8 (2017) 1364. DOI: https://doi.org/10.1038/s41467-017-01583-4
M. Jiang, H. Asahara, S. Sato, T. Kanaki, H. Yamasaki, S. Ohya and M. Tanaka, Efficient full spin–orbit torque switching in a single layer of a perpendicularly magnetized single-crystalline ferromagnet, Nat. Commun. 10 (2019) 2590. DOI: https://doi.org/10.1038/s41467-019-10553-x
A. Manchon, J. Zelezny, I. M. Miron, T. Jungwirth, J. Sinova, A. Thiaville, K. Garello and P. Gambardella, Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems, Rev. Mod. Phys. 91 (2019) 035004. DOI: https://doi.org/10.1103/RevModPhys.91.035004
S. Bhatti, R. Sbiaa, A. Hirohata, H. Ohno, S. Fukami and S. N. Piramanayagam, Spintronics based random access memory: a review, Mater. Today 20(9) (2017) 530. DOI: https://doi.org/10.1016/j.mattod.2017.07.007
E. I. Rashba, Spin currents in thermodynamic equilibrium: The challenge of discerning transport currents, Phys. Rev. B 68 (2003) 241315(R). DOI: https://doi.org/10.1103/PhysRevB.68.241315
H. -J. Drouhin, G. Fishman and J. E. Wegrowe, Spin currents in semiconductors: Redefinition and counterexample, Phys. Rev. B 83 (2011) 113307. DOI: https://doi.org/10.1103/PhysRevB.83.113307
P. M. Haney and M. D. Stiles, Current-induced torques in the presence of spin-orbit coupling, Phys. Rev. Lett. 105 (2010) 126602. DOI: https://doi.org/10.1103/PhysRevLett.105.126602
W. Cao, M. Wei-Yuan Tu, J. Xiao and W. Yao, Giant spin transfer torque in atomically thin magnetic bilayers, Chinese Physics Letters 37(10) (2020) 107210. DOI: https://doi.org/10.1088/0256-307X/37/10/107201
N. S. Al-Shameri and H. Dakhlaoui, Spin-current oscillations in diluted magnetic semiconductor multibarrier GaMnAs/GaAs: Role of temperature and bias voltage, Coatings 12(4) (2022) 504. DOI: https://doi.org/10.3390/coatings12040504
N. S. Al-Shameri and H. Dakhlaoui, Numerical investigation of quantum tunneling time and spin-current density in GaAs/GaMnAs/GaAs barriers: Role of an applied bias voltage, Physica B 628 (2022) 413555. DOI: https://doi.org/10.1016/j.physb.2021.413555
M. Tanaka, S. Ohya and Pham Nam Hai, Recent progress in III-V based ferromagnetic semiconductors: Band structure, Fermi level, and tunneling transport, App. Phys. Rev. 1 (2014) 011102. DOI: https://doi.org/10.1063/1.4840136
D. To, T. Dang, Hoai Nguyen, V. Safarov, J. George, H. -J. Drouhin and H. Jaffr`es, Spin-orbit currents, spintransfer
torque and anomalous tunneling in III–V heterostructures probed by advanced 30- and 40-bands k.p tunneling methods, IEEE Trans. Magn. 55(7) (2019) 1400707. DOI: https://doi.org/10.1109/TMAG.2019.2894571
Duy-Quang To, Advanced multi-band k.p methods for semiconductor-based spintronics, Ph.D dissertation, Institut
Polytechnique de Paris (2019).
Guy Fishman, Semi-conducteurs: les bases de la th´eorie k.p, Les ´ Edition de l’ ´ Ecole Polytechnique (2010).
S. Richard, F. Aniel and G. Fishman, Energy-band structure of Ge, Si, and GaAs: A thirty-band k.p method, Phys. Rev. B 70 (2004) 235204. DOI: https://doi.org/10.1103/PhysRevB.70.235204
T. L. Hoai Nguyen, H. -J. Drouhin, and G. Fishman, Spin trajectory along an evanescent loop in zinc-blende semiconductors, Phys. Rev. B 80 (2009) 075207. DOI: https://doi.org/10.1103/PhysRevB.80.075207
Y. Ando and T. Ito, Calculation of transmission tunneling current across arbitrary potential barriers, J. Appl. Phys. 61 (1987) 1497. DOI: https://doi.org/10.1063/1.338082
Nguyen Thi Loan and Nguyen Thi Lam Hoai, Hong Duc University Journal of Science, 45 (2019) 95. DOI: https://doi.org/10.51316/jca.2020.015
A. Kalitsov, Spin-polarized current-induced torque in magnetic tunnel junctions, J. Appl. Phys. 99(8) (2006) 08G501. DOI: https://doi.org/10.1063/1.2151796
D. C. Ralph and M. D. Stiles, Spin transfer torques, J. Magn. Magn. Mater. 320 (2008) 1190. DOI: https://doi.org/10.1016/j.jmmm.2007.12.019
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with CIP agree with the following terms:- The manuscript is not under consideration for publication elsewhere. When a manuscript is accepted for publication, the author agrees to automatic transfer of the copyright to the editorial office.
- The manuscript should not be published elsewhere in any language without the consent of the copyright holders. Authors have the right to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of their work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are encouraged to post their work online (e.g., in institutional repositories or on their websites) prior to or during the submission process, as it can lead to productive exchanges or/and greater number of citation to the to-be-published work (See The Effect of Open Access).
Funding data
-
Vietnam Academy of Science and Technology
Grant numbers ICP.2021.12
Accepted 08-07-2022
Published 06-09-2022