Berry Approach to Intrinsic Anomalous Hall Conductivity in Dilute Magnetic Semiconductors (Ga1-xMnxAs)

Sintayehu Mekonnen; P. Singh

doi:10.4236/wjcmp.2015.53019

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World Journal of Condensed Matter Physic... > Vol.5 No.3, August 2015

Berry Approach to Intrinsic Anomalous Hall Conductivity in Dilute Magnetic Semiconductors (Ga_1-xMn_xAs) ()

Sintayehu Mekonnen, P. Singh

Department of Physics, Addis Ababa University, Addis Ababa, Ethiopia.

DOI: 10.4236/wjcmp.2015.53019 PDF HTML XML 3,488 Downloads 4,190 Views Citations

Abstract

We develop a model Hamiltonian to treat intrinsic anomalous Hall conductivity in dilute magnetic semiconductor (DMS) of type (III, Mn, V) and obtain the Berry potential and Berry curvature which are responsible for intrinsic anomalous Hall conductivity in Ga_1-xMn_xAs DMS. Based on Kubo formalism, we establish the relation between Berry curvature and intrinsic anomalous Hall conductivity. We find that for strong spin-orbit interaction intrinsic anomalous Hall conductivity is quantized which is in agreement with recent experimental observation. In addition, we show that the intrinsic anomalous Hall conductivity (AHC) can be controlled by changing concentration of magnetic impurities as well as exchange field. Since Berry curvature related contribution of anomalous Hall conductivity is believed to be dissipationless, our result is a significant step toward achieving dissipationless electron transport in technologically relevant conditions in emerging of spintronics.

Keywords

Berry Potential, Berry Curvature, Kubo Formalism, Anomalous Hall Conductivity

Share and Cite:

Mekonnen, S. and Singh, P. (2015) Berry Approach to Intrinsic Anomalous Hall Conductivity in Dilute Magnetic Semiconductors (Ga_1-xMn_xAs). World Journal of Condensed Matter Physics, 5, 179-186. doi: 10.4236/wjcmp.2015.53019.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Hall, E. (1879) On a New Action of the Magnet on Electric Currents. American Journal of Mathematics, 2, 287-292. http://dx.doi.org/10.2307/2369245
[2]	Tsui, D.C., Stormer, H.L. and Gossard, A.C. (1982) Two-Dimensional Magneto Transport in the Extreme Quantum Limit. Physical Review Letters, 48, 1559. http://dx.doi.org/10.1103/PhysRevLett.48.1559
[3]	Chen, H., Niu, Q. and MacDonald, A.H. (2014) Anomalous Hall Effect Arising from Noncollinear Antiferromagnet. Physical Review Letters, 112, Article ID: 017205. http://dx.doi.org/10.1103/PhysRevLett.112.017205
[4]	Hsu, S., Lin, C.P., Sun, S.J. and Chou, H. (2010) The Role of Anomalous Hall Effect in Diluted Magnetic Semiconductors. Applied Physics Letters, 96, Article ID: 242507. http://dx.doi.org/10.1063/1.3431294
[5]	Idrish Miah, M. (2007) Observation of the Anomalous Hall Effect in GaAs. Journal of Physics D: Applied Physics, 40, 1659. http://dx.doi.org/10.1088/0022-3727/40/6/013
[6]	Mitra, P., Misra, R., Hebard, A.F., Muttalib, K.A. and Wölfle, P. (2007) Weak-Localization Correction to the Anomalous Hall Effect in Polycrystalline Fe Films. Physical Review Letters, 99, Article ID: 046804. http://dx.doi.org/10.1103/PhysRevLett.99.046804
[7]	Jungwirth, T., Niu, Q. and MacDonald, A.H. (2002) Anomalous Hall Effect in Ferromagnetic Semiconductors. Physical Review Letters, 88, Article ID: 207208. http://dx.doi.org/10.1103/PhysRevLett.88.207208
[8]	Karplus, R. and Luttinger, J.M. (1954) Hall Effect in Ferromagnetism. Physical Review, 95, 1154. http://dx.doi.org/10.1103/PhysRev.95.1154
[9]	Nunner, T.S., Zaránd, G. and von Oppen, F. (2008)Anomalous Hall Effect in a Two Dimensional Electron Gas with Magnetic Impurities. Physical Review Letters, 100, Article ID: 236602. http://dx.doi.org/10.1103/PhysRevLett.100.236602
[10]	Liu, S., Yan, Y.-Z. and Hu, L.-B. (2012) Characteristics of Anomalous Hall Effect in Spin-Polarized Two-Dimensional Electron Gases in the Presence of Both Intrinsic, Extrinsic, and External Electric-Field Induced Spin—Orbit Couplings. Chinese Physics B, 21, Article ID: 027201. http://dx.doi.org/10.1088/1674-1056/21/2/027201
[11]	Sundaram, G. and Niu, Q. (1999) Wave-Packet Dynamics in Slowly Perturbed Crystals: Gradient Corrections and Berry-Phase Effects. Physical Review B, 59, 14915-14925.
[12]	Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A.H. and Ong, N.P. (2010) Anomalous Hall Effect in Antiferromagnetic Systems. Reviews of Modern Physics, 82, 1539. http://dx.doi.org/10.1103/RevModPhys.82.1539
[13]	Boldrin, D. and Wills, A.S. (2012) Anomalous Hall Effect in Geometrically Frustrated Magnets. Advanced Condensed Matter Physics, 2012, Article ID: 615295. http://www.hindawi.com
[14]	Chang, C.-Z., et al. (2013) Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator. Science Magazine, 340, 167-170. http://www.sciencemag.org/content/340/6129/167.abstract
[15]	Gradhand, M., Fedorov, D.V., Pientka, F., Zahn, P., Mertig, I. and Györffy, B.L. (2012) First-Principle Calculations of the Berry Curvature of Bloch States for Charge and Spin Transport of Electrons. Journal of Physics: Condensed Matter, 24, Article ID: 213202. http://dx.doi.org/10.1088/0953-8984/24/21/213202
[16]	Crépieux, A. and Bruno, P. (2001) Theory of the Anomalous Hall Effect from the Kubo Formula and the Dirac Equation. Physical Review B, 64, Article ID: 014416.
[17]	Bestwick, A.J., Fox, E.J., Kou, X.F, Pan, L., Wang, K.L. and Goldhaber-Gordon, D. (2015) Precise Quantization of the Anomalous Hall Effect Near Zero Magnetic Field. Mesoscale and Nanoscale Physics, 114, Article ID: 187201.
[18]	Chang, C.-Z., et al. (2013) The Complete Quantum Hall Trio. Science, 340, 153-154. http://www.sciencemag.org/content/early/recent / 14 March 2013 / Page 10.1126/science.1234414
[19]	Sinitsyn, N.A., MacDonald, A.H., Jungwirth, T., Dugaev, V.K. and Sinova, J. (2007) Anomalous Hall Effect in a Two-Dimensional Dirac Band: The Link between the Kbo-Streda Formula and the Semiclassical Boltzmann Equation Approach. Physical Review B, 75, Article ID: 045315. http://dx.doi.org/10.1103/PhysRevB.75.045315