The Magnetic Domain Structure Properties in Diluted Magnetic Semiconductors
Keywords:magnetic domain structure, diluted magnetic semiconductor
We present a comprehensive analysis of the domain structure formation in the ferromagnetic
phase of diluted magnetic semiconductors (DMS) of the p-type. Our analysis is carried out
on the base of the effective magnetic free energy of DMS calculated by us earlier. This free
energy, substituting DMS (a disordered magnet) by an effective ordered substance, permits us
to apply the standard phenomenological approach to the domain structure calculation. Using
the coupled system of Maxwell equations with those obtained by the minimization of the free
energy functional, we show the existence of the critical ratio vcr of concentration of charge
carriers and magnetic ions such that the sample critical thickness Lcr (such that the sample
is monodomain at L < Lcr) diverges as v → vcr. At v > vcr, the sample is monodomain. This
feature makes DMS different from conventional ordered magnets, as it gives a possibility to
control the sample critical thickness and the emerging domain structure period by a variation
of v. As the concentration of magnetic impurities grows, vcr → ∞, restoring a conventional
behavior of ordered magnets. Above facts have been revealed by the examination of the tem-
perature of the transition to an inhomogeneous magnetic state (stripe domain structure) in
the slab of a p-type DMS with finite thickness L. Our theory can be easily generalized for an
arbitrary disordered magnet.
A.V. Komarov, S.M. Ryabchenko, O.V. Terletskii, I.I. Zheru, R.D. Ivanchuk. Magneto-optical studies and the double opticomagnetic resonance of the exciton band in Mn/2+/-doped CdTe. Sov. Phys. JETP 46, 318 (1977).
E.A. Pashitskii, S.M. Ryabchenko. Magnetic ordering in semiconductors with magnetic impurities. Fiz. Tverd. Tela 21, (1979), 545 [Sov. Phys. Solid State 21, 322 (1979)].
T. Dietl, H. Ohno. Dilute ferromagnetic semiconductors: Physics and spintronic structures. Rev. Mod. Phys. 86, 187 (2014). https://doi.org/10.1103/RevModPhys.86.187
Introduction to the Physics of Diluted Magnetic Semiconductors. Edited by J. Kossut, J.A. Gaj (Springer, 2010).
M. Tanaka. Ferromagnet (MnAs)/III-V semiconductor hybrid structures. Semicond. Sci. Tech. 17, 327 (2002). https://doi.org/10.1088/0268-1242/17/4/306
T. Dietl. Ferromagnetic semiconductors. Semicond. Sci. Tech. 17, 377 (2002). https://doi.org/10.1088/0268-1242/17/4/310
T. Dietl, J. K¨onig, A.H. MacDonald. Magnetic domains in III-V magnetic semiconductors. Phys. Rev. B 64, 241201 (2001). https://doi.org/10.1103/PhysRevB.64.241201
T. Shono, T. Hasegawa, T. Fukumura, F. Matsukura, H. Ohno. Observation of magnetic domain structure in a ferromagnetic semiconductor (Ga, Mn) As with a scanning Hall probe microscope. Appl. Phys. Lett. 77, 1363 (2000). https://doi.org/10.1063/1.1290273
L.D. Landau, E.M. Lifshitz. Electrodynamics of Continuous Media (Wiley, 1984). https://doi.org/10.1016/B978-0-08-030275-1.50007-2
V.V. Tarasenko, E.V. Chenskii, I.E. Dikshtein. Theory of inhomogeneous magnetic states in ferromagnetic substances in vicinity of phase-transitions of 2nd kind. Zh. Eksp. Teor. Fiz. 70, 2178 (1976) [Sov. Phys. JETP 43, 1136 (1976)].
L.D. Landau, E.M. Lifshitz. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Zs. UdSSR, 8, 153 (1935).
M.Ya. Shirobokov. On the mechanism of magnetization of ferromagnetics. Zh. Eksp. Teor. Fiz. 15, 57 (1945).
V.G. Bar'yakhtar, B.A. Ivanov. Phase diagram of a ferromagnetic plate in an external magnetic field. Zh. Eksp. Teor. Fiz. 72, 1504 (1977) [Sov. Phys. JETP 45, 789 (1977)].
T. Dietl, H. Ohno, F. Matsukura. Hole-mediated ferromagnetism in tetrahedrally coordinated semiconductors. Phys. Rev. B 63, 195205 (2001). https://doi.org/10.1103/PhysRevB.63.195205
Yu. Semenov, V. Stephanovich. Enhancement of ferromagnetism in uniaxially stressed dilute magnetic semiconductors. Phys. Rev. B 67 195203 (2003). https://doi.org/10.1103/PhysRevB.67.195203
Yu.G. Semenov, V.A. Stephanovich. Suppression of carrier-induced ferromagnetism by composition and spin fluctuations in diluted magnetic semiconductors. Phys. Rev. B 66 075202 (2002). https://doi.org/10.1103/PhysRevB.66.075202
L.N. Bulaevskii, V.L. Ginzburg. Temperature dependence of the shape of the domain wall in ferromagnetics and ferroelectrics. Zh. Eksp. Teor. Fiz. 45, 772 (1963).
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