Molecular-Field Approximation in the Theory of Ferromagnetic Phase Transition in Diluted Magnetic Semiconductors
DOI:
https://doi.org/10.15407/ujpe66.6.503Keywords:
diluted magnetic semiconductors, ferromagnetic ordering, mean- field approximation, RKKY interactionAbstract
In this pedagogical paper, the comparative analysis of two common approaches describing the ferromagnetic phase transition in diluted magnetic semiconductors (DMS) is expounded in terms of the Weiss field approximation. Assuming a finite spin polarization of the magnetic ions, the treatment of carrier-ion exchange interaction in the first order evokes a homogeneous Weiss molecular field that polarizes the spins of free carriers. In turn, this spin polarization of the free carriers exerts the effective field that may stabilize the DMS spin polarization belowa critical temperature TC. The treatment of such self-consistent spontaneous DMS magnetization can be done in terms of the spin-spin interaction independent of the inter-ion distance and the infinitesimal in thermodynamic limit. On the other hand, by additionally accounting for the second-order effects of the carrier-ion exchange interaction, we can treat a Weiss field in terms of the Ruderman–Kittel–Kasuya–Yosida indirect spin-spin interaction, which oscillates and does not disappear at finite inter-ion distances in the case of a finite concentration of carriers. These both approaches result in the same Curie temperature TC provided a non-correlated homogeneous random distribution of the localized spin moments over the sample volume. We discuss the origin of such coincidence and show when this is not a case in other more realistic models of the conducting DMSs.
References
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 Mn2+-doped CdTe. JETP 46, 318 (1977), [translate from Zh. Exp. Teor. Fiz. 73, 608 (1977)].
Introduction to the Physics of Diluted Magnetic Semiconductors. Edited by J. Kossut, J.A. Gaj (Springer, 2010).
E.A. Pashitskii, S.M. Ryabchenko. Magnetic ordering in semiconductor with magnetic impurities. Sov. Phys. Solid State 21, 322 (1979).
C. Zener. Interaction between the d-shells in the transition metals. Phys. Rev. 81, 440 (1951).
https://doi.org/10.1103/PhysRev.81.440
C. Zener. Interaction between the d-shells in the transition metals. III. Calculation of the Weiss factors in Fe, Co, and Ni. Phys. Rev. 83, 299 (1951).
https://doi.org/10.1103/PhysRev.83.299
M.A. Ruderman, C. Kittel. Indirect exchange coupling of nuclear magnetic moments by conduction electrons. Phys. Rev. 96, 99 (1954).
https://doi.org/10.1103/PhysRev.96.99
T. Kasuya. A theory of metallic ferro- and antiferromagnetism on Zener's model. Progress of Theoretical Physics 16, 45 (1956).
https://doi.org/10.1143/PTP.16.45
K.Yosida. Magnetic properties of Cu-Mn alloys. Phys. Rev. 106, 893 (1957).
https://doi.org/10.1103/PhysRev.106.893
J.H. Van Vleck. Note on the interactions between the spins of magnetic ions or nuclei in metals. Rev. Mod. Phys. 34, 681 (1962).
https://doi.org/10.1103/RevModPhys.34.681
T. Story, G. Karczewski, L. Swierkowski, R.R. Galazka. Magnetism and band structure of the semimagnetic semiconductor Pb-Sn-Mn-Te. Phys. Rev. B 42, 10477 (1990).
https://doi.org/10.1103/PhysRevB.42.10477
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
Y.G. Semenov, S.M. Ryabchenko. Exactly solvable model for carrier-induced paramagnetic-ferromagnetic phase
transition in diluted magnetic semiconductors. Physica E 10, 165 (2001).
https://doi.org/10.1016/S1386-9477(01)00075-3
Y.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
Y.G. Semenov, V.A. Stephanovich. Enhancement of ferromagnetism in uniaxially stressed dilute magnetic semiconductors. Phys. Rev. B 67, 195203 (2003). https://doi.org/10.1103/PhysRevB.67.195203
P. Grunberg, R. Schreiber, Y. Pang, U. Walz, M.B. Brodsky, H. Sowers. Layered magnetic structures: Evidence for antiferromagnetic coupling of Fe layers across Cr interlayers. J. Appl. Phys. 61, 3750 (1987). https://doi.org/10.1063/1.338656
M. Getzlaff. Fundamentals of Magnetism (Section 15.1 Interlayer Exchange Coupling (IEC) Across a Non-Magnetic Spacer Layer) (Springer, 2008) [ISBN: 978-3-540-31152-2].
P.J.H. Bloemen. Interlayer exchange coupling and giant magnetoresistance in magnetic multilayers. Acta Physica Polonica A, 89, 277 (1996). https://doi.org/10.12693/APhysPolA.89.277
F. Stobiecki, T. Luciсski, R. Gontarz, M. Urbaniak. Influence of the annealing process on the gmr effect in per-malloy/copper multilayers. Materials Science Forum 287-288, 513 (1998). https://doi.org/10.4028/www.scientific.net/MSF.287-288.513
Y.G. Semenov, V.G. Abramishvili, A.V. Komarov, S.M. Ryabchenko. Magneto-optical investigations of diluted Cd1−xMnxS magnetic semiconductors in the B-exciton region. Phys. Rev. B 56, 1868 (1997). https://doi.org/10.1103/PhysRevB.56.1868
S.M. Ryabchenko, Yu.G. Semenov, O.V. Terletski. Exchange-scattering effects on band energies in magnetically mixed semiconductors. Phys. Stat. Sol. (b) 144, 661 (1987). https://doi.org/10.1002/pssb.2221440225
J. Cibert, D. Scalbert. Diluted magnetic semiconductors: Basic physics and optical properties. In: Spin Physics in Semiconductors. Edited by M.I. Dyakonov (Springer, 2008), 157, p. 389.
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
