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Volumn 67, Issue 4, 2003, Pages

Disorder-induced noncollinear ferromagnetism in models for (III, Mn)V semiconductors

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL; MANGANESE;

EID: 0037438656     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.045202     Document Type: Article
Times cited : (31)

References (69)
  • 1
    • 85038925217 scopus 로고    scopus 로고
    • J. K. Furdyna and J. Kossut, Diluted Magnetic Semiconductors, Vol. 25 of Semiconductor and Semimetals (Academic Press, New York, 1988)
    • J. K. Furdyna and J. Kossut, Diluted Magnetic Semiconductors, Vol. 25 of Semiconductor and Semimetals (Academic Press, New York, 1988).
  • 2
    • 0032516694 scopus 로고    scopus 로고
    • H. Ohno, Science 281, 951 (1998).
    • (1998) Science , vol.281 , pp. 951
    • Ohno, H.1
  • 5
    • 85038965013 scopus 로고    scopus 로고
    • J. König, J. Schliemann, T. Jungwirth, and A. H. MacDonald, in Electronic Structure and Magnetism of Complex Materials, edited by D. J. Singh and D. A. Papaconstantopoulos (Springer-Verlag, Berlin, 2002)
    • J. König, J. Schliemann, T. Jungwirth, and A. H. MacDonald, in Electronic Structure and Magnetism of Complex Materials, edited by D. J. Singh and D. A. Papaconstantopoulos (Springer-Verlag, Berlin, 2002).
  • 10
    • 85038924293 scopus 로고    scopus 로고
    • Semiconductor Spintronics and Quantum Computation, edited by D. D. Awschalom, D. Loss, and N. Samarth (Springer, Berlin, 2002)
    • Semiconductor Spintronics and Quantum Computation, edited by D. D. Awschalom, D. Loss, and N. Samarth (Springer, Berlin, 2002).
  • 25
    • 0343777323 scopus 로고    scopus 로고
    • Interacting Electrons in Nanostructures, edited by R. Haug and H. Schoeller (Springer, Berlin, 2001)
    • J. König, H. H. Lin, and A. H. MacDonald, Phys. Rev. Lett. 84, 5628 (2000);in Interacting Electrons in Nanostructures, edited by R. Haug and H. Schoeller (Springer, Berlin, 2001).
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 5628
    • König, J.1    Lin, H.H.2    MacDonald, A.H.3
  • 32
    • 85038887100 scopus 로고    scopus 로고
    • S.-R. E. Yang and A. H. MacDonald, cond-mat/0202201 (unpublished)
    • S.-R. E. Yang and A. H. MacDonald, cond-mat/0202201 (unpublished);
  • 33
    • 0037101425 scopus 로고    scopus 로고
    • J. Sinova, T. Jungwirth, S.-R. E. Yang, J. Kucera, and A. H. MacDonald, Phys. Rev. B 66, 041202 (2002)
    • J. Sinova, T. Jungwirth, S.-R. E. Yang, J. Kucera, and A. H. MacDonald, Phys. Rev. B 66, 041202 (2002).
  • 40
    • 85038942794 scopus 로고    scopus 로고
    • cond-mat/0111504 (comment) Phys. Rev. Lett. (to be published)
    • see, however, C. Timm, F. Schäfer, and F. von Oppen, cond-mat/0111504 (comment) Phys. Rev. Lett. (to be published);
    • Timm, C.1    Schäfer, F.2    von Oppen, F.3
  • 41
    • 85038941413 scopus 로고    scopus 로고
    • cond-mat/0112165 (reply) Phys. Rev. Lett. (to be published)
    • M. Berciu and R. N. Bhatt, cond-mat/0112165 (reply) Phys. Rev. Lett. (to be published).
    • Berciu, M.1    Bhatt, R.N.2
  • 61
    • 85038950243 scopus 로고    scopus 로고
    • W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, Berlin, 1999)
    • W. W. Chow and S. W. Koch, Semiconductor-Laser Fundamentals (Springer, Berlin, 1999).
  • 65
    • 85038971360 scopus 로고    scopus 로고
    • Note that the expression (20) has, just as (Formula presented) dimension of energy, since the (Formula presented) there are dimensionless. This is different from Eq. (11) where the quantities (Formula presented) have the dimension of the inverse temperature such that (Formula presented) is dimensionless
    • Note that the expression (20) has, just as (Formula presented) dimension of energy, since the (Formula presented) there are dimensionless. This is different from Eq. (11) where the quantities (Formula presented) have the dimension of the inverse temperature such that (Formula presented) is dimensionless.
  • 66
    • 85038935153 scopus 로고    scopus 로고
    • We note that the summation over (Formula presented) and (Formula presented) in Eq. (23) is unrestricted, i.e., is performed over all single-particle states. If one would restrict the summation to, say, states (Formula presented) that are occupied in the ground state and states (Formula presented) that are unoccupied, a factor of (Formula presented) would occur
    • We note that the summation over (Formula presented) and (Formula presented) in Eq. (23) is unrestricted, i.e., is performed over all single-particle states. If one would restrict the summation to, say, states (Formula presented) that are occupied in the ground state and states (Formula presented) that are unoccupied, a factor of (Formula presented) would occur.
  • 68
    • 85038900761 scopus 로고    scopus 로고
    • If the spin flip is performed with respect to the (Formula presented) plane, the corresponding operator acting on the carrier states is just the operator (Formula presented) of complex conjugation which changes the sign of (Formula presented) but leaves the other Pauli matrices invariant. In the case of the (Formula presented) plane or (Formula presented) plane the spin-flip operator is (Formula presented) and (Formula presented) respectively. For a general orientation of this plane one has to use the appropriate linear combination of these operators. If all Mn spins lie in such a plane, the parabolic-band Hamiltonian is invariant under this spin-flip operation
    • If the spin flip is performed with respect to the (Formula presented) plane, the corresponding operator acting on the carrier states is just the operator (Formula presented) of complex conjugation which changes the sign of (Formula presented) but leaves the other Pauli matrices invariant. In the case of the (Formula presented) plane or (Formula presented) plane the spin-flip operator is (Formula presented) and (Formula presented) respectively. For a general orientation of this plane one has to use the appropriate linear combination of these operators. If all Mn spins lie in such a plane, the parabolic-band Hamiltonian is invariant under this spin-flip operation.
  • 69
    • 85038888143 scopus 로고    scopus 로고
    • Note that the sum rules, Eqs. (33) and (34), are independent of our choice to take all wave functions to be real since possible common phases in the up or down spins cancel in each term in the summation over (Formula presented)
    • Note that the sum rules, Eqs. (33) and (34), are independent of our choice to take all wave functions to be real since possible common phases in the up or down spins cancel in each term in the summation over (Formula presented)


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