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Volumn 67, Issue 6, 2003, Pages

Magnetic domain walls in single-phase and phase-separated double-exchange systems

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL; MANGANESE DERIVATIVE;

EID: 0037304005     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.064404     Document Type: Article
Times cited : (18)

References (86)
  • 8
    • 85038955011 scopus 로고    scopus 로고
    • H. S. Wang and Qi Li (unpublished) (the latter was received upon completion of the present work)
    • H. S. Wang and Qi Li (unpublished) (the latter was received upon completion of the present work).
  • 17
    • 85038887511 scopus 로고    scopus 로고
    • (formula presented) and (formula presented) directed along the principal directions of the inverse lattice, are not to be mixed with diagonally directed and rescaled (formula presented) and (formula presented) introduced later in the article
    • (formula presented) and (formula presented) directed along the principal directions of the inverse lattice, are not to be mixed with diagonally directed and rescaled (formula presented) and (formula presented) introduced later in the article.
  • 18
    • 85038901221 scopus 로고    scopus 로고
    • L.D. Landau and E.M. Lifshits, Theoretical Physics, 8 (Pergamon, New York, 1984)
    • L.D. Landau and E.M. Lifshits, Electrodynamics of Continuous Media, Theoretical Physics, Vol. 8 (Pergamon, New York, 1984).
  • 21
    • 85038889381 scopus 로고    scopus 로고
    • We neglect the magnetostatic energy associated with the domain wall in a film. In this limit the wall has the same structure as in the 3D case considered in Ref., and is more properly called the Landau-Lifshits wall [see, e.g., A. Aharoni, (Oxford University Press, Oxford, 2000)]. Our treatment remains valid when the anisotropy axis is parallel to the film, although the spin rotation then takes place in a different plane in spin space (Néel wall)
    • We neglect the magnetostatic energy associated with the domain wall in a film. In this limit the wall has the same structure as in the 3D case considered in Ref. 14, and is more properly called the Landau-Lifshits wall [see, e.g., A. Aharoni, Introduction to the Theory of Ferromagnetism (Oxford University Press, Oxford, 2000)]. Our treatment remains valid when the anisotropy axis is parallel to the film, although the spin rotation then takes place in a different plane in spin space (Néel wall).
  • 22
    • 0014585889 scopus 로고
    • Fiz. Tverd. Tela, 2779 (1969)
    • E L. Nagaev, Fiz. Tverd. Tela 11, 2779 (1969) [Sov. Phys. Solid State11, 2249 (1970)].
    • (1970) Sov. Phys. Solid State , vol.11 , pp. 2249
    • Nagaev, E.L.1
  • 23
    • 85038897967 scopus 로고    scopus 로고
    • We stress that the magnetic properties of these two systems are by no means identical, which can be seen from Eq. (3), yielding a Heisenberg (cosine) dispersion law at (formula presented) but not for any finite (formula presented) value
    • We stress that the magnetic properties of these two systems are by no means identical, which can be seen from Eq. (3), yielding a Heisenberg (cosine) dispersion law at (formula presented) but not for any finite (formula presented) value.
  • 24
    • 85038928262 scopus 로고    scopus 로고
    • E.L. Nagaev, (Imperial College Press, London, 2002), and references therein
    • E.L. Nagaev, Colossal Magnetoresistance and Phase Separation in Magnetic Semiconductors (Imperial College Press, London, 2002), and references therein.
  • 27
    • 85038903852 scopus 로고    scopus 로고
    • D.I. Golosov (unpublished)
    • D.I. Golosov (unpublished).
  • 30
    • 85038914956 scopus 로고    scopus 로고
    • The integration variable (formula presented) corresponds to (formula presented) We also assume that (formula presented) is negative; the (formula presented) case is treated similarly
    • The integration variable (formula presented) corresponds to (formula presented) We also assume that (formula presented) is negative; the (formula presented) case is treated similarly.
  • 31
    • 85038885790 scopus 로고    scopus 로고
    • Bloch wall energy, i.e., the change in the thermodynamic potential associated with the Bloch wall, can also be evaluated in a similar way, thus confirming the classical result (2)
    • Bloch wall energy, i.e., the change in the thermodynamic potential associated with the Bloch wall, can also be evaluated in a similar way, thus confirming the classical result (2).
  • 32
    • 85038920888 scopus 로고    scopus 로고
    • When the principal contribution to the spin stiffness, originates from a large, superexchange, (formula presented) the Bloch wall remains stable even when the inequality (20) is violated. Due to the absence of carriers near the center of the wall, the domain wall then becomes impenetrable for electrical current
    • When the principal contribution to the spin stiffness D originates from a large ferromagnetic superexchange, (formula presented) the Bloch wall remains stable even when the inequality (20) is violated. Due to the absence of carriers near the center of the wall, the domain wall then becomes impenetrable for electrical current.
  • 33
    • 85038915367 scopus 로고    scopus 로고
    • The limit of low hole doping, (formula presented) one similarly finds (formula presented)
    • In the limit of low hole doping, (formula presented) one similarly finds (formula presented)
  • 34
    • 85038949182 scopus 로고    scopus 로고
    • By using the Hamiltonian (1), which does not include Coulomb interactions
    • By using the Hamiltonian (1), which does not include Coulomb interactions.
  • 35
    • 85038915706 scopus 로고    scopus 로고
    • This holds for both finite and infinite values of Hund’s rule coupling. In the case of (formula presented) the carrier wave functions must vanish at the wall, whereas at finite values of (formula presented) the exponential tail of the spin-up wave function extends into the spin-down magnetic domain and vice versa [see Eq. (10)
    • This holds for both finite and infinite values of Hund’s rule coupling. In the case of (formula presented) the carrier wave functions must vanish at the wall, whereas at finite values of (formula presented) the exponential tail of the spin-up wave function extends into the spin-down magnetic domain and vice versa [see Eq. (10)].
  • 36
    • 85038971660 scopus 로고    scopus 로고
    • Three dimensions, one finds that the energy per unit area of partition is (formula presented) [see Eq. (A20)
    • In three dimensions, one finds that the energy per unit area of partition is (formula presented) [see Eq. (A20)].
  • 37
    • 85038891950 scopus 로고    scopus 로고
    • It is because of the 1D character of the perturbation that one is able to introduce a spectral shift function in this way; Eq. (27) generalizes the standard Lifshits-Krein trace formula (Ref
    • It is because of the 1D character of the perturbation that one is able to introduce a spectral shift function in this way; Eq. (27) generalizes the standard Lifshits-Krein trace formula (Ref. 33).
  • 39
    • 85038936923 scopus 로고    scopus 로고
    • I.M. Lifshits, S.A. Gredeskul, and L.A. Pastur, (Wiley, New York, 1988), Chap. 5
    • I.M. Lifshits, S.A. Gredeskul, and L.A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988), Chap. 5;
  • 40
    • 85038968149 scopus 로고    scopus 로고
    • M.G. Krein, (Birkhäuser, Basel, 1983), 107–172
    • M.G. Krein, Topics in Differential Equations and Operator Theory (Birkhäuser, Basel, 1983), pp. 107–172.
  • 42
    • 85038927254 scopus 로고    scopus 로고
    • At these values of, the uniform ferromagnetic state is typically unstable with respect to phase separation
    • At these values of J, the uniform ferromagnetic state is typically unstable with respect to phase separation.
  • 43
    • 85038904083 scopus 로고    scopus 로고
    • We emphasize that this statement applies to the intermediate doping range (formula presented)
    • We emphasize that this statement applies to the intermediate doping range (formula presented)
  • 44
    • 85038916552 scopus 로고    scopus 로고
    • Adding a nonzero superexchange, (formula presented) would (i) result in the diagonal (rather than vertical) abrupt wall being preferred at low, and (ii) give rise to a phase-separation instability within a certain low-(formula presented) region
    • Adding a nonzero superexchange, (formula presented) would (i) result in the diagonal (rather than vertical) abrupt wall being preferred at low x and (ii) give rise to a phase-separation instability within a certain low-(formula presented) region.
  • 46
    • 0000616009 scopus 로고    scopus 로고
    • It is likely that it also occurs in electron-doped monolayered compounds, like (formula presented) and
    • It is likely that it also occurs in electron-doped monolayered compounds, like (formula presented) [A. Maignan, C. Martin, G. van Tendeloo, M. Hervieu, and B. Raveau, J. Mater. Chem.8, 2411 (1998)].
    • (1998) J. Mater. Chem. , vol.8 , pp. 2411
    • Maignan, A.1    Martin, C.2    van Tendeloo, G.3    Hervieu, M.4    Raveau, B.5
  • 47
    • 0001347951 scopus 로고    scopus 로고
    • E L. Nagaev, Phys. Rep.346, 387 (2001), and references therein.
    • (2001) Phys. Rep. , vol.346 , pp. 387
    • Nagaev, E.L.1
  • 51
    • 85038915045 scopus 로고    scopus 로고
    • Such a wave function does not necessarily have to be a Bloch wave. In a purely 1D case, this would be a cosine wave, and it is also important that its wave vector will have to be related to the energy of the localized state by the usual tight-binding dispersion relation. We note that the choice of the basic set of electron energy eigenstates used in the Lifshits-Krein trace formalism [cf. Eqs. (29) and (31)] is, in principle, arbitrary
    • Such a wave function does not necessarily have to be a Bloch wave. In a purely 1D case, this would be a cosine wave, and it is also important that its wave vector will have to be related to the energy of the localized state by the usual tight-binding dispersion relation. We note that the choice of the basic set of electron energy eigenstates used in the Lifshits-Krein trace formalism [cf. Eqs. (29) and (31)] is, in principle, arbitrary.
  • 52
    • 85038913721 scopus 로고    scopus 로고
    • We consider the single-band case [cf. Eq. (1)], when the carriers originate solely from doping, and not from band overlap
    • We consider the single-band case [cf. Eq. (1)], when the carriers originate solely from doping, and not from band overlap.
  • 53
    • 85038959400 scopus 로고    scopus 로고
    • Some possible examples of antiferromagnetic phases are discussed in Ref
    • Some possible examples of antiferromagnetic phases are discussed in Ref. 22.
  • 57
    • 85038951526 scopus 로고    scopus 로고
    • This requirement is perhaps somewhat relaxed in the case of a thin film, due to the power-law (rather than exponential—see Appendix B) decay of the screened Coulomb potential
    • This requirement is perhaps somewhat relaxed in the case of a thin film, due to the power-law (rather than exponential—see Appendix B) decay of the screened Coulomb potential.
  • 60
    • 85038894377 scopus 로고    scopus 로고
    • D. S. Dessau and Z.-X. Shen, in, edited by Y. Tokura (Gordon and Breach, New York, 2000), and references therein
    • D. S. Dessau and Z.-X. Shen, in Colossal Magnetoresistive Oxides, edited by Y. Tokura (Gordon and Breach, New York, 2000), and references therein.
  • 61
    • 85038968182 scopus 로고    scopus 로고
    • Strictly speaking, there is also a surface charge (and hence Coulomb energy) associated with the interphase boundary itself, which in this respect is similar to the abrupt domain walls considered in Sec. III. Throughout Sec. IV we omit these electrostatic corrections to the energies of abrupt and Bloch domain walls and interphase boundaries. They are expected to be much smaller than the electrostatic energies of the large charged islands considered here
    • Strictly speaking, there is also a surface charge (and hence Coulomb energy) associated with the interphase boundary itself, which in this respect is similar to the abrupt domain walls considered in Sec. III. Throughout Sec. IV we omit these electrostatic corrections to the energies of abrupt and Bloch domain walls and interphase boundaries. They are expected to be much smaller than the electrostatic energies of the large charged islands considered here.
  • 62
    • 85038891043 scopus 로고    scopus 로고
    • The numerical smallness of, (which can be estimated as half the energy of an abrupt domain wall; see in the text below) and the fact that the actual values of (formula presented) are large result in the value of (formula presented) [see Eq. (41)] being small and, more generally, in (formula presented) It is therefore consistent to assume (formula presented) when evaluating abrupt wall energies and
    • The numerical smallness of W (which can be estimated as half the energy of an abrupt domain wall; see in the text below) and the fact that the actual values of (formula presented) are large result in the value of (formula presented) [see Eq. (41)] being small and, more generally, in (formula presented) It is therefore consistent to assume (formula presented) when evaluating abrupt wall energies and W.
  • 63
    • 85038958277 scopus 로고    scopus 로고
    • We recall that the interphase boundaries are expected to be abrupt (Ref
    • We recall that the interphase boundaries are expected to be abrupt (Ref. 22).
  • 64
    • 0000172889 scopus 로고
    • Zh. Eksp. Teor. Fiz., 2105 (1974)
    • V A. Kashin and E L. Nagaev, Zh. Eksp. Teor. Fiz. 66, 2105 (1974) [Sov. Phys. JETP39, 1036 (1974)];
    • (1974) Sov. Phys. JETP , vol.39 , pp. 1036
    • Kashin, V.A.1    Nagaev, E.L.2
  • 66
    • 85038932378 scopus 로고    scopus 로고
    • This method is exact for the stripe phase in 3D
    • This method is exact for the stripe phase in 3D.
  • 68
    • 85038936252 scopus 로고    scopus 로고
    • This holds within the Wigner-cell approximation for the stripe phase. Within a more rigorous treatment, (formula presented) will vanish at a certain point near (formula presented)
    • This holds within the Wigner-cell approximation for the stripe phase. Within a more rigorous treatment, (formula presented) will vanish at a certain point near (formula presented)
  • 69
    • 85038927918 scopus 로고    scopus 로고
    • Thus, the interphase boundaries within the film, be oriented perpendicularly to the film plane
    • Thus, the interphase boundaries within the film can be oriented perpendicularly to the film plane.
  • 72
    • 85038911111 scopus 로고    scopus 로고
    • Although under certain conditions stripe wall formation may be possible in the opposite case of a thick film or bulk crystal (see below and Appendix B), there is no reason to expect that these conditions are satisfied for the thicker samples studied in Ref
    • Although under certain conditions stripe wall formation may be possible in the opposite case of a thick film or bulk crystal (see below and Appendix B), there is no reason to expect that these conditions are satisfied for the thicker samples studied in Ref. 6.
  • 75
    • 36049056269 scopus 로고
    • The change of domain wall structure in the film may be further assisted by the well-known structural phase transition in strontium titanate, which takes place at about the same temperature [see, and, and references therein
    • The change of domain wall structure in the film may be further assisted by the well-known structural phase transition in strontium titanate, which takes place at about the same temperature [see G. Shirane and Y. Yamada, Phys. Rev.177, 858 (1969), and references therein;
    • (1969) Phys. Rev. , vol.177 , pp. 858
    • Shirane, G.1    Yamada, Y.2
  • 77
    • 85038897045 scopus 로고    scopus 로고
    • For very large values of Hund’s rule coupling, (formula presented) abrupt walls can also be stabilized at low hole doping, (formula presented) Because of an effective antiferromagnetism associated with the finite value of (formula presented) in real systems (and reflected, e.g., in the antiferromagnetic ordering commonly observed in manganates at (formula presented) it is unlikely that this situation can be realized experimentally
    • For very large values of Hund’s rule coupling, (formula presented) abrupt walls can also be stabilized at low hole doping, (formula presented) Because of an effective antiferromagnetism associated with the finite value of (formula presented) in real systems (and reflected, e.g., in the antiferromagnetic ordering commonly observed in manganates at (formula presented) it is unlikely that this situation can be realized experimentally.
  • 83
    • 23044532976 scopus 로고    scopus 로고
    • Fiz. Met. Metalloved., (3), 50 (2002)
    • A P. Nosov and P. Strobel, Fiz. Met. Metalloved. 93 (3), 50 (2002) [Phys. Met. Metallogr.93, 239 (2002)].
    • (2002) Phys. Met. Metallogr. , vol.93 , pp. 239
    • Nosov, A.P.1    Strobel, P.2
  • 86
    • 85038930499 scopus 로고    scopus 로고
    • Equations (A12) and (A13) correct misprints in expressions for related quantities, (formula presented) and (formula presented) published earlier in Ref
    • Equations (A12) and (A13) correct misprints in expressions for related quantities, (formula presented) and (formula presented) published earlier in Ref. 22.


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