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85038913466
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J.-C. Tolédano and P. Tolédano, (World Scientific, Singapore, 1987)
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J.-C. Tolédano and P. Tolédano, The Landau Theory of Phase Transitions (World Scientific, Singapore, 1987).
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8
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85038891501
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The approximations are often the consequences of the complexity of the calculational problem and are made to make the problem tractable
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The approximations are often the consequences of the complexity of the calculational problem and are made to make the problem tractable.
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10
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4243072904
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P H. Dederichs, S. Blügel, R. Zeller, and H. Akai, Phys. Rev. Lett.53, 2512 (1984).
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36149047977
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Györffy, B.L.1
Pindor, A.J.2
Staunton, J.3
Stocks, G.M.4
Winter, H.5
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12
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25544474582
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The property that the state providing the minimum of the functional under the symmetry restrictions does not need a stabilizing field can also be proved in a more general form, without referring to the Kohn-Sham minimization procedure. It can be shown that the energy functional has a zero-variational derivative at the density that supplies the minimum of the energy functional under the constraining symmetry conditions. Gunarsson and Lundqvist [, and, considered the case of a Hamiltonian commuting with the operator of an observable and discussed the minimization of the total energy functional for different eigenvalues (formula presented) of the observable. They have shown that in this case the constrained minimization of a universal functional is replaced by an unconstrained minimization of a (formula presented)-dependent functional that is carried out separately for each (formula presented)
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The property that the state providing the minimum of the functional under the symmetry restrictions does not need a stabilizing field can also be proved in a more general form, without referring to the Kohn-Sham minimization procedure. It can be shown that the energy functional has a zero-variational derivative at the density that supplies the minimum of the energy functional under the constraining symmetry conditions. Gunarsson and Lundqvist [O. Gunarsson and B I. Lundqvist, Phys. Rev. B13, 4274 (1976)] considered the case of a Hamiltonian commuting with the operator of an observable and discussed the minimization of the total energy functional for different eigenvalues (formula presented) of the observable. They have shown that in this case the constrained minimization of a universal functional is replaced by an unconstrained minimization of a (formula presented)-dependent functional that is carried out separately for each (formula presented).
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Phys. Rev. B
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Gunarsson, O.1
Lundqvist, B.I.2
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15
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85038928032
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Deviation of the propagation vector of the magnetic structure of Cr from 0.5 was not taken into account in early calculations
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Deviation of the propagation vector of the magnetic structure of Cr from 0.5 was not taken into account in early calculations.
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17
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0002833491
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R. J. Elliott, Plenum Press, London, in, edited by, p
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W C. Koehler, in Magnetic Properties of Rare Earth Metals, edited by R. J. Elliott (Plenum Press, London, 1972), p. 81.
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Koehler, W.C.1
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20
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85038906828
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B. R. Cooper, in, (Ref. p. 17
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B. R. Cooper, in Magnetic Properties of Rare Earth Metals, (Ref. 17), p. 17.
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25
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85038947706
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In this respect, the results of the early paper by Lyons and Kaplan are worth noting (Ref. The authors have shown that the ground state of the system of equivalent classical Heisenberg spins is always a helix. Since the classical Heisenberg exchange energy is invariant with respect to generalized translations this result is in agreement with our arguments. Although Lyons and Kaplan did not refer directly to the generalized translations, they emphasized the relation between the symmetry of the energy expression and the helical ground state. An important difference between the present discussion and the discussion in Ref., is in the treatment of collinear magnetic states. Whereas the conclusions of Lyons and Kaplan are valid in the case the collinear ferromagnetism and collinear antiferromagnetism are considered as particular cases of helices, our statements are made for, helical structures. In contrast to incommensurate helices, the collinear magnetic structures can be stable in the relativistic case
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In this respect, the results of the early paper by Lyons and Kaplan are worth noting (Ref. 7). The authors have shown that the ground state of the system of equivalent classical Heisenberg spins is always a helix. Since the classical Heisenberg exchange energy is invariant with respect to generalized translations this result is in agreement with our arguments. Although Lyons and Kaplan did not refer directly to the generalized translations, they emphasized the relation between the symmetry of the energy expression and the helical ground state. An important difference between the present discussion and the discussion in Ref. 7 is in the treatment of collinear magnetic states. Whereas the conclusions of Lyons and Kaplan are valid in the case the collinear ferromagnetism and collinear antiferromagnetism are considered as particular cases of helices, our statements are made for incommensurate helical structures. In contrast to incommensurate helices, the collinear magnetic structures can be stable in the relativistic case.
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27
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0033600285
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P. Strange, A. Svane, W M. Temmerman, Z. Szotek, and H. Winter, Nature (London)399, 756 (1999).
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Strange, P.1
Svane, A.2
Temmerman, W.M.3
Szotek, Z.4
Winter, H.5
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