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85038289981
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Perhaps the absolute value of (Formula presented) is not a serious problem as it can be easily adjusted by adding a phenomenological antiferromagnetic superexchange interaction between the localized spins (Refs. 37 48
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Perhaps the absolute value of (Formula presented) is not a serious problem as it can be easily adjusted by adding a phenomenological antiferromagnetic superexchange interaction between the localized spins (Refs. 48).
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21
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4244101029
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Y. Tomioka and Y. Tokura, in Colossal Magnetoresistive Oxides, edited by Y. Tokura (Gordon and Breach Science Publishers, Tokyo, 2000).
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0035130866
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48
-
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85038287618
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-
Note that the attempt to average Eq. (1) with the distribution function (2) will yield an unphysical result, where the CPA self-energy depends linearly on (Formula presented) The linear term will then contribute to the free energy (6), that contradicts to the stationarity condition in the PM state
-
Note that the attempt to average Eq. (1) with the distribution function (2) will yield an unphysical result, where the CPA self-energy depends linearly on (Formula presented) The linear term will then contribute to the free energy (6), that contradicts to the stationarity condition in the PM state.
-
-
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-
49
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4244150730
-
-
The PM-FM transition in the pure DE model is typically of the second order. However, an additional antiferromagnetic superexchange interaction between the localized spins can lead to the first-order transition: J. L. Alonso, L. A. Fernández, F. Guinea, V. Laliena, and V. Martín-Mayor, Phys. Rev. B 63, 064416 (2001).
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(2001)
Phys. Rev. B
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-
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Alonso, J.L.1
Fernández, L.A.2
Guinea, F.3
Laliena, V.4
Martín-Mayor, V.5
-
50
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85038303150
-
-
All calculations have been performed using the mesh consisting of 374660 nonequivalent (Formula presented) points, which corresponds to the (Formula presented) divisions of the reciprocal lattice vectors
-
All calculations have been performed using the mesh consisting of 374660 nonequivalent (Formula presented) points, which corresponds to the (Formula presented) divisions of the reciprocal lattice vectors.
-
-
-
-
52
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85038286024
-
-
Note that the matrix multiplication in Eq. (12) is not restricted by a finite cluster (the dimer, in our case). This is the main difference from the so-called cluster CPA (Refs. 353659). Our CPA scheme is compatible with the symmetry constraints, because all dimers are equivalent and equally contribute to the T matrix. This equivalence is artificially broken in the case of cluster CPA, which takes into account the contributions of only those sites which belong to a given cluster
-
Note that the matrix multiplication in Eq. (12) is not restricted by a finite cluster (the dimer, in our case). This is the main difference from the so-called cluster CPA (Refs. 59). Our CPA scheme is compatible with the symmetry constraints, because all dimers are equivalent and equally contribute to the T matrix. This equivalence is artificially broken in the case of cluster CPA, which takes into account the contributions of only those sites which belong to a given cluster.
-
-
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-
53
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85038312744
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-
cond-mat/0207544 (unpublished). Note that in the present paper we use reversed order of the (Formula presented) orbitals, which corresponds to the interchange of the orbital indices 1 and 2 in all formulas for the degenerate DM model
-
I. V. Solovyev, cond-mat/0207544 (unpublished). Note that in the present paper we use reversed order of the (Formula presented) orbitals, which corresponds to the interchange of the orbital indices 1 and 2 in all formulas for the degenerate DM model.
-
-
-
Solovyev, I.V.1
-
54
-
-
85038341991
-
-
We retain both (Formula presented) and (Formula presented) but only for the sake of convenience, because formally (Formula presented) can be expressed through (Formula presented) using identity (11)
-
We retain both (Formula presented) and (Formula presented) but only for the sake of convenience, because formally (Formula presented) can be expressed through (Formula presented) using identity (11).
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-
55
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0000526531
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P. Bruno, J. Kudrnovský, V. Drchal, and I. Turek, Phys. Rev. Lett. 76, 4254 (1996).
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Bruno, P.1
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-
56
-
-
85038294574
-
-
Note that the first order expansion with respect to (Formula presented) corresponds to the following set of parameters in Eq. (17): (Formula presented) and (Formula presented) Then, after replacing (Formula presented) by (Formula presented) one obtains (Formula presented) where (Formula presented) is the energy of the PM state in the theory of de Gennes, which is related to the energy of fully polarized FM state as (Formula presented)
-
Note that the first order expansion with respect to (Formula presented) corresponds to the following set of parameters in Eq. (17): (Formula presented) and (Formula presented) Then, after replacing (Formula presented) by (Formula presented) one obtains (Formula presented) where (Formula presented) is the energy of the PM state in the theory of de Gennes, which is related to the energy of fully polarized FM state as (Formula presented)
-
-
-
-
57
-
-
85038308933
-
-
For example, for (Formula presented) and (Formula presented) we obtain (Formula presented) and (Formula presented) respectively. Unfortunately, different authors reported very different estimates of (Formula presented) based on the DMFT. Using SC DOS, Furukawa alone reported two different values of (Formula presented) at (Formula presented) (Formula presented) (Ref. 16). Anyway, all these values seems to be overestimated in comparison with results of nonlocal CPA calculations
-
For example, for (Formula presented) and (Formula presented) we obtain (Formula presented) and (Formula presented) respectively. Unfortunately, different authors reported very different estimates of (Formula presented) based on the DMFT. Using SC DOS, Furukawa alone reported two different values of (Formula presented) at (Formula presented) (Formula presented) (Ref. 16). Anyway, all these values seems to be overestimated in comparison with results of nonlocal CPA calculations.
-
-
-
-
59
-
-
85038309961
-
-
The energy of the phenomenological SE interaction between nearest neighbors (Formula presented) is typically defined as (Formula presented) For three-dimensional manganites, (Formula presented) is of the order of 60–70 meV.5
-
The energy of the phenomenological SE interaction between nearest neighbors (Formula presented) is typically defined as (Formula presented) For three-dimensional manganites, (Formula presented) is of the order of 60–70 meV.5
-
-
-
-
60
-
-
85038287426
-
-
According to Monte Carlo calculations, (Formula presented) is reduced till (Formula presented) at (Formula presented) (Ref. 28, and references therein)
-
According to Monte Carlo calculations, (Formula presented) is reduced till (Formula presented) at (Formula presented) (Ref. 28, and references therein).
-
-
-
-
61
-
-
85038324982
-
-
Transformations of the (Formula presented) orbitals in the cubic lattice can be described by the unitary matrices (Formula presented) where (Formula presented) and (Formula presented) correspond to the (Formula presented) rotations around the x and y axes, respectively
-
Transformations of the (Formula presented) orbitals in the cubic lattice can be described by the unitary matrices (Formula presented) where (Formula presented) and (Formula presented) correspond to the (Formula presented) rotations around the x and y axes, respectively.
-
-
-
-
66
-
-
0001588470
-
-
K. Wildberger, P. Lang, R. Zeller, and P. H. Dederichs, Phys. Rev. B 52, 11 502 (1995).
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(1995)
Phys. Rev. B
, vol.52
, pp. 11 502
-
-
Wildberger, K.1
Lang, P.2
Zeller, R.3
Dederichs, P.H.4
-
67
-
-
85038282864
-
-
In practical terms, we start iterations at (Formula presented) with two different sets for the self-energy, which guarantee two different CPA solutions, and then at each consecutive pole (Formula presented) start with the self-consistent CPA solutions obtained for (Formula presented) (and so on until the merging of the two solutions)
-
In practical terms, we start iterations at (Formula presented) with two different sets for the self-energy, which guarantee two different CPA solutions, and then at each consecutive pole (Formula presented) start with the self-consistent CPA solutions obtained for (Formula presented) (and so on until the merging of the two solutions).
-
-
-
-
68
-
-
85038277976
-
-
Equation (25) is obtained from the Lloyd formula for the integrated DOS and is the generalization of Eq. (16) for the two-orbital case, which includes also the trace over the orbital indices. The latter is responsible for the factor 2 in the first term and gives rise to two different contributions to the second term
-
Equation (25) is obtained from the Lloyd formula for the integrated DOS and is the generalization of Eq. (16) for the two-orbital case, which includes also the trace over the orbital indices. The latter is responsible for the factor 2 in the first term and gives rise to two different contributions to the second term.
-
-
-
-
69
-
-
85038302046
-
-
Note that if the concentration of the FM phase is as large as (Formula presented) it is natural to expect that the system is above the percolation threshold. Then, the behavior in the interval (Formula presented) should correpond to the proper FM order, rather than to the superferromagnetism (small FM islands in the PM matrix)
-
Note that if the concentration of the FM phase is as large as (Formula presented) it is natural to expect that the system is above the percolation threshold. Then, the behavior in the interval (Formula presented) should correpond to the proper FM order, rather than to the superferromagnetism (small FM islands in the PM matrix).
-
-
-
-
70
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85038277755
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Y. Tomioka (private communication)
-
Y. Tomioka (private communication).
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72
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85038266014
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A. J. Millis, in Colossal Magnetoresistive Oxides, edited by Y. Tokura (Gordon and Breach Science Publishers, Tokyo, 2000)
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A. J. Millis, in Colossal Magnetoresistive Oxides, edited by Y. Tokura (Gordon and Breach Science Publishers, Tokyo, 2000).
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