Electronic structure of Chevrel-phase high-critical-field superconductors

Ole Krogh Andersen, W. Klose, H. Nohl

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Abstract

Using muffin-tin orbitals and the atomic-sphere approximation, we have studied the band structures of Chevrel-phase molybdenum chalcogenides, MmMo6X8-x. Generally, these compounds exist for a broad variety of elements, M=Pb,Sn,Ag,Cu and X=S,Se,Te. m may be between 0 and 2, depending on the element M. We present level schemes, computed for a range of Mo and X potentials, for three Mo6X14 clusters appropriate for the crystal structures of Mo6S8, Mo6Se8, and PbMo6S7.5, respectively. Self-consistent Mo and X potentials have been estimated. The cluster levels give the positions of the Mo 4d-like bands, while the widths and dispersions are estimated analytically in the tight-binding approximation taking the covalent mixing with the X p states into account. The 30 Mo d bands are grouped into narrow subbands derived from the levels for an isolated Mo6 octahedron. The Fermi level falls in a doubly degenerate Eg band with Mo wave functions of x2-y2 character and the Eg bandwidths vary between 65 and 35 mRy in the compounds considered. The Eg band is probably crossed by a five times wider, singly degenerate A1g band of predominantly 3z2-r2 character. The Eg and A1g bands are the only ones crossing the Fermi level in the ternaries but, in the binaries, the octahedra are elongated and a 50-35 mRy wide Au band, split off from a triply degenerate T2u band, furthermore overlaps the Eg band. The susceptibilities measured for SnMo5S6 and PbMo5S6 are in good agreement with our estimates, N(0)=11 states/(spin Mo-atom Ry) and IMoStoner=40 mRy, of the band density of states and the effective exchange-interaction parameter. From the measured electronic-specific-heat coefficients we deduce the value λ=2.5 for the electron-phonon enhancement. In accord with experimental phonon spectra we estimate frequencies of 10 and 15 meV for a rocking mode of Mo6Se8 and Mo6S8 units, respectively. For the average electron-phonon matrix element in the Gaspari-Gyorffy and atomic-sphere approximations we find 〈I2〉=3×10-3 (Ry/bohr (Ry/bohr radius)2. The magnitude and extreme sensitivity to local environment effects of the spin-orbit coupling in the Eg band offer an explanation for the high critical magnetic fields measured in the ternaries.
Original languageEnglish
JournalPhysical Review B
Volume17
Issue number3
Pages (from-to)1209-1237
ISSN2469-9950
DOIs
Publication statusPublished - 1978

Bibliographical note

Copyright (1978) by the American Physical Society.

Cite this

Andersen, Ole Krogh ; Klose, W. ; Nohl, H. / Electronic structure of Chevrel-phase high-critical-field superconductors. In: Physical Review B. 1978 ; Vol. 17, No. 3. pp. 1209-1237.
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abstract = "Using muffin-tin orbitals and the atomic-sphere approximation, we have studied the band structures of Chevrel-phase molybdenum chalcogenides, MmMo6X8-x. Generally, these compounds exist for a broad variety of elements, M=Pb,Sn,Ag,Cu and X=S,Se,Te. m may be between 0 and 2, depending on the element M. We present level schemes, computed for a range of Mo and X potentials, for three Mo6X14 clusters appropriate for the crystal structures of Mo6S8, Mo6Se8, and PbMo6S7.5, respectively. Self-consistent Mo and X potentials have been estimated. The cluster levels give the positions of the Mo 4d-like bands, while the widths and dispersions are estimated analytically in the tight-binding approximation taking the covalent mixing with the X p states into account. The 30 Mo d bands are grouped into narrow subbands derived from the levels for an isolated Mo6 octahedron. The Fermi level falls in a doubly degenerate Eg band with Mo wave functions of x2-y2 character and the Eg bandwidths vary between 65 and 35 mRy in the compounds considered. The Eg band is probably crossed by a five times wider, singly degenerate A1g band of predominantly 3z2-r2 character. The Eg and A1g bands are the only ones crossing the Fermi level in the ternaries but, in the binaries, the octahedra are elongated and a 50-35 mRy wide Au band, split off from a triply degenerate T2u band, furthermore overlaps the Eg band. The susceptibilities measured for SnMo5S6 and PbMo5S6 are in good agreement with our estimates, N(0)=11 states/(spin Mo-atom Ry) and IMoStoner=40 mRy, of the band density of states and the effective exchange-interaction parameter. From the measured electronic-specific-heat coefficients we deduce the value λ=2.5 for the electron-phonon enhancement. In accord with experimental phonon spectra we estimate frequencies of 10 and 15 meV for a rocking mode of Mo6Se8 and Mo6S8 units, respectively. For the average electron-phonon matrix element in the Gaspari-Gyorffy and atomic-sphere approximations we find 〈I2〉=3×10-3 (Ry/bohr (Ry/bohr radius)2. The magnitude and extreme sensitivity to local environment effects of the spin-orbit coupling in the Eg band offer an explanation for the high critical magnetic fields measured in the ternaries.",
author = "Andersen, {Ole Krogh} and W. Klose and H. Nohl",
note = "Copyright (1978) by the American Physical Society.",
year = "1978",
doi = "10.1103/PhysRevB.17.1209",
language = "English",
volume = "17",
pages = "1209--1237",
journal = "Physical Review B (Condensed Matter and Materials Physics)",
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}

Electronic structure of Chevrel-phase high-critical-field superconductors. / Andersen, Ole Krogh; Klose, W.; Nohl, H.

In: Physical Review B, Vol. 17, No. 3, 1978, p. 1209-1237.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Electronic structure of Chevrel-phase high-critical-field superconductors

AU - Andersen, Ole Krogh

AU - Klose, W.

AU - Nohl, H.

N1 - Copyright (1978) by the American Physical Society.

PY - 1978

Y1 - 1978

N2 - Using muffin-tin orbitals and the atomic-sphere approximation, we have studied the band structures of Chevrel-phase molybdenum chalcogenides, MmMo6X8-x. Generally, these compounds exist for a broad variety of elements, M=Pb,Sn,Ag,Cu and X=S,Se,Te. m may be between 0 and 2, depending on the element M. We present level schemes, computed for a range of Mo and X potentials, for three Mo6X14 clusters appropriate for the crystal structures of Mo6S8, Mo6Se8, and PbMo6S7.5, respectively. Self-consistent Mo and X potentials have been estimated. The cluster levels give the positions of the Mo 4d-like bands, while the widths and dispersions are estimated analytically in the tight-binding approximation taking the covalent mixing with the X p states into account. The 30 Mo d bands are grouped into narrow subbands derived from the levels for an isolated Mo6 octahedron. The Fermi level falls in a doubly degenerate Eg band with Mo wave functions of x2-y2 character and the Eg bandwidths vary between 65 and 35 mRy in the compounds considered. The Eg band is probably crossed by a five times wider, singly degenerate A1g band of predominantly 3z2-r2 character. The Eg and A1g bands are the only ones crossing the Fermi level in the ternaries but, in the binaries, the octahedra are elongated and a 50-35 mRy wide Au band, split off from a triply degenerate T2u band, furthermore overlaps the Eg band. The susceptibilities measured for SnMo5S6 and PbMo5S6 are in good agreement with our estimates, N(0)=11 states/(spin Mo-atom Ry) and IMoStoner=40 mRy, of the band density of states and the effective exchange-interaction parameter. From the measured electronic-specific-heat coefficients we deduce the value λ=2.5 for the electron-phonon enhancement. In accord with experimental phonon spectra we estimate frequencies of 10 and 15 meV for a rocking mode of Mo6Se8 and Mo6S8 units, respectively. For the average electron-phonon matrix element in the Gaspari-Gyorffy and atomic-sphere approximations we find 〈I2〉=3×10-3 (Ry/bohr (Ry/bohr radius)2. The magnitude and extreme sensitivity to local environment effects of the spin-orbit coupling in the Eg band offer an explanation for the high critical magnetic fields measured in the ternaries.

AB - Using muffin-tin orbitals and the atomic-sphere approximation, we have studied the band structures of Chevrel-phase molybdenum chalcogenides, MmMo6X8-x. Generally, these compounds exist for a broad variety of elements, M=Pb,Sn,Ag,Cu and X=S,Se,Te. m may be between 0 and 2, depending on the element M. We present level schemes, computed for a range of Mo and X potentials, for three Mo6X14 clusters appropriate for the crystal structures of Mo6S8, Mo6Se8, and PbMo6S7.5, respectively. Self-consistent Mo and X potentials have been estimated. The cluster levels give the positions of the Mo 4d-like bands, while the widths and dispersions are estimated analytically in the tight-binding approximation taking the covalent mixing with the X p states into account. The 30 Mo d bands are grouped into narrow subbands derived from the levels for an isolated Mo6 octahedron. The Fermi level falls in a doubly degenerate Eg band with Mo wave functions of x2-y2 character and the Eg bandwidths vary between 65 and 35 mRy in the compounds considered. The Eg band is probably crossed by a five times wider, singly degenerate A1g band of predominantly 3z2-r2 character. The Eg and A1g bands are the only ones crossing the Fermi level in the ternaries but, in the binaries, the octahedra are elongated and a 50-35 mRy wide Au band, split off from a triply degenerate T2u band, furthermore overlaps the Eg band. The susceptibilities measured for SnMo5S6 and PbMo5S6 are in good agreement with our estimates, N(0)=11 states/(spin Mo-atom Ry) and IMoStoner=40 mRy, of the band density of states and the effective exchange-interaction parameter. From the measured electronic-specific-heat coefficients we deduce the value λ=2.5 for the electron-phonon enhancement. In accord with experimental phonon spectra we estimate frequencies of 10 and 15 meV for a rocking mode of Mo6Se8 and Mo6S8 units, respectively. For the average electron-phonon matrix element in the Gaspari-Gyorffy and atomic-sphere approximations we find 〈I2〉=3×10-3 (Ry/bohr (Ry/bohr radius)2. The magnitude and extreme sensitivity to local environment effects of the spin-orbit coupling in the Eg band offer an explanation for the high critical magnetic fields measured in the ternaries.

U2 - 10.1103/PhysRevB.17.1209

DO - 10.1103/PhysRevB.17.1209

M3 - Journal article

VL - 17

SP - 1209

EP - 1237

JO - Physical Review B (Condensed Matter and Materials Physics)

JF - Physical Review B (Condensed Matter and Materials Physics)

SN - 1098-0121

IS - 3

ER -