Electronic structure of Calcium hexaborides Page: 2 of 14
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The discovery of ferromagnetism in lightly doped CaB6 and SrB has fueled intense
investigation on these materials over the last several years. The remarkably high transition
temperature (T, ~ 600K) with a very low magnetic moment (< 0.07 B per atom) has raised
many speculations on the origin of the magnetism, including ferromagnetic phase within
dilute electron gas  and doped excitonic insulators [3-5]. Although it now seems quite
conclusive that the ferromagnetism is originated from the external impurities on the surface
of the samples [6, 7] rather than from an intrinsic property of the system, the electronic
band structure of the bulk systems is still under debate. While Fermi surface measurements
 imply that CaB6 is a semimetal, angle-resolved photoemission spectroscopy (ARPES),
momentum-resolved inelastic x-ray scattering , and transport  measurements indicate
that CaB6 is a semiconductor with a gap larger than 1.0 eV. Theoretically, the local density
approximation (LDA) has predicted a semimetallic band structure for CaB6 with a small
overlap of boron-bands at the X point of the Brillouin zone [11-14], but it is well known
that LDA calculations often underestimate the eigenenergy gap. On the other hand, more
accurate many-body GW calculations have reported many different results. While a pseu-
dopotential GW calculation led to a 0.8 eV band gap  for CaB6, different full-potential
LMTO GW calculations yielded 0.35 , -0.4 eV , and -0.7 eV .
One possible reason for the large differences in the theoretical results is the high sensitivity
of the band gap to the crystal geometry parameters. Divalent hexaborides, including CaB6,
have a simple cubic unit cell with metal ions (Ca) located at the cubic corners and boron
octahedral cages at the cubic center. The two relevant structural parameters are the lattice
constant a and the positional parameter x of the boron atoms. The positions of boron
atoms are +(, 1, x), +(, x, 1), +(x, , j) in the unit of lattice constant. When x = 0.207,
the intra-octahedral and inter-octahedral B-B distances are equal. As demonstrated below,
the band gap of the system depends sensitively on the values of a and x. Unfortunately,
the experimentally measured results for a and x have not shown a complete agreement.
The experimentally measured CaB6 lattice constant varies from 4.145 to 4.153 A ,
while LDA calculations predicts a lattice constant between 4.08 and 4.105 A [11, 13, 19].
The internal parameter x has been observed experimentally from 0.200 to 0.207  while
LDA predictions vary from 0.201 to 0.2024. We shall show that, within the experimental
uncertainty of x, the calculated band gap can change by as much as 0.5 eV. This might
partially explain the differences in the GW calculated band gaps.
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Lee, Byounghak & Wang, Lin-Wang. Electronic structure of Calcium hexaborides, article, June 15, 2005; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc891739/m1/2/: accessed February 21, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.