3,622 research outputs found
Screening of Coulomb interactions in transition metals
We discuss different methods of calculation of the screened Coulomb
interaction in transition metals and compare the constraint local-density
approximation (LDA) with the GW approach. We clarify that they offer
complementary methods of treating the screening and should serve for different
purposes. In the GW method, the renormalization of bare on-site Coulomb
interactions between 3d electrons occurs mainly through the screening by the
same 3d electrons, treated in the random phase approximation (RPA). The basic
difference of the constraint-LDA method is that it deals with the neutral
processes, where the Coulomb interactions are additionally screened by the
``excited'' electron, since it continues to stay in the system. This is the
main channel of screening by the itinerant () electrons, which is
especially strong in the case of transition metals and missing in the GW
approach, although the details of this screening may be affected by additional
approximations, which typically supplement these two methods. The major
drawback of the conventional constraint-LDA method is that it does not allow to
treat the energy-dependence of . We propose a promising approximation based
on the combination of these two methods. First, we take into account the
screening of Coulomb interactions in the 3d-electron-line bands located near
the Fermi level by the states from the subspace being orthogonal to these
bands, using the constraint-LDA methods. The obtained interactions are further
renormalized within the bands near the Fermi level in RPA. This allows the
energy-dependent screening by electrons near the Fermi level including the same
3d electrons.Comment: 25 pages, 5 figures, 2 table
Lattice Distortion and Magnetism of 3d- Perovskite Oxides
Several puzzling aspects of interplay of the experimental lattice distortion
and the the magnetic properties of four narrow -band perovskite oxides
(YTiO, LaTiO, YVO, and LaVO) are clarified using results of
first-principles electronic structure calculations. First, we derive parameters
of the effective Hubbard-type Hamiltonian for the isolated bands using
newly developed downfolding method for the kinetic-energy part and a hybrid
approach, based on the combination of the random-phase approximation and the
constraint local-density approximation, for the screened Coulomb interaction
part. Then, we solve the obtained Hamiltonian using a number of techniques,
including the mean-field Hartree-Fock (HF) approximation, the second-order
perturbation theory for the correlation energy, and a variational superexchange
theory. Even though the crystal-field splitting is not particularly large to
quench the orbital degrees of freedom, the crystal distortion imposes a severe
constraint on the form of the possible orbital states, which favor the
formation of the experimentally observed magnetic structures in YTiO,
YVO_, and LaVO even at the HF level. Beyond the HF approximation, the
correlations effects systematically improve the agreement with the experimental
data. Using the same type of approximations we could not reproduce the correct
magnetic ground state of LaTiO. However, we expect that the situation may
change by systematically improving the level of approximations for dealing with
the correlation effects.Comment: 30 pages, 17 figures, 8 tables, high-quality figures are available
via e-mai
First-principle Wannier functions and effective lattice fermion models for narrow-band compounds
We propose a systematic procedure for constructing effective lattice fermion
models for narrow-band compounds on the basis of first-principles electronic
structure calculations. The method is illustrated for the series of
transition-metal (TM) oxides: SrVO, YTiO, VO, and
YMoO. It consists of three parts, starting from LDA. (i)
construction of the kinetic energy Hamiltonian using downfolding method. (ii)
solution of an inverse problem and construction of the Wannier functions (WFs)
for the given kinetic energy Hamiltonian. (iii) calculation of screened Coulomb
interactions in the basis of \textit{auxiliary} WFs, for which the
kinetic-energy term is set to be zero. The last step is necessary in order to
avoid the double counting of the kinetic-energy term, which is included
explicitly into the model. The screened Coulomb interactions are calculated in
a hybrid scheme. First, we evaluate the screening caused by the change of
occupation numbers and the relaxation of the LMTO basis functions, using the
conventional constraint-LDA approach, where all matrix elements of
hybridization involving the TM orbitals are set to be zero. Then, we switch
on the hybridization and evaluate the screening associated with the change of
this hybridization in RPA. The second channel of screening is very important,
and results in a relatively small value of the effective Coulomb interaction
for isolated bands. We discuss details of this screening and consider
its band-filling dependence, frequency dependence, influence of the lattice
distortion, proximity of other bands, and the dimensionality of the model
Hamiltonian.Comment: 35 pages, 25 figure
Fingerprints of Spin-Orbital Physics in Crystalline O
The alkali hyperoxide KO is a molecular analog of strongly-correlated
systems, comprising of orbitally degenerate magnetic O ions. Using
first-principles electronic structure calculations, we set up an effective
spin-orbital model for the low-energy \textit{molecular} orbitals and argue
that many anomalous properties of KO replicate the status of its orbital
system in various temperature regimes.Comment: 4 pages, 2 figures, 1 tabl
Construction of Wannier functions from localized atomic-like orbitals
The problem of construction of the Wannier functions (WFs) in a restricted
Hilbert space of eigenstates of the one-electron Hamiltonian (forming
the so-called low-energy part of the spectrum) can be formulated in several
different ways. One possibility is to use the projector-operator techniques,
which pick up a set of trial atomic orbitals and project them onto the given
Hilbert space. Another possibility is to employ the downfolding method, which
eliminates the high-energy part of the spectrum and incorporates all related to
it properties into the energy-dependence of an effective Hamiltonian. We show
that by modifying the high-energy part of the spectrum of the original
Hamiltonian , which is rather irrelevant to the construction of WFs in
the low-energy part of the spectrum, these two methods can be formulated in an
absolutely exact and identical form, so that the main difference between them
is reduced to the choice of the trial orbitals. Concerning the latter part of
the problem, we argue that an optimal choice for trial orbitals can be based on
the maximization of the site-diagonal part of the density matrix. The main idea
is illustrated for a simple toy model, consisting of only two bands, as well as
for a more realistic example of bands in VO. An analogy with
the search of the ground state of a many-electron system is also discussed.Comment: 13 pages, 6 figure
Lattice Distortion and Magnetic Ground State of YTiO and LaTiO
Effects of lattice distortion on the magnetic ground state of YTiO and
LaiO are investigated on the basis accurate tight-binding parametrization
of the electronic structure extracted from the local-density
approximation. The complexity of these compounds is related with the fact that
the -level splitting, caused by lattice distortions, is comparable with
the energies of superexchange and spin-orbit interactions. Therefore, all these
interactions are equally important and should be treated on an equal footing.
The Hartree-Fock approximation fails to provide a coherent description
simultaneously for YTiO and LaTiO, and it is essential to go beyond.Comment: 4 pages, 3 figures (good quality figures are available via e-mail
Ferromagnetic zigzag chains and properties of the charge ordered perovskite manganites
The low-temperature properties of the so-called ''charge ordered'' state in
50% doped perovskite manganites are described from the viewpoint of the
magnetic spin ordering. In these systems, the zigzag antiferromagnetic
ordering, combined with the double-exchange physics, effectively divides the
whole sample into the one-dimensional ferromagnetic zigzag chains and results
in the anisotropy of electronic properties. The electronic structure of one
such chain is described by an effective 33 Hamiltonian in the basis of
Mn() orbitals. We treat this problem analytically and consider the
following properties: (i) the nearest-neighbor magnetic interactions; (ii) the
distribution of the Mn() and Mn() states near the Fermi level, and
their contribution to the optical conductivity and the resonant x-ray
scattering near the Mn -absorption edge. We argue that the anisotropy of
magnetic interactions in the double-exchange limit, combined with the isotropic
superexchange interactions, readily explains both the local and the global
stability of the zigzag antiferromagnetic state. The two-fold degeneracy of
levels plays a very important role in the problem and explains the
insulating behavior of the zigzag chain, as well as the appearance of the
orbital ordering in the double-exchange model. Importantly, however, the charge
ordering itself is expected to play only a minor role and is incompatible with
the ferromagnetic coupling within the chain. We also discuss possible effects
of the Jahn-Teller distortion and compare the tight-binding picture with
results of band structure calculations in the local-spin-density approximation.Comment: 35 pages, 8 figure
Superexchange Interactions in Orthorhombically Distorted Titanates RTiO3 (R= Y, Gd, Sm, and La)
Starting from the multiorbital Hubbard model for the t2g-bands of RTiO3 (R=
Y, Gd, Sm, and La), where all parameters have been derived from the
first-principles calculations, we construct an effective superexchange (SE)
spin model, by treating transfer integrals as a perturbation. We consider four
approximations for the SE interactions: (i) the canonical crystal-field (CF)
theory, where the form of the the occupied t2g-orbitals is dictated by the CF
splitting, and three extensions, namely (ii) the relativistic one, where
occupied orbitals are confined within the lowest Kramers doublet obtained from
the diagonalization of the crystal field and relativistic spin-orbit (SO)
interactions; (iii) the finite-temperature extension, which consider the effect
of thermal orbital fluctuations near the CF configuration; (iv) the
many-electron extension, which is based on the diagonalization of the full
Hamiltonian constructed in the basis of two-electron states separately for each
bond of the system. The main results are summarized as follows. (i) Thermal
fluctuations of the orbital degrees of freedom can substantially reduce the
value of the magnetic transition temperature. (ii) The anisotropic and
antisymmetric Dzyaloshinsky-Moriya interactions are rigorously derived and
their implications to the magnetic properties are discussed. (iii) The CF
theory, although applicable for YTiO3 and high-temperature structures of GdTiO3
and SmTiO3, breaks down in LaTiO3. Instead, the combination of the
many-electron effects and SO interaction can be responsible for the AFM
character of interatomic correlations in LaTiO3. (iv) The SE interactions in
YTiO3 strongly depend on the details of the crystal structure. Distortions in
the low-temperature structure tend to weaken the ferromagnetic interactions.Comment: 23 pages, 9 tables, 4 figure
Long-Range Magnetic Interactions Induced by the Lattice Distortions and the Origin of the E-type Antiferromagnetic Phase in the Undoped Orthorhombic Manganites
With the increase of the lattice distortion, the orthorhombic manganites
MnO ( La, Pr, Nd, Tb, and Ho) are known to undergo the phase
transition from the layered A-type antiferromagnetic (AFM) state to the zigzag
E-type AFM state. We consider the microscopic origin of this transition. Our
approach consists of the two parts. First, we construct an effective lattice
fermion model for the manganese 3d-bands and derive parameters of this model
from the first-principles electronic structure calculations. Then, we solve
this model in the Hartree-Fock approximation (HFA) and analyze the behavior of
interatomic magnetic interactions. We argue that the nearest-neighbor
interactions decrease with the distortion and at certain stage start to compete
with the longer range (particularly, second- and third-neighbor) AFM
interactions in the orthorhombic ab-plane, which lead to the formation of the
E-phase. The origin of these interactions is closely related to the orbital
ordering, which takes place in the distorted orthorhombic structure. The model
is able to capture the experimental trend and explain why LaMnO develops
the A-type AFM order and why it tends to transform to the E-type AFM order in
the more distorted compounds. Nevertheless, the quantitative agreement with the
experimental data crucially depends on other factors, such as the magnetic
polarization of the oxygen sites and the correlation interactions beyond HFA.Comment: 26 pages, 15 figure
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