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Magnetic structure of noncentrosymmetric perovskites PbVO3 and BiCoO3
It is well known that if a crystal structure has no inversion symmetry, it
may allow for Dzyaloshinskii-Moriya magnetic interactions, operating between
different crystallographic unit cells, which in turn should lead to the
formation of long-periodic spin-spiral structures. Such a behavior is
anticipated for two simple perovskites PbVO3 and BiCoO3, crystallizing in the
noncentrosymmetric tetragonal P4mm structure. Nevertheless, we argue that in
reality PbVO3 and BiCoO3 should behave very differently. Due to the fundamental
Kramers degeneracy for the odd-electron systems, PbVO3 has no single-ion
anisotropy. Therefore, the ground state of PbVO3 will be indeed the spin spiral
with the period of about one hundred unit cells. However, the even-electron
BiCoO3 has a large single-ion anisotropy, which locks this system in the
collinear easy-axis C-type antiferromagnetic ground state. Our theoretical
analysis is based on the low-energy model, derived from the first-principles
electronic structure calculations.Comment: 16 pages, 7 figures, 3 table
Magnetization induced local electric dipoles and multiferroic properties of Ba2CoGe2O7
Ba2CoGe2O7, crystallizing in the noncentrosymmetric but nonpolar structure,
belongs to a special class of multiferroic materials, whose properties are
predetermined by the rotoinversion symmetry. Unlike inversion, the
rotoinversion symmetry can be easily destroyed by the magnetization. Moreover,
due to specific structural pattern, the magnetic structure of Ba2CoGe2O7 is
relatively soft. Altogether, this leads to the rich variety of multiferroic
properties, where the magnetic structure can be easily deformed by the magnetic
field, inducing the electric polarization in the direction, which depends on
the direction of the magnetic field. In this paper, we show that all these
properties can be successfully explained on the basis of realistic low-energy
model, derived from the first-principles electronic structure calculations for
the magnetically active Co 3d bands, and the Berry-phase theory of electric
polarization. Particularly, we argue that the magnetization induced electric
polarization in Ba2CoGe2O7 is essentially local and expressed via the
expectation values of some dipole matrices, calculated in the Wannier basis of
the model, and the site-diagonal density matrices of the magnetic Co sites.
Thus, the basic aspects of the behavior of Ba2CoGe2O7 can be understood already
in the atomic limit, where both magnetic anisotropy and magnetoelectric
coupling are specified by density matrix. Then, the macroscopic polarization
can be found as a superposition of electric dipoles of the individual Co sites.
We discuss the behavior of interatomic magnetic interactions, main
contributions to the magnetocrystalline anisotropy and the spin canting, as
well as the similarities and differences of the proposed picture from the
phenomenological model of spin-dependent p-d hybridization.Comment: 27 pages, 8 figure
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
Superexchange theory of electronic polarization driven by relativistic spin-orbit interaction at the half-filling
By applying Berry-phase theory for the effective half-filled Hubbard model,
we derive an analytical expression for the electronic polarization driven by
the relativistic spin-orbit (SO) coupling. The model itself is constructed in
the Wannier basis, using the input from the first-principles electronic
structure calculations in the local-density approximation, and then treated in
the spirit of the superexchange theory. The obtained polarization has the
following form: , where
is the direction of the bond ,
and are the directions of spins in this
bond, and is the pseudovector containing all the
information about the crystallographic symmetry of the considered system. The
expression describes the ferroelectric activity in various magnets with
noncollinear but otherwise nonpolar magnetic structures, which would yield no
polarization without SO interaction, including the magnetoelectric (ME) effect,
caused by the ferromagnetic canting of spins in the external magnetic field,
and spin-spiral multiferroics. The abilities of this theory are demonstrated
for the the analysis of linear ME effect in CrO and BiFeO and
properties multiferroic MnWO and -MnO. In all considered
examples, the theory perfectly describes the symmetry properties of the induced
polarization. However, in some cases, the values of this polarization are
underestimated, suggesting that other effects, besides the spin and electronic
ones, can also play an important role.Comment: 31 pages, 10 figure
Self-consistent linear response for the spin-orbit interaction related properties
In many cases, the relativistic spin-orbit (SO) interaction is regarded to be
small and can be treated using perturbation theory. The major obstacle on this
route comes from the fact that the SO interaction can also polarize the
electron system and produce additional contributions to the perturbation
theory, arising from the electron-electron interactions. In electronic
structure calculations, it may even lead to necessity to abandon the
perturbation theory and return to the self-consistently solution of
Kohn-Sham-like equations with the effective potential , incorporating
the effects of the electron-electron interactions and the SO coupling, even
though the latter is small. In this work, we present the theory of
self-consistent linear response (SCLR), which allows us to get rid of numerical
self-consistency and formulate it analytically in the first order of the SO
coupling. This strategy is applied to the Hartree-Fock solution of the
effective Hubbard model, derived from electronic structure calculations in the
Wannier basis. By using , obtained from SCLR, one can successfully
reproduce results of ordinary calculations for the orbital magnetization and
other properties in the first order of the SO coupling. Particularly, SCLR
appears to be extremely useful for calculations of antisymmetric
Dzyaloshinskii-Moriya (DM) interactions based on the magnetic force theorem.
Furthermore, due to the powerful 2n+1 theorem, the SCLR theory allows us to
calculate the magnetic anisotropy energy up to the third order of the SO
coupling. The fruitfulness of this approach is illustrated on a number of
example, including the spin canting in YTiO and LaMnO, formation of
spiral magnetic order in BiFeO, and the magnetic inversion symmetry
breaking in BiMnO, which gives rise to both ferroelectric activity and DM
interactions, responsible for the ferromagnetism.Comment: 42 pagse, 5 figure, 6 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
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