First- and Second-Principles Studies of Perovskites

The Metal-Insulator transition (MIT) upon cooling at elevated temperatures is a fascinating
effect that is observed in some ABX 3 perovskite compounds with specific electronic
configurations on the transition metal B cation d states. These compounds behave
completely oppositional to ordinary metals who become better conductors upon cooling.
At the MIT temperature these specific perovskite compounds show electron localization
accompanied by cooperative lattice distortions that deform the BX 6 corner shared
octahedral network. Since the discovery of these MITs, theoretical concepts about its
origin have been proposed and debated. In this work we study from ab initio density
functional theory (DFT) calculations LaMnO 3 and the alkaline earth ferrite series AFeO 3
who all have a formal d 4 occupation. As a basis to our discussion we introduce canonical
notations, that were missing until now, for lattice distortions in perovskites that distort the
X anion octahedra and are connected to MITs. While LaMnO 3 shows electron localization
through orbital ordering - the appearance of a static order of Mn d orbital occupations-,
CaFeO 3 shows electron localization through charge ordering - the appearance of a static
order of formal Fe charges-. From DFT calculations we can show that both mechanisms
are compatible with the concept of a Peierls transition and are enabled by octahedral
rotations. From Monte-Carlo simulations we show furthermore that spin disorder in
the paramagnetic phase is a key ingredient to explain the high MIT temperatures. Last
we study the influence of external epitaxial strain on these compounds. Here, our
canonical notations help to discriminate internal relaxations and external constraints. Our
calculations show that in LaMnO 3 epitaxial strain alone can provoke a change from an
antiferromagnetic to an ferromagnetic order without the necessity of Oxygen vacancies
as has been often speculated. In CaFeO 3 epitaxial strain can provoke a change from the
bulk charge ordering MIT to an orbital ordering MIT, which explains the experimental
finding of a strongly elevated MIT in CaFeO 3 thin films.
In the second part of this work, we present methodological developments for generating
effective lattice potentials by a polynomial expansion that describe electronic potential
energy surfaces in which atomic nuclei move. This is the so-called second-principles
approach. The aim thereby is to replace the computational intensive self consistent DFT
procedure by an lightweight evaluation of a polynomial depending on nuclear positions.
If successful, this approach provides a mean to achieve a scale-transfer retaining the
accuracy of ab initio calculations applicable to large scale systems with many thousand
atoms and statistical simulations. In a proof of concept study we apply this approach to
the perovskite CaTiO 3 . The retained effective potential reproduces with good accuracy
a number of ab initio quantities. Moreover, in the low to average temperature range
(T<=1000K) the lattice dilatation of CaTiO 3 is well described. In the highest temperature
range the effective potential deviates from the experimentally measured lattice dilatation
and proposed phase transition sequence that is itself, however, debated. We conclude
that the lattice dilatation properties can be refined by extending the lattice expansion
and that a reexamination of the high temperature phase sequence of CaTiO 3 due the the
information of our effective potential might be meaningful. Finally, we also highlight that
there exists a strongly ferroelectric low energetic phase of CaTiO 3 whose stabilization
through external constraints is part of ongoing research.