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Environmentally benign $(1\text{\ensuremath{-}}x)\mathrm{Ba}({\mathrm{Ti}}_{0.8}{\mathrm{Zr}}_{0.2}){\mathrm{O}}_{3}\text{\ensuremath{-}}x({\mathrm{Ba}}_{0.7}{\mathrm{Ca}}_{0.3}){\mathrm{TiO}}_{3}$ (BZT-BCT) ceramics are promising materials due to their remarkable high piezoresponse [Liu and Ren, Phys. Rev. Lett. 103, 257602 (2009)]. In this Letter, by focusing on local and average structure in combination with macroscopic electromechanical and dielectric measurements we demonstrate the structure property relationship in the tetragonal BZT-BCT ceramic. During high-temperature cubic to tetragonal phase transformation, polar nanoregions are manifested through the spontaneous volume ferroelectrostriction at temperatures below $\ensuremath{\sim}477$ K. Temperature-dependent local structural investigations across the Zr $K$ edge extended x-ray absorption fine-structure spectroscopy reveal an anomalous collaboration between the ${\mathrm{ZrO}}_{6}$ and ${\mathrm{TiO}}_{6}$ octahedra. These octahedra compromise their individuality during polarization development. The presence of domains of submicron size embedded inside the macroscopic ferroelectric regions below ${T}_{m}$, as well as their hierarchical arrangement, is observed by piezoresponse force microscopy. Effects of the existence of the structural/polar heterogeneities below ${T}_{m}$ are observed also when polarizabilities of the poled and unpoled samples are compared; the poled sample is found to be more susceptible to the electric field. In addition, by using electric field dependent x-ray diffraction studies we also show that this ceramic under field exhibits a reduction of tetragonal distortion, which is consistent with earlier reports.

${[{\mathrm{Ca}}_{2}{\mathrm{CoO}}_{3}]}_{0.62}[{\mathrm{CoO}}_{2}]$, a two dimensional misfit metallic compound, is famous for its rich phases accessed by temperature, i.e., high temperature spin-state transition, metal-insulator transition (MIT) at intermediate temperature ($\ensuremath{\sim}100\phantom{\rule{4pt}{0ex}}\mathrm{K}$), and low temperature spin density wave (SDW). It enters into a SDW phase below ${T}_{\text{MIT}}$ which becomes long range at 27 K. Information on the independent role of misfit layers (rocksalt/${\mathrm{Ca}}_{2}{\mathrm{CoO}}_{3}$ and triangular/${\mathrm{CoO}}_{2}$) in these phases is scarce. By combining a set of complementary macroscopic (DC magnetization and resistivity) and microscopic (neutron diffraction and x-ray absorption fine structure spectroscopy) measurements on pure (CCO) and Tb substituted in the rocksalt layer of CCO (CCO1), magnetic correlations in both subsystems of this misfit compound are unraveled. CCO is found to exhibit glassiness, as well as exchange bias (EB) effects, while CCO1 does not exhibit glassiness, albeit it shows weaker EB effect. By combining local structure investigations from extended x-ray absorption fine structure (EXAFS) spectroscopy and neutron diffraction results on CCO, we confirm that the SDW arises in the ${\mathrm{CoO}}_{2}$ layer. Our results show that the magnetocrystalline anisotropy associated with the rocksalt layer acts as a source of pinning, which is responsible for EB effect. Ferromagnetic clusters in the ${\mathrm{Ca}}_{2}{\mathrm{CoO}}_{3}$ layer affects the SDW in ${\mathrm{CoO}}_{2}$ and ultimately glassiness arises.

The quadruple perovskite CaMn$_7$O$_{12}$ is a topical multiferroic, in which the hierarchy of electronic correlations driving structural distortions, modulated magnetism, and orbital order is not well known and may vary with temperature. x-ray resonant elastic scattering (XRES) provides a momentum-resolved tool to study these phenomena, even in very small single crystals, with valuable information encoded in its polarization- and energy-dependence. We present an application of this technique to CaMn$_7$O$_{12}$. By polarization analysis, it is possible to distinguish superstructure reflections associated with magnetic order and orbital order. Given the high momentum resolution, we resolve a previously unknown splitting of an orbital order superstructure peak, associated with a distinct \textit{locked-in} phase at low temperatures. A second set of orbital order superstructure peaks can then be interpreted as a second-harmonic orbital signal. Surprisingly, the intensities of the first- and second-harmonic orbital signal show disparate temperature and polarization dependence. This orbital re-ordering may be driven by an exchange mechanism, that becomes dominant over the Jahn-Teller instability at low temperature.

Layered misfit cobaltate ${[{\mathrm{Ca}}_{2}{\mathrm{CoO}}_{3}]}_{0.62}[{\mathrm{CoO}}_{2}]$, which emerged as an important thermoelectric material [A. C. Masset et al. Phys. Rev. B 62, 166 (2000)], has been explored extensively in the last decade for the exact mechanism behind its high Seebeck coefficient. Its complex crystal and electronic structures have inhibited consensus among such investigations. This situation has arisen mainly due to difficulties in accurate identification of the chemical state, spin state, and site symmetries in its two subsystems (rocksalt $[{\mathrm{Ca}}_{2}{\mathrm{CoO}}_{3}]$ and triangular $[{\mathrm{CoO}}_{2}]$). By employing resonant photoemission spectroscopy and x-ray absorption spectroscopy along with charge transfer multiplet simulations (at the Co ions), we have successfully identified the site symmetries, valencies, and spin states of the Co in both layers. Our site-symmetry observations explain the experimental value of the high Seebeck coefficient and also confirm that the carriers hop within the rocksalt layer, which is in contrast to earlier reports where hopping within triangular ${\mathrm{CoO}}_{2}$ layer has been held responsible for the large Seebeck coefficient.

The origin of multiferroicity in ${\mathrm{NdCrTiO}}_{5}$ has been examined. A first-order phase transition, due to breaking of the inversion symmetry, near the low-temperature antiferromagnetic ordering (${T}_{N}\ensuremath{\sim}21$ K) where spontaneous electric polarization also appears, is confirmed. From synchrotron x-ray powder diffraction measurements, the structure at low temperatures is found to be noncentrosymmetric (space group $Pba2$), justifying the polar behavior of this compound below ${T}_{N}$. Temperature-dependent Raman measurements reveal that the lattice is strongly coupled with the spins, pointing to the spin lattice correlations in a noncentrosymmetric space group being responsible for invoking the ferroelectricity below 21 K. Through time-of-flight neutron powder diffraction experiments, it is confirmed that the magnetic sublattices, both Nd and Cr, simultaneously order at ${T}_{N}$, and at temperatures below 15 K the Cr moments are found to be saturated while the Nd moments continue to grow until 6 K.

${\mathrm{VO}}_{2}$ exhibits several insulating phases (monoclinic $M1,M2$, and triclinic $T)$, and the study of these phases is important for understanding the true nature of the insulator-to-metal transition (IMT) in ${\mathrm{VO}}_{2}$. These insulating phases have small but discernible crystallographic differences in the vanadium chains forming the dimers. Peculiarities of the electron localizations in the dimerized chains for many of the probes such as NMR make it difficult to characterize the true character of these phases [T. J. Huffman et al., Phys. Rev. B 95, 075125 (2017); J. Pouget et al., Phys. Rev. B 10, 1801 (1974)]. Here we present structural, electrical, ultrafast-reflectivity, and electronic structure studies of the $T$ phase Cr-doped ${\mathrm{VO}}_{2}$ and the $M1$ phase pure ${\mathrm{VO}}_{2}$ thin films, both grown by pulsed laser deposition under identical conditions. An intermediate $M2$ structure is observed in the Cr-doped ${\mathrm{VO}}_{2}$, while the pure ${\mathrm{VO}}_{2}$ directly goes from the insulating monoclinic $M1$ structure to a metallic rutile $R$ structure, manifested by temperature-dependent Raman spectroscopy. Temperature-dependent electronic structure studies utilizing x-ray near-edge absorption spectroscopy reveal that all these insulating phases (monoclinic $M1$ and $M2$ and triclinic $T)$ have similar electronic structures which place these insulating phases into the list of Mott-Hubbard insulators. This is a first combined experimental report on the electronic structure of all the three insulating phases, monoclinic $M1,M2$, and triclinic $T$.