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The coupling between spins and charge disproportionation states has been investigated in the $\mathrm{LaC}{\mathrm{a}}_{2}\mathrm{F}{\mathrm{e}}_{3}{\mathrm{O}}_{9}$ oxide with neutron powder diffraction. This $A$-site layer ordered triple perovskite $\mathrm{LaC}{\mathrm{a}}_{2}\mathrm{F}{\mathrm{e}}_{3}{\mathrm{O}}_{9}$ undergoes charge disproportionation on cooling and shows two different charge ordering patterns. At 230 K, $\mathrm{F}{\mathrm{e}}^{3.67+}$ disproportionates into a 2:1 ratio of $\mathrm{F}{\mathrm{e}}^{3+}:\mathrm{F}{\mathrm{e}}^{5+}$, which order in a layered manner along the $\ensuremath{\langle}010\ensuremath{\rangle}$ direction of the pseudocubic unit cell. At lower temperatures $(Tl170\phantom{\rule{0.16em}{0ex}}\mathrm{K})$, the charge ordering pattern changes to a layered arrangement along the $\ensuremath{\langle}111\ensuremath{\rangle}$ direction. Neutron powder diffraction data show that in the intermediate temperature range ($170\phantom{\rule{0.16em}{0ex}}\mathrm{K}lTl230\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) the spins order into a cycloidal structure on the $ac$ plane for the $\mathrm{F}{\mathrm{e}}^{3+}$ cations while the $\mathrm{F}{\mathrm{e}}^{5+}$ cations remain paramagnetic. For the lowest temperature range ($2\phantom{\rule{0.16em}{0ex}}\mathrm{K}lTl190\phantom{\rule{0.16em}{0ex}}\mathrm{K}$), the spin structure follows the charge ordering and evolves to a $\ensuremath{\langle}111\ensuremath{\rangle}$ layered magnetic structure.

The $A$-site-ordered cubic perovskite $\mathrm{LaC}{\mathrm{u}}_{3}\mathrm{C}{\mathrm{r}}_{4}{\mathrm{O}}_{12}$, where a partial Cu-Cr intersite charge transfer transition occurs at ${T}_{\mathrm{CT}}=220\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, was found to be an unconventional metallic and $G$-type antiferromagnetic oxide. Neutron powder diffraction revealed a $G$-type antiferromagnetic ordering at the Cr sites and no ordered moments at the Cu sites. Ab initio electronic structure calculations revealed that the narrowing of the Cr-O-Cr bands due to heavy tilting of the $\mathrm{Cr}{\mathrm{O}}_{6}$ octahedra and the strong hybridization of the $\mathrm{Cu}\text{\ensuremath{-}}3d,\mathrm{Cr}\text{\ensuremath{-}}3d$, and $\mathrm{O}\text{\ensuremath{-}}2p$ orbitals near the Fermi level give an unusual electronic structure in the vicinity of a localized-electron regime. The $G$-type magnetic structure is primarily stabilized by nearest-neighbor antiferromagnetic superexchange interactions of the near-localized Cr spins. The ferromagnetic ${1\phantom{\rule{0.28em}{0ex}}1\phantom{\rule{0.28em}{0ex}}1}$ layers of the $G$-type antiferromagnetic Cr-spin sublattice allow the spin-polarized electron transfer through the strongly hybridized Cu orbitals.

$B$-site-disordered perovskite $\mathrm{CaF}{\mathrm{e}}_{0.5}\mathrm{M}{\mathrm{n}}_{0.5}{\mathrm{O}}_{3}$ with unusually high valence $\mathrm{F}{\mathrm{e}}^{4+}$ was synthesized using a high-pressure technique. $\mathrm{F}{\mathrm{e}}^{4+}$ randomly distributed at half of the $B$ sites shows charge disproportionation to $\mathrm{F}{\mathrm{e}}^{3+}$ and $\mathrm{F}{\mathrm{e}}^{5+}$. The spins of $\mathrm{F}{\mathrm{e}}^{3+},\phantom{\rule{0.16em}{0ex}}\mathrm{F}{\mathrm{e}}^{5+}$, and $\mathrm{M}{\mathrm{n}}^{4+}$ order below 90 K. Analysis of low-temperature neutron powder-diffraction data revealed a $G$-type antiferromagnetic structure\char22{}where all the nearest-neighboring spins of $\mathrm{F}{\mathrm{e}}^{3+},\phantom{\rule{0.16em}{0ex}}\mathrm{F}{\mathrm{e}}^{5+}$, and $\mathrm{M}{\mathrm{n}}^{4+}$ couple antiparallel\char22{}and the small ordered moment of $0.58\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$ reveals local charge ordering that gives rise to predominant $\mathrm{F}{\mathrm{e}}^{3+}$-O-$\mathrm{F}{\mathrm{e}}^{5+}$ antiferromagnetic arrangements. Despite the identical chemical compositions of $\mathrm{CaF}{\mathrm{e}}_{0.5}\mathrm{M}{\mathrm{n}}_{0.5}{\mathrm{O}}_{3}$ and $\mathrm{C}{\mathrm{a}}_{2}\mathrm{FeMn}{\mathrm{O}}_{6}$, the magnetic structure of the present $\mathrm{CaF}{\mathrm{e}}_{0.5}\mathrm{M}{\mathrm{n}}_{0.5}{\mathrm{O}}_{3}$ is very different from the noncollinear one of layered $B$-site-ordered $\mathrm{C}{\mathrm{a}}_{2}\mathrm{FeMn}{\mathrm{O}}_{6}$.

The magnetism of the A-site-ordered perovskite $\mathrm{LaM}{\mathrm{n}}_{3}{\mathrm{V}}_{4}{\mathrm{O}}_{12}$ is studied comprehensively by means of neutron powder diffraction experiments and theoretical calculations. Magnetic neutron diffraction results show that a rhombohedral 60\ifmmode^\circ\else\textdegree\fi{} spin structure emerges on the cubic lattice below a 44-K N\'eel transition. Ab initio electronic structure calculations confirm that high-spin ${\mathrm{Mn}}^{2+}$ moments are localized while V $3d$-band states are itinerant, and that the noncollinear 60\ifmmode^\circ\else\textdegree\fi{} spin structure is more stable than collinear ferromagnetic or G-type antiferromagnetic alternatives. Effective Heisenberg model calculations reveal that the appearance of such a nontrivial spin structure can be attributed to significant next-nearest-neighbor and third-nearest-neighbor magnetic interactions.

To gain insight into the unconventional superconductivity of Fe pnictides with no electron pockets, we measure the thermal conductivity $\ensuremath{\kappa}$ and penetration depth $\ensuremath{\lambda}$ in the heavily hole-doped regime of Ba${}_{1\ensuremath{-}x}$K${}_{x}$Fe${}_{2}$As${}_{2}$. The residual thermal conductivity ${(\ensuremath{\kappa}/T)}_{T\ensuremath{\rightarrow}0\phantom{\rule{0.28em}{0ex}}\mathrm{K}}$ and $T$ dependence of $\ensuremath{\lambda}$ consistently indicate the fully gapped superconductivity at $x=0.76$ and the (line) nodal superconductivity at higher hole concentrations. The magnitude of $\frac{\ensuremath{\kappa}}{T}\phantom{\rule{0.16em}{0ex}}{T}_{c}{|}_{T\ensuremath{\rightarrow}0\phantom{\rule{0.28em}{0ex}}\mathrm{K}}$ and the slope of $\ensuremath{\lambda}(T)$ at low temperatures, both of which are determined by the properties of the low-energy excitations, exhibit a highly unusual nonmonotonic $x$ dependence. These results indicate a dramatic change of the nodal characteristics in a narrow doping range. We suggest that the observed $x$ dependence is naturally explained by a doping crossover of the gap function between the $s$-wave states with and without sign reversal between $\ensuremath{\Gamma}$-centered hole pockets.

We have investigated the superconducting(SC)-gap anisotropy for several Ba-doped KFe$_2$As$_2$ samples using laser-based angle-resolved photoemission spectroscopy. We show that the SC-gap anisotropy and node positions drastically change with a small amount of Ba doping. Our results totally exclude a possibility of $d$-wave symmetry and strongly suggest that both spin and orbital fluctuations are important for the paring interaction in the Ba-doped K122.

Using small angle neutron scattering, the anisotropy of the magnetic vortex lattice (VL), in the heavily hole-doped pnictide superconductor KFe2As2, was studied. Well-ordered VL scattering patterns were measured with fields applied in directions between B parallel to c and the basal plane, rotating either towards [100] or [110]. Slightly distorted hexagonal patterns were observed when B parallel to c. However, the scattering pattern distorted more strongly as the field was rotated away from the c axis. At low field, the arrangement of vortices is affected by the anisotropy of penetration depth in the plane perpendicular to the field. By fitting the distortion with the anisotropic London model, we obtain an estimate of similar to 3.4 for the anisotropy factor gamma between the in-plane and c-axis penetration depths at the lowest temperature studied. The results further reveal VL phase transitions as a function of field direction. We discuss these transitions using the "hairy ball" theorem.

We performed a laser angle-resolved photoemission spectroscopy (ARPES) study on a wide doping range of Ba${}_{1\ensuremath{-}x}$K${}_{x}$Fe${}_{2}$As${}_{2}$ (BaK) and precisely determined the doping evolution of the superconducting gaps in this compound. The gap size of the outer hole Fermi-surface (FS) sheet around the Brillouin zone (BZ) center shows an abrupt drop with overdoping (for $x\ensuremath{\gtrsim}$ 0.6) while the inner and middle FS gaps roughly scale with ${T}_{c}$. This is accompanied by the simultaneous disappearance of the electron FS sheet with similar orbital character at the BZ corner. These results indicate the different contributions of ${X}^{2}\ensuremath{-}{Y}^{2}$ and $XZ/YZ$ orbitals to superconductivity in BaK and can hardly be completely reproduced by the available theories on iron-based superconductors.

By neutron scattering, we have observed a well-ordered magnetic vortex lattice (VL) in KFe${}_{2}$As${}_{2}$ single crystals. With the field along the $c$ axis, a nearly isotropic hexagonal VL is formed, with no symmetry transitions up to high fields, indicating a small anisotropy of the superconducting state around this axis. This rules out line nodes parallel to the $c$ axis, and thus $d$-wave or anisotropic $s$-wave pairing. However, the strong temperature dependence of the signal at $T\ensuremath{\ll}{T}_{c}$ shows that extremely small gap values exist; these may arise from nodal lines perpendicular to the $c$ axis.

The ionic states of Cu and Mn ions and the magnetic structure in an $A$-site-ordered perovskite ${\text{BiCu}}_{3}{\text{Mn}}_{4}{\text{O}}_{12}$ were investigated by powder neutron diffraction and soft x-ray absorption and magnetic circular dichroism spectroscopy experiments. A substitution by ${\text{Mn}}^{3+}$ was found at the square-planar ${A}^{\ensuremath{'}}$ ${\text{Cu}}^{2+}$ site, leading to a composition $\text{Bi}{(\text{Cu}^{2+}{}_{0.8}\text{Mn}^{3+}{}_{0.2})}_{3}\text{Mn}^{3.6+}{}_{4}{\text{O}}_{12}$. This compound is a ferrimagnet with a collinear spin configuration below ${T}_{\text{C}}=350\text{ }\text{K}$, and the magnetic structure is stabilized by a strong ferromagnetic coupling between the ${A}^{\ensuremath{'}}$ and $B$ site Mn ions and an antiferromagnetic coupling between Cu and Mn ions, leading to a near zero net moment at the ${A}^{\ensuremath{'}}$ site.

Among the iron-based pnictide superconductors the material ${\text{KFe}}_{2}{\text{As}}_{2}$ is unusual in that its Fermi surface does not consist of quasinested electron and hole pockets. Here we report measurements of the temperature dependent London penetration depth of very clean crystals of this compound with residual resistivity ratio $g1200$. We show that the superfluid density at low temperatures exhibits a strong linear-in-temperature dependence which implies that there are line nodes in the energy gap on the large zone-centered hole sheets. The results indicate that ${\text{KFe}}_{2}{\text{As}}_{2}$ is an unconventional superconductor with strong electron correlations.