We present measurements of the spin and orbital magnetic moments of ${\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4$ by using SQUID and magnetic circular dichroism in soft x-ray absorption. The measurements show that ${\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4$ has a noninteger spin moment, in contrast to its predicted half-metallic feature. ${\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4$ also exhibits a large unquenched orbital moment. Calculations using the local density approximation including the Hubbard $U$ method and the configuration interaction cluster-model suggest that strong correlations and spin-orbit interaction of the $3d$ electrons result in the noninteger spin and large orbital moments of ${\mathrm{F}\mathrm{e}}_3{\mathrm{O}}_4$.

The material class of rare earth nickelates with high Ni³⁺ oxidation state is generating continued interest due to the occurrence of a metal-insulator transition with charge order and the appearance of non-collinear magnetic phases within this insulating regime. The recent theoretical prediction for superconductivity in LaNiO₃ thin films has also triggered intensive research efforts. LaNiO₃ seems to be the only rare earth nickelate that stays metallic and paramagnetic down to lowest temperatures. So far, centimeter-sized impurity-free single crystal growth has not been reported for the rare earth nickelates material class since elevated oxygen pressures are required for their synthesis. Here, we report on the successful growth of centimeter-sized LaNiO₃ single crystals by the floating zone technique at oxygen pressures of up to 150 bar. Our crystals are essentially free from Ni²⁺ impurities and exhibit metallic properties together with an unexpected but clear antiferromagnetic transition.

Using $\mathrm{Co}\mathrm{\text{−}}{L}_{2,3}$ and $\mathrm{O}\mathrm{\text{−}}K$ x-ray absorption spectroscopy, we reveal that the charge ordering in ${\mathrm{La}}_{1.5}{\mathrm{Sr}}_{0.5}{\mathrm{CoO}}_4$ involves high spin ($S=3/2$) ${\mathrm{Co}}^{2+}$ and low spin ($S=0$) ${\mathrm{Co}}^{3+}$ ions. This provides evidence for the spin-blockade phenomenon as a source for the extremely insulating nature of the ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CoO}}_4$ series. The associated $e_g^2$ and $e_g^0$ orbital occupation accounts for the large contrast in the Co-O bond lengths and, in turn, the high charge ordering temperature. Yet, the low magnetic ordering temperature is naturally explained by the presence of the nonmagnetic ($S=0$) ${\mathrm{Co}}^{3+}$ ions. From the identification of the bands we infer that ${\mathrm{La}}_{1.5}{\mathrm{Sr}}_{0.5}{\mathrm{CoO}}_4$ is a narrow band material.

In the realm of ferroelectric memories, HfO₂-based ferroelectrics stand out because of their exceptional CMOS compatibility and scalability. Nevertheless, their switchable polarization and switching speed are not on par with those of perovskite ferroelectrics. It is widely acknowledged that defects play a crucial role in stabilizing the metastable polar phase of HfO₂. Simultaneously, defects also pin the domain walls and impede the switching process, ultimately rendering the sluggish switching of HfO₂. Herein, we present an effective strategy involving acceptor-donor co-doping to effectively tackle this dilemma. Remarkably enhanced ferroelectricity and the fastest switching process ever reported among HfO₂ polar devices are observed in La³⁺-Ta⁵⁺ co-doped HfO₂ ultrathin films. Moreover, robust macro-electrical characteristics of co-doped films persist even at a thickness as low as 3 nm, expanding potential applications of HfO₂ in ultrathin devices. Our systematic investigations further demonstrate that synergistic effects of uniform microstructure and smaller switching barrier introduced by co-doping ensure the enhanced ferroelectricity and shortened switching time. The co-doping strategy offers an effective avenue to control the defect state and improve the ferroelectric properties of HfO₂ films.

By using x-ray absorption spectroscopy at the $\text{Rh}{L}_{2,3}$, $\text{Co}{L}_{2,3}$, and $\text{Fe}{L}_{2,3}$ edges, we find a valence state of ${\text{Co}}^{2+}/{\text{Rh}}^{4+}$ in ${\text{Ca}}_3{\text{CoRhO}}_6$ and of ${\text{Fe}}^{3+}/{\text{Rh}}^{3+}$ in ${\text{Ca}}_3{\text{FeRhO}}_6$. X-ray magnetic circular dichroism spectroscopy at the $\text{Co}{L}_{2,3}$ edge of ${\text{Ca}}_3{\text{CoRhO}}_6$ reveals a giant orbital moment of about $1.7{\mu }_B$, which can be attributed to the occupation of the minority-spin $d_0{d}_2$ orbital state of the high-spin ${\text{Co}}^{2+}$ $\left(3d^7\right)$ ions in trigonal prismatic coordination. This active role of the spin-orbit coupling explains the strong magnetocrystalline anisotropy and Ising-type magnetism of ${\text{Ca}}_3{\text{CoRhO}}_6$.