The microscopic origin of ultrafast modification of the ratio between the symmetric ($J$) and antisymmetric ($D$) exchange interaction in antiferromagnetic iron oxides is revealed, using femtosecond laser excitation as a pump and terahertz emission spectroscopy as a probe. By tuning the photon energy of the laser pump pulse we show that the effect of light on the $D/J$ ratio in two archetypical iron oxides ${\mathrm{FeBO}}_3$ and ${\mathrm{ErFeO}}_3$ is maximized when the photon energy is in resonance with a spin and parity forbidden $d-d$ transition between the crystal-field split states of ${\mathrm{Fe}}^{3+}$ ions. The experimental findings are supported by a multielectron model, which accounts for the resonant absorption of photons by ${\mathrm{Fe}}^{3+}$ ions. Our results reveal the importance of the parity and spin-change forbidden, and therefore often underestimated, $d-d$ transitions in ultrafast optical control of magnetism.

The relationship is established between quantum phase transitions and complex geometric phases for open quantum systems governed by a non-Hermitian effective Hamiltonian with accidental crossing of the eigenvalues. In particular, the geometric phase associated with the ground state of the one-dimensional dissipative Ising model in a transverse magnetic field is evaluated, and it is demonstrated that the related quantum phase transition is of the first order.

We have investigated the x-ray diffraction (XRD) structure, magnetic susceptibility, and heat capacity of GdCoO${}_3$ in a wide temperature range. A model of phase separation of the low-spin (LS) and high-spin (HS) states has been proposed based on the analysis of XRD peak shape anomalies in the temperature range 200–800 K. From magnetic measurements we separated the HS Co${}^{3+}$ contribution and fitted it with the temperature-dependent spin gap. We found a smooth LS-HS crossover at $T=800$ K. The possible contribution of the intermediate spin (IS) state to the thermodynamics is excluded by the calculation IS-LS excitation energy within the modified crystal-field approach. In the two-phase model, with HS/LS probabilities calculated from the found spin gap and the LS and HS volumes calculated by the DFT-GGA method, we were able to reproduce the temperature dependence of the unit-cell volume and thermal expansion. Thus, we conclude that in GdCoO${}_3$ the main mechanism of the lattice expansion is not the conventional lattice anharmonicity, but the HS/LS fluctuations. The electronic structure has been calculated by the LDA+GTB method. At zero temperature, we have obtained the charge-transfer insulator with the charge gap $E_g=0.5$ eV. The thermal population of the HS term results in the in-gap band formation inside the insulator gap and smooth insulator-metal transition at $T_{\text{IMT}}=780$ K. Heat-capacity measurements revealed a smooth maximum near the $T_{\text{IMT}}$.

We have investigated the spin and oxidation states of Co in ${\mathrm{Co}}_3{\mathrm{BO}}_5$ using x-ray magnetic circular dichroism (XMCD) and dc magnetic susceptibility measurements. At low temperatures, XMCD experiments have been performed at the Co $K$-edge in ${\mathrm{Co}}_3{\mathrm{BO}}_5$ and ${\mathrm{Co}}_2{\mathrm{FeBO}}_5$ single crystals in the fully ferrimagnetically ordered phase. The Co ($K$-edge) XMCD signal is found to be related to the ${\mathrm{Co}}^{2+}$ magnetic sublattices in both compounds, providing strong experimental support for the low-spin (LS) ${\mathrm{Co}}^{3+}$ scenario. The paramagnetic susceptibility is highly anisotropic. An estimation of the effective magnetic moment in the temperature range 100–250 K correlates well with two ${\mathrm{Co}}^{2+}$ ions in the high-spin (HS) state and some orbital contribution, while ${\mathrm{Co}}^{3+}$ remains in the LS state. The crystal structure of the ${\mathrm{Co}}_3{\mathrm{BO}}_5$ single crystal has been solved in detail at the $T$ range 296–703 K. The unit cell parameters and volume show anomalies at 500 and 700 K. The octahedral environment of the Co4 site strongly changes with heating. The generalized gradient approximation with Hubbard $U$ correction calculations have revealed that, at low-temperatures, the system is insulating with a band gap of 1.4 eV, and the ${\mathrm{Co}}^{2+}$ ions are in the HS state, while ${\mathrm{Co}}^{3+}$ are in the LS state. At high temperatures ($T$ > 700 K), the charge ordering disappears, and the system becomes metallic with all Co ions in $3d^7$ electronic configuration and HS state.