Magnetic properties of FeBO$_3$ in the low-spin state

Changes in the magnetic properties of FeBO$_3$ single crystals in the course of spin crossover occurring with increasing pressure up to 63 GPa are studied both experimentally and theoretically. Simultaneous measurements of the nuclear diffraction and nuclear forward scattering spectra make it possible to detect the antiferromagnetic high-spin state at low pressures up to 48 GPa and to reveal the antiferromagnetic state within the range characterized by the coexistence of Fe$^{3+}$ ions in the high-spin and low-spin states, which occurs at pressures from 48 to 54 GPa, where the hysteresis takes place. Above 58 GPa, only the low-spin state is observed, whereas the magnetic order is absent down to 9 K. An analysis of changes in the exchange interactions manifesting themselves at spin crossover suggests that there exist competing ferromagnetic and antiferromagnetic contributions nearly compensating each other. A possible Néel temperature in the low-spin state does not exceed 7 K; thus, an ordered state cannot be observed in our experiments.