Magnetic and quadrupole effects at the crossover in a strong magnetic field in rare-earth tetragonal compounds

Anomalies of the magnetic and magnetoelastic properties of rare-earth (RE) tetragonal paramagnetic materials with zircon and scheelite structures resulting from the interaction of the energy levels (crossover) of an RE ion in a strong magnetic field up to 400 kOe are discussed. Using the example of HoPO$_4$, the specific features of magnetic properties are compared for a crossover with and without a gap in the magnetic field along the [100] and [110] axes. Anomalies of linear magnetostriction at a crossover in a strong magnetic field with DyPO$_4$ are discussed. Calculations within the formalism of the crystal field are shown to give an adequate description of magnetic and magnetoelastic anomalies and critical parameters of the crossover of the investigated crystals when using known interaction parameters, under the assumption of an adiabatic magnetization process in pulsed fields. Taking HoVO$_4$ as example, the anomalous magnetocaloric effect near the crossover is discussed when a crystal is cooled to temperatures of approximately 0.1 K as the field increases, with the starting temperature being $T_{\rm st}=4.2$ K. The step-like change of the contribution of the quadrupole interactions in a number of the crystals caused by the change of the quadrupole moments at the crossover is noted as an analogue of the induced quadrupole transition.