Pressure-induced commensurate magnetic order in multiferroic $HoMn_2O_5$

The pressure ($p$) -- temperature ($T$) phase diagram for microscopic magnetism in the multiferroic compound HoMn$_{2}$O$_{5}$ was established using neutron diffraction measurements under a hydrostatic pressure up to 1.25 GPa. At ambient pressure, incommensurate--commensurate--incommensurate magnetic phase transitions occur successively with decreasing temperature. Upon applying pressure, the incommensurate phase at the lowest temperature almost decreases and the commensurate phase appears. The $p$ -- $T$ phase diagram established shows excellent agreement with the recently reported $p$ -- $T$ dielectric phase diagram, where ferroelectricity is induced by applying pressure. We also found that the $p$ -- $T$ magnetic phase diagram is quite similar to the previously obtained magnetic field-temperature phase diagram.