Anisotropic phase diagram of ferroquadrupolar ordering in the trigonal chiral compoundDyNi3Ga9

Abstract

The rare-earth chiral compound ${\mathrm{DyNi}}_{3}{\mathrm{Ga}}_{9}$ with trigonal structure shows successive phase transitions at 10, 9, 5.5, and 2.5 K. We previously reported that the transverse elastic modulus ${C}_{66}$ exhibits significant softening toward ${T}_{\mathrm{Q}}=10$ K and the phase transition at ${T}_{\mathrm{Q}}$ is ferroquadrupolar ordering due to the quasidegenerate quartet under a crystal electric field (CEF). To investigate the order parameter and magnetic field-temperature phase diagrams of the ferroquadrupolar ordering, we performed ultrasonic measurements under magnetic fields. ${T}_{\mathrm{Q}}$ decreases drastically at low fields in the magnetic field in the $c$ plane. In contrast, ${T}_{\mathrm{Q}}$ remains even at high fields in the field along the $c$ axis. We found anisotropic and complex phase diagrams, and this anisotropy of the diagrams originates from the field dependences of the CEF energies and a quadrupole interaction. From our calculated results, we propose that the order parameter of the ferroquadrupolar ordering will be the electric quadrupole ${O}_{xy}$. There are first-order successive phase transitions in the field sweep in the $c$ plane, and a magnetic-field-induced phase appears in the phase diagram for the $a$ axis.