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Field-Orientation Effect on Ferro-Quadrupole Order in PrTi2Al20

Ferro-quadrupole (FQ) order in the non-Kramers $Γ_3$ doublet system PrTi$_2$Al$_{20}$ has been investigated via angle-resolved measurements of the specific heat, rotational magnetocaloric effect, and entropy, under a rotating magnetic field within the $(1\bar{1}0)$ plane. The FQ transition occurring at 2 K is robust when the magnetic field $B$ is applied precisely along the $[111]$ direction. By contrast, the magnetic field of larger than 1 T tilted away from the $[111]$ direction sensitively changes the FQ transition to a crossover. The energy gap between the ground and first-excited states in the FQ order increases remarkably with the magnetic field in $B \parallel [001]$, but hardly depends on the magnetic-field strength, at least up to 5 T, in the field orientation between the $[111]$ and $[110]$ axes. These features can be reproduced by using a phenomenological model for FQ order assuming an anisotropic field-dependent interaction between quadrupoles, which has been recently proposed to explain the field-induced first-order phase transition in PrTi$_2$Al$_{20}$. The present study demonstrates the great potential of the field-angle-resolved measurements for evaluating possible scenarios for multipole orders.