Quadrupole susceptibility by magnetostriction and thermal expansion measurements for the non-magnetic ground state doublet in a cubic Pr-based compound PrMgNi₄

Cubic praseodymium-based intermetallic compounds with 4f ² electrons have received much interests because the quadrupolar degrees of freedom of the nonmagnetic Γ₃ doublet ground state under the crystalline electric field shows a variety of phenomena. Recently, we reported that PrMgNi₄ crystallizing in the cubic MgSnCu₄-type structure with an fcc sublattice of the Pr ions has the Γ₃ doublet ground state [1,2]. At around 0.7 K, both magnetic specific heat C_m(T) and electrical resistivity ρ (T) exhibit a shoulder, which could be ascribed to the short-range quadrupole order.

In the present work, we measured the thermal expansion ∆L(T)/L₀ and magnetostriction ∆L(B)/L₀ of PrMgNi₄ at T > 0.3 K. The thermal expansion coefficient d(∆L(T)/L₀)/dT shows a broad peak at around 5 K, which is consistent with the doublet-triplet Schottky anomaly in C_m(T) [2]. Upon further cooling, a clear peak manifests at 0.7 K, due to quadrupole order.

The second derivative of magnetostriction d²(ΔL(B)/L₀)/dB² in the zero-field limit is proportional to the quadrupole susceptibility χ_Q. We qualitatively derive the temperature dependence of χ_Q from d²(ΔL(B)/L₀)/dB² at various temperatures. χ_Q(T) for B || [001] divergently increases on cooling, whereas χ_Q(T) for B || [111] tends to saturate below 5 K. These results indicate that Γ₃-type quadrupole moments which couple with tetragonal distortion are active.

[1] Y. Kusanose et al., J. Phys. Soc. Jpn. 88, 083703 (2019).

[2] Y. Kusanose et al., JPS Conf. Proc. 30, 011160 (2020).