Tuning of the two successive phase transitions with pressure in URhSn

Electron correlations involving 5$f$-orbitals are rather highly tunable with external stimulus. Suppressing phase transitions by hydrostatic pressure to realize a quantum critical point has been a lucrative interest for many researchers in recent decades. Such efforts have fruitfully brought up exotic electronic phases owing to unconventional quantum fluctuations near the associated quantum phase transitions. Here we present a case when there are two successive phase transitions at $T_{\rm C}$ = 18 K and $T_{\rm O}$ = 54 K in URhSn, where $T_{\rm C}$ stands for the Curie temperature below which a ferromagnetic ordering takes place; while the order parameter for the phase transition at $T_{\rm O}$ remains unknown till date. A recent study by Shimizu et al. has established a reinforcement of the this hidden order under magnetic fields; based on which a quadrupolar order or a helical order is suggested below $T_{\rm O}$. A high quality single crystal of URhSn with RRR = 40 and $\rho_0$=6.5 $\mu\Omega$ cm was obtained by Czocharalski method followed by annealing under high vacuum (10$^{-6}$ Torr). Electrical transport under pressures up to 11 GPa and temperature range 2.5-300 K were performed at a dedicated high pressure facility in ISSP, The University of Tokyo. Hydrostaticity of the pressure was enforced by use of cubic anvil cell which uses an in-situ load maintenance mechanism applied via six faces of the cubic MgO gasket. Use of a 1:1 mixture of Flourinert FC-70/FC-77 and pressurization only at room temperature further ensures homogeneity of the pressure transmission across the sample.
The two successive phase transitions in URhSn suppress under pressure in a correlated manner till 6.25 GPa, above which the anomalies in resistivity show an increase for the both phase transitions. This infers a pair of bicritical points at 25.1 K and 33.7 K, associated to the orders at $T_{\rm C}$ and $T_{\rm O}$, respectively. This scheme is further supported by a step/sharp peak in $\rho$($P$) curves at 6.25 GPa, an indication of first order nature of the phase boundary for the line joining the two bicritical points down to absolute zero temperature. A gradual appearance of –ln$T$ slope above $T_{\rm O}$ in 5$f$-electron derived resistivity ($\rho_{5f}$), increase in the quadratic temperature coefficient of resistivity ($A$-coefficient) by an order of magnitude, an increase in the residual resistivity ($\rho_0$) concurrently suggest an enhancement in the c-f hybridization with pressure in URhSn. In the pressure induced phase above the $P_{\rm C}$, resistivity varies as $T^{5/3}$ in a large window of the $P-T$ plane, which makes it akin to a marginal Fermi liquid state that in itinerant electron weak ferromagnet ZrZn$_2$. An intricate regulation of magnetic frustration incorporated by uranium quasi-kagome lattice together with electron correlations imparted by the $c-f$ hybridization is likely to play a crucial role in stabilizing the unique $P-T$ phase diagram of URhSn.