  Resistivity measurements were performed for the itinerant Ising-type
ferromagnet URhAl at temperatures down to 40 mK under high pressure up to 7.5
GPa, using single crystals. We found that the critical pressure of the Curie
temperature exists at around $P_c$ ~ 5.2 GPa. Near $P_c$, the $A$-coefficient
of the $AT^{2}$ Fermi-liquid resistivity term below $T^*$ is largely enhanced
with a maximum around 5.2-5.5 GPa. Above $P_c$, the exponent of the resistivity
$\rho(T)$ deviates from 2. At $P_c$, it is close to $n = 5/3$, which is
expected by the theory of three-dimensional ferromagnetic spin fluctuations for
a 2nd-order quantum-critical point (QCP). However, $T_C(P)$ disappears as a
1st-order phase transition, and the critical behavior of resistivity in URhAl
cannot be explained by the theory of a 2nd-order QCP. The 1st-order nature of
the phase transition is weak, and the critical behavior is still dominated by
the spin fluctuation at low temperature. With increasing pressure, the
non-Fermi-liquid behavior is observed in higher fields. Magnetic field studies
point out a ferromagnetic wing structure with a tri-critical point (TCP) at ~
4.8-4.9 GPa in URhAl. One open possibility is that the switch from the
ferromagnetic to the paramagnetic states does not occur simply but an
intermediate state arises below the TCP as suggested theoretically recently.
Quite generally, if a drastic Fermi-surface change occurs through $P_c$, the
nature of the interaction itself may change and lead to the observed
unconventional behavior.
