Effect of simultaneous application of field and pressure on magnetic transitions in La${}_{0.5}$Ca${}_{0.5}$MnO${}_3$

We study combined effect of hydrostatic pressure and magnetic field on the magnetization of La${}_{0.5}$Ca${}_{0.5}$MnO${}_3$. We do not observe any significant effect of pressure on the paramagnetic to ferromagnetic transition. However, pressure asymmetrically affects the thermal hysteresis across the ferro-antiferromagnetic first-order transition, which has strong field dependence. Though the supercooling (T*) and superheating (T**) temperatures decrease and the value of magnetization at 5K (M${}_{5K}$) increases with pressure, T* and M${}_{5K}$ shows abrupt changes in tiny pressure of 0.68kbar. These anomalies enhance with field. In 7Tesla field, transition to antiferromagnetic phase disappears in 0.68kbar and M${}_{5K}$ show significant increase. Thereafter, increase in pressure up to $\sim$10kbar has no noticeable effect on the magnetization.