ar X iv : c on d - m at / 0 40 84 24 v 1 1 9 A ug 2 00 4 Quantum Phase Transitions in the Itinerant

We report a study of the ferromagnetism of ZrZn2, the most promising material to exhibit ferromagnetic quantum criticality, at low temperatures T as function of pressure p. We find that the ordered ferromagnetic moment disappears discontinuously at pc=16.5 kbar. Thus a tricritical point separates a line of first order ferromagnetic transitions from second order (continuous) transitions at higher temperature. We also identify two lines of transitions of the magnetisation isotherms up to 12T in the p − T plane where the derivative of the magnetization changes rapidly. These quantum phase transitions (QPT) establish a high sensitivity to local minima in the free energy in ZrZn2, thus strongly suggesting that QPT in itinerant ferromagnets are always first order.