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We report a study of the ferromagnetism of ZrZn$_{2}$, the most promisingmaterial to exhibit ferromagnetic quantum criticality, at low temperatures $T$as function of pressure $p$. We find that the ordered ferromagnetic momentdisappears discontinuously at $p_c$=16.5 kbar. Thus a tricritical pointseparates a line of first order ferromagnetic transitions from second order(continuous) transitions at higher temperature. We also identify two lines oftransitions of the magnetisation isotherms up to 12 T in the $p-T$ plane wherethe derivative of the magnetization changes rapidly. These quantum phasetransitions (QPT) establish a high sensitivity to local minima in the freeenergy in ZrZn$_{2}$, thus strongly suggesting that QPT in itinerantferromagnets are always first order

physical review letters

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Quantum Phase Transitions in the Itinerant FerromagnetZrZn2