Field induced first order phase transition in the antiferromagnet Yb$_{3}$Pt$_{4}$

Yb$_{3}$Pt$_{4}$ is an antiferromagnet that orders at T$_{N}$=2.4K. Magnetic fields B suppress T$_{N}$, and the B-T phase line T$_{N}$(B) terminates almost vertically at T=0, B$_{C}$=2.0 T. Specific heat measurements find a mean-field transition at T$_{N}$(B), and the magnetocaloric effect shows that the antiferromagnetic transition is continuous at all fields, with no associated latent heat. However, neutron diffraction measurements performed for B$\sim $B$_{C}$ find that a distinct step in the magnetization $\Delta $M occurs near the transition, with a magnitude that increases for T$<$1 K. The field dependent magnetization M(B) similarly has a metamagnetic-like step at T$_{N}$(B) below 1 K, accompanied by a sharp peak in the susceptibility whose magnitude increases but does not diverge as T$\to $0. We argue that a nonzero magnetization step $\Delta $M is required to give $\Delta $S=0 for T=0, since the vertical phase line at T=0 implies dT$_{N}$/dB=-$\Delta $M/$\Delta $S$\to -\infty $. We argue that T$_{N}$ (B) terminates at B$_{C}$ in a T=0 first order transition.