Reentrant Phase Diagram of $rm{Yb_2Ti_2O_7}$ in $langle 111 rangle$ Magnetic Field

We present a magnetic phase diagram of rare-earth pyrochlore $rm{Yb_2Ti_2O_7}$ in a $langle 111 rangle$ magnetic field. Using heat capacity, magnetization, and neutron scattering data, we show an unusual field-dependence of a first-order phase boundary, wherein a small applied field increases the ordering temperature. The zero-field ground state has ferromagnetic domains, while the spins polarize along $langle 111 rangle$ above 0.65T. A classical Monte Carlo analysis of published Hamiltonians does account for the critical field in the low T limit. However, this analysis fails to account for the large bulge in the reentrant phase diagram, suggesting that either long-range interactions or quantum fluctuations govern low field properties.