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In the quest to realize a quantum spin liquid (QSL), magnetic long-range order is hardly welcome. Yet it can offer deep insights into a complex world of strong correlations and fluctuations. Much hope was placed in the cubic pyrochlore Yb$_2$Ti$_2$O$_7$ as a putative U(1) QSL but a new class of ultra-pure single crystals make it abundantly clear the stoichiometric compound is a ferromagnet. Here we present a detailed experimental and theoretical study of the corresponding field-temperature phase diagram. We find it to be richly anisotropic with a critical endpoint for $\vec{B}\,\parallel\,\langle 100\rangle$, while field parallel to $\langle 110 \rangle$ and $\langle 111 \rangle$ enhances the critical temperature by up to a factor of two and shifts the onset of the field-polarized state to finite fields. Landau theory shows that Yb$_2$Ti$_2$O$_7$ in some ways is remarkably similar to pure iron. However, it also pinpoints anomalies that cannot be accounted for at the classical mean-field level including a dramatic enhancement of $T_{\mathrm{C}}$ and reentrant phase boundary by fields with a component transverse to the easy axes, as well as the anisotropy of the upper critical field in the quantum limit.

We document the coexistence of ferro- and anti-ferromagnetism in pyrochlore $\rm Yb_2Ti_2O_7$ using three neutron scattering techniques on stoichiometric crystals: elastic neutron scattering shows a canted ferromagnetic ground state, neutron scattering shows spin wave excitations from both a ferro-and an antiferro-magnetic state, and field and temperature dependent small angle neutron scattering reveals the corresponding anisotropic magnetic domain structure. High-field $\langle 111 \rangle$ spin wave fits show that $\rm Yb_2Ti_2O_7$ is extremely close to an antiferromagnetic phase boundary. Classical Monte Carlo simulations based on the interactions inferrred from high field spin wave measurements confirm $\psi_2$ antiferromagnetism is metastable within the FM ground state., Comment: 11 pages and 11 figures, 8 pages appendices with 10 additional figures

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., Comment: 5 pages, 5 pages supplementary information