Phase Diagram of $\alpha$-RuCl$_3$ in an in-plane Magnetic Field

The low-temperature magnetic phases in the layered honeycomb lattice material $\alpha$-RuCl$_3$ have been studied as a function of in-plane magnetic field. In zero field this material orders magnetically below 7 K with so-called zigzag order within the honeycomb planes. Neutron diffraction data show that a relatively small applied field of 2 T is sufficient to suppress the population of the magnetic domain in which the zigzag chains run along the field direction. We found that the intensity of the magnetic peaks due to zigzag order is continuously suppressed with increasing field until their disappearance at $\mu_o$H$_c$=8 T. At still higher fields (above 8 T) the zigzag order is destroyed, while bulk magnetization and heat capacity measurements suggest that the material enters a state with gapped magnetic excitations. We discuss the magnetic phase diagram obtained in our study in the context of a quantum phase transition.