${\mathrm{PbCuTe}}_2{\mathrm{O}}_6$ is considered to be one of the rare candidate materials for a three-dimensional quantum spin liquid (QSL). This assessment was based on the results of various magnetic experiments, performed mainly on polycrystalline material. More recent measurements on single crystals revealed an even more exotic behavior, yielding ferroelectric order below $T_{\text{FE}}\approx 1\text{K}$, accompanied by distinct lattice distortions, and a somewhat modified magnetic response which is still consistent with a QSL. Here we report on low-temperature measurements of various thermodynamic, magnetic, and dielectric properties of single-crystalline ${\mathrm{PbCuTe}}_2{\mathrm{O}}_6$ in magnetic fields $B\le 14.5\text{T}$. The combination of these various probes allows us to construct a detailed $B\text{−}T$ phase diagram including a ferroelectric phase for $B\le 8$ T and a $B$-induced magnetic phase at $B\ge 11$ T. These phases are preceded by or coincide with a structural transition from a cubic high-temperature phase into a distorted noncubic low-temperature state. The phase diagram discloses a ferroelectric quantum critical point at $B_{c1}=7.9\text{T}$, where the second-order phase transition line associated with ferroelectric order is suppressed to zero. In addition, a magnetic quantum phase transition is revealed at $B_{c2}=11\text{T}$. The corresponding phase transition to a field-induced magnetic order at $B>B_{c2}$ is likely to be of first order. Field-induced lattice distortions, observed in the state at $T>1$ K and which are assigned to the effect of spin-orbit interaction of the ${\mathrm{Cu}}^{2+}$ ions, are considered as the key mechanism by which the magnetic field couples to the dielectric degrees of freedom in this material.

• Received 27 February 2023
• Revised 9 May 2023
• Accepted 6 June 2023

DOI:https://doi.org/10.1103/PhysRevB.107.235133