We present a theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid ${}^3\mathrm{He}\text{−}\mathrm{B}$. Based on a strong-coupling Ginzburg-Landau functional that accounts for the relative stability of the bulk A and B phases of ${}^3\mathrm{He}$ at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid ${}^3\mathrm{He}\text{−}\mathrm{B}$. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of $H=284\text{G}$ parallel to the rotation axis, $\mathbf{H}\parallel \mathit{\Omega }$, are reported, as well as the supercooling transition line, $T_{\text{V}}^{*}(p,H)$. In zero field the vortex phases of ${}^3\mathrm{He}\text{−}\mathrm{B}$ are separated by a first-order phase transition line $T_{\text{V}}\left(p\right)$ that terminates on the bulk critical line $T_c\left(p\right)$ at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and $\beta$ phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, $T_{\text{V}}^{*}(p,H)$, below which it is globally unstable to an array of D-core vortices. For $H\gtrsim 60\text{G}$ external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating ${}^3\mathrm{He}\text{−}\mathrm{B}$, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating ${}^3\mathrm{He}\text{−}\mathrm{B}$.

• Received 18 March 2019
• Revised 14 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.024517