A two-dimensional electron gas (2DEG) in two-valley semiconductors has two discrete degrees of freedom given by the spin and valley quantum numbers. We analyze the zero-temperature magnetic instabilities of two-valley semiconductors with SOI, in-plane magnetic field, and electron-electron interaction. The interplay of an applied in-plane magnetic field and the SOI results in noncollinear spin quantization in different valleys. Together with the exchange intervalley interaction this results in a rich phase diagram containing four nontrivial magnetic phases. The negative nonanalytic cubic correction to the free energy, which is always present in an interacting 2DEG, is responsible for first order phase transitions. Here, we show that nonzero ground state values of the order parameters can cut this cubic nonanalyticity and drive certain magnetic phase transitions second order. We also find two tricritical points at zero temperature which together with the line of second order phase transitions constitute the quantum critical sector of the phase diagram. The predicted magnetic phases can be observed in a monolayer $\mathrm{Mo}{\mathrm{S}}_2$ at electron densities $n\lesssim 5\times {10}^{12}{\mathrm{cm}}^{-2}$.

• Received 17 August 2020
• Revised 14 December 2020
• Accepted 16 December 2020

DOI:https://doi.org/10.1103/PhysRevB.103.024401