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We use a variational technique to study the many-body phase diagram ofelectrons and holes in $n$-doped and $p$-doped monolayer transition metaldichalcogenides (TMDs). We find a total of four different phases. $i$) A fullyspin polarized and valley polarized ferromagnetic state. $ii$) A state with noglobal spin polarization but with spin polarization in each valley separately,i.e. spin-valley locking. $iii$) A state with spin polarization in one of thevalleys and little to no spin polarization in the other valley. $iv$) Aparamagnetic state with no valley polarization. These phases are separated byfirst-order phase transitions and are determined by the particle density andthe dielectric constant of the substrate. We find that in the presence of aperpendicular magnetic field the four different phases persist. In the case of$n$-doped MoS$_2$, a fifth phase, which is completely valley polarized but notspin polarized, appears for magnetic fields larger than 7 T and for magneticfields larger than 23 T completely replaces the second phase.

Rich many-body phase diagram of electrons and holes in doped monolayer transition metal dichalcogenides