Emergence of half-metallic ferromagnetism and valley polarization in transition metal substituted WSTe monolayer

Two-dimensional (2D) Janus materials hold a great importance in spintronic and valleytronic applications due to their unique lattice structures and emergent properties. They intrinsically exhibit both in-plane inversion and out-of-plane mirror symmetry breakings, which provide a new degree of freedom to electrons in the material. One of the main limitations in the multifunctional applications of these materials is, however, that they are usually nonmagnetic in nature. Here, using first-principles calculations, we propose to induce magnetic degrees of freedom in nonmagnetic WSTe via substituting transition metal (TM) elements---Mn, Fe, and Co. Further, we comprehensively probe the electronic, spintronic, and valleytronic properties in TM-WSTe systems. Our simulations predict intrinsic Rashba- and Zeeman-type spin splittings in pristine WSTe. The obtained Rashba parameter is $\ensuremath{\sim}422\phantom{\rule{0.16em}{0ex}}\mathrm{meV}\phantom{\rule{0.16em}{0ex}}\AA{}$ along the $\mathrm{\ensuremath{\Gamma}}\ensuremath{-}K$ direction. The Rashba spin splitting is observed to show a strong dependence on uniaxial and biaxial strains. The electronic structure of TM-WSTe reveals a half-metallic nature for 6.25% and 18.75% of Fe, 25% of Mn, and 18.75% and 25% of Co structures, which leads to a 100% spin polarization. The structural asymmetry, strong spin-orbit coupling, and broken inversion symmetry are found to lead to valley polarization in TM-WSTe systems. Further, our calculations predict a strain-dependent tunability of valley polarization, where we find an increasing(decreasing) trend with uniaxial and biaxial tensile(compressive) strains. We observed a maximum enhancement of $\ensuremath{\sim}172%$ for 6.25% of Fe doping on application of 3% biaxial tensile strain. The ability to control valley degrees of freedom, along with spin and charge, could open new prospects for next-generation spintronic and valleytronic devices.