The spin orientation of electronic wave functions in crystals is an internal degree of freedom, typically insensitive to electrical knobs. We argue from a general symmetry analysis and a $\mathbf{k}·\mathbf{p}$ perspective, that monolayer $1T^{\prime }-{\mathrm{WTe}}_2$ possesses a gate-activated canted spin texture that produces an electrically tunable bulk band quantum geometry. In particular, we find that due to its out-of-plane asymmetry, an applied out-of-plane electric field breaks inversion symmetry to induce both in-plane and out-of-plane electric dipoles. These in-turn generate spin-orbit coupling to lift the spin degeneracy and enable a bulk band Berry curvature and magnetic moment distribution to develop. Further, due to its low symmetry, Berry curvature and magnetic moment in $1T^{\prime }-{\mathrm{WTe}}_2$ possess a dipolar distribution in momentum space, and can lead to unconventional effects such as a current induced magnetization and quantum nonlinear anomalous Hall effect. These render $1T^{\prime }-{\mathrm{WTe}}_2$ a rich two-dimensional platform for all-electrical control over quantum geometric effects.

• Received 24 September 2018

DOI:https://doi.org/10.1103/PhysRevB.99.035403