Giant enhancement of Rashba spin splitting and anisotropy in thermodynamically stable Janus <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Ta</mml:mi> <mml:mi>Q</mml:mi> <mml:mi>X</mml:mi> </mml:mrow> </mml:math> monolay

Structural symmetry breaking in two-dimensional systems introduces additional electronic degrees of freedom, fostering exotic quantum phenomena such as the Rashba effect, magnetic anisotropy, and nontrivial topological states, thereby advancing their relevance in spintronic, valleytronic, and quantum information technologies. In the present density functional theory investigation on $\mathrm{Ta}QX$ $(Q=\mathrm{O}, \mathrm{S}; X=\mathrm{F}, \mathrm{Cl}, \mathrm{Br})$ Janus monolayers, possessing intrinsic mirror asymmetry and permanent out-of-plane dipole moments, we aim at boosting Rashba dynamics via application of external electric field and biaxial strain. All six systems are not only phonon-stable across a broad strain window but also thermodynamically durable as per room-temperature ab initio molecular dynamics and exhibit spontaneous formation potential. Phonon dispersion and factor group analysis reveal simultaneously Raman and infrared (IR)-active vibrational modes $({E}^{1,2},{A}_{1}^{1,2})$, reaffirming the absence of an inversion center. All monolayers are semiconductors with indirect (except TaOF) band gaps, spanning from the near-IR to visible range, promising for optospintronic applications. Foremost, strong spin-orbit coupling facilitates substantial Rashba-type spin splitting near the $\mathrm{\ensuremath{\Gamma}}$ point at the valence band maximum, with Rashba coefficients ranging between ${\ensuremath{\alpha}}_{R}=122\phantom{\rule{0.16em}{0ex}}\text{and}\phantom{\rule{0.16em}{0ex}}330\phantom{\rule{0.16em}{0ex}}\mathrm{meV}\phantom{\rule{0.16em}{0ex}}\AA{}$. Application of out-of-plane electric field and in-plane biaxial strain modulates ${\ensuremath{\alpha}}_{R}$, maximizing it up to 4.25 times $(\ensuremath{\sim}1.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV}\phantom{\rule{0.16em}{0ex}}\AA{})$ for TaOF. Furthermore, huge strain-induced Rashba anisotropy emerges along the $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}K$ and $\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}M$ directions, reaching 58 meV \AA{} in 5% tensed TaOF. Elevated ${\ensuremath{\alpha}}_{R}$ coupled with pronounced anisotropy in structurally robust TaOF unlocks crystallographically dictated spin splitting, directional manipulation of spin-momentum locking, nonreciprocal spin transport, and spin filtering, essential for next-generation spintronic integration.