Enhancement of the linear and nonlinear planar Hall effect by altermagnets on the surface of topological insulators

We investigate the planar Hall effect (PHE) in topological insulators (TIs) in proximity to an altermagnet (AM). We find that, due to the interplay between altermagnetism and spin-momentum locking, in-plane magnetic fields can induce PHE in the TI surface states by modulating the anisotropy of the Fermi velocity, the characteristic vectors associated with spin-momentum locking, and the tilt of the Dirac cone. Both linear and nonlinear PHE can be significantly enhanced by the adjacent AM, particularly when the N\'eel vector lies within the TI surface. Notably, the planar Hall conductivities are tunable by the spin-momentum locking properties and change sign as the N\'eel vector rotates by ${180}^{\ensuremath{\circ}}$ in the TI surface. Therefore, the PHE can serve as a powerful tool for detecting both the N\'eel vector and the spin-momentum locking characteristics.