Magnetic control of Goos-H\"anchen shifts and group delay time in monolayer WSe$_2$

We study the influence of an external magnetic field on the Goos-H\"anchen (GH) shift and the group delay time (GDT) in monolayer WSe$_2$ in the presence of a magnetic barrier. The transport properties of Dirac-like carriers are obtained by solving the effective low-energy Hamiltonian and evaluating the corresponding transmission amplitudes. The GH shift and the GDT are subsequently extracted from the phase of the transmission coefficient. We systematically analyze their dependence on the magnetic field strength, incident energy, angle of incidence, and barrier width, with particular emphasis on the spin and valley degrees of freedom associated with the $K$ and $K'$ valleys. Our results show that the magnetic barrier strongly modulates both the GH shift and the GDT, leading to oscillatory behavior and pronounced spin-valley-dependent transport characteristics. Remarkably, the magnetic field enables selective control of the lateral shift and traversal time of carriers for each spin and valley channel, allowing for tunable spatial and temporal separation of electronic wave packets. This provides a mechanism for manipulating fermionic trajectories after transmission through the barrier in a highly controllable manner. Such tunability opens promising avenues for designing nanoscale devices based on spin and valley filtering, as well as for potential applications in information storage and processing within spintronic and valleytronic platforms.