Magnetic Properties of Titanium Hydride (TiH) Diatomic Molecule with Modified Kratzer Energy-Dependent Screened Coulomb Potential in the Presence of Magnetic and Aharonov-Bohm Flux Fields

In this study, the modified Kratzer energy-dependent screened Coulomb potential is analyzed in the presence of external magnetic and Aharonov–Bohm (AB) flux fields. The Schrödinger equation is solved using the Nikiforov–Uvarov Functional Analysis (NUFA) method, yielding closed-form expressions for the energy eigenvalues and the corresponding wavefunctions. These solutions are applied to investigate the magnetic properties of the titanium hydride (TiH) diatomic molecule, including the partition function, magnetization, magnetic susceptibility, and persistent current. The effects of the slope parameter are examined in detail and found to play a significant role in controlling the magnitude, ordering, and convergence behavior of all magnetic observables. Negative slope values enhance the magnetic and thermodynamic responses of the system, while positive slope values suppress them, with the zero-slope case acting as an intermediate regime. The magnetic field induces divergence and saturation effects, whereas the AB-flux field governs sharp transitions, minima, and convergence characteristics. Overall, the results demonstrate that both the slope parameter and external fields provide effective mechanisms for tuning the magnetic behavior of the TiH diatomic molecule.