Investigation of magnetic order influenced phonon and electron dynamics in MnBi$_{2}$Te$_{4}$ and Sb doped MnBi$_{2}$Te$_{4}$ through terahertz time-domain spectroscopy

MnBi$_{2}$Te$_{4}$, the first topological insulator with inherent magnetic ordering, has attracted significant attention recently for providing a platform to realize several exotic quantum phenomena at relatively higher temperatures. In this work, we have carried out an exhaustive investigation of MnBi$_{2}$Te$_{4}$ and Sb doped MnBi$_{2}$Te$_{4}$ thin films using THz time-domain spectroscopy. The extracted real THz conductivity displays a strong IR active E$_u$ phonon absorption peak (at $\sim$1.5 THz) merged on top of the Drude-like contributions from bulk and surface electrons. The extracted parameters from the THz conductivity data fitted to the Drude-Fano-Lorentz model, show significant changes in their temperature dependence around the magnetic ordering N\'eel temperature of $\sim$ 25K, which is suggestive of the coupling between magnetic ordering and electronic band structure. The frequency of the E$_u$ phonon displays an anomalous blue-shift with increasing temperatures by $\sim$ 0.1 THz ($\sim$7 %) for MnBi$_{2}$Te$_{4}$ and $\sim$0.2 THz ($\sim$13 %) for Sb doped MnBi$_{2}$Te$_{4}$ between 7K and 250K. The line-shape of the E$_u$ phonon mode in Sb doped MnBi$_{2}$Te$_{4}$ shows significant Fano asymmetry compared to that of MnBi$_{2}$Te$_{4}$, indicating that Sb doping plays an important role in the Fano interference between the phonons and the electrons, in this system. These results indicate that the anomalous phonon behaviour seen in MBT arise mainly from positive cubic anharmonicity induced self energy parameter, whereas both anharmonicity and the electron phonon coupling are at play in making the relatively higher anomalous blue shift of phonons in MBST. Our studies provide the first comprehensive understanding of the phonon and electron dynamics of MnBi$_{2}$Te$_{4}$ and Sb doped MnBi$_{2}$Te$_{4}$ in the THz range using time-domain THz spectroscopy.