Unveiling the driving force for a phase transition is normally difficult when multiple degrees of freedom are strongly coupled. One example is the nematic phase transition in iron-based superconductors. Its mechanism remains controversial due to a complex intertwining among different degrees of freedom. In this paper, we report a method for measuring the nematic susceptibly of FeSe$_{0.9}$S$_{0.1}$ using angle-resolved photoemission spectroscopy (ARPES) and an $in$-$situ$ strain-tuning device. The nematic susceptibility is characterized as an energy shift of band induced by a tunable uniaxial strain. We found that the temperature-dependence of the nematic susceptibility is strongly momentum dependent. As the temperature approaches the nematic transition temperature from the high temperature side, the nematic susceptibility remains weak at the Brillouin zone center while showing divergent behavior at the Brillouin zone corner. Our results highlight the complexity of the nematic order parameter in the momentum space, which provides crucial clues to the driving mechanism of the nematic phase transition. Our experimental method which can directly probe the electronic susceptibly in the momentum space provides a new way to study the complex phase transitions in various materials.
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