Phase Shift and Magnetic Anisotropy Induced Field Splitting of Impurity States in (Li_{1-x}Fe_{x})OHFeSe Superconductor.

Revealing the energy and spatial characteristics of impurity-induced states in superconductors is essential for understanding their mechanism and fabricating a new quantum state by manipulating impurities. Here, by using high-resolution scanning tunneling microscopy and spectroscopy, we investigate the spatial distribution and magnetic field response of the impurity states in (Li_{1-x}Fe_{x})OHFeSe. We detect two pairs of strong in-gap states on the "dumbbell-shaped" defects. They display damped oscillations with different phase shifts and a direct phase-energy correlation. These features have long been predicted for the classical Yu-Shiba-Rusinov (YSR) state and are demonstrated here with unprecedented resolution for the first time. Moreover, upon applying magnetic field, all in-gap state peaks remarkably split into two rather than shift, and the splitting strength is field orientation dependent. Via detailed numerical model calculations, we find such an anisotropic splitting behavior can be naturally induced by a high-spin impurity coupled to an anisotropic environment, highlighting how magnetic anisotropy affects the behavior of YSR states.