Title: Record high superconducting transition temperature in Ti$_{1-x}$Mn$_x$ alloy with rich magnetic element Mn

Abstract: It is well-known that magnetic moments are very harmful to superconductivity. A typical example is the element Mn whose compounds usually exhibit strong magnetism. Thus, it is very hard to achieve superconductivity in materials containing Mn. Here, we report enhanced superconductivity with the superconducting transition temperature ($T_\text{c}$) up to a record high-value of about 26 K in a beta-phase Ti$_{1-x}$Mn$_x$ alloy containing rich magnetic element Mn under high pressures. This is contrary to the intuition that the magnetic moments always suppress superconductivity. Under high pressures, we also found that in the middle-pressure regime, the Pauli limit of the upper critical field is surpassed. The synchrotron X-ray diffraction data shows an unchanged beta-phase with a continuous contraction of the cell volume, which is well supported by the first-principles calculations. Although the theoretical results based on electron-phonon coupling (EPC) can interpret the $T_\text{c}$ value in a certain pressure region, the monotonic enhancement of superconductivity by pressure cannot seek support from the theory. Our results show a surprising enhancement of superconductivity in Ti$_{1-x}$Mn$_x$ alloy with a considerable Mn content.