Discovery of a bi-critical point between antiferromagnetic and superconducting phases in pressurized single crystal Ca$_{\mathrm{0.73}}$La$_{\mathrm{0.27}}$FeAs$_{\mathrm{2}}$

One of the most strikingly universal features of the high-temperature superconductors is that the superconducting phase emerges in the close proximity of the antiferromagnetic phase, and the interplay between these two phases poses a long-standing challenge. It is commonly believed that, as the antiferromagnetic transition temperature is continuously suppressed to zero, there appears a quantum critical point, around which the existence of antiferromagnetic fluctuation is responsible for the development of the superconductivity. In contrast to this scenario, we report the discovery of a bi-critical point identified at 2.88 GPa and 26.02 K in the pressurized high-quality single crystal Ca$_{\mathrm{0.73}}$La$_{\mathrm{0.27}}$FeAs$_{\mathrm{2}}$ by complementary \textit{in-situ} high pressure measurements. At the critical pressure, we find that the antiferromagnetism suddenly disappears and superconductivity simultaneously emerges at almost the same temperature, and that the external magnetic field suppresses the superconducting transition temperature but hardly affects the antiferromagnetic transition temperature.