Scanning Tunneling Microscopy Observation of a Square Abrikosov Lattice in ${\mathrm{LuNi}}_2{B}_{2}C$

We present scanning tunneling microscopy measurements of the (001) surface of a ${\mathrm{LuNi}}_2{\mathrm{B}}_2\mathrm{C}$ borocarbide single crystal at 4.2 K. In zero field, the conductance versus voltage characteristics recorded at various locations on the sample reproducibly provide a gap value of 2.2 meV. In a magnetic field of 1.5 and 0.375 T, the recordings of the conductance as a function of position reveal a regular square vortex lattice tilted by $45°$ with respect to the crystalline $a$ axis. This unusual result is correlated with an in-plane anisotropy of the upper critical field $H_{c2\mathrm{}}^{\parallel }\left(45°\right)/H_{c2\mathrm{}}^{\parallel }\left(0\right)=0.92\mathrm{}$ at 4.2 K and is analyzed within the framework of Ginzburg-Landau theory.