Angle - dependent upper critical field of overdoped Ba(Fe$_{1-x}$Ni$_x$)$_2$As$_2$

In-plane resistivity measurements were used to study the upper critical field, $H_{c2}$, of single crystals of iron-based superconductor Ba(Fe$_{1-x}$Ni$_{x}$)$_{2}$As$_{2}$ ($x=0.054$ and $x=0.072$). An applied magnetic field (up to 35 T) was precisely aligned (with the accuracy better than 0.1$^{o}$) parallel to the Fe-As layers and the measurements were taken for $H\parallel ab-$ plane and $H\parallel c-$axis as function of temperature. The determined $H_{c2}(T)$ clearly differs for the two principal directions. The dependence of the upper critical field on the angle $\Theta$ between the field direction and the $ab-$plane was measured in isothermal conditions at temperatures close to $T_{c0}$ and at low temperatures $T\ll T_{c}(H=0)$. In both temperature regimes $H_{c2}(\Theta)$ clearly deviates from sinusoidal function, expected for orbital $H_{c2}$ [1]. We discuss the origin of this behavior as possible reflection of the angular modulation of the superconducting gap magnitude and the complex warping of the Fermi surface along the $c$-axis. Work in Ames was supported by the Department of Energy Office of Science, Basic Energy Sciences under Contract No. DE-AC02-O7CH11358.\\[4pt] [1] V. G. Kogan and R. Prozorov, Rep. Prog. Phys. \textbf{75}, 114502 (2012).