Anisotropic $H_{c2}$ determined up to 92 T and the signature of multi-band superconductivity in Ca${}_{10}$(Pt${}_4$As${}_8$)((Fe${}_{1-x}$Pt${}_x$)${}_2$As${}_2$)${}_5$ superconductor

The upper critical fields, $H_{c2}$($T$), of single crystals of the superconductor Ca${}_{10}$(Pt${}_{4-\delta }$As${}_8$)((Fe${}_{0.97}$Pt${}_{0.03}$)${}_2$As${}_2$)${}_5$ ($\delta$ $\approx$ 0.246) are determined over a wide range of temperatures down to $T$ = 1.42 K and magnetic fields of up to ${\mu }_{0}H$ $\simeq$ 92 T. The measurements of anisotropic $H_{c2}$($T$) curves are performed in pulsed magnetic fields using radio-frequency contactless penetration depth measurements for magnetic field applied both parallel and perpendicular to the $\mathbf{\text{ab}}$-plane. Whereas a clear upward curvature in $H_{c2}^{\parallel \mathbf{\text{c}}}$($T$) along $\mathbf{\text{H}}$$\parallel$$\mathbf{\text{c}}$ is observed with decreasing temperature, the $H_{c2}^{\parallel \mathbf{\text{ab}}}$($T$) along $\mathbf{\text{H}}$$\parallel$$\mathbf{\text{ab}}$ shows a flattening at low temperatures. The rapid increase of the $H_{c2}^{\parallel \mathbf{\text{c}}}$($T$) at low temperatures suggests that the superconductivity can be described by two dominating bands. The anisotropy parameter, ${\gamma }_H$ $\equiv$ $H_{c2}^{\parallel \mathbf{\text{ab}}}\mathrm{/}{H}_{c2}^{\parallel \mathbf{\text{c}}}$, is $\sim$7 close to $T_c$ and decreases considerably to $\sim$1 with decreasing temperature, showing rather weak anisotropy at low temperatures.