Vortex Core Size in ${}^3$He-${}^4$He films with Monolayer Superfluid ${}^4$He

The superfluid transition of ${}^3$He-${}^4$He mixture films adsorbed on alumina powder is studied, with a ${}^4$He superfluid coverage near one layer. With up to 1.3 layers of ${}^3$He added, the transition becomes strongly broadened, indicating a linear increase in the vortex core size for ${}^3$He coverages below one layer. Annealing of the sample mixture at 4.2 K is found to be critically important in ensuring a homogeneous film across the porous substrate.