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We have determined the superconducting and magnetic properties of foursamples of Lu$_x$Zr$_{1-x}$B$_{12}$ ($x=0.04$, $0.07$, $0.17$, and $0.8$) usingmuon spin rotation ($\mu$SR) and magnetometry measurements. We observed astrong magnetic signal in both the $\mu$SR and magnetometry data in one sample($x=0.07$), likely caused by the formation of static moments of size $\approx1\,\mu_{\rm B}$ due to a clustering effect of the Lu$^{3+}$ ions. In all othersamples, we find only a small magnetic signal in the $\mu$SR data thought tooriginate from boron nuclei in the B$_{12}$ cages. The superconductivity isfound to evolve with $x$, with a decrease in $x$ resulting in an increase incritical temperature and a decrease of the penetration depth. Most remarkably,we find the formation of nodes in the superconducting gap for $x \leq 0.17$,providing a new example of an $s$-to-$d$-wave crossover in a superconductor.

Observation of a crossover from nodal to gapped superconductivity in Lu$_x$Zr$_{1-x}$B$_{12}$