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Superconductivity in noncentrosymmetric LaNiC$_2$ is expected to be inducedby electron--phonon interactions due to its lack of magnetic instabilities. Thenon-Bardeen-Cooper-Schrieffer (BCS) behaviors found in this material call intoquestion the long-standing idea that relates unconventional superconductivitywith magnetic interactions. Here we report magnetic penetration-depthmeasurements in a high-purity single crystal of LaNiC$_2$ at pressures up to2.5 GPa and temperatures down to 0.04 K. At ambient pressure and below 0.5$T_c$the penetration depth goes as $T^4$ for the in-plane and $T^2$ for theout-of-plane component, firmly implying the existence of point nodes in theenergy gap and the unconventional character of this superconductor. The presentstudy also provides first evidence of magnetism in LaNiC$_2$ by unraveling apressure-induced antiferromagnetic phase inside the superconducting state attemperatures below 0.5 K, with a quantum critical point around ambientpressure. The results presented here maintain a solid base for the notion thatunconventional superconductivity only arises near magnetic order orfluctuations.

Unconventional superconductivity and an ambient-pressure magnetic quantum critical point in single-crystal LaNiC$_2$