  Although superconductivity in the vicinity of antiferromagnetic (AFM)
instability has been extensively explored in the last three decades or so,
superconductivity in compounds with a background of ferromagnetic (FM) spin
fluctuations is still rare. We report 75As nuclear quadrupole resonance
measurements on the A2Cr3As3 family, which is the first group of Cr-based
superconductors at ambient pressure, with A being alkali elements. From the
temperature dependence of the spin-lattice relaxation rate (1/T1), we find that
by changing A in the order of A=Na, Na0.75K0.25, K, and Rb, the system is tuned
to approach a FM quantum critical point (QCP). This may be ascribed to the
Cr2-As2-Cr2 bond angle that decreases towards 90 degrees, which enhances the FM
interaction via the Cr2-As2-Cr2 path. Upon moving away from the QCP, the
superconducting transition temperature Tsc increases progressively up to 8.0 K
in Na2Cr3As3, which is in sharp contrast to the AFM case where Tsc usually
shows a maximum around a QCP. The 1/T1 decreases rapidly below Tsc with no
Hebel-Slichter peak, and ubiquitously follows a T5 variation below a
characteristic temperature T*=0.6 Tsc, which indicates the existence of point
nodes in the superconducting gap function commonly in the family. These results
suggest that the A2Cr3As3 family is a possible solid-state analog of superfluid
3He.
