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We present a $^{31}$P nuclear magnetic resonance (NMR) investigation ofBaCdVO(PO$_4$)$_2$ focusing on the nearly saturated regime between$\mu_0H_{c1}$ = 4.05 T and $\mu_0H_{c2}$ = 6.5 T, used to be considered as apromising candidate for a spin-nematic phase. NMR spectra establish the absenceof any dipolar order there, whereas the weak field dependence of themagnetization above $H_{c1}$ is accounted for by Dzyaloshinskii-Moriyainteraction terms. The low-energy spin dynamics (fluctuations), measured bynuclear spin-lattice relaxation rate ($T_1^{-1}$), confirms the continuity ofthis phase and the absence of any low-temperature phase transition.Unexpectedly, the spin dynamics above $H_{c1}$ is largely dominated bytwo-magnon processes, which is expected above the saturation field of aspin-nematic phase, but not inside. This shows that BaCdVO(PO$_4$)$_2$ isindeed close to a spin-nematic instability, however, this phase is notstabilized. We thus confirm recent theoretical predictions that thespin-nematic phase can be stabilized, at most, in an extremely narrow fieldrange close to saturation or is rather narrowly avoided [Jiang et al., Phys.Rev. Lett. 130, 116701 (2023)].

Narrowly avoided spin-nematic phase in BaCdVO(PO$_4$)$_2$: NMR evidence