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

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