Exotic quantum magnetization process observed in the \{Cu$_3$\} triangular spin ring

We present a comprehensive set of pulsed field magnetization, ESR, and NMR measurements on the triangle spin ring system [Cu$_{3}$(H$_{2}$O)$_{3}(\alpha $-XW$_{9}$O$_{33})_{2}$]$^{12- }$(X=As, Sb). We observed half step magnetization and hysteresis loops for X=As in a fast sweeping magnetic field of $\sim $10$^{4}$T/s at 0.4 K. These features become less pronounced for X=Sb. A comparative ESR study of both compounds reveals that Dzyaloshinskii-Moriya (DM) interactions are weaker in X=Sb than X=As because of the size difference between the diamagnetic heteroatom X. This leads to a reduction of an anti-level crossing gap in X=Sb compared to X=As. This is consistent with the NMR results which show an appreciable peak of the spin-lattice relaxation rate 1/T$_{1}$ at anti-level crossing fields of 2 and 4.4 T only for X=Sb. Our work suggests that the dependence of half step magnetization on X in a nanocluster system arises from a delicate balance between the adiabatic magnetization and the relaxation rate, relying on DM interactions.