Magneto-elastic coupling in molecule-based materials: [Ru$_2$(O$_2$CMe)$_4$]$_3$[Cr(CN)$_6$] and Mn[N(CN)$_2$]$_2$*

We measured the infrared vibrational response of two prototypical molecule-based magnets, [Ru$_2$(O$_2$CMe)$_4$]$_3$[Cr(CN)$_6$] and Mn[N(CN)$_2$]$_2$. We find that both temperature and magnetic field driven transitions impact spin-lattice interactions in these materials. For instance, through the N\'eel transition, Cr--CN stretching and bending modes as well as Ru-O stretching mode in [Ru$_2$(O$_2$CMe)$_4$]$_3$[Cr(CN)$_6$] display sudden frequency shifts and a strong hysteresis that reveal local structure changes around Cr and Ru centers in response to magnetic ordering. On the other hand, the dicyanamide ligands in Mn[N(CN)$_2$]$_2$ display pronounced sensitivity to the 30 T magnetic quantum critical transition, in line with our calculations that point toward the importance of N--C--N and C--N--C angles for the mediation of Mn$\cdots$Mn spin exchange interactions.