Magnetic-field-induced quantum phase transition in multiferroic BiMn$_{2}$O$_{5}$

Multiferroic BiMn$_{2}$O$_{5}$ exhibits both antiferromagnetic and ferroelectric ordering below $\sim $40 K. We have systematically investigated the electric/magnetic phase of BiMn$_{2}$O$_{5}$ by magnetization (M), dielectric constant ($\varepsilon )$, electric polarization (P) and specific heat (C$_{p})$ measurements down to 0.6 K and magnetic field (H) up to 45 tesla. At 4 K, BiMn$_{2}$O$_{5}$ shows a single magnetic-field-induced transition near H$_{c}\sim $18 T as evidenced by a sharp increase in M. Interestingly, $\varepsilon $ vs H shows a sharp peak at H$_{c}$, of which magnitude systematically increases as critical temperature T$_{c}$ approaches proximity to 0 K. Furthermore, P changes its sign with increasing H from positive to negative near H$_{c}$ with no hysteresis. The trajectory of which above three transitions occur follows the scaling relation T$_{c}$(H)$\sim $(H-H$_{c})^{1/2}$. The shape of C$_{p}$ vs H curve indicates that this transition is 2$^{nd}$ order down to 0.6 K, consistent with the absence of hysteresis in M, $\varepsilon $, and P measurements. Temperature dependent $\varepsilon $ measurements under fixed H near H$_{c}$ reveal that $\varepsilon $ increases on cooling to 5 K and slightly decreases down to 0.6 K, as similarly observed in a quantum paraelectric SrTiO$_{3}$. All of these observations support an interesting possibility that BiMn$_{2}$O$_{5}$ can be the first system to exhibit quantum fluctuation of ferroelectricity tuned by magnetic field.