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Verwey transition in Fe$_{3}$O$_{4}$ at high pressure: quantum critical behavior at the onset of metallization

We provide evidence for the existence of a {\em quantum critical point} at the metallization of magnetite Fe$_{3}$O$_{4}$ at an applied pressure of $p_{c} \approx 8$ GPa. We show that the present ac magnetic susceptibility data support earlier resistivity data. The Verwey temperature scales with pressure $T_{V}\sim (1-p/p_{c})^ν$, with $ν\sim 1/3$. The resistivity data shows a temperature dependence $ρ(T)=ρ_{0}+AT^{n}$, with $n\simeq 3$ above and 2.5 at the critical pressure, respectively. This difference in $n$ with pressure is a sign of critical behavior at $p_{c}$. The magnetic susceptibility is smooth near the critical pressure, both at the Verwey transition and near the ferroelectric anomaly. A comparison with the critical behavior observed in the Mott-Hubbard and related systems is made.