Verwey transition in Fe${}_3$O${}_4$ at high pressure: quantum critical behavior at the onset of metallization

Abstract

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 $T_V\sim (1-p/p_c{)}^{\nu }$, with $\nu \sim 1/3$. The resistivity data shows a temperature dependence $\rho (T)={\rho }_0+A{T}^n$, 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.

5 pages, 5 figures