Quantum percolation phase transition and magnetoelectric dipole glass in hexagonal ferrites

Abstract

Hexagonal ferrites not only have enormous commercial impact (\textsterling{}2 billion/year in sales) due to applications that include ultrahigh-density memories, credit-card stripes, magnetic bar codes, small motors, and low-loss microwave devices, they also have fascinating magnetic and ferroelectric quantum properties at low temperatures. Here we report the results of tuning the magnetic ordering temperature in $\mathrm{PbF}{\mathrm{e}}_{12\ensuremath{-}x}\mathrm{G}{\mathrm{a}}_{x}{\mathrm{O}}_{19}$ to zero by chemical substitution $x$. The phase transition boundary is found to vary as ${T}_{N}\ensuremath{\sim}{(1\ensuremath{-}x/{x}_{c})}^{2/3}$ with ${x}_{c}$ very close to the calculated spin percolation threshold, which we determine by Monte Carlo simulations, indicating that the zero-temperature phase transition is geometrically driven. We find that this produces a form of compositionally tuned, insulating, ferrimagnetic quantum criticality. Close to the zero-temperature phase transition, we observe the emergence of an electric dipole glass induced by magnetoelectric coupling. The strong frequency behavior of the glass freezing temperature ${T}_{m}$ has a Vogel-Fulcher dependence with ${T}_{m}$ finite, or suppressed below zero in the zero-frequency limit, depending on composition $x$. These quantum-mechanical properties, along with the multiplicity of low-lying modes near the zero-temperature phase transition, are likely to greatly extend applications of hexaferrites into the realm of quantum and cryogenic technologies.