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Hexagonal ferrites do not only have enormous commercial impact ({\pounds}2billion/year in sales) due to applications that include ultra-high densitymemories, credit card stripes, magnetic bar codes, small motors and low-lossmicrowave devices, they also have fascinating magnetic and ferroelectricquantum properties at low temperatures. Here we report the results of tuningthe magnetic ordering temperature in PbFe$_{12-x}$Ga$_x$O$_{19}$ to zero bychemical substitution $x$. The phase transition boundary is found to vary as$T_N \sim (1-x/x_c)^{2/3}$ with $x_c$ very close to the calculated spinpercolation threshold which we determine by Monte Carlo simulations, indicatingthat the zero-temperature phase transition is geometrically driven. We findthat this produces a form of compositionally-tuned, insulating, ferrimagneticquantum criticality. Close to the zero temperature phase transition we observethe emergence of an electric-dipole glass induced by magneto-electric coupling.The strong frequency behaviour of the glass freezing temperature $T_m$ has aVogel-Fulcher dependence with $T_m$ finite, or suppressed below zero in thezero frequency limit, depending on composition $x$. These quantum-mechanicalproperties, along with the multiplicity of low-lying modes near to thezero-temperature phase transition, are likely to greatly extend applications ofhexaferrites into the realm of quantum and cryogenic technologies.

Quantum percolation phase transition and magneto-electric dipole glass in hexagonal ferrites