Uniaxial ferroelectric quantum criticality in multiferroic hexaferrites BaFe₁₂O₁₉ and SrFe₁₂O₁₉

BaFe₁₂O₁₉ is a popular M-type hexaferrite with a Néel temperature of 720 K and is of enormous commercial value ($3 billion/year). It is an incipient ferroelectric with an expected ferroelectric phase transition extrapolated to lie at 6 K but suppressed due to quantum fluctuations. The theory of quantum criticality for such uniaxial ferroelectrics predicts that the temperature dependence of the electric susceptibility χ diverges as 1/T³, in contrast to the 1/T² dependence found in pseudo-cubic materials such as SrTiO₃ or KTaO₃. In this paper we present evidence of the susceptibility varying as 1/T³, i.e. with a critical exponent γ = 3. In general γ = (d + z – 2)/z, where the dynamical exponent for a ferroelectric z = 1 and the dimension is increased by 1 from d_eff = 3 + z to d_eff = 4 + z due to the effect of long-range dipole interactions in uniaxial as opposed to multiaxial ferroelectrics. The electric susceptibility of the incipient ferroelectric SrFe₁₂O₁₉, which is slightly further from the quantum phase transition is also found to vary as 1/T³.