Uniaxial ferroelectric quantum criticality in multiferroic hexaferrites BaFe 12 O 19 and SrFe 12 O 19

BaFe 12 O 19 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/ T 3 , in contrast to the 1/ T 2 dependence found in pseudo-cubic materials such as SrTiO 3 or KTaO 3 . In this paper we present evidence of the susceptibility varying as 1/ T 3 , 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 SrFe 12 O 19 , which is slightly further from the quantum phase transition is also found to vary as 1/ T 3 .