Abstract
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 deff = 3 + z to deff = 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.
Highlights
Transition for BaFe12O19 at about 3.0 K. In this context it is important to note that SrFe12O19 and (Ba,Sr)Fe12O19 are n-type semiconductors[11] with bandgaps at approximately Eg = 0.63 eV and rather heavy electrons and holes: m(light e) = 5.4 me; m(heavy e) = 15.9 me; m(light h) = 10.2 me; m(heavy h) = 36.2 me and highly anisotropic conductivity, so it is important to discriminate between true ferroelectric hysteresis and leakage current artefacts
M-type hexaferrite single crystals were prepared by the flux method
The single-crystal x-ray diffraction (XRD) patterns at room temperature shown in Fig. 1c suggest that our samples are single-phase M-type with c = 23.18 Å for BaFe12O19 and 23.04 Å for SrFe12O19, respectively, agreeing with the original 1959 single-crystal value of Brixner[15,16]
Summary
Transition for BaFe12O19 at about 3.0 K. The proximity to the quantum critical point is evident from a rapidly rising dielectric susceptibility as the temperature is lowered and a soft A2u-symmetry q = 0 long wavelength phonon mode with a frequency that decreases to 42 cm−1 as T approaches zero[6]; we designate this frequency gap (minimum in the transverse-optical phonon frequency in the low temperature limit at q = 0) as Δ.
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