Resolving the quantum criticality paradox in O-18 isotopic SrTiO3

Scott, J. F. and Pirc, R. and Levstik, A. and Filipic, C. and Blinc, R. (2006) Resolving the quantum criticality paradox in O-18 isotopic SrTiO3. Journal of Physics: Condensed Matter, 18. L205. DOI 10.1088/0953-8984/18/16/L01

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Abstract

Recently there has been considerable interest in the displacive ferroelectric phase transition near T = 28 K in O-18 isotopic strontium titanate. Special efforts have been made to combine the quantum criticality exponents α = −2 (2D) or −3 (3D), δ = 3, and γ = 2 with the thermodynamic inequalities of Rushbrooke, Griffiths, Widom et al, which become exact equalities under the hypothesis of scaling. In particular, these have led others to the inference that γ = 2.0 and β = 1.2 in SrTiO3. First we show that this is mathematically incorrect and explain why (quantum criticality is exact only at T = 0, whereas the thermodynamic (in)equalities are valid everywhere except T = 0). Second, we show that the inferred values strongly violate a new equality, γ−2β = ν(4−d−2η)>0, we derive from hyperscaling. Third, we show that the existing soft mode frequency data ω(T) from Takesada et al (2006 Phys. Rev. Lett. at press) yield above Tc (from the Lyddane–Sachs–Teller relationship) γ = 1.0. Fourth, we remeasure β from the polarization P(T) and find β = 0.50 ± 0.02. Fifth, we remeasure the electric susceptibility and find that it perfectly satisfies the Salje–Wruck–Thomas equation, which requires γ = 1.0. The important conclusions are: (a) O-18 SrTiO3 near Tc is mean-field; (b) the thermodynamic scaling equalities of Rushbrooke, Griffiths et al are mathematically incompatible with quantum criticality theory; (c) a new hyperscaling relationship makes β = 1.2 and β>γ/2 impossible.

Item Type: Article
Uncontrolled Keywords: 2006 AREP IA51 2006 P
Subjects: 03 - Mineral Sciences
Divisions: 03 - Mineral Sciences
Journal or Publication Title: Journal of Physics: Condensed Matter
Volume: 18
Page Range: L205
Identification Number: 10.1088/0953-8984/18/16/L01
Depositing User: Sarah Humbert
Date Deposited: 16 Feb 2009 13:03
Last Modified: 23 Jul 2013 10:08
URI: http://eprints.esc.cam.ac.uk/id/eprint/676

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