The order parameter entropy relation in some universal classes: experimental evidence

Abstract

The asymptotic behaviour near phase transitions can be suitably characterized by the scaling of ∆s/Q 2 with ǫ = 1 − T /T c , where ∆s is the excess entropy and Q is the order parameter. As ∆s is obtained by integration of the experimental excess specific heat of the transition ∆c, it displays little experimental noise so that the curve log(∆s/Q 2 ) versus log ǫ is better constrained than, say, log ∆c versus log ǫ. The behaviour of ∆s/Q 2 for different universality classes is presented and compared. In all cases, it clearly deviates from being a constant. The determination of this function can then be an effective method to distinguish asymptotic critical behaviour. For comparison, experimental data for three very different systems, Rb 2 CoF 4 , Rb 2 ZnCl 4 and SrTiO 3 , are analysed under this approach. In SrTiO 3 , the function ∆s/Q 2 does not deviate within experimental resolution from a straight line so that, although Q can be fitted with a non mean-field exponent, the data can be explained by a classical Landau mean-field behaviour. In contrast, the behaviour of ∆s/Q 2 for the antiferromagnetic transition in Rb 2 CoF 4 and the normal-incommensurate phase transition in Rb 2 ZnCl 4 is fully consistent with the asymptotic critical behaviour of the universality class corresponding to each case. This analysis supports, therefore, the claim that incommensurate phase transitions in general, and the A 2 BX 4 compounds in particular, in contrast with most structural phase transitions, have critical regions large enough to be observable.

Studies on magnetic properties of unique molecular magnet {[FeII(pyrazole)4]2[NbIV(CN)8]∙4H2O}n

“…The value of the effective magnetic moment μ eff and the saturation value M S which both were found between the limiting values for antiferromagnetic and ferromagnetic arrangement, may be explained by a non-collinear magnetic system. The value of γ=1.42±0.07 from the classical scaling agrees well with the 3D Heisenberg model (≈1.4 [3]). Also the result of the Kouvel-Fisher method points to this behaviour (γ=1.45±0.06).…”

“…Both the high value of χ ' ac and the low coercivity confirm the soft magnet behaviour. Classical scaling relation in the form: (3) was used to extract critical exponent γ from the ac susceptibility, figure 4. The obtained value of γ=1.42±0.07.…”

Critical behavior of the Mn2[Nb(CN)8] molecular magnet

“…For ν, one obtains 0.73(3), which is close to the value of 0.71(2) expected for (1) and the 3D Heisenberg model (2). 28 The values of exponents κ and κ were calculated for the first two entries using the relations given by Eqs. (16) and (18).…”

“…This crucial information can be combined with that gleaned from the complementary calorimetric measurement to further characterize the critical behavior. The critical laws for specific heat and order parameter imply the validity of a combined scaling of excess entropy and the square of order parameter 28 below the transition point T c :…”

“…These values are close to 0.26 and 1.31, respectively, predicted for the 3D Heisenberg model. 28 Using Eqs. (16) and (18) for α < 0 and the value of β = 0.38 (1) found in μSR experiment, one obtains κ = 0.24(2) and κ = 1.32 (3), which are both consistent with the values determined from the scaling analysis.…”