The most prominent feature of spin fluctuation in YBCO6+x system is the 41 meV resonance peak which appears below the Tc of the optimal sample. This feature (and strong spin fluctuation for all x values in this system) has been considered as an important experimental evidence for the magnetic interaction pairing of HTSCs although its role on the pairing interaction and the details of the mechanism of superconductivity are not still clear. In this study scientists from the USA and the UK have studied this resonance peak in YBCO system and presented an interesting relation of this peak and the specific heat in this system. Inelastic neutron scattering is used to study the frequency and wave vector dependent magnetic structure of YBCO6+x with x=0.6, 0.7, 0.8, 0.93 (Tc=62.7-92.5 K).
Results and discussion:
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In x=0.6 sample a resonance peak at 34 meV appears in the acoustic mode (in-phase magnetic fluctuation of the coupled CuO2 planes) of the local [∫dqxdqyχ"(ω,q)] magnetic susceptibility by reducing temperature which is the most important feature of this measurement (Fig. 1).
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Well below the resonance peak the magnetic scattering is suppressed and a true spin-gap is developed in the superconducting state, while above it there is a broad feature extending at least to 220 meV with a maximum around 75 meV (Fig. 1).
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The resonance peak also exist in the temperature above Tc at 75-150 K for x=0.6 (Fig. 2). By increasing the temperature it broadens and its intensity decreases and finally vanishes at 200 K.
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The onset of the resonance occurs at T* which almost coincides with the Tc in optimal doped and is larger of Tc for underdoped samples as 115±15 K for x=0.8 and 150±20 K for x=0.6. This temperature is comparable with the temperatures that the dρ(T)/dT (electrical resistivity) and the Cu nuclear 1/(T1T) relaxation rate reaches a broad maxima in this system, due to the formation of the pseudogap in this system.
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It is very interesting that the behavior of d<m2res>/dT versus the doping and temperature is very similar with the behavior of electronic part of the specific heat (Cel(x,T); Fig. 3D-E). <m2res>=(3h/4π2)∫dω χ”res(ω)/[1-exp(hω/kBT)] is the mean-squared (fluctuating) moment associated with the resonant part.
The authors have noticed this evidence as a track of the magnetic resonance fluctuation in the thermodynamics of the HTSCs. They have estimated the effect of the magnetic fluctuation on the thermodynamic properties of the HTSCs by calculating the dEJ/dT, where EJ is the exchange part of the simple t-J Hamiltonian. By some simple analytic calculation and considering the resonance peak as a dominant effect the following relation could be found:
CJres≈dEJres/dT=-(3hJ/8π2µ2B) d(∫dω χ”res(ω)/[1-exp(hω/kBT)])/dT
= -(J/2µ2B) d<m2res>/dT
By J=125±20 meV for x=0.6 the pattern of this calculation is comparable with the experimental results of the Cel(x,T). The difference of the calculated CJres and the experimental one could be reduced by considering the other parts of temperature dependence of the magnetic fluctuation, spin-gap and pseudogap, and the part related to the kinetic energy of the t-J Hamiltonian. Finally, this agreement suggests that a large part of the specific heat near Tc and its associated entropy are due to resonant spin fluctuation.
Ref.: P. Dai, H.A. Mook, S.M. Hayden, G. Aeppli, T.G. Perring, R.D. Hunt, F. Dogan, Science 284 (1999) 1344.
