Dramatic changes in the magnetic excitation spectrum by going to the superconducting state of HTSCs, known as the “resonance” peak, have been considered as a strong evidence for the magnetic pairing mechanism of superconductivity in these systems. The resonance peak occurs at Eres=41 and 34 meV [at q=(0.5, 0.5) in the CuO2 reciprocal lattice units (rlu)] respectively for optimal doped YBCO6..93 and underdoped YBCO6.6, and below the Eres the peaks are formed at the incommensurate positions (0.5±δ,0.5) and (0.5±δ,0.5), δ≈0.105 for YBCO6.6. It is difficult to believe the resonance peak as the only origin of the electron pairing because it has only small part of the total spectral magnetic weight. To know about higher-energy excitations, a group of scientists from the UK and the US have measured the energy and momentum dependence of the spin fluctuation by neutron scattering measurements in different temperature and energy (E>Eres) in YBCO6.6 (Tc=62.7 K, Eres=34 meV).
Their most important results summarized as:
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At E=85 meV, there is a single peak at T=300 K centered at q=(0.5,0.5) but with decreasing the temperature a quartet of peaks is formed at Qε=(0.5±ε,0.5±ε) and (0.5±ε,0.5-±ε), with ε=0.12±0.01 rlu (Fig. 1a-c). These peaks have different characteristic with the low energy incommensurate peaks, because they are rotated by 45 degree relative to low energy peaks (0.5±δ,0.5). The coherency of excitations develops in temperature between 300 and Tc which could be related to the pseudogap temperature.
- By reducing the temperature to 66 K (Tc+3.3 K), the magnetic response becomes strong near (0.5,0.5) and Eres=34 meV, and then (T=10 K) the resonance becoming stronger and incommensurate peaks are developed below Eres (Fig.1 g-i). In contrast, the high-energy incommensurate peaks are fully developed at Tc. Both the low-energy and the high-energy incommensurate peaks develop through a loss of spectral weight near (0.5,0.5) and at their respective energies as the temperature is lowered.
- There is a square structure with the vertices of the square pointing along the (110) and (1-10) directions in the E=66-105 meV region (Fig. 2a-q). The incommensurate peaks are most developed in the 70-90 meV energy range. These data rule out a spin-wave like dispersion for higher-energy excitations, because we expect the continuous rings of scattering at the constant energy (rather than square shape in this study) for a spin-wave.
- The value of <m2> has been derived to be 0.12±0.02 μ2B/f.u. (formula unit) for the resonance and sub-resonance structure (24<E<44 meV) and 0.26±0.05 μ2B/f.u. for high energy scattering (60<E<120 meV). The significantly greater contribution (~<m2>) of the higher-energy excitation to the total fluctuating moment than the resonance structure, these excitations should be considered in a magnetically mediated pairing mechanism of HTSCs.
The authors have discussed that existence of the similar pattern for high energy magnetic excitations in La1.875Ba0.125CuO4 indicates a universality of this phenomenon for HTSCs compounds. Candidates for the common origin of this phenomenon include an incipient spin-charge separation leading to unidirectional stripes and the underlying electronic structure.
Ref.: S.M. Hayden, H.A. Mook, P. Dai, T.G. Perring & F. Dogan; Nature 429 (2004) 531.
