Magnetic resonant excitations in High-Tc superconductors

More than fifteen years after the high temperature superconductivity discovery, antiferromagnetic (AF) fluctuations pairing mechanism[1] is still highly controversial. However, inelastic neutron scattering (INS) measurements have successfully brought to light the existence of unusual AF excitations that develop below Tc and could be the hallmark of an unexpected spin-1 collective mode, tightly bound to the superconducting (SC) state. Whatever the role of that mode for superconductivity, it has to be derived from the same microscopic model used to discuss superconductivity. We here review its characteristic features in a few cuprates and discuss its possible origin in light of different theoretical models. In optimally doped YBa2Cu3O6+x (YBCO) (Tc=93 K) where it has been discovered [2] (Fig. 1.a), the spin excitation spectrum is dominated in the SC state by a sharp magnetic excitation at an energy of ∼40 meV and at the planar antiferromagnetic wave vector qAF = (π/a, π/a), the so-called magnetic resonance peak [2, 3, 4, 5]. Its intensity decreases with increasing temperature and vanishes steeply at Tc, without any significant shift of its characteristic energy Er. In the underdoped regime, Er monotonically decreases with decreasing hole concentration [6, 7] so that Er ≃ 5 kBTc (Fig. 2). Besides, it is possible to vary Tc without changing the carrier concentration through impurity substitutions of Cu in the CuO2 planes. This is the case in YBa2(Cu1−yNiy)3O7 (y=1%, Tc=80 K), where the magnetic resonance peak shifts to lower energy with a preserved Er/kBTc ratio (Fig. 1.b) [8]. In optimally doped Bi2Sr2CaCu2O8+δ (BSCO) (Tc=91 K), a similar magnetic resonance peak has been observed at 43 meV (Fig. 1.d) [9]. Furthermore, Er shifts down to 38 meV in the overdoped regime (Tc=80 K) [10], preserving a constant ratio with Tc: Er ≃ 5.4 kBTc (Fig. 2). Thus, whatever the hole doping, the energy position of the magnetic resonance peak always scales with Tc. In contrast to YBCO, where the resonance peak is resolution limited in energy, the resonance peak in BSCO exhibits an energy width of ∼13 meV. In addition, the momentum width of the excitation is twice broader . A similar energy and momentum broadening has been also reported inYBa2(Cu1−yNiy)3O7 [8] (Fig. 1.b) and can therefore be ascribed to disorder, such as impurities or inhomogeneities. Furthermore, the observation of a spatial distribution of the SC gap in Bi2Sr2CaCu2O8+δ by Scanning Tunneling Microscopy measurements [11] provides evidence in favor of an intrinsic disorder in this system. Further, the magnetic resonance peak has been observed in optimally doped Tl2Ba2CuO6+δ(Tc=90 K) at Er=47 meV (Fig. 1.c) [12]. This yields a ratio Er/kBTc ≃ 6 slightly larger than YBa2Cu3O6+x. Nevertheless, as in YBa2Cu3O7, the excitation is limited by the resolution in energy and displays a momentum width of 0.25 Å (half width at half maximum). Meanwhile, the energy integrated intensity of