Crossover to non-Fermi-liquid spin dynamics in cuprates

Abstract

The antiferromagnetic spin correlation function SQ, the staggered spin susceptibility χQ and the energy scale ωF L = SQ/χQ are studied numerically within the t-J model and the Hubbard model, as relevant to cuprates. It is shown that ωF L, related to the onset of the non-Fermi-liquid spin response at T > ωF L, is very low in the regime below the 'optimum' hole doping c h < c * h ∼ 0.16, while it shows a steep increase in the overdoped regime. A quantitative analysis of NMR spin-spin relaxation-rate 1/T2G for various cuprates reveals a similar behavior, indicating on a sharp, but continuous, crossover between a Fermi-liquid and a non-Fermiliquid behavior as a function of doping. PACS numbers: 71.27.+a, The understanding of the phase diagram of cuprates continues to exemplify one of the major theoretical and experimental challenges [1]. Besides superconductivity (SC) and antiferromagnetic (AFM) ordering, several regimes with distinct electronic properties have been identified within the normal metallic phase. The behavior of spin degrees of freedom, which are the subject of this paper, has been intensively studied using the inelastic neutron scattering (INS) [2,3] and NMR relaxation experiments [4]. They clearly reveal that in underdoped cuprates magnetic properties are not following the usual Fermi-liquid (FL) scenario within the metallic state above the SC transition T > T c .Within a normal FL one expects a dynamical spin susceptibility χ ′′ q (ω) to be T -independent at low T, ω. On the contrary, INS results show that q-integrated spin susceptibility exhibits in a broad range of ω and T an anomalous, but universal behavior χ ′′ L (ω) ∝ f (ω/T ), first established in La 2−x Sr x CuO 4 (LSCO) at low doping [3,5]. This behavior can be even followed to lowest T in YBaCu 3 O 6+x (YBCO), where T c has been suppressed by Zn doping [6]. At the same time, low-energy INS reveals at low T the saturation of the inverse AFM correlation length κ = 1/ξ, at least in YBCO [2] and in LSCO at low doping [3,5]. Anomalous T -dependence of 63 Cu NMR spin-lattice relaxation rate 1/T 1 and of the spin-spin relaxation rate 1/T 2G in underdoped cuprates is in general compatible with INS [4], in particularOn the other hand, cuprates at optimum doping and, moreover, in the overdoped regime show a strong reduction of the spin response at low energies ω. This is evident from the loss of INS intensity in the normal state (as well as in a weak resonant peak for T < T c ) and low NMR relaxation rates 1/T 1 , 1/T 2G . At the same time, NMR confirms the approach to the normal FL behavior, 1/(T 1 T ) ∼ const. and 1/T 2G ∼ const. [4]. There are other indications that the normal FL behavior is approached in the overdoped regime. Recently, the angle-resolved photoemission spectroscopy (ARPES) on BiSrCaCuO (BSCCO) system gave evidence for the existence of coherent electronic excitations for T < T X at higher doping [7], i.e., the FL-like phase is found in the normal state only in the overdoped regime where T X shows a steep increase with hole doping...

Magnetic Response of Nonmagnetic Impurities in Cuprates

“…The consequence is that the local magnetic response is an image of the anomalous staggered susceptibility in a homogeneous system. Consequently, the onset of a finite Kondo scale is related to the doping-driven crossover of the bulk spin dynamics from a non-Fermi-liquid spin dynamics to a Fermi-liquid one [16].In a homogeneous doped AFM the dynamical spin susceptibility q ! ÿhhS z q ; S z q ii !…”

Spin-fluctuation mechanism of superconductivity in cuprates

“…Equations involve the dynamical spin susceptibility which we consider as an input taken from the inelastic-neutron-scattering (INS) and NMRrelaxation experiments in cuprates. The analysis of these experiments [12] reveals that in the metallic state the AFM staggered susceptibility is strongly enhanced at the crossover from the overdoped (OD) regime to optimum (OP) doping and is increasing further in underdoped (UD) cuprates, while at the same time the corresponding spin-fluctuation energy scale is becoming very soft. Direct evidence for the latter is the appearance of the resonant magnetic mode [13,14] within the SC phase indicating that the AFM paramagnon mode can become even lower than the SC gap.…”

“…For UD, OP and OD regime, i.e., c h = 0.12, 0.17, 0.22, respectively, we use furtheron the following values: χ 0 Q t = 15.0, 4.0, 1.0, Γ 0 Q /t = 0.03, 0.1, 0.18 (appropriate at low T ), and κ = 0.5, 1.0, 1.2. It is evident, that in the UD regime the energy scale Γ 0 Q becomes very small (and consequently χ 0 Q ∝ 1/Γ 0 Q large, in spite of modest κ [12]), supported by a pronounced resonance mode [14]. We take into account also the T dependence, i.e., Γ Q (T ) ∼ Γ 0 Q + T [12], being significant only in the UD regime.…”

“…Although one can attempt to calculate them using the analogous framework [16], we use here the experimental input for cuprates. We refer to results of the recent analysis [12], where NMR T 2G relaxation and INS data were used to extract κ, χ 0 Q (T ) and Γ Q (T ) for various cuprates, ranging from the UD to the OD regime. For comparison with the t-J model, we use usual parameters t = 400 meV ∼ 4500 K, J = 0.3t.…”

Spin-fluctuation mechanism of superconductivity in cuprates

“…Although one can attempt to calculate them using the analogous framework, 21 we use here the experimental input for cuprates. We refer to results of the recent analysis, 17 where NMR T 2G relaxation and INS data were used to extract κ, χ 0 Q (T ) and Γ Q (T ) for various cuprates, ranging from the UD to the OD regime. For comparison with the t-J model, we use usual parameters t = 400 meV, J = 0.3t.…”