ELSEVIER Physica B 199&200 11994) 330-332 PHYSICA Theoretical study of NMR-Ti- 1 on the basis of the extended t-J model Hiroshi Kohno*, Tetsufumi Tanamoto Hidetoshi Fukuyama Department of Physics. Faculty of Science. University o.I" Tokyo. 7-3-1 Bongo, Bunkyo-ku, Tokyo 113. Japan Abstract The Knight shift, K, and the relaxation rate, Ti- t of NMR is calculated in the slave-boson mean-field approximation based on the t-t'-J model. Comparison with the experimental results suggests that singlet formation is related to the drop in (T~ T)-~ rather than to that in K. Characteristic behaviours of spin fluctuations in high- T~ cuprates have been observed by NMR and neutron scattering. In particular, careful analyses [1] of NMR results have revealed two characteristic temperatures, Ts and TR, which are defined as temperatures where the Knight shift, K, and the rate R =(Tt T)-~ start to de- crease with decreasing temperature, respectively. While Ts and Te are located far above T,, the superconducting critical temperature, for samples in the low-doping (L-) region, the;,' are slightly above or coincide with T~ in the high-doping (H-) region. In this paper, we report calculated results for the NMR shift, K, and the rate, T~-~, in the extended t-J model which is given [2] by straint, b~b~ + ~.,f~J~'s = I. While J is assumed only for the neighbouring sites, t..~has a finite spatial extent with values, t {nearest neighbour) and t' (next-nearest neigh- bour). As explained in Ref. [2], we assume t/J = 4, t'/t = -1/6 for LSCO and t/J = 4, t'/t = -1/2 for YBCO. (Note that the present choice of parameters for YBCO is different from that adopted in Ref. [2], but reproduces similar Fermi surfaces.) We exploit the mean- field approximation (MFA) with order parameters, ~(.f~j,,)and * * (f~rfJ~) for the uniform (u-) and singlet (s-) RVB with the d~2_~2-symmetry, respectivel~ and loosen the local constraint to the global one. The (dimen- sionless) NMR shift, K, and the rate, (T~ T)-~, are cal- culated as i.j;3 (i,j) ~1) in the slave boson representation with holon (bO and spinon (f~) operators, supplemented by the local con- * Corresponding author. I Present address: Toshiba R&D Center, 1 Komukai Toshiba- cho, Saiwai-ku, Kawasaki 210, Japan. K = .I'Z( q --* O. f,_~ = 0). t'h ( 7"17"}- t = ~F(q) lira lm/'(q" ~,JI (3) q (,) ~ 0 (,9 with the dynamical spin susceptibility [3], z{q, to)= Xo (q, ~}/[I + Jtcosqx + cosq,.Jzo(q, co)] in RPA for the J-term in Eq. (I I, where "/.o{q, "~) is that of free spinons in the u- or s-RVB state. In Eq. ~3}, F [q) is the form factor. 0921-4526/94507.00 ~C) 1994 Elsevier Science B.V. All rights reserved SSDI 0921-4526193}E0282-L