Spin-gap and magnetic excitations in the cuprate superconductors

Physiea C 235-240 (1994) 1681-1682 North-Holland

PHYSICA

Spin-gap and magnetic excitations in the cuprate superconductors* (; S t e m m a n n . M Lavagna and C.Pdpin CEA. D6partement de la Recherche Fondamentale sur la Mat,6re Condens6e. SPSMS-MDN, 17, rue des Martyrs, 38054 Grenoble Cedex 9, France We have analysed the spin-excitation spectrum as observed by neutron and NMR expeqrnents In ]'Ba2Cu30~,+.~ in the frame of a bidimensional t-t'-J modal. Next-nearest neighbour hopping term t" is introduced m order to fit the shape of the Fermi surface revealed by photoemlssion Within the slave-boson approach, we study as well the d-wave superconducting state, as the singlet-RVB state which is expected to describe the normal phase of heavily-doped systems In the superconducting state, d-wave pairing leads to the predictmn of a resonance and a gap-structure in the spin-excitation spectrum, in good agremen! with neutron dzffractmn results for z = 1192 and x = 1.0 Our calculations show a smooth evolution of the speclrum from one phase to the other the value of the threshold of excitatmns E~ increases with doping, while the temperature T,, at which the spin-gap open~ regularly decreases, reaching Tc only in the overdoped regime Th~s very atypical combined variation of Eo and Tm wzth doping results of strong-correlation effects in presence of the reahstw band-structure considered here

Experimentally, it is well a d m i t t e d that while long range antiferromagnetic order is destroyed above z = 0.4 m YBa2Cua06+~,, the neutron scattering signal keeps its m a x i m u m of amplitude around the antfferromagnetlc wavevector (~ = (,% ,'r). At low temperatures, the magnetzc form factor S(Q,,,z) shows a depression of intensity when decreasing frequency, with a finite cutoff of order 50meV. A so-called pseudo-gap (or spin-gap) appears [1,2]. the value of which contmuously increases with doping ( EG = 4, 16.28 and 26meV at x = 0.51.0.69,0.92 and 1.0). This pseudo-gap persists above Tc for heavily-doped systems (x = 0.51, 0.69 and 0.92), up to a temperature scale Tm whxch decreases with doping. For overdoped systems (x = 1.0) the gap disappears lmmedmtely above Tc, as in usual superconductors. In addition to the existence of a pseudogap, a resonance appears m the superconducting phase in S(Q.oa) at ~o = 4 i r n e V (z = 0 92 or 1.0) for T = 5 K [1,3] This resonance is accompamed by an enhancement of the magnetzc correlation length m its vlmmty NMR results are consistent with the or)enmg of a pseudo-gap with the presence of a m a x i m u m of (T1T) -1 on 6aCu at a temperature Tm > Tc (with T m = Tc In overdoped

systems). In the weak-couphng hnut. we have studied ,n a previous paper [4] the superconducting ~tate with a d-~ave symmetr3 of the p a m n g parameter A0 The slriklng resemblance found between the spectrum o[ spin-excitations of the superconducting state m the weak-couphng: hnnt, and the spectrum expermu'ntall3 ,~Lser~ed m the normal phase of heax ~[3-doped %x,<,~,ns ~nc.'ted u~ 1o extend the d-wave pairing to the smglet-RVB state above To, in the strong couphng limit of the t - i "-,.] model In the slave-boson representauon, we can ~ rite the t-t'-J h a m d t o m a n as

*Supported by European Uztion under contract No ERB 4050 PL 920925. 0921-453a/94/$07 00 © 1994 - ElsevmrScmnce B V All nght~ reserved SSDI0921-4534(94)01407-8

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1 W,, ha~,, num~ rLcally solved the system of saddle-point equatlun.[5], and studmd the effect of d-wa~e pairing m both superconducting state, m whwh holon~ t, are partially condensed (T < TI3E), and H\'B state, m v,h~ch the first excited lexe!s arv occuprod (T > TBE) We have computed lhe spin susceptibility \ " (q', w) within this scheme mclud-

G Stemmann et al /Physwa C 235-240 (1994) 168i-1682

1682

mg RPA renormalization. The strong-coupling effects make themselves felt through the renormahsatton of the various parameter, entering the expression of the suscept~biht~ We have plotted m Fig.1 the frequency-dependence of \"(0",~) at T = 0 for two values of doping. Let us note the presence of a gap, the value of which increases w~th doping In addition, the overdoped case shows a resonance at higher frequency in agreement w~th the neutron diffracUon results th~s resonance is analyzed as a Kohn anomaly of the second kind in the Cooper channel

hawng included self-consistent effects contained in the strong-couphng limit in order ~o recover the decrease of 7;,~ w~th doping, experimentalb observed by neutron scattering experiments. We have also explored the q-dependence of the magnetic susceptibility ~"(0",,~0) 6o0 < < Ea). It is quite remarkable that the result predxets a peak in the signal around the antiferromagnetie wavevectot Q = Or, ,-r), accompamed by a characteristic enhancement of the magnetic correlation length around the resonance trequenc~

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REFERENCES \~," were able to eslabhsh the analytw exl>re.~,,ion of the ~pm-gap according to Ip

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J Ro.,,sat-Mlgnod, L P Regnaull. (' \'ettter, P Buffet J Y llenr~ (i Lapertot. PlDslca B 169 58 ( 1!)91 ) 2. P 'M (h'hrm~ J ,M franquada, (; Slnram, .I R I) ('oph'y.R W Erwm.M Salo,S ,~halllOtO Ph~,lh'~ B 11%~11 (1991) 3 lt.A Mook \I Yellural(; Aepph,T EMason, I. . ~...... . . ~....... . . . .p ; , , , n,,,.. ~,,~ . . . 70,3490 . . . (l'aoa~..,

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