Spin-gap and magnetic excitations in the cuprate superconductors

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Spin-gap and magnetic excitations in the cuprate

superconductors

G Stemmann, M. Lavagna, C. Pépin

To cite this version:

G Stemmann, M. Lavagna, C. Pépin. Spin-gap and magnetic excitations in the cuprate

superconduc-tors. Physica C: Superconductivity, North-Holland, 1994, 235-240, pp.1681 - 1682.

�10.1016/0921-4534(94)92062-1�. �hal-01896260�

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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 F o n d a m e n t a l e 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 = 11 92 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 t h a t 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 ampli- tude a r o u n d the antfferromagnetlc wavevector (~ = (,% ,'r). At low t e m p e r a t u r e s , the magnetzc form factor

S(Q,,,z)

shows a depression of inten- sity when decreasing frequency, with a finite cut- off of order

50meV.

A so-called pseudo-gap (or spin-gap) appears [1,2]. the value of which con- t m u o u s l y 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 a n d 0.92), up to a temperature scale Tm whxch decreases with doping. For overdoped systems (x = 1.0) the gap disappears l m m e d m t e l y above

Tc, as

in usual superconductors. In addition to the existence of a pseudo- gap, a resonance appears m t h e 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 N M R 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 *Supported by European Uztion under contract No ERB 4050 PL 920925.

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 param- eter A0 The slriklng resemblance found between the spectrum o[ spin-excitations of the superconducting state m the weak-couphng: h n n t , and the spectrum expermu'ntall3 ,~Lser~ed m the normal phase of heax ~[3-doped %x,<,~,ns ~nc.'ted u~ 1o ex- tend 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

u

0,;}

1 W,, ha~,, num~ rL- cally 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 occu- prod (T >

TBE)

We have computed lhe spin susceptibility \ " (q', w) within this scheme mclud-

SSDI

0921-4534(94)01407-8

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

mg RPA renormalization. T h e strong-coupling effects make themselves felt through the renor- mahsatton of the various p a r a m e t e r , 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 agree- ment 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 wavevec-

tot Q = Or, ,-r), accompamed by a characteristic

enhancement of the magnetic correlation length

around the resonance trequenc~

2 . 5 2 '~' 1 . 5

¢?

1 0.5

o6

i . I , 10 2 0 3 0 40 $0

[meVl

l:m, ure [ Sp,.clral ~,.ighl \'((~.-,'0) ,,er,,u,, treqm,ncy ,.,, (a) overdoped ~,~',|('m', (b) hea~fl~- doped .',) b t e l l l b O0

%

0.75 0,5 0.2S 0 7 I " " " I .... • . I . , " " , - . . I " "~200 :' ... - ~ / 4 ~ 5 0 t ,.4

11 °

9 11 13 15 17 19 21 I p.l

[meVl

l:lgure 2 ('ombm('d ,~ar]at~on of the ~pm-gap

Ec;

and 7',,,. a:. a fun('t~on of th,' chelmcal potential

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

I p - ~ )._,

Flus resull enable.,, u.', to umh'r.,,land the char,~c-

lex l~t t( Increa,,,e of

E,,

'~ it h dOl)lng ('~en though ...k() decrease.,, In the n w a n w h i l e (,,('e FI~, 2) T h e

( , t l t l l l a l l O l l ' . . , ha~,e [)Cell a,'.., %(,11 [ ) l . l l s u e d a | h l l l l ~ '

lelllpi,ralur~, l'he ,,pln-gap I,, graduall~ filh,d Ill, aim lh(' re',onan(e d1.,,appear.,, when lhe lemper- alllre lllCreabe:., Fig 2 reporls Ill(' e\oiu|lOll ,,~llh (tol)mg of lhe leinperalure scale I,,, al ~lu('h lh(, gap opens "flus study s h o ~ the mq)urtauct ot

R E F E R E N C E S

1 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~.., 12A511~t(~I)

5 (',Si~,mmann (' Pdpm \1 l,a~agna, to be published m t'h~, th'~ B