Physica C 235-240 (1994) 2191-2192 North-Holland PP]YSiCA

Comparison of two sets of parameters for multi-band Hubbard models of high-Tc compounds using ferro-antiferro mixed phases in spin disordered configurations*

G e r a r d o M a r t f n e z ~'

alnstituto de Fisica,'Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre, Brasil

We compare two sets of parameters proposed in the literature for the multi-band Hubbard model of high-Tc materials, one obtained by finite cluster analyses and other with band theory calculations. The comparison is done using a configuration mixing of ferro and antiferromagnetic Cu-Cu bonds in mean-field alloy theory. Both sets give qualitatively different results concerning the magnetic phases close to half-filling. A spin disordered phase is obtained upon doping with holes. Nevertheless, quantities fike magnetic moments and charge transfers are rather different reflecting the difference of density of states close to the Fermi level in both cases.

There has recently been put much attention in correctly describing the magnetic phases close to the half-filled situation in the high-To com- pounds. It seems that an accurate description of the low-energy excitations is essential for un- derstanding such remarkable materials. A well known model for dealing with the electronic structure of the CuO2 planes in the prototypi- cal lanthanum cuprate 214 superconductor is the mult i-band Hubbard model, proposed by Emery [1]. The Emery model is written as

H = E E dp t + H.c.) + b p + (ij) ~ (ij)

t j j ,(pjapj, a -b -1- ~p P (jj') ¢' j,,,

P P it (1) Up E nj tn j l + ¢d E n~z + Ua E naiT na j i ,a i

where ~he Cu sites i form a square lattice with the O sites j at the bridges between the Cu atoms. They include Cu-3d and O-2p orbitals, respec- tively. In this work we make a comparison of two independently proposed sets of parameters for this model, one obtained by finite cluster anal- yses [2] and other by using local density approxi- mation of band theory calculations [3]. We apply

"Work financed by CNPq (Brasil).

a model calculation [4] where the antiferromag- netic order is destroyed by a spin disordered phase at a small doping. We define an order parameter p which counts the balance of ferro and antifer- romagnetic Cu-Cu bonds of the doped system. Introducing two sublattices A and B, the local propagator Io~ Cu-atom orbitals in sublattice A is given by tt:e following expression

G A ~ ( ~ , ) = p G A A ( ~ ) + ( 1 - - R ) G A ~ ( ~ ') (2)

where the 'bond' propagators G AA and Gd %B are defined in [4]. They describe a configuration where nearest neighbor Cu-atoms are ferromag- netic aligned (G AA) or antiferromagnetic aligned (GAB). A similar expression run for G~,~(w). Eq. (2) represents thus a mixture of configurations whose parameter p must be found by minimiz- ing the total energy for different dopant concen- trations. The propagators were obtained in a Bethe lattice for a Hartree-Fock decoupling of the namH~outo.n terms Ud and rr ~,. p~ .... ~,.¢

selected were taken from the work of Tjeng-Eskes- Sawatsky [2]: t ap = 1.47 eV, cp - ea = 2.5 eV, Ud = 9.7 eV, Up = 5.7 eV: and from the work of I-Iybertsen-Schl/iter-Christiansen [3]: t ap = 1.30 eV, ep - ¢ d = 3.6 eV, Ud = 10.5 eV, Up = 4.0 eV. In both cases we took tPP = Udp = 0. We believe that this restriction would not affect the main conclusions of this work.

The results in Figs. ! and 2 show that at half-

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2 1 9 2 G. Martinez/Physica C 235-240 (1994) 2191-2192

filling (6 = 0) there is perfect antiferromagnetic alignement since the minima lie at p = 0 for both sets. When we dope with holes the order param- eter is different from zero, giving rise to a dis- ordered configuration where the long range AF order is lost on the average. The destroy of AF or- der happens more quickly for LDA than for TES parameters as is shown in Fig. 2. This may be a combination of two things like a larger charge transfer energy cp-¢d and a larger ratio Ud/tpd in

i ETO r (p ) - ETO T (o1 [ e V ] 012 " o.,oLt /

0.08 ~- 5:0

0.06

/ o.o, / / .-

6:0.25

-o.o2 ! L - " T ' - T - - , 5:o. , t ' [ ~ ! ,

-o .o~ c ' '

i _-z-

0 0.I 0.2 0.3 0.4 0.5 0.6 p

(a)

I E r o r l P i - E r o r ( O l [eVl OtO - -

0.08 - / 5:0

' 3 0 6 - /

0 . 0 4 5 : 0 . 0 5

o L

0

- 0 . 0 2

-0.04 0.25

-oo6 F- I t , 6

I / I . . . . ',

0 0.I 0.2 0.3 0/. 05 O.d p

(b)

Figure 1. Total energy as a function of the order parameter p for different hole doping 6 using (a) TES parameters [2] and (b) LDA parameters [3]. Arrows indicate the equilibrium values of p.

.20 L

.~ . :5

m

; 1 0 :0 '

~ .05

L

/ / . . , F ' J ~ ' ' ' ' I ; ' ' , : I

.05 .~0 .15

dopant concentration

Figure 2. Order parameter p at the minima in Fig. 1 (a) and (b) as a function of hole dopant concentration 6.

the LDA parameters. Both situations contribute to a larger AF gap at half-filling and to narrow bands close to the Fermi level. The magnetic mo- ments obtained a r e m T E S - - ( n f - n d)~ - 0 . 6 ~ B

and m L D A - - 0.81 /~B- They are reduced by 20% when doping with holes. Charge goes mainly to oxygen sites in a proportion of 70% to 80% for both parameters, respectively.

In conclusion, we got a spin disordered phase using both sets of parameters in the Emery model when doping with holes. To answer if this is biased by the Hartree-Fock approximation some calculations of second-order self-energy correc- tions in Ua are in progress [5].

Refe rences

1. V.J . Emery, Phys. Rev. Lett. 58 (1987) 2794. 2. L. H. Tjeng, H. Eskes, and G. A. Sawatsky,

in Strong Correlation and Superconductivity, Springer Series of Solid State and Sciences, vol. 89 (1989), p. 33.

3. M.S. Hybertsen, M. Schliiter, and N.E. Chris- tiansen, Phys. Rev. B 39 (1989) 9028.

4. F. Yndurain and G. Martinez, Phys. Rev. B 43 (1991) 3691.

5. G. Martinez, J. R. Iglesias, and E. V. Anda, Physica B 199&200 (1994) 341.