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The EFG Analysis of La2CuO4 and YBa2Cu3O7 Based Superconductors
Ivan Kupčić, Slaven Barišić, Eduard Tutiš
To cite this version:
Ivan Kupčić, Slaven Barišić, Eduard Tutiš. The EFG Analysis of La2CuO4 and YBa2Cu3O7 Based Superconductors. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.2291-2297.
�10.1051/jp1:1996218�. �jpa-00247312�
The EFG Analysis of La2Cu04 and YBa2Cu307 Based
Superconductors
Ivan Kupéié (~.*), Slaven Bari§ié (~) and Eduard Tuti§ (~)
(~) Department of Physics, PCB 162, Faculty of Sciences, Zagreb, Croatia (~) Institute of Physics of the University, PCB 304, Zagreb, Croatia
(Received 30 August 1996, accepted 3 September 1996)
PACS.76.60.-k Nuclear magnetic resonance and relaxation PACS.74.72.Bk Y.based cuprates
PACS.î4.72.Dn La.based cuprates
Abstract. It is shown that the 3d~~?_~? orbital of the in-plane copper aud the 2pz apex oxygen orbital are absent at the Ferini level of La2-~Sr~Cu04, at variance with proposais giving
importance to copper-apex oxygen hybridization. At the in-plane oxygen site a sizable 2pz admixture is found at the Fermi le~~el of YBa2Cu307. The additional hales are shared among copper and oxygeu ~ites in similar proportions. This is shown compatible with the large Uà Emery model provided that the dilference between the p and d atomic energies is comparable
to the first neighbor overlap energy.
The symmetry of trie localized atomic orbitals which huila up valence bands in trie high-T~
superconductors (HTSC), and trie occupation of these orbitals by charge carriers, still attracts
great attention, m spite of numerous expenmental and theoretical studies of these topics carried out so far [1-10j. In finis respect, trie investigation of electric field gradients (EFG'S) V«a at
various nuclei in trie HTSC materais, and in particular at trie Cu and O sites m trie conducting planes, is of great interest. Trie local contributions of trie 3dz?-~? and 3d~z2-r; copper orbitals to trie EFG are of trie opposite sign, and by measuring trie change of trie EFG upon doping it is
possible to determine which of these two orbitals takes trie dominant part of trie excess charge
on copper, which was trie question raised in reference [loi. Similarly, trie admixture of trie
2p~(~) orbital to trie 2pa orbital of trie in-plane oxygen breaks trie umaxial symmetry of trie EFG and is thus subject to observation. Almost equally iniportant is trie study of trie charge
distribution (CD and trie resulting EFG on trie apex oxygen, since some theories attribute an important rote to trie 3d3z2-r2(Cu) 2p=(apex oxygen) hybridization.
In these studies, it is important to separate trie contribution to trie EFG of trie local charge
distribution (LCD). associated with trie partially filled orbitals at trie site considered. froin trie contributions of other sites in trie crystal lattice. This separation is achieved by using trie
well-known semiempiric Sternheimer expression
~~~ " Ii R)~ÎÎ~~' + 11 ~)vlitUce 11
(*) Author for correspondence le-mail: kupcic@phy.hr)
Q Les Éditions de Physique 1996
2292 JOURNAL DE PHYSIQUE I N°12
Equation (il was originally derived [11,12] for ionic insulators. ~j$~~~ and ~'jf~~~~ in equa- tion (1) are, respectively, the bare contribution of the LCD and of the surrounding lattice. R
arises from the polarization of the closed shells due to the presence of electrons or hales, addi- tional to those shells, on the considered site. As for ~, in general it is a tensor, which however tums into a scalar in two cases relevant to the present analysis. First, this occurs ~v.hen the ionic configuration in the crystal results from polarizing the closed shells of a free ion. E-g-,
this occurs on the in-plane O sites in La2Cu04 and YBa2Cu3Off when the CU-O hybridization
is neglected. Second, ~ is a scalar when there is a 4-fold symmetry axis at the considered site. This is easily understood on noting that bath ~[~ and Vjf~~~~ have to satisfy the Laplace equation. Such is the case at the CU site in HTT phase of La2-xSr~Cu04. The HTT/LTO
transition in this material is net expected to affect much the electronic spectra [14], and thus
~, in agreement with the NMR and NQR results [4,13,15]. A similar conclusion holds for the
buckling of Cu02 planes in YBa2Cu306. When the hybridization between ions is tumed on, its main effect on equation il is to replace the integer charges by fractional values. In particular,
this turns ~ into a teiisor on the in-plane O sites, but the estimated corrections to the scalar value of ~ amount to only a few percent, even in the doped materials. Such corrections con be
safely neglected and equation iii used in the high-T~ ionic conductors as well, with fractional charges affecting only the values of Vj$~~~ and Vjf~~~~
In Table I we give the results of the EFG analysis in Lai s5Sro
là Cu04. Ail approximations in
Dur paper are consistent with 1 in 10 accuracy in the hale distribution over the orbitals. Since the O-NMR measurements show that the EFG'S on the apex oxygen are independent of the strontium content (at least in the range between 0.075 and 0.24 [4,13], no 2pz apex oxygen orbitals in this material fait on the Fermi level. For the in-plane nuclei we indude in equation il), in the first step, only the a-orbitals (2p~-O(2), 2p~-O(3) and 3d~2_~2-Cu(2)), in agreement with the basic assumption of the Emery pd mortel for the HTSC materials in which only the in-plane a-orbitals play an active Yole [16]. The values of parameters used in the analysis are
determined as follo~vs. The bare local contribution 17j$~~~ at the 1-th crystal position, due to an orbital characterized by quantum numbers n,1 and ~, is calculated from the expression
n~ec([(1/r3)nj, where n~ is the number of holes on this orbital. Factors C)$ for orbitals relevant in the considered materials have the well-known values Cfj = -2C(j = -2C(j
=
4/5, and CÎ(?~~~ = -2CÎ[~~~?
= -2Cjj~~~~ = -4/7. We suppose that the parameters il/r3)ni, and especially their dependence on the effective charge of the considered ion, are
well descnbed by Sl~ter-type wave functions [lî]. The effective charges of nuclei, determining
these ~vave functions, are chosen to give Il/r~)
ni m accordance with those estimated from the
Knight shift analysis m YBa2Cu307 [2.3]. Further on, for factors R(Ol and R(Cu) we use the rounded theoretical values 0.1 and 0.2 [12]. This results in Il Ri Il/r3)
ni values approximately independent of the material. With one notable exception mentioned later, we calculate the bare lattice part in the point charge approximation, ~j["~~~
= ~~ q~(3R(~ R)1/R)j here q~
is the effective charge of the ion, and R~ is its position. The factor ~(Cu) is conveniently estimated by fitting the measured EFG at the in-chain CU nuclei in YBa2Cu306 [18] (this CU atom has a closed 3d shell, qcuji) " +1 and ~(Cu) m -5.24). On the contrary, the estimate of ~(O) is rather uncertain because ii is diliicult to distinguish between the lattice and the
local contribution at the O nudei. The value of ~(O) is chosen equal to -6, which explains consistently ail NMR and NQR spectra in La2-~Sr~Cu04 materais (Tab. I, Figs. 2 and 3).
The values ~[Ba) and ~(La) are estimated directly from the expenmental EFG. One obtains
respectively ~(Ba) = -59 and ~(La) = -81. Note that large values of ~ correspond, however,
to small iomc polanzabilities [12]. Finally, occupations of the a orbitals are fitted to the largest compouent of the EFG tensor ai each crystal site.
Table I. Estimated EFG'S (m umts of10~~ V/m~), effective charge of ions q~ and num- ber of haies m corresponding a-orbitais n~ for Lai.85Sro.15C~04 and YBa2 Cu307 mater~ais.
Elperimentai values gmen m parentheses for Lai.s5Sro_15Cu04 are from reference f~j and for YBa2Cu3 07 are frein Refs. (il (O nuciei) and /2j (CU nuciei). At trie sites where n~ # 0, trie
contnbutio~s il ~)Vj$"~~~ ta ~[~ are given m trie second TOM.
atom Îa Vbb Îc q~ (n~j
Lai 8ôSro.15Cu04
Cu(2) 6.96 (7.0) 6.96 (7.0) -13.92 (-14.0) 1.î02
-2.46 -2.46 4.92 [0.702]
O(2) î.45 (7.3) -4.39 (-5.0) -3.06 (-2.3) -1.816
2.69 -2.01 -0.68 [0.184]
La ~ 8.25 8.25 -16.50 2.925
O(1) -1.04 (-1.0) -1.04 (-1.0) 2.07 (2.0) -1.960
-0.54 -0.54 1.07 [0.04j
YBa2Cu307
Cu(2) 5.85 (6.2) 6.58 (6.2) -12.43 (-12.4) 1.64
-2.71 -1.99 4.70 [0.64]
O(2) 10.35 (10.5) -4.66 (-6.3) -5.69 (-4.1) -1.72
2.9î -0.9î 2.00 [0.28]
O(3) -4.23 (-6.3) 9.63 (10.2) -5.40 (-3.9) -1.72
-0.54 2.24 -1.70 [0.28]
Ba ~ -8.50 0.55 7.95 2.00
O(1) -4.34 (-4.0) -6.02 (-7.6) 10.36 [11.6) -1.71
-0.52 -2.19 2.71 [0.29]
Cu(1) -6.59 (-7.4) 4.71 (7.5) 1.88 (0.0) 1.54
7.76 -2.47 -5.29 [0.54]
O(4) -7.17 (-5.1) 16.96 (17.3) -9.79 (-12.1) -1.52
-0.58 3.7î -3.19 [0.48j
~~ ~ 0.065 ù-II -0.lis 3.00
~ In the calculation of the Vj$~~~~~ contributions, the spatially averaged charge on La sites is used to
msure the charge neutrality of the system, (n~ = o). In reference [22] ic
= + 16.7 X lo~~ V/m~ at La
site m La2-~Sr~Cu04, x < o.08, is reported.
~ We take that the expenmental values from reference [23] correspond approximately to the antisym-
metric EFG tensor with values (-8.7, o, 8.7), (n~ = o).
~ We give here only the bare Iattice contribution, because there
is no 1 > 1/2 Y nuclei, (n~ = o).
An overall numencal agreement between the measured and calculated values of V~~ is Db- tained in this way, except ai the m-chain Cu[1) position of YBa2Cu307. where the description
of ~ by a scalar is presumably toc crude, because there is no 4-fold symmetry mxis at this
2294 JOURNAL DE PHYSIQUE I N°12
site. However, due to a large number of fitting parameters, this agreement may net be very convincing and we are led therefore to qualitative considerations.
First, our analysis shows undeniably that the electronic mortel used at the O(2) site of
YBa2Cu307 requires qualitative corrections, which is net the case in La2-~Sr~Cu04. This is best seen by considering the quantity ~'
= (V~~ Vbbl/Îa. According to Table I its ex-
perimental values in Lai.85Sro_iôCu04 and YBa2Cu307 are q' m 0A and ~' m 0.2, while the
corresponding mortel predictions are $ 1 0.2 and ~' m -0.1. In order to understand this
discrepancy, it should be noted that due to the a-axis uniaxial symmetry of the 2pa orbital at the O(21 site, the LCD contribution cancels ont in the numerator of ~'. The sign of ~' is thus
entirely determined by the lattice contribution in the considered electronic mortel. $ was there- fore recalculated in YBa2Cu307 beyond the point charge approximation, using the spread-eut charge distributions on the sites in the neighborhood of O(2), but it remained negative. This
can be remedied by noting that the crystal field in the z-direction admixes the 2pz orbital to the wave function ai the O(2) site of YBa2Cu307, thus breaking the a-axis uniaxial symmetry of the LCD contribution to V~~ and making ~' positive. The estimated occupation of the 2pz
orbital is somewhat less than ù-1 hales (compared to n2pa G3 0.3). This agrees qnalitatively
with the results of band calculations of EFG, reported by Schwarz et ai. [5]. In contrast to
that, in Lai 8ôSro.iôCu04 the conducting plane is the mitron symmetry plane, the crystal field
m the z-direction is absent, and therefore there is no 2pz admixture at the O(2) site.
Furthermore, ouf analysis shows that bonds neon the Fermi level of YBa2Cu307, which correspond to the oui-of-plane atoms, consist predominantly of 3d~2-=2-Cu(1), 2pz-O(apex oxygen) and 2p~-O(4) orbitals, verifying the bond structure results of Massidda et ai. [19].
In terms of CD, this means that the two hales pet unit cell, generated by putting an oxygen
atom on the O(4) position, remain mostly attached to the eut-of-plane sites, leading to a fractional population of the 2pz-O(1) orbital comparable to the population of the two in-plane 2pa orbitals (à m 0.2). Unfortunately, the doping dependence of ~[~ on O-sites is not available for this family of materais. On the other hand, there are some data for the Cu(2) site, but they hâve been obtained by different authors on samples from different batches, and cannot
therefore be compared in a meaningful way. Thus, the important question of Cu[2) apex O
hybridization remains open m YBa2Bu307, which brings us to the La2-~Sr~Cu04 compounds.
Actually, the descnbed corrections to the Emery mortel of YBa2Bu307 illustrate well the accuracy of ouf approach and allow us to take the main qualitative result of the present analysis
more confidently, namely to assert that no 3d3z2-r2 states at the Cu site of La2-xSr~Cu04
occur at the Fermi level. The argument is again based on symmetry-sign considerations.
Table II. Distribution of trie additionai hale in YBa2Cu307 (~hpd QS 2tpd) and La2Cu04 (/hpd G3 3tpd) based materials. ô is trie doping of the plane obtained in EFG analysis. In
YBa2Cu3 Off ~d là obtamed using the ezper~mental EFG (18j, whùe np foiiows alter trie as- sumption that à
= 0.
~ ~ ~add ~add à
P d
p d
YBa2Cu306 0.225 0.55 ù-o
YBa2Cu307 0.28 0.64 27.5~ 45~ 0.2
Lai.8ôSro.iôCu04 0.184 0.î02 0.07
Lai.76Sro.24Cu04 0.2275 0.715 43.5 ~ 13 ~ 0.17
à = 0.2 t~~ = i-o 0.80
n
~ n
~
°.6° ~'~~
t~~ = .0
°.~~
A~~ = 3.0
~~~0.0 0.2 0.4
ô 0.40
1-o 2.0 3.0 4.0 5.0 6.0
A~j
Fig. 1. The dependence of nd on energy dioEerence àpd (main figure) and doping à (msert) in the
regime of parameters which is appropriate to the La2Cu04 based materials.
Figure 2 shows that the 63vQ resonant frequency increases steeply upon doping. On the other hand, 6~vQ is proportional to Vzz (see caption of Fig. 2). Assuming that beside the 3d~2-~>
there is a 3d3z2-r2 contribution at the Fermi level, we find that the corresponding variation of l§z upon doping is proportional to the variation of the difference n(3d~2-y2 n(3d3z>-r2
m occupation of those two d-states, because their C)[ factors (defined above) are equal in
magnitude but opposite in sign. At the same time the lattice contribution approximately
cancels eut in trie variation of l§z. The mcrease of 6~vQ is therefore consistent only with the
excess charge going primarily to the 3d~2_~2 state, contrary to the recent proposai [loi that
the excess charge on Cu is small and its change with doping mostly associated with the change
of the 3d3z2-r2 occupation. If this latter assumption were true, 6~vQ would decrease slowly
upon doping.
Dur discussion of equation il and the associated experimental results shows that the Emery model takes mto account ail quahtatively important tight-binding states. The question which nevertheless remains is, whether the EFG results can be reconciled with the large Ud assump- tion of this model. Actually, Table II (derived from Tab. I and Figs, 2, 3) sho~vs that the holes doped into the Cu02 planes are shared in nearly equal proportions by Cu and each of O
ions, which may seem to contradict the large Ud assumption. This last question is therefore
exammed by starting from the Hamiltonian [20,21]
~ ~~~~~ ~ ~~ ~ ~~~~ ~~~~~"~~~" ~ ~~P l~)PlsaPysa
~~~~ ~ ~ l~)fia/saj + ~
(b~ 1)
~~
+ ~j btô [(plw +p[~a) fs+ôa + fia lP~s+ôa +Pys+ôa)j 12j
~aô
The Hamiltoman (?) is the result of the saddle point approximation m the slave boson approach
to the large Coulomb repulsion on the in-plane Cu site (Ud ~ co) in the Emery model. and b
are auxiliary fields which have to be optimized by mmimization of the related thermodynamic
2296 JOURNAL DE PHYSIQUE I N°12
41 .0 ~pd " .°
39.0
§ ,
37.0
~
~ A
~~ 35.0 ~~
0.2
33.0 ~~
O.O 0.2 0.4
x
~~'i.05 O.15 0.25 0.35 0.45
x (Sr content)
Fig. 2. The calculated dependence of the ~~vQ frequency on x (fuit Iine), compared with the
frequencies of the main ~~Cu-NQR signal (filled triangles secondary signal, to be discussed elsewhere
is not shown) measured in La2_~Sr~Cu04, reference [15]. [For ~~vQ gwen m àlHz units and ir[z in 10~~ V/m~ holds ~~vQ = 2.55 i[z.) Insert of figure shows relation à to x.
t~~ = 1.o
A~~ = 3.0
( O.g
j
~~
0.7
x (Sr
content)
Fig. 3. The calculated dependence of the ~~vaa frequency on x (fuit fine). [~~v~a = o.0943 Vaal Experimental values for La2-~Sr~Cu04 (filled diamondsl are from references [4,13].
potential fl [21]. The results are dependent only on two parameters: doping of the conducting planes à, and the energy diiference ~hpd between the 2pa and 3d~2-~> levels (/hpd " Ep Ed ),
measured in terms of the pd overlap energy tpd Since the nearest neighbor Coulomb interaction is not included explicitly, ouf /hpd should be taken as an effective value, which takes its eifect
into account [loi. Since trie EFG'S are nearly independent on the temperature, we solve the related equations, ôfl/ôb
= 0, ôfl/ôà
= o, -ôfl/ô~
= Nil + à), at T
= 0, for simplicity. In
Figure 1 we sho~v ho~v the CD, described in terms of the number of holes on the 3d~2-~>-Cu
orbital (nd), depends on two relevant parameters of the mortel, for two special cases, à = 0.2
and uhpd " 3.0tpd. The most pronounced qualitative result is the saturation of nd with respect
to the changes of à or /hpd, already for not too large à and /hpd. Such saturation is a direct consequence of a large Ud.
In Figures 2 and 3 we compare the results of this theoretical calculation with the measured NMR and NQR spectra in La2-~Sr~Cu04 materials. For ~(Cu)
= -5.24 the dependence of the frequency of the main Cu6~-NQR signal (filled triangles m Fig. 2 [15]) on z is descI.ibed well by /hpd G3 3tpd. /hpd = 3tpd leads further to the estimate of the Sternheimer factor
~(O) m -6 (Fig. 3). Linear dependences of both resonant frequencies ~~vzz and 6~vQ on z
confirm qualitatively the picture of doping of the conducting planes by holes, which is obtained
m the hmit Ud ~ co. Namely, in the considered regime of parameters of the Hamiltonian (2),
holes doped into the conducting planes go on the Cu and O sites in nearly equal proportions.
This shows that the Emery model with large Ud is entirely consistent with EFG measurements,
assuming that trie bare bond splittings and bond widths are of the same order of magnitude.
Acknowledgments
We are grateful to V.J. Emery for calhng ouf attention to reference [loi.
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