Plasma frequency determination in YBa2Cu3O6+x as a function of oxygen content

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Plasma frequency determination in YBa2Cu3O6+x as a function of oxygen content

N. Bontemps, D. Fournier, A.C. Boccara, P. Monod, H. Alloul, J. Arabski, G.

Deutscher

To cite this version:

N. Bontemps, D. Fournier, A.C. Boccara, P. Monod, H. Alloul, et al.. Plasma frequency determination in YBa2Cu3O6+x as a function of oxygen content. Journal de Physique, 1989, 50 (18), pp.2895-2901.

�10.1051/jphys:0198900500180289500�. �jpa-00211110�

Plasma frequency determination in YBa2Cu3O6 + x

^{as a}

^function

of _oxygen content

N. Bontemps

(1),

^{D. Fournier}

(1),

A. C. Boccara

(1),

^{P. Monod}

(2),

^{H. Alloul}

(2),

J. Arabski

(2)

and G. Deutscher

(3)

(1) Laboratoire d’Optique Physique, ^{ESPCI, 10 rue} Vauquelin, 75231 Paris Cedex 05, ^France (2) Laboratoire de Physique ^des Solides, Université Paris-Sud, 91405 Orsay Cedex, ^France

(3) ^{School of} Physics ^and Astronomy, ^Tel-Aviv University, ^Ramat Aviv, ^Tel Aviv, ^Israël (Reçu le 23 mai 1989, révisé le 15 juin 1989, accepté ^{le 16} juin 1989)

Résumé. ²⁰¹⁴ La réflectivité optique ^{d’un ensemble de} céramiques polycrystallines ^de YBa2Cu3O6+x a été mesurée dans la gamme 0,5-1,5 ^eV pour 0 x 1. Nous proposons ^une

analyse détaillée de l’effet de l’anisotropie ^{de la constante} diélectrique pour calculer le spectre ^de réflexion d’un échantillon polycristallin ^et le comparer ^{à un} monocristal. Nous avons déterminé la

fréquence ^de plasma afin d’en tirer la densité des porteurs ^{dans le} plan (a, b). ^{Nous trouvons} que contrairement à la variation de la susceptibilité de Pauli obtenue à partir de celle du déplacement

de Knight ^de Y89 (qui diminue fortement entre x = 1 et x ⁼ 0,5) la densité des porteurs ^décroit seulement de 5,8 ^x 1021 cm-3 pour x = 1 ^à 3,2 1021 cm-3 _{pour x} ⁼ 0,5.

Abstract. ²⁰¹⁴ We have measured the optical reflectivity ^{of a set of} YBa2Cu3O6+x polycrystalline samples ^{for 0 x} 1. We have worked out a rigorous approach ^{of the} anisotropy ^{in order to} compute ^the reflectivity spectrum ^{of a} polycrystalline sample compared ^{to the} single crystal. ^We

have focused our analysis ^on the search of the plasma frequency, ^{hence the} density ^of carriers, in the copper-oxygen planes. ^{We find} that, ^{in contrast} with the Pauli susceptibility, ^{as revealed} by

the variation of the Knightshift ^of Y89, ^which drops sharply ^{between x = 1 and x = 0.5, the} density of free carriers decreases from 5.8 x 1021 cm-3 for x = 1 to 3.2 1021 cm-3 for

x ⁼ 0.5.

Classification

Physics ^Abstracts

78.20D ^- 78.30E ^- 72.30 ^- 74.70V

The basic microscopic information contained in the optical conductivity ^{in the} complex

dielectric function of the high Tc superconductors ^has stimulated ^a large ^amount of work. The

optical reflectivity has been measured on single crystals

[1, 3],

thin films

[4],

plain

[5, 6]

^and

textured

[7]

ceramics of

YBa2CU307

^or La1-xSrxCu04

[8].

^Of prime importance ^{are the}

measurements performed ^on La1-xSrxCu04 ^{as a} function of doping

[9, 10]

^{or on}

YBa2Cu306 + x

^when monitoring the oxygen concentration

[1, 11],

though little is known in the latter case. Indeed, ^{one can} expect ^{from such} experiments ^{as well as} from Hall effect and London penetration depth measurements, ^to determine the variation of the density ^{of free}

carriers versus doping, ^{hence to} infer how the band structure builds up in these compounds.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500180289500

2896

It is difficult to control the oxygen ^content in

YBa2CU306 .,

single crystals ^{within a}

thickness of a few thousands A at the surface which is the

depth

probed by ^the electromagnetic ^{wave in a} reflectivity measurement. On the contrary, ^the homogeneity ^of

ceramic samples is better controlled and can be checked experimentally, ^as explained ^further.

We have therefore measured the optical reflectivity of ceramic samples

YBa2Cu306+x (0

^{-- x :}

1).

^{As it was crucial to take} properly ^{into account the} anisotropy ^{of these} materials,

we have computed ^the reflectivity ^{of each} single anisotropic crystal according ^{to its}

orientation with respect ^{to the} light propagation

[12].

^{When the} wavelength ^{À of} light ^remains

small compared ^{to the} grain ^size L, ^the light ^reflected by ^a polycrystal ^{is the sum of} the energy contributions of each individual crystallite. By assuming ^{a set of} randomly ^oriented crystallites

and by summing ^{over all their} contributions, ^we have obtained the reflectivity spectrum ^{of a} ceramic. This calculation will not hold as soon as À - L, therefore we have not attempted ^to

extend the wavelength range below 2 ^IL, 10 IL being ^an average

grain

^size. By fitting ^{to out} experimental spectra, ^we have extracted the plasma frequency.

Disc-shaped

samples

(diameter

^{12 mm, thickness 2.5}

mm)

^of

YBa2CU307

^{have been} prepared by the standard ceramic technique. Their oxygen ^{content x} has been adjusted by annealing under various conditions of temperature and oxygen partial pressure

[13]. x

^was

determined by measuring ^their weight change. ^We have controlled the transition temperatures Te ^{of the} samples by ^{a 4} point ^a.c. resistivity measurement and checked that the onset of the Meissner effect was consistent with the resistivity measurement. The T, dependence upon

x follows the well known pattern

[14].

These characteristics are listed in table I.

Table I. ^- Transition temperatures, corresponding plasma

frequencies l.ùp ^(defined

^within

±0.1

eV),

density ⁿ o f free ^carriers for ^{the various x values.} TeR ^{is the} temperature ^{at the 50 %} value

o f the

^normal resistance at the onset

o f

^the

drop,

à T,, ^is the total width o f ^the resistivity transition, TeM de fines ^{the onset} o f the ^Meissner effect. ^{For x = 0.28 and} 0.34, ^the resistivity ^has

increased by ^more than 6 orders

of

magnitude ^with respect ^{to the} metallic species.

The samples ^{have been} mechanically dry-polished. Although ^{it is} possible ^{to achieve a}

mirror-like surface, ^{we have}

preferred

^to keep ^{a residual} roughness of the surface. We have indeed noticed that the contact resistance between the pellet ^and mechanically pressed golden

electrodes was increasing abruptly ^when polishing ^{the surface} beyond ^{a 20 ±} 10 g granulomet-

ry. As ^a consequence, when ^we calibrate the reflection coefficient with respect ^{to a} gold mirror, ^we underestimate the absolute value of the reflection coefficient. We shall take this into account by introducing ^{in our} fitting procedure ^a systematic multiplicative ^{factor, which is}

kept ^constant

(within

^{± 5}

%)

whatever the oxygen ^{content or} the wavelength. Therefore it will not affect the shape ^{of the} spectra.

Our reflectivity spectra ^{at room} temperature ^{are shown in} figure ^1.

Fig. ^{1. -} Reflectivity spectra ^of YBa2Cu306+x ^ceramics for various x concentrations for linearly polarised light within the incident plane ^at i = 60° incidence (Brewster angle). For the sake of clarity ^we

have selected (....) x = 1 (.-.-.-) ^{x = 0.71} (----) ^{x = 0.56} (..--) ^{x = 0.5} (+++) ^{x = 0.28. The} corresponding ^fitted spectra ^are displayed ^with large symbols (circles, squares and triangles) using equation (3) with the values of w p of table 1 and a damping constant y = 1 eV. It is noteworthy ^{that the} plasma « edge » ( £1 = 0 ) ^{visible on the} spectra between 1 and 1.5 eV corresponds ^{to a} plasma frequency ^{of 2 to} 2.7 eV because of the high ^{value of} e. ⁼ 4.5 used in equation (3). ^The inset shows the geometry used for the reflexion coefficient measurement.

For these experiments, light ^was linearly polarized within the plane ^defined by ^{the wave}

vector k and the normal N to the surface

(the

^incident

plane).

^{k was at an} angle i ¹ adjusted ^{in order to} minimize the reflection coefficient

(Rv)

in the visible range

(E

> 12 000

cm - 1).

^{When tan} i = n

(n

is the real index of the

medium) i 1

is the so-called Brewster angle. ^{We find} Rv ’" 2 % ^for il", 600, ^{to be} compared ^{to -} 10 % under normal incidence. This confirms that the index n is approximately 2 in the visible range, hence

E. - 4

(3.8-4.5

^{in the}

literature),

and also that the extinction coefficient is not zero in this range.

The data show two distinct behaviors : one set of curves exhibit a typical rise in the infra-red

(IR)

^{which has} commonly been observed in the oxygenated samples

(x

> 0.5

).

^{The other set}

of curves

(x

^:

0.5)

remains flat in the corresponding IR range. We shall refer ^to the rise as

the ^« metallic » edge. Indeed, this feature disappears right when the oxygen concentration

drops ^{from 6.5 to 6.34} which, from various techniques

[14],

corresponds ^to the transition from the metallic

(superconducting)

phase

(6.5)

^{to the} insulating phase

(6.34).

Qualitatively, ^the

metallic edge ^{shifts as} expected

[11]

towards lower energies ^as the oxygen ^content is decreased.

It was important ^to check that the oxygen concentration is the ^{same at} the surface and in the bulk. For samples with oxygen ^content 0.30 x : 0.77 which can be expected ^{to be the most} inhomogeneous, ^we have removed half a millimeter from the surface and remeasured the

2898

reflectivity. ^The largest change ^{that we} have found

(corresponding

^{to a} weaker oxygen concentration on the as-prepared surface than in the

bulk)

is less than the difference between two closest x values. This indicates that the samples ^are homogeneous enough ^to provide ^a

reliable analysis ^{of our data versus} the oxygen concentration.

We proceed ^{now to a} quantitative analysis ^{of our results.}

Following ^Orenstein

[12],

^{we shall assume that the} single crystallites ^are uniaxial, ^{i.e. that}

for the optics, ^{the a and b axes are}

equivalent.

Then the dielectric tensor has 2 principal components s;) and E,. When the wave vector lies along ^{a direction at} angle 0 ^{with the c axis,}

two different modes can propagate : the so-called ^« ordinary ^{» and «} extraordinary ^{» waves.}

One needs to know the associated indices no and n ^or similarly eo

= n 0 2

^{and E = n 2 in order to}

calculate the reflection coefficient

[15] :

e , is the dielectric constant in the a, b plane ^and defines the propagation ^{of the} ordinary ^wave

(k

parallel ^{to the c}

axis).

cj; is the dielectric ^constant along ^{the c} axis and defines the

propagation ^{of the} extraordinary ^{wave, k} lying ^{in the a, b} plane. 6 ^{is the} angle ^{between k and}

c

(see

^{inset of} Fig.

1).

In the a, b plane, ^we have assumed the usual Drude contribution. The simplest phenomenological description to account for the absorption beyond ^{1.5 eV is to include a}

bound carrier contribution. Hence :

(Op ^{is the} plasma frequency :

co p 2

^{= 4 7Tne}

^{2/m *,}

^{where n} is the number of free carriers per unit

volume, ^{m * their mass} and e their charge. ^{y is the} damping factor of the free carriers,

lù a is the resonance frequency of the bound carrier, yj ^its damping factor and lù j its oscillator

strength.

Along ^{the c} axis, ^{we have} neglected ^a possible Drude contribution. Indeed, in the similar

compound La2Nio4

[16],

^{as well as in}

YBa2CU307

single crystals

[17],

^the reflectivity spectrum does not display ^{in the} corresponding spectral range any ^« metallic edge ^» when the electric field lies parallel ^{to the c} axis. Hence :

The notation is similar to that of

(3).

^The frequency, oscillator strength ^and damping ^factor

of the bound carrier may differ in both directions but ^we have taken the same

value.

From

(1), (2), (3)

^and

(4),

^{we can work out the} indices no and n then compute the reflection coefficient R,, when the incident wave is not normal to the surface. Assuming ^{a random}

distribution of the orientations of the c axes, ^we find :

ro ⁼

Ero/E;o ^{and re}

⁼

Erel Eie

^{are the} amplitudes of reflection coefficients and are complex

numbers. They ^are defined for each polarisation of the electric field

(E;o

^or

E;e)

^{in the}

incidence plane

(rI!)

^and perpendicular ^to the incidence plane

(r-L )

^and involve the incident

angle condition. The stars denote the complex conjugate

quantities.

Under normal incidence,

we recover the expression ^found by Orenstein et al.

[12].

We have checked by X-ray analysis ^{that our} samples ^{do not} exhibit any preferential

orientation on the surface. Therefore we have used

(5)

^to compute ^the expected spectrum ^of

our ceramic samples

for i 1=

^60°.

Starting ^{from x = 0.28 and} 0.34, ^we have first identified a bound carrier contribution at 1.7 eV and adjusted £00 ^at 4.5. We have then kept E. and _Wc constant versus x. For

x : 0.5, ^{we can} put ^an upper value ^to w p

(1.3 eV)

consistent with the fact that we do not observe any metallic rise in ^our spectral range.

For x:> 0.5, ^we have introduced the Drude contribution and gradually changed ^the

characteristics of the bound carrier in the visible range in order ^to reproduce ^the experimental spectra. Considering ^our restricted spectral range and the experimental ^error bars, ^{it did not}

look meaningful ^{to achieve a best fit on the} damping ^{factor y} for each x concentration.

Conversely, ^{y cannot be} changed significantly

(typically

^{from 1 to 1.5}

eV)

^without altering

the

quality

of the fits. We have thus assumed that it remains constant versus x and selected the value which yields ^{an overall} satisfactory ^{fit : y = 1 eV.} Finally, ^the multiplicative ^factor

mentioned earlier is 1.4 ± 0.06.

Examples of these fits are shown in figure ^{1. The set of} _wp values for the various oxygen contents are listed in table I. Table II summarises all the parameters of the fits relevant to the bound carriers.

Table II. ^- Bound carrier characteristics (resonance

frequencies,

oscillator

strengths,

damping factors) ^{in the a, b} plane ^and

along

^{the c axis, used} for

fitting

^the spectra ^{as a}

function o f x.

^For x : 0.5, ^the fit corresponds ^{to an} experimentally ^{rather well}

identified

transition. For 0.5 : x « 1, ^{we have} used this bound carrier as a

phenomenological

description of possibly

more complicated spectroscopic

features

(see text).

For x = 1, ^the parameters ^{are similar to} those which have been found on single crystals ^and

films in a broader energy range.

For x ⁼ 0.58, ^{we have} compared ^the reflectivity spectrum ^{of the} polycrystal ^{to the} reflectivity ^{of an} as-grown single crystal i.e. which was not reoxygenated

(2 x 2

^mm

platelet).

Its transition temperature

(onset

of the Meissner

effect)

^{was 50} K, ^{which is similar to the}

onset of the Meissner effect for ^{our x =} 6.58 polycrystal. ^{In the case of the} crystal, ^{because of}

the high optical quality ^{of the} surface, ^the fitting procedure ^{does not}

require

any correction factor

(compared

^{to the} factor 1.4 for the

ceramic).

^{The fit} yields ^{the same} plasma frequency

on the single crystal lù p ⁼

(2.5 ±

^0.1

eV )

and the ceramic

(2.4 ± 0.1 eV ).

It has been suggested ^{that an} IR transition was responsible for the rise in reflectivity

observed in the

YBa2CU307

compounds

[7].

^We have indeed checked that for x ⁼ 6.9-7, ^our

2900

IR spectrum

(below

^1.5

eV)

^{could be as} well fitted with the parameters of reference

[7]

(cdp

^{= 0.74 eV, y = 0.037 eV, lùa = 0.26 eV,} y j ^{= 1} eV, lùj ⁼ 2.6 eV. It shows that the

parametrization ^{of the} reflectivity spectrum ^{is not} unique. ^{Thomas et al.}

[3]

^have recently suggested ^{a different} interpretation which appears ^to be consistent with ours. According ^to

their analysis, ^{y and m *} change ^{with the} frequency ^and approach respectively ^{1 eV and}

mo

(the

free electron

mass)

in the visible range. We indeed find the ^{same y} value in this

spectral range. Moreover ^our data show that there exists ^a correlation between the reflectivity

rise in the infrared range and the metallic behavior and that the simple Drude model provides

the proper shapes ^{of our} reflectivity spectra.

We now show in figure ^{2 the variation versus x of the} density of free carriers

n deduced from

w p

^{assuming m * = mo}

(consistent

^{with Ref.}

[3]).

^{Our most} striking ^{result is}

that the density of carriers

( w p )

^changes very little with ^x, e. g. n ⁼ 5.8 x 1021 cm- 3 for

x = 1, ^{3.2 x} 1021 cm- 3 for x = 0.5, ^then drops abruptly ^{for x 0.5.}

At this point, ^{it is} tempting ^to relate the variation of the density of carriers to that of the Pauli susceptibility ^{as can be} deduced from the Knightshift variation AK of Y89

(measured

ⁱⁿ

Ref.

[18]).

Indeed, ^{these room} temperature ^NMR data have been taken as a function of oxygen ^content in a series of powder samples processed ^{in an} identical way ^as those of the present ^work.

The Pauli susceptibility ^{was found to} drop ^{to zero at x = 0.4. The} variation of the density ^of

carriers that we find around x ⁼ 0.4 is consistent with the susceptibility ^data.

In figure ^{3 we have} plotted the variation of the Knighshift ^{OK as a} function of the density

n of free carriers. This plot ^shows the variation of the density ^{of states} NF ^at the Fermi level

versus n, provided ^the Knightshift ^{is a fair} representation ^of NF. ^{None of the usual} expected

variations in the 1-, 2-, 3-dimension cases seem to describe properly ^the experimental ^one.

The present findings ^{shed a new} point ^{of view on the} dependence upon n of Tc ^and

AK. Such behaviors could be consistent with the localization of the carriers.

Fig. 2. Fig. 3.

Fig. ^{2. -} Variation of the density n of free carriers versus x deduced from the

w §

values listed in table I.

The full symbols correspond ^{to the} explicit ^Drude contributions, the shaded ones to the upper estimate

of ú)p for x - 0.5.

Fig. ^{3. -} Plot of the variation of the Knight ^shift (- I1K) ^{of Y89 at room} temperature ^for

YBa2Cu306+x ^{as a} function of the density of the free carriers obtained through

w§

^{(Tab. 1 and text).}

In summary, ^we have described a rigorous approach ^{of the} reflectivity spectra ^of polycrystalline samples ^{that we have} applied successfully ^{to a set of}

YBa2Cu306 +x

^ceramic compounds. ^{We find a modest} drop ^{in the} plasma frequency ^as the oxygen ^content is decreased down to 0.5. Below x ⁼ 0.5, ^the plasma edge ^shifts beyond ^our spectral range,

implying ^a sharp decrease of the plasma frequency.

Acknowledgements.

We are

grateful

^{to F.} Queyroux and M. Nanot for their X-ray analysis ^{of our} samples, ^{to A.}

Revcolevschi and J. Jegoudez ^for providing ^{us with a} high quality single crystal. ^{We thank}

Prof. J. Friedel for an illuminating discussion.

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