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ESR of YBa2Cu3O7 single crystals : on the nature of the magnetic centres
A. Deville, B. Gaillard, H. Noël, M. Potel, P. Gougeon, J.C. Levet
To cite this version:
A. Deville, B. Gaillard, H. Noël, M. Potel, P. Gougeon, et al.. ESR of YBa2Cu3O7 single crys- tals : on the nature of the magnetic centres. Journal de Physique, 1989, 50 (17), pp.2357-2374.
�10.1051/jphys:0198900500170235700�. �jpa-00211067�
ESR of YBa2Cu3O7 single crystals : on the nature of the magnetic centres
A. Deville (1), B. Gaillard (1), H. Noël (2), M. Potel (2), P. Gougeon (2)
and J. C. Levet (2)
(1) Laboratoire d’Electronique des Milieux Condensds, CNRS UA 784, Université de Provence, Centre St-Jérôme, 13397 Marseille Cedex 13, France
(2) Laboratoire de Chimie Minérale, CNRS UA 254, Université de Rennes, avenue Général Leclerc, 35042 Rennes Cedex, France.
(Reçu le 26 février 1988, révisé le 5 mai 1989, accepté le 12 mai 1989)
Résumé.
2014Les résultats antérieurs fournis en RPE par des poudres de YBa2Cu3O7 sont
contradictoires. Nous présentons des résultats sur des monocristaux de YBa2Cu3O7, avec des
mesures systématiques d’intensité, comparaison des spectres en bandes X et Q, examen de l’influence du broyage des cristaux, comparaison aux spectres d’autres oxydes Y/Ba/Cu. Nous n’avons pas détecté la RPE des électrons de conduction. Bien qu’anisotrope, le spectre RPE n’est pas dû à YBa2Cu3O7, mais à des inclusions orientées de Y2BaCuO5. A 300 K, le champ rf subit
dans le cristal une atténuation modérée et isotrope, qui disparaît après broyage. La variation
thermique de l’intensité est très différente avant et après broyage : avant broyage elle décroît fortement en dessous de Tc, reflet de l’expulsion du champ rf. L’absence de RPE des ions
Cu2+ de la phase YBa2Cu3O7 pourrait être due à la formation de paires d’échange non magndtiques dans l’état fondamental.
Abstract.
2014Previous ESR results from YBa2Cu3O7 powders are contradictory. We present results on YBa2Cu3O7 single crystals, obtained through systematic intensity measurements, a
comparison of X and Q-band spectra, a comparison with the spectra from other related Y/Ba/Cu oxides, and a study of the influence of grinding the crystals. The ESR of conduction electrons was not detected. Although anisotropic, the ESR spectrum is not produced by YBa2Cu3O7, but by
oriented inclusions of Y2BaCuO5. At 300 K the rf field in the crystal undergoes a moderate, isotropic attenuation which disappears after grinding. The thermal variation of the ESR intensity
is quite different before and after grinding. Before grinding it strongly decreases below
Tc, which reflects the expulsion of the rf field. The absence of ESR from the Cu2+ of the
YBa2Cu3O7 phase could be due to the formation of exchange-pairs with a non magnetic ground
state.
Classification
Physics Abstracts
74.70
-76.30
1. Introduction.
In order to get materials with a critical temperature 7c higher than that of Nb3Ge, Bednorz
and Müller focused on the Ba-La-Cu-0 system [1, 2] because, due to the presence of itinerant
states between the non Jahn-Teller Cu3 + and the J.T. Cu2 + ions, this system was expected to
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198900500170235700
have considerable electron-phonon coupling and metallic conductivity. Since then, La has
been replaced by Y [3], the superconducting phase YBa2CU307 (Tc == 90 K) has been
identified and its crystalline structure obtained [4-7]. The true origin of the mechanism responsible for the behaviour of these oxides is still in debate. Among the various theories which have been proposed, it has been suggested that the magnetic coupling between the copper ions could play a decisive role [8-10]. It is quite natural to try and get information, on
the magnetic properties of these materials with ESR, and this paper presents the ESR results
we have obtained from YBa2CU307 single crystals (preliminary results have been presented at
the Interlaken Conference [11]). The first question we had to answer was : what magnetic
centers can one hope to detect ? If Tu 7c (for instance 300 K) one can a priori think of conduction electrons, and of the more or less localized spins associated with Cu2 +
(S
=1/2) or Cu3 + (S
=1) (1 ), if the spin-spin and spin-orbit couplings are not too strong.
One can also think of chemical impurities or of structural defects which could act as local
probes. When we started these experiments, we had clearly in mind that the use of ESR could in fact be a difficult task, even above T, - for instance at room temperature - because of the
probable damping of the rf field by the skin effect. We initially hoped to at least partially
overcome this problem by taking advantage of the strong anisotropy of the electrical
conductivity in YBa2CU307. Our purpose was to have the penetration of the rf field into the
sample governed not by the conductivity in the Cu-O-Cu planes, but by that in the direction
perpendicular to these planes, which is known to be much lower - this by an adequate choice
of the orientation of the sample in the cavity. We will show that we have in fact observed a
moderate, isotropic, attenuation of the rf field. This last point we will relate to the
inhomogeneous nature of the material. The experiments discussed below try therefore to elucidate the origin of the ESR signal in a YBa2CU307 single crystal, and to give informations
on the rf penetration in the material, before and after grinding. We were also led to examine
the ESR of Y/Cu oxides, especially the so-called green phase. By now numerous papers have
appeared, mainly on sintered materials, with contradictory conclusions (compare for instance
[12-14] with [15]). We hope that this will not increase the confusion, but will allow some
clarification.
In section 2, we recall the local symmetry for the copper ions in YBa2CU307, as known from
structure studies, and discuss about the expected magnetic moment in the ground level of the copper ions. The sample preparation and our experimental conditions for ESR are described in section 3. In section 4 we present the experimental results and discuss the origin of the ESR signal. We discuss about the propagation of the rf field in section 5. A discussion of the
magnetic properties of YBa2CU307, including a comparison of our ESR results with those from other experimental technics, is given in section 6.
2. Local symmetry and magnetic moment of the copper ions in YBa2CU307.
YBa2CU307 is known to have a perovskite-like structure ([4-7], and [16] for a short review).
More generally the YBaZCu307 - à compounds with à 0.4 are orthorhombic. The primitive
cell of YBa2Cu309 can be viewed as consisting of the piling of three cubes, an yttrium atom being at the center of the middle cube, and barium at that of the extreme cubes. The vertices of these cubes are occupied by copper, and the middle of the edges by oxygen.
a, b and c, the dimensions of the cell, thus verify a - b - c /3. The structure can also be
viewed as a piling of planes perpendicular to the c axis ; in YBa2CU307, the oxygen vacancies
(1) If one accepts a ionic description for YBa2CU307, with Y3 + , Ba 2+@ p2 - then, when
à
=0.9, 27 % of the copper ions are Cu3 + .
are thought to be in the extreme Cu-O-Cu planes of the cell, and in the yttrium containing plane (Fig. 1). One third of the copper ions have four oxygen neighbours in a square planar configuration (the plane being parallel to c) and two thirds have five oxygen neighbours in a pyramidal configuration (the axis of the pyramid being parallel to c). In order to get some idea about the behaviour of copper in such a local symmetry, it is useful to consider first that it
originates from octahedral symmetry, and to distinguish moreover between Cu2 + and
Cu3 + . In an intermediate field of octahedral symmetry, the Cu2 + ion (ground state 3d9, ground term 2D) has a r 3 doublet orbital ground level ; if a weaker tetrahedral distorsion is added, this level splits into two orbital singlets ; the Cu2 + ion will then have a magnetic
moment associated with a S
=1/2 spin, and zero orbital moment. In an intermediate field of octahedral symmetry, the Cu3 + ion (3d 8 3F) has a r 2 singlet orbital level. With this or lower symmetry, the Cu3 + ion will then have a magnetic moment associated with a S
=1 spin, and
zero orbital magnetic moment (although the level originates from a L
=2 term, the matrix
elements of L within the singlet are zero : the orbital moment is quenched) [17].
Fig. 1.
-The primitive cell of YBa2CU307 (from [16]).
3. Sample préparation, experimental conditions.
Crystals of YBaZCu307 were grown by a mineralization process from a stoichiometric
composition, at a temperature slightly lower than that corresponding to the peritectic décomposition). After annealing at 450 °C under oxygen flow for twelve hours, the crystals
exhibited a high quality superconducting behaviour with a critical temperature Tc =-..z 90 K and
a transition width ATc -- 1 K as measured by DC conductivity. Calling o-c the conductivity along c and u ab that in the plane perpendicular to c, uâbl for these crystals lies in the 500- 700 fJ.O-cm, depending on the sample and on the quality of the electrical contacts ; moreover
at 300 K u ab/ u c == 30 in YBa2CU307 [18]. The corresponding values at 100 K are 200-400 fJ.O-
cm and == 60. The barium-copper oxide BaCu02 and the green phase Y2BaCuO5 were prepared from the corresponding stoichiometric mixtures of Y203, BaC03 and CuO, in a
muffle furnace at 950 °C for twelve hours.
ESR experiments at X-band (9.3 GHz) were performed with a E112 Varian spectrometer
and a variable temperature gas flow cryostat (Oxford ESR9). The intensity measurements of
the resonance signal were made by comparing the signal from the sample at the temperature of experiment with that given by a reference sample (strong pitch) kept at room temperature, using a double rectangular TE,04 cavity. The derivative of the absorption was first recorded
(usual field modulation and lock-in detection). The output of the spectrometer was coupled to
a computer (Nova 4 from Data General) which performed a first numerical integration, leading to the absorption signal, and a second integration giving the area under the absorption
curve. This double integration was carried out for both the sample under study, at variable temperature, and the reference sample at room temperature. It gave a quantity which we will
call I, the normalized intensity. Its determination uses the values of the rf power, field modulation and gain settings, for both samples. I is independent of rf power (in the absence of saturation), of field modulation and gain settings, and is proportional to the sample mass (at least for a sample without skin-effect). During the intensity measurements, in order to
correct for any possible variation of the Q of the cavity due to the thermal variation of the electrical conductivity of the sample, we systematically recorded the spectrum of the reference sample after each measurement made on the YBa2CU307 sample. When choosing
the amplitude of the field modulation and the rf power, care was taken to avoid overmodulation of the ESR line and partial saturation. In order to get the number of spins
from these data, it is necessary to know the value of the spin of the paramagnetic centres, and
the absorption law. The analysis is more difficult in the presence of the skin-effect (then not
all the spins are detected, and the signal is a mixture of absorption and dispersion
-Dysonian
lines -). In our first experiments, the crystal was positioned with a small teflon holder put in
a quartz ESR tube. The holder gave a small spurious signal. In subsequent experiments, we
sticked the sample at one end of an ESR quartz capillary, using a General Electric varnish which had been verified to give a negligible signal in our temperature range. The magnetic
field values were obtained from the Varian Hall probe, and the calibration checked with the
pitch resonance signal.
The Q-band experiments were made using the E110 Varian microwave bridge, and a cylindrical cavity. The magnet could then be rotated around the vertical axis.
4. Expérimental results. Nature of the magnetic centres.
The ESR spectrum obtained at X band from YBa2CU307 single crystals has the following
characteristics :
1) The spectrum is clearly anisotropic. This is shown in figure 2, which displays the 300 K spectrum at X-band for c vertical (Fig. 2a), and for c colinear with the driving field Ho (Fig. 2b)
-the choice of these directions will be justified in section 5. The spectrum was obtained from a single crystal which we will call Cl. Ci was a 0.45 mm thick plate, in the form of a nearly isocel (1.9 mm) right-angled triangle, and its mass was 4.4 mg. Figure 3 shows the
angular variation of the ESR spectrum from Cl when the sample is rotated around the vertical
c axis. Figure 4 shows the corresponding angular variation of the low field extremum
Hm.
2) When the temperature is lowered down from 300 K, I, the normalized intensity, progressively deviates from the Curie law, and strongly decreases near T,,, as shown in figure 5, which corresponds to c vertical and to crystal Cl. The superconducting transition was
also detected in a most sensitive manner, in zero field, by a strong change of the reflection
coefficient T of the cavity near T,.
3) Although the shape of the ESR spectrum is anisotropic, I, the intensity, is the same at
300 K for the two orientations already considered in 1), and the thermal variation of
I is the same in both cases, within experimental accuracy.
Fig. 2.
-ESR spectrum of an YBa2CU307 single crystal for a) c axis vertical (corresponds to
0
=120° in Fig. 3) b) c axis horizontal and parallel to the static field Ho. The same units are used for the
amplitude in a) and b).
Fig. 3. - Variation of the ESR spectrum of the YBa2Cu307 single crystal of figure 2, when the sample is
rotated around the c axis ( T
=295 K, f
=9.391 GHz, P
=100 mW, Hmod
=20 Gpp).
4) The magnetic centres observed with ESR are time-stable. This was established by repeating the intensity measurement of the 300 K ESR signal from Cl, after a one year
interval, with the same equipement and the same experimental conditions. The same result
was then obtained, within experimental accuracy.
Fig. 4. Fig. 5.
Fig. 4.
-Angular variation of the field Hm in a Fig. 5.
-Thermal variation of 1, the normalized rotation around the vertical c axis of the intensity (area under the absorption curve) for the YBa2CU307 single crystal (0 and Hm are defined in YBa2CU307 single crystal, with c vertical and the insert (T
=295 K, f
=9.381 GHz, 0 =120° ( f
=9.392 GHz, P = 100 mW (no par- P = 100 mW, Hmod
=20 G pp ). tial saturation), Hmod
=20 Gpp). Solid line : Curie
law.
5) After grinding an YBa2CU307 single crystal into a powder, the normalized intensity, for
the same mass of material, is increased by a factor of about 5, for the crystals of a few mg we used in our experiments. This was not observed with Cl, which was kept unground, but with
three other crystals from the same fabrication run, which we will call C2 (5.7 mg), C3 (5.2 mg), and C4 (9.6 mg), and which displayed a behaviour similar to that described for
Cl in 1), 2) and 3). More precisely, the ratio of the normalized intensities for the same mass of
crystal and powder was found to be :
(precisions upon the normalized intensity of these crystals will be given later on). The mass of
the powder obtained from C2, C3 and C4 and used in these experiments was 3.0, 1.4 and
6.5 mg respectively. We are not able to decide whether the attenuation factor is the same for
quite different masses of samples, or whether it seems so because the sizes of the samples are
not much different (the masses of C2, C3 and C4 differ by a factor less than 2). We verified with C2 that when the powder is subsequently diluted into a paraffin powder, no new intensity change is observed. Since the ESR spectrum is time-stable and since the intensity increase is the same for several samples, we will consider that this increase does not come from some
chemical change accompanying the grinding operation, but is associated with the existence of
a moderate attenuation of the rf field in the crystal, which we discuss in more detail in 5.
6) At 300 K, the introduction of the YBa2CU307 crystal into the dual cavity affects
somewhat the distribution of the microwave field within the cavity, and that in a non-uniform
way. This was established by first recording the ESR spectrum from a trace of DPPH placed
in the center of the first half of the cavity, and that from the Varian pitch simultaneously placed in the second half of the cavity, and then repeating both recordings when Cl was placed against the DPPH trace. It was found that the introduction of Cl multiplies the amplitude of the magnetic field acting on the pitch by a factor of 0.79, and that acting on Cl by 0.60. As a consequence, if a true determination of the concentration of magnetic centres in
an YBa2Cu307 crystal is needed, one should use not I, the normalized intensity, but a quantity which we will call the corrected normalized intensity 1 c
=1.311.
We now discuss the origin of the resonance signal, and present the results of experiments
we made to elucidate this question. After some comments upon the presence of the conduction electrons, we give some information on the Q-band spectrum from YBa2CU307.
We then give precisions on the spin concentration and its possible dependence with YBa2CU307 sample. Our results invited us to compare the ESR spectrum from YBa2CU307
with that possibly obtained from other Y/Ba oxides, which led us to examine Y2BaCuO5 in
greater detail. ESR spectrum intensity results, X-fluorescence measurements and the ESR results already described finally suggest a reasonable conclusion about the origin of these
centres.
Several facts indicate that this resonance signal cannot be attributed to conduction electrons : 1) When T > Tc, I, the intensity, is not too far from a Curie law, instead of being temperature independent. 2) The position and the width of the spectrum are not compatible
with that of a nearly free electron, which is confirmed by Q-band measurements to be described later on. 3) ESR detection of conduction electrons is neither frequent nor easy.
The spectrum of figure 2, which does not originate from a powder but from a single crystal,
cannot be attributed to just one king of S = 1/2 spins even with an anisotropic g tensor, but has a more complex origin. We will assume that it corresponds to a mixture of different centres with S = 1/2 (for instance CU2+ in several unequivalent sites). We have examined the Q-band (35 GHz) ESR spectrum from Cl with the hope that a better resolution could help separating the different contributions to the ESR spectra and then help identifying the magnetic centres. The observed Q-band spectrum is in fact complex and such an identification has not been possible yet. Several points should however be noted : 1) The spectrum, given in figure 6, cannot be explained by considering just two unequivalent S = 1/2 spins. The copper nucleus has a 1= 3/2 spins, and one has to examine whether a hyperfine coupling can explain
the spectrum. However as the experimental spectrum has more than eight lines, this is in fact not possible. 2) If we define OH
=HM - H., where Hm and HM are the field values for the extrema at the lowest and highest values of the field (Fig. 4), and if we consider the maximum value i1HM of the somewhat orientation-dependent quantity 0394H, we find that à
(35 GHz)/i1HM (9.4 GHz )
=3.61, while the ratio of the rf frequencies is 3.73 : the spectrum is field dependent. The most important features come not from the hyperfine structure, or from quantities like DS;, but from the Zeeman coupling.
We will consider that the assumption of a Curie law for our ESR signal in an YBa2CU307 crystal is not too unrealistic at 300 K. From the value of the corrected normalized
intensity for C2 powder, we obtain that the concentration of the S = 1/2 spins in C2 is (7.9 ± 1.6 ) 102° spins/cm3. It is (6.8 ± 1. 4 )1020/CM3 in C3 and (2.1 ± 0.4 )1020/CM3 in C4.
Supposing that the same factor of 5.3 exists for Cl after grinding, the corresponding
concentration in Cl is (8.5 ± 1.7 ) 102o/cm3. In YBa2Cu307 the copper concentration is 1.7 x 1022 atoms/cm3. It follows that in C2 for instance the (number of spins/ number of
copper atoms) ratio is only 0.05. This result suggests that we detect traces of a spurious phase containing copper which can be detected by ESR, or that in our YBa2CU307 crystals only a
small proportion of the copper can be detected by ESR. We shall soon discuss this point. We
Fig. 6.
-Q-band spectrum of the YBa2CU307 single crystal, for different values of the 0’ angle, the c
axis being vertical (T
=295 K, f
=35.01 GHz, P = 10 mW, Hmod
=40 Gpp).
note beforehand that the difference between the concentration of C2 and C4 is well beyond
that which could result from the experimental accuracy, which suggests that the spin
concentration is sample dependent. We were able to confirm this point. We could first select three small YBa2CU307 single crystals, with well-defined faces. Putting them all into an ESR quartz tube (total mass : 1.7 mg) we obtained a signal which was 7 times weaker than that
predicted by assuming the proportionality between intensity and mass and the same intensity
for the same mass of that crystals and of Cl. We moreover did not detect any ESR signal from
a small well-shaped single crystal (0.5 mg), while under the same assumptions the Signal-to-
Noise Ratio should have been about 7. We checked that this sample was however truly superconducting at 90 K, by observing the sudden spectacular change in the power reflected from the cavity at this temperature. These small well-shaped crystals had been prepared by
the same method as the previous ones. We will explain later on why such samples were
chosen.
At this stage we examined directly whether the ESR signal could come from traces of a spurious phase in the YBa2CU307 host, by comparing the results for YBa2CU307 with that possibly obtained from other yttrium/copper oxides, which were obtained as powders. A
direct comparison between the ESR spectrum from a single crystal and from a powder is not possible. Moreover the presence of a given paramagnetic species is not significant by itself, if
its proportion is unknown. We therefore systematically made quantitative measurements. We first used a BaCu02 powder sample. We obtained an ESR spectrum (Figs. 7a and b), but with
a very weak intensity. Calling y’ (BaCu02 ) the amplitude of the derivative of the absorption,
and y’ (C2 ) that of crystal C2, expressed for the same masses and same experimental
conditions for both samples, we obtained : y(BaCu02)/Y(C2)
=0.028, which indicates that the signal in YBaZCu307 cannot come from the presence of BaCu02 in the sample. Repeating
the experiment with YBa2Cu306 (Fig. 8) we obtained y’ (YBaZCu306)/y’ (Cz) = 1.5, indicat-
ing that the same conclusion holds for YBa2CU306. Had we taken account of the
Fig. 7.
-ESR spectrum of BaCu02 (powder, 75 mg) a) T
=295 K, f
=9.385 GHz, P
=100 mW, Hmod
=20 Gpp ; b) same conditions as in figure 7a except the driving field.
Fig. 8.
-ESR spectrum of a YBa2Cu306 crystal (arbitrary direction ; 8.3 mg) ( T
=295 K,
f
=9.388 GHz, P
=100 mW, Hmod = 20 Gpp ).
5.3 x 1.3 factor, we would have obtained 4 x 10- 3 instead of 0.028 and 0.2 instead of 1.5. We
can therefore safely conclude that we detect neither BaCu02 nor YBa2Cu306 traces. We then
examined Y2BaCu05, the so-called green phase - the colour is probably due to the presence of Cu2 + ions. The ESR spectrum at X-band, given in figure 9, is similar to that from an
YBaZCu307 crystal powder. For a better resolution the experiments were also made at
35 GHz. The spectra for Y2BaCU5 and Y2BaCU307, presented in figure 10a and b, are quite
similar. The slight difference is not significant but could be due to a small unwanted contribution of the cavity or sample-holder in the spectrum of YBaZCu3070 The ESR
spectrum from the green phase is intense. For the same mass and experimental conditions we
Fig. 9. - ESR spectrum of Y2BaCuO5 (powder 7 mg) (T
=295 K, f
=9.388 GHz, P
=100 mW, Hmod
=20 Gpp). The receiver gain is 100 times weaker than in figure 2.
Fig. 10.
-ESR spectrum of a) Y2BaCuO5 (same sample as in Fig. 9) (T
=295 K, f
=35.14 GHz,
P
=0.1 mW, H.,,
=4 Gpp, receiver gain 125) ; b) a YBa2CU307 powder obtained from a single crystal
(T
=295 K, f
=35.14 GHz, P
=10 mW, Hmod
=40 Gpp, receiver gain 800).
obtained Y’(y2BaCuO5)IYC’(C2)
=39 (where Yc’(C2) is the amplitude of the derivative of
absorption from C2 after correction by the 1.3 factor), and therefore Y’(y2BaCuO5)IYC’(C2 powder)
=7.4 (because of the 5.3 increase after grinding). This result
means that if the ESR in YBa2CU307 is attributed to the presence of Y2BaCuO5, one has to
suppose the presence of 13.5 % (mass proportion) of oriented microcrystallites of this phase
distributed in the whole sample. The corresponding mass proportion for C3 is 11.6 % . This
seems a high proportion indeed. Truly, traces of the green phase were found under binocular observation, and crushing a sample into pieces confirmed that they seem to be present in the whole crystal. The presence of small amounts of the green phase was confirmed by X-rays powder measurements on ground crystals. It was these results and observations which initially suggested to choose the well-shaped crystals mentionned when studying the sample dependence of the ESR signal from YBa2CU307 crystals, because they seemed to be simultaneously free of the green phase traces. It is of interest to observe that [Cu]/[Y], the
ratio of the copper to yttrium atomic concentrations, is quite different in YBa2Cu307 and in
the green phase Y2BaCu05 - 3 and 0.5 respectively. We have therefore measured this ratio
using X-rays fluorescence microanalysis. It was not possible to determine the Cu and Y atomic concentrations in the C2 powder, because of the presence of the paraffin. Measure-
ments were therefore made with the C3 powder. Observation of several 40 lim x 40 03BCm windows of the sample powder showed that the material is far from being homogeneous (measurements from five different regions gave the following [Cu ]/ [Y ] ratios : 2.95, 2.56, 3.70, 1.92, 2.74, 1.73). These values are moreover all in the 0.5-3 range, except the 3.70 one.
Measurements for the whole surface (roughly a 2 mm x 2 mm square) of the powder used in
the microanalysis experiments gave [Cu ]/ [Y ]
=2.62. It is generally estimated that the
precision of these measurements is about 1 %, and this last result confirms that the mean
[Cu ]/ [Y ] value is far from 3. The value of 2.62 corresponds to a mass proportion of 5.6 % of
the green phase. Remembering the possible sources of errors in our comparison of ESR
spectra which needed several corrections, the fact that not the whole powder used in the ESR experiments could be used in the X-rays fluorescence measurements, and last but not least the fact that the fluorescence method explores only the surface of our non-homogeneous material, we consider that the difference between the two values
-2.3 and 2.62
-is not
surprising, and we estimate that this result does confirm the presence of the green phase. We
will therefore conclude from the whole set of experiments that the ESR signal in our YBa2CU307 crystals unambiguously comes from traces of the green phase, which have epitaxially grown, and which are distributed in a non-homogeneous manner in the whole
sample.
When examining the possibility of the presence of the green phase, we were led to examine
in detail the thermal variation of the intensity of its ESR signal. We found (Fig.11) that it
deviates from a Curie law and has a maximum value around 55 K. Below 30 K the line
broadens, and when reaching 15 K the intensity strongly decreases while the line strongly
broadens. The line cannot be detected below 15 K. This behaviour is characteristic of an
antiferromagnetic material, and we identified 15 K as TN. This result confirms that obtained from static susceptibility measurements by Troc et al. [19] (TN = 13 K). The existence of a
maximum of the ESR intensity around 55 K has also been observed by Mehran et al. [20], but
is not detected in static measurements, and its origin is unclear. Comparing I, the ESR intensity at 300 K with that from a reference sample (strong pitch) and assuming
S
=1/2 and a Curie law, we find that the spin concentration is 4.4 x 1021 spins/cm2 while one
should find 8.9 x 1021 (density : 6.2 [21]). This discrepancy probably means that the assumption of a Curie law for Y2BaCuO5 is a poor assumption at 300 K. The relative
measurements made when comparing the spectra from YBa2CU307 and Y2BaCuO5 are of
Fig. 11.
-Thermal variation of the intensity (height x square of the peak-to-peak width of the derivative of the absorption) for the green phase Y2BaCuO5 ( f
=9.390 GHz, P = 100 mW (no partial saturation), Hmod
=20 GPP). Solid line : Curie law.
course more precise than this absolute determination of the spin concentration in
YZBaCu05.
Although the ESR signal in YBa2CU307 crystals and in the Y2BaCU05 powder are due to
the same magnetic centres, their thermal variation is quite different (compare Figs. 5 and 11).
This has a simple explanation : the intensity decrease below Tc in the YBa2Cu307 crystals simply reflects the progressive expulsion of the rf field. This is confirmed by the following
fact : once the crystal is ground, this intensity decrease below T, is no more present (Fig. 12).
Fig. 12.
-Thermal variation of I, the normalized intensity (area under the absorption curve) for the
YBa2CU307 crystal C3, after grinding ( f
=9.39 GHz, P
=20 mW (no partial saturation) Hmod
=20 G ).
The ground material is then still superconducting below
=90 K, as can be seen from the behaviour of the ESR signal (appearance of noise and of a field-dependent offset (Fig. 13),
reminiscent of the one we have observed with sintered materials, but the propagation of the if
field under 7c is quite different within these grains and for the crystals.
We have finally to observe that an ESR signal in the ground crystal is still present below 15 K (Fig. 12). Complementary experiments with samples relatively free of the green phase
are necessary to determine whether this difference comes from a low-temperature signal due
to the YBa2Cu307 matrix, or just means that the magnetic behaviour of small antiferromagne-
tic grains of Y 2,BaCuOs diluted in the YBa2CU307 matrix is different from that of pure
Y2BaCuO5.
Fig. 13.
-ESR spectrum of the YBa2CU307 ground crystal C3 (T
=50 K, f
=9.39 GHz,
P
=20 mW, Hmod
=20 Gpp). The existence of noise and of a field-dependent offset, not present above 90 K, are clearly seen. A jump of the signal when the field begins and stops its time-variation is also apparent.
5. The propagation of the rf field.
We now examine the question of the penetration of the rf field above T,, for instance 300 K,
in our crystals. We call as usual a, b and d the dimensions of the TE104 rectangular cavity in the
x (vertical) y and z directions respectively : the sample under study was centered at A(a/2, b/2, d/4) and the reference sample at B(a/2, b/2, 3 d/4) (Fig. 14) ; in this mode, the
electric field is along y. At A, the electric field vanishes and the magnetic field is vertical. It is useful to consider that the rf field in the cavity results in fact of two progressive waves and to
examine the penetration of the incident wave only, which around A has its H component vertical and its E component horizontal along y (neglecting the perturbation of the field
configuration by the sample). We momentarily assume that the sample under study is
continuous and homogeneous, and that its electrical conductivity is the same at 10 GHz and at
zero frequency, and is therefore anisotropic, with axial symmetry. It is then clear that the rf behaviour will depend upon the orientation of the sample in the cavity (Appendix). We will
for simplification consider an YBa2CU307 square (length f) slab of thickness e, with the c axis
perpendicular to the plane of the square. We saw in section 3 that the DC conductivity in
these crystals decreases between 300 and 100 K, as in a metal. If one accepts to describe the
propagation of the rf field at 300 K in the same way as in a good conductor then, when E is in
Fig. 14.
-Positionings of the sample and reference in the TE104 dual-cavity.
the CuOCu plane the skin depth is 8a6
=(21/-Lo Ù) 0,b)112 -= 12 03BC at 10 GHz, and when E is
along the c axis it is 8 c = (2/03BC0 WO c )1/2
=66 it. We will then consider the following positionings of the sample in the cavity :
Case 1: the slab is horizontal (c axis vertical) ; the skin depth is then 8ab ; if a side of the square is perpendicular to z, the effective volume of the sample is 2 8 ab Qe (the factor of 2
comes from the penetration of the reflected wave at the opposite face).
Case 2 : the slab is vertical ; then
2 a : if c is colinear with z, the effective volume is 2 sab Q2
2 b : if c is colinear with y (i.e. colinear with the driving field Ho) this volume is
2 03B4, Le ; thus if one rotates the sample around the vertical axis, the intensity variation is not
expected to be high since with the crystals used (8ab fi 8c e) == 1 ; on the contrary the
intensity in case 2b is expected to be about (8 ci 8 ab) = (u abl U c )1/2
-=5.5 times stronger than
in case 1. We have already said that our experimental results did not confirm this prevision :
the normalized intensity of the ESR signal is isotropic. From this experimental result one is
first tempted to deduce the absence of skin-effect in our crystals (and this we did in [11]), but
this is not the only possibility, and is not exactly the one presently encountered. We have
explained that an intensity increase by a factor of about 5 was observed after grinding of the crystals, and that a subsequent dilution in paraffin resulted in no new intensity change, indicating a moderate attenuation of the rf field during its propagation through the crystal. In
other words, there is some skin-effect, but which cannot be described by the usual theory for a good conductor. This theory assumes 1) a local relation between the electric field and the current density (Ohm’s law), 2) thé o- > eo w condition (conduction current > displacement current), 3) the w T « 1 condition (T : mean time between collisions). YBa2CU307 is a type II superconductor. Below Tc, the relation between j and A, the vector potential, is therefore a
local one. This is even particularly true here, since the anisotropic coherence length seems to
be very small : for instance Worthington et al. [22] have found eab (0)
=34 Â (in the ab
plane), and gc(O)
=7 Â. Ohm’s law j
=QE seems a fortiori a good approximation above
Tc, the collisions being probably more efficient then. At 300 K, in our material 03C3 / E° w = 3 x 105 so that the second condition is also fulfilled. It is more difficult to discuss the w03C4 « 1 condition ; accepting the u
=neg relation and using the value n
=1021/cm3 from Hall experiments ([23] and [24] give 1.1 and 1.5 x 10Z1/cmz respectively) then 03BC= 10 CM2/V/S.
If one supposes then that 1£
=eT /meff and takes for meff the electron mass m, then
T= 5 x 10- 15 s, and the condition w 03C4 1 is fulfilled. The previous relations between
u and Tare perhaps invalid, but is seems reasonable to conclude that r is anyway shorter than
10-1° s, and that the three relations are therefore valid. However the theory of the skin effect
assumes at the start the presence of a homogeneous medium, and it is probably this assumption which is presently unrealistic. It is known that YBa2CU307 samples have generally
many large-scale defects, and our results have confirmed that our crystals do contain many chemical defects. If we modelize the Y2BaCuO5 regions as insulating zones, and if we recall their relatively high proportion, we have then to examine the rf propagation in a conducting
medium containing a significant proportion of insulating regions randomly distributed (the
fact that each region has a definite orientation relative to the host material, as suggested by ESR, is not relevant here). This is a difficult problem which, as far as we know, is still
unsolved. Thus, in a study of percolation in conductivity made some years ago [25], the
discussion of experiments at 3 GHz in a parent situation was made with the assumption of a homogeneous medium, in a context where it was thought to be reasonable then. We suspect that the present situation can lead to a moderate isotropic attenuation of the rf field if the
mean size of the insulating regions and their mean distance are at most of the order of the skin
depth of the homogeneous (i.e. without the insulating regions) conductor. It would be of interest to study model situations in more detail to test this opinion.
6. Discussion.
We will limit the discussion to the magnetic properties of the materials. In section 4 we have shown that the ESR signal in the YBa2CU307 crystals is due to traces of the green phase, and it
is therefore necessary to examine why the resonance of the copper ions from the host material is not presently detected. We note beforehand that our negative result confirms those obtained in static susceptibility and NMR measurements :
-
Junod et al. [26] have interpreted their measured static susceptibility as a sum of three
terms, two being temperature-independent quantities (a diamagnetic and a Pauli term). The
last term was Curie-like and was attributed to traces of BaCU02 (between 2 and 6 % according
to the sample). They did not detect any localized Cu2 + moment from the matrix. McGuire et al. [27] have measured the static susceptibility of four samples. Only one, which had the lowest diamagnetic shielding, showed a paramagnetic moment. They concluded that there is
an absence of any localized moment on the copper, or that there is an antiferromagnetic state
with the copper having a small magnetic moment 0 - 11£ B or 0.2 9 B,
-
in NMR and NQR experiments, Furo et al. [28] did not detect the presence of localized
moments. Similar results were found for instance by Lütgemeier et al. [29].
Our results also confirm the feeling of Vier and Schultz [15] for the origin of their high- temperature ESR signal (we are however surprised of their attribution of their low- temperature signal to BaCu02). On the contrary, our results disagree with [12-14], who
conclude that their magnetic centres have an intrinsic origin. It is highly desirable that future
work indicate the measured concentration, and how it was measured.
The first point to examine now is the presence of electronic magnetic moments. It is true
that the existence of Cu3 + in YBa2CU307 and the nature of the Cu3 + state seems still
controversial (compare for instance [30, 31] with [32, 33]). On the contrary the existence of
the more usual CU2 + is generally accepted. The 3d9 configuration for copper has been identified from X-rays absorption and X-rays photoemission, first in La2-xSrxCu04 ([30]),
, then in YBa2CU307 ([31, 32]). One has therefore to understand why the magnetic moment
associated with the S = 1/2 spin of CU2 + is not detected in ESR at room temperature, and
even at 100 K. There are in fact a priori several reasons which could preclude this observation
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