Hypert'me Interactions 77 (1993) 277-299
277
Two-dimensional spin freezing in
Yl_zCazBa2Cu3_xFex07
A. R y k o v , A. Ducouret, N. Nguyen, V. Caignaert, F. Studer
and B. R a v e a u
Laboratoire CRISMAT, CNRS URA 1318, ISMRA, Universithde Caen,
14050 Caen Cedex, France
Received 7 January 1993
Hyperfme electric and magnetic interactions in Yl_zCa:Ba2Cu3_zFexOr+y compounds
have been studied for different rates of Fe and Ca substitution (x = 0.09 and 0.24; z = 0.24;
y = 0-1) by STFeMrssbauer spectroscopy of powder samples obtained by different thermal
treatments. Calculations of the Fe3+ EFG tensor have been performed for different coordination polyhedra in Cul and Cu2 sites. Variations of the direction, amplitude and of the sign of
the principal component of the EFG are reported versus the iron displacement from the ideal
Cu sites inside the pyramidal and tetrahedral coordination polyhedra. Calculated AEa and
*7values are compared with the experimental ones. For the Cu2 site, faithfully probed in both
oxygen-depleted and oxygen-saturated samples by fairly large fraction of residing iron atoms,
the mutual orientations of the axes of the principal EFG component and that of easiest magnetization are deduced from interrelations between quadrupole parameters for paramagnetic
quadrupolar and magnetic Zeeman MSssbauer spectra. In the desoxygenated samples, the
coexistence of a long range 2D antiferromagnetie order and of a spin-glass order has been evidenced. For the oxygen-saturated samples, the two-dimensional spin-glass order is observed
below Tf = 10 K. The Mrssbauer spectra under applied fields at 4.2 K show an easy polarization of the spins in the Cu2 sites.
1. I n t r o d u c t i o n
M a n y experimental and theoretical studies have been focused on the interplay
b e t w e e n superconductivity and magnetism since the discovery o f high-temperature
superconductors. The study of the competition between these p h e n o m e n a and o f
their c o m p l e m e n t a r y nature was performed in RBa2Cu306+y (R = rare-earth element) b y M f s s b a u e r spectroscopy using 57Fe and 57C0 local probes substituted
into C u sites [1-12]. The doping with magnetic impurity suppresses locally the
superconducting pairing and reinforces the magnetic coupling. However, Fe a n d
C o substituents m a y enter in both C u l "chain site" and Cu2 "plane-site", which
take non-equal parts in the establishment o f superconductivity or magnetic order.
© J.C. Baltzer AG, SciencePublishers
278
A. Rykov et al. / Two-dimensional spinfreezing
The evidence of the primordial role of pyramidal copper layers in superconductivity was given recently on the example of Yl-xCaxBa2Cu3_xFex07,prepared by a
non-conventionalmethod [13]. In this method of preparation [13, I4], the driving of
iron atoms into Cu2 sites resulted in a dramatic decrease of Tc and even in the suppression of superconductivity. For conventionally prepared samples it has been
shown [2], that the magnetic transition detected in the temperature variation of
M6ssbauer spectra is not affected by large changes in oxygen content. Since the
local environment around the majority of Fe-atoms (,-, 90%) occupying Cul sites
does not influence the magnetic transition, Tamaki et al. [2] proposed the important role of Cu2. On the other hand, the temperature of the magnetic transition in
superconducting samples decreases with decreasing doping rate and tends to zero
in the limit x = 0 of pure YBa2Cu307 [1]. These two results suggest that the magnetic transition may be governed by a small fraction (,,~ 10%) of iron atoms occupying the Cu2 sites. The latter may easily polarize the copper spins in the Cu2
planes. However, in probing the Cu2 site, the M6ssbauer spectroscopy of conventionally prepared samples [1-12] faces the problem of extraction of too small a contribution of this site (,,~ 10%) out of the total spectrum. Moreover, the high
dispersion of the proposed theoretical approaches for processing the spectra makes
that different methods may lead to very acceptable fitting for the same complex
hyperfine spectrum. For instance, assuming a slow frequency of iron spin relaxation [3-6], an hyperfine field distribution [7], or a simple superposition of four
Zeeman sextets [8,9] could give an equally satisfactory fit of spectra measured at
different temperatures near the transition point. Thus, the analysis of M6ssbauer
spectra of conventionallyprepared samples with iron atoms residing preferentially
(,,~ 90%) on the Cul site leaves still unknown the origin of the magnetic transition
in superconducting oxides. Moreover, the mechanism responsible for the occurrence of hyperfine splitting in superconducting oxides is still not understood; the
most consistent approach suggests that static hyperfine field may arise from spinglass freezing coexisting with superconductivity [12,15-17].
In the present study we have investigated the superconducting properties, electric and magnetic hyperfine interactions in two iron substituted superconductors
Yl_zCazBa2Cu3_xFexO6+y(x = 0.09 and 0.24; z = 0.24), using different methods
of preparation in order to induce a variation in the occupancy of copper sites by
iron. For the first time we have successfully extracted the contribution of the Cu2
site from the M6ssbauer spectra; consequently, a complete analysis of iron on the
Cul sites, using electric field gradient calculations, could be performed. The
detailed study of magnetic hyperfine spectra in the temperature range 300-4.2 K
allows a two-dimensional spin freezing model to be proposed.
2. Sample characterization and X-ray diffraction study
The starting solid solutions were prepared from Y203,BaCO3,CaCO3,CuO
A. Rykov e t al. / Two-dimensional spinfreezing
279
and Fe203 enriched with 57Fe isotope (95°,4). The initial treatment consists of heating in air at 950°C for 60 h with two intermediate grindings. The starting material
was then exposed to a sequence of "high-temperature" and "low-temperature"
thermal treatment in Ar or Oz gas flows. The distribution of iron over copper sublattice was modified by applying the "high-temperature" treatment at 850-950°C,
while a low-temperature treatment at 380-400°C in O2 gas flow was used for oxygen saturation. After each high-temperature treatment the samples were slowly
cooled with a cooling rate of 1-2°C/min. For the sake of convenience we denote the
samples according to the sequence of thermal treatment. Both the gas atmosphere
and the temperature of the treatment are used for labelling of samples. The gas is
specified in square brackets by the corresponding symbol, while the treatment at
relatively low temperatures (380-400°C) is distinguished by subscript LT. Thus,
[OOL'r], [Ar], [ArOLT] and [Airq] refer to the four following protocols of gas-heat
treatment sequences:
[OOLT]: annealing in O2 gas at 980°C, slow cooling (1 °C/min) to 400°C and oxygenation at 400°C for 9 h;
[Ar]: annealing at 850°C in flowing Ar gas for 12 h and slow cooling (2°C/min)
to room temperature in Ar;
[ArOLT]: treatment [Ar] followed by annealing at 400°C in O2 gas;
[Airq]: heating in air at 950°C, followed by quenching in liquid nitrogen.
The powder X-ray diffraction data were collected by step scanning over an angular range 22-102 ° (269) with increment 0.02 ° (26)) by means of a high resolution diffractometer Seifert using Cu K~I radiation. The powder diffraction patterns of
the samples [Ar], [Airq] and [OOLr] were indexed in a tetragonal cell (S.G. P4/
mmm), while the orthorhombic symmetry was observed for [ArOLa-] sample (S.G.
Pmmm). This variation of symmetry in Fe-doped oxygen-saturated samples,
depending on the oxygen fugacity on the stage of intermediate high-temperature
treatment, was explained previously [18,19]. The tetragonal symmetry of [OOLT]
samples results from the preferential occupancy of Cul sites by iron; the latter
tends to take the tetrahedral coordination, forming microdomains, which favours
an apparent tetragonal symmetry. The tetragonal symmetry of the [Ar] sample is
due to the removal of oxygen from the level of Cul sites, so that the latter exhibits a
two-fold coordination and consequently can only be occupied by copper. The
restoration of orthorhombic symmetry in the [ArOLT] sample is easily explained by
the fact that iron in the [Ar] sample has not migrated back to the CuI site after oxygen annealing; these Cul sites are only occupied by copper forming rows of CuO4
planar groups and, consequently, one observes the classical orthorhombic structure of YBazCu3OT.
The results of the refinement of the lattice parameters and z-coordinates of Ba,
Cu2, and oxygen atoms are given in table 1. These data are used for interpretation
of the M6ssbauer spectra. Note, that the close values of the scattering factors of
Cu and Fe do not allow any distinction to be made, so that the distribution of iron
in copper sites presented in table 1 is deduced from our M6ssbauer study. Though
280
A. Rykov et al. / Two-dimensional spinfreezing
Table 1
Room-temperature crystallographic parameters of [Aft, [OLx] and [ArOLr] samples of
Yo.TsCao.24Ba2Cu2.91Feo.0906+y.
treatment
S.G.
P4/mmm
a(A)
b(A)
c (A)
atom
Y/Ca
Ba
Cul/Fel
Cu2/Fe2
02(02/03)
04
O1
occupancy
z
occupancy
z
occupancy
z
z
occupancy
Rwp
/~
Rx
d(cu2/Fe2)_O4(~k)
oxygen
content
6 +yb
site
ld
2h
Ia
28
4i
2g
2f
[Ar]
P4/mmm
3.8581(a)
3.8581(1)
11.8027(2)
[OOLT]
P4/mmm
3.8554(1)
3.8554(1)
11.6978(3)
0.76/0.24 a
0.1946(1)
0.99/0.01 =
0.3603(3)
0.96/0.04 *
0.378(1)
0.159(2)
0.33(5)
8.58
6.63
5.38
2.376
0.76/0.24 a
0.1867(2),
0.92/0.08 =
0.3579(4)
0.995/0.005 *
0.378(1)
0.161(2)
0.8(1)
14.4
13.32
4.89
2.303
6.38(!0)
6.89(10)
~mm
site
lh
2t
Ia
2q
2r/2s
2q
lb
[ArOL-r]
Pmmm
3.8241(1)
3.8797(1)
I 1.6689(2)
0.76/0.24
0.1846(1) a
0.98/0.02 a
0.3548(3)
0.965/0.35 *
0.376(1)
0.160(2)
1.0(I)
10.9
8.06
5.26
2.273
6.94(10)
* Fixed values (see text for details of explanation).
b Measured by thermogravimetry.
the atomic coordinates of the oxygen atoms are not very accurate, one observes a
behaviour similar to that of the compensated seriesstudied by neutron diffraction
[I3].Indeed, the (CUP.,Fe2)-O4 apicaldistance in the orthorhombic [ArOLT] phase
is smaller than that of the [OOLT] phase in agreement with the factthat in the formet sample the pyramidal copper sitesare preferentiallyoccupied by iron,whereas
in the latteriron ismainly located on the Cul sites.
The superconducting properties of [OOLT] and [ArOLT] samples have been studied by susceptibilitymeasurements. The T¢ values of 10 K (x = 0.24,z = 0.24) and
of 49 K (x = 0.09,z = 0.24) for orthorhombic [ArOLT] phases are significantly
lower than those of 74 K (x = 0.24,z = 0.24) and of 78 K (x = 0.09,z = 0.24) for
tetragonal [OOLT] phases. This resultwas explained previously [13,19]by the detrimental effecton Tc induced by iron occupying the Cu2 siterather than the Cul
site. Other properties of these samples, especially pinning properties, wiU be
reported elsewhere.
281
A. Rykov et al. / Two-dimensional spin freezing
3. Room-temperature Mfssbauer study
The Mfssbauer measurements were carried out by using 50 mCi 57Co in Rh as
the 7-ray source. Calibrations of the isomer shift and of the hyperfine field for each
source velocity were performed by using the spectra of an a-Fe foil at room
temperature. In our previous work [19], for the Yl_zCazBazCu3_xFexO6+ywe have
distinguished four quadrupole sites denoted A, B, C and D in order of increasing
modules for the quadrupole splittings AEQ (table 2). Both subspectra B and C were
assigned to Fe substituted at the Cul site in a five-fold pyramidal coordination.
The subspectrum C was attributed to isolated pyramids FeO5 and the broadened
subspectrum B was related to series of small clusters composed of corner-sharing
FeOs-pyramids, like Fe209, Fe3013, etc. The subspectrum D was assigned to a
tetrahedral coordination of iron since it vanishes when orthorhombicity develops
after [ArOLr] treatment. Doublet A, having the smallest quadrupole splitting,
originates from Fe 3+ ions residing in Cu2 pyramidal sites. The evidence of
the assignment of subspectrum A to the Cu2 site follows from antiferromagnetic
ordering in the Cu2 planes observed for a long time in YBa2Cu3_x57FexO6+y
(x = 0.0I-0.03, y = 0.0-0.3) [20,21]. Fig. 1 reproduces the room temperature powder M6ssbauer spectra of Y0.76Ca0.24Ba2Cu2.91Fe0.09OT. Attempts were made to
Table 2
Isomer shifts relative to a-Fe(rIs), absolute value of quadrupole splitting (IAEQI),full width at half
maximum linewidths (/~) and relative spectral areas (%) of STFe Mfissbauer subspectra observed at
room temperature in Yl-zCazBa2Cu3-xFexOr+y for different (x, z) values.
x,z
Treatment
Subspectra
~s (ram/s)
0.24, 0.24
[Airq]
A
B
D
0.30(1)
0.16(1)
0.096(3)
0.24, 0.24
[Ar]
A
B
D
0.09,0.24
[ooLr]
0.09,0.24
0.09, 0.24
[AEQI(ram/s)
r(mm/s)
%
0.93(1)
1.09(4)
2.017(6)
0.38(1)
0.74(8)
0.36(1)
44
20
35
0.255(6)
0.293(4)
0.11(3)
-0.56(6) a
0.936(8)
1.93(5)
_
0.56(1)
0.53(5)
58
30
12
A
B
C
D
0.293(2)
--0.028(2)
-0.047(3)
0.049(2)
0.636(4)
1.11(1)
1.84(2)
1.974(5)
0.266(5)
0.46(1)
0.35(3)
0.285(2)
13
33
8
45
JAr]
A
D
0.309(1)
0.068(5)
0.924(1)
1.94(1)
0.404(2)
0.42(4)
89
11
[ArOLT]
A
B
D
0.275(1)
-0.06(1)
0.07(2)
0.624(2)
1.2(1)
1.98(5)
0.321(3)
0.54(5)
0.30(3)
79
17
4
a The given value is the quadrupolar shift 2e = AEQ(3 cos 2 0 - 1)/2 of the A subspeetrum.
282
A. Rykov et aL / Two-dimensional spinfreezing
100
95
90
85
DC
B VA
Z
0
t~
100
z
95
JAr]
e~
t-
>
90
85
e~
lO0
98
[ArO1.r]
96
94
92
-2
-1
0
1
VELOCITY (ram/s)
2
3
Fig. 1. Room temperature Mossbauer spectra of Y0.76Ca0.24Ba2Cu2.91Fe0.0906+y,prepared by
[OOLr],[Ar],and [ArOLr]methods. See text for details of preparation.
fit all the spectra with the same four quadrupole sites. However, the doublet C
was not found in samples prepared by methods JAr] and [ArOLr], while the doublet
B is absent for [Ar]-treatment. The change in the shape of the spectra from the top
to the bottom of this figure implies that a majority of Fe atoms have migrated
from the Cul to the Cu2 sites during [Ar]-treatment. At the next stage, the annealing of this sample in an oxygen flow at low temperature (400°C) allowed the back
migration of the cations to be avoided. Only a small fraction of Fe (,-, 10%) was
found to undergo a backward migration from Cu2 to Cul. We observed earlier
[19], for the compensated substitution "Y/Ca--Cu/Fe" in Yl-xCaxBa2Cu3_xFex07
(x = 0.09 and 0.24), that a substantial fraction of clustered ion atoms (,-, 30-40%)
survived in Cul-sites after [Ar]-treatment. For the "non-compensated"
(x = 0.09; z = 0.24) sample, the intensity of the A-subspectrum runup to 89% after
[Ar] treatment. Thus, the excess of Ca with respect to Fe allowed us to drive out
still about 30% of Fe cations from the Cul sites into the Cu2 sites.
A. Rykov et al. / Two-dimensional spinfreezing
283
Consideration of fig. 1 shows the AEQ dependence of the A-subspectrum upon
the oxygen content. We can suppose that the geometry of the pyramidal coordination which is accommodated by Fe in the Cu2 sites varies dramatically with the oxygen uptake or removal. The elongation of the FeOs-pyramids, which was
observed in Rietveld refinement (see table 1), explains the increase of AEQ in the
[Ar] sample with respect to the [ArOL-r] sample.
Three types of coordination (a tetrahedral and two pyramidal), proposed for
Fe on Cul sites, are well distinguished on the M6ssbauer spectra since the quadrupole splittings AEQ of the corresponding B, C, D subspectra differ significantly
from each other. Only the relative intensity of the quadrupole doublets B, C and D
varies, depending dramatically on the oxygen and iron contents and on the thermal
history of samples, while the quadrupole splitting AEQ of each individual doublet
does not vary significantly from sample to sample. The significantly different AEQ
values between B, C and D subspectra lead to a favorable situation to examine the
dependence of AEQ upon the geometry of the iron coordination polyhedra, which
will be done in the section 4, via electric field gradient (EFG) calculations.
4. E F G calculation
The determination of the EFG tensor acting on the metallic ion in different environments is of considerable interest in view of the assignment of MSssbauer subspectra to several coordinations of iron. The knowledge of the sign, direction and
magnitude of the principal component Vzz of the EFG tensor as well as that of the
asymmetry parameter of the metallic ion environment, r~, allows AEQto be completely calculated (module and sign); these results combined with hyperfine magnetic
interactions permit the interpretation of low-temperature M6ssbauer spectra.
Except in self-consistent charge density ab initio methods [22] where, by solving
the Poisson equation, the EFG is derived from an all electron band structure calculation [23], conventionally, the EFG tensor is generally estimated as the sum of
two contributions:
(i) a "valence term" coming from the electronic shells of the metallic ion, often
estimated in the crystal field model for ionic compounds or with molecular orbitals
calculations for more covalent situations;
(ii) a "lattice term" reflecting the geometry of the local environment, either
extended to a full lattice summation or limited to the polyhedron of first neighbors
of the central ion.
In the case of Cu2+ or Cu3+, the asymmetry of the 3s and 4p valence shells makes
the valence contribution the dominant one, as verified by Ambrosch-Draxl et al.
[23], while, in the case of high spin Fe3+ (S = 5/2) or Cu + (S = 0) the valence contribution can be neglectedwith respect to the lattice one. A more complicated situation occurs for Fe4+ (S = 2) [24] with a large valence term opposite in sign to the
lattice term, the result being a majoritary valence term (octahedral, pyramidal, tet-
284
A. Rykov et al. / 75vo-dimensional spinfreezing
rahedral environments), or a quasicancellation of the two terms (dumpbell, triangular, square coordinations). The case of the intermediate spin Fe3+ (S = 3/2) is
the most delicate since the relative importance of the valence contribution has not
yet been estimated became of too large uncertainties on the crystal field parameters; furthermore, the separation between lattice and valence terms has probably
no longer a physical meaning in such excited electronic configurations [25], where
the spatially extended metallic 4s and 4p orbitals could be involved and contribute
to the hybridization with the neighboring ligand orbitals. Nevertheless, the lattice
term might reflect the real situation, especially in cases where strong deformation
of the iron environmentcould be involved.
In a recent study of iron-substituted YBa2CuaO6+y[19], the S = 5/2 state was
attributed to Fe 3+ in the pyramidal Cu2 sites (A subspectrum) and the S = 3/2
state to Fe 3+ in the pyramidal (B, C subspectra) and tetrahedral ~ subspectrum)
Cul sites. Consequently, in the present work, we have only computed lattice contributions to the EFG tensor of Fe3+; as results from the above discussion, this would
be a quite correct treatment for the A site, while for the B, C and D sites it should
be considered only as a first qualitative approach to the problem.
Since each iron site differs from the corresponding copper site by its position
and by the geometry of its coordination polyhedron, it would be considered as a
structural defect. So, calculations of the lattice sum, in the point charge model,
using the non-modified Cul and Cu2 positions and coordinations, are no longer
correct for iron environment. A more precise calculation of Vzz for real oxygen
ligand coordination was proposed by Smith et al. [26]; the only contribution of the
innermost 02- ions was taken for a lattice sum approximation, resulting in reasonable AEQ values. However, the assumption of equal distances (ra = rb = re) for
each set of oxygen coordinations (V2, V3, V4, V,~,Vs, V6) seems to be oversimplified
owing to the distortions of iron tetrahedra and pyramids. These distortions, as
well as the variations of the iron location might modify significantly the calculated
EFG values. Neglecting these distortions leads to erroneous trends in the calculated values of AEQ which explains the misleading assignment of M6ssbauer C, D
subspectra to different four-fold coordinations [26], including an unrealistic
square-planar coordination of iron.
To promote a correct qualitative interpretation of the M6ssbauer spectroscopic
data, we have taken into account the real situation for the FeO4 and FeO5 polyhedra. The iron monopolar EFG lattice tensor has been calculated for the three different oxygen coordinations: pyramidal Cu2, pyramidal Cul and tetrahedral Cul.
For the sake of simplicity and owing to the crudeness of the model in the S = 3/2
case, we have introduced neither the dipolar contributions of the oxygen ions, nor
the monopolar contribution of more distant cations and anions. Several values of
the oxygen charges have been tested to take account for some covalence effects.
The results are not qualitatively affected by changes in the oxygen charges. The
most plausible results are obtained, assuming that oxygens are 02- except the O1
around the pyramidal Cul site with an average (-5/3) charge to take into account
A. Rykov et al. / Two-dimensional spin freezing
285
the holes residing on the chains. The same distribution of charge was used by
Pennington et al. [27].
The calculations are made in the Cartesian system Oxyz, simply deduced from
the crystallographic axes (with Ox[]a,OyHb,Oz[Ic in the pyramidal coordination or
with OxH [I I0], Oy[[[110], Oz]]c in the tetrahedral coordination). In the three cases,
the EFG tensor is diagonal in the Cartesian system, so its eigenvalues
Vxx, Vrr, Vzz are directly given by the set of Vxx, Vyy,V= put in the increasing
order of their absolute values, i.e. ]Vxx[<.[Vrr] ~<]Vzz]; this convention gives for
the asymmetry parameter r] = ( V x x - Vrr)/Vzz a positive value in the range
0 ~<r/~<1. AEQ = 1/2(1 - %o)eQVzz(1 + ~ / 3 ) 1/2 is then calculated using an antishielding Sternheimer factor %0 for high spin Fe 3+ of 10.14 [28] and a reasonable
value of 0.2 barn [29] for the 5VFequadrupolar moment Q. Note, that the Q value is
controversed in the literature [30], from 0.08 barn [31] to 0.28 barn, inducing a supplementary difficulty in the estimation of AEg. In the same way, the Sternheimer
factor is unknown for Fe 3+ (S = 3/2), probably greater than for Fe ~+ (S = 5/2)
because of the enhancement of the antishielding effect of the lattice charges due to a
greater spread of the iron p-orbitals. Consequently, our calculated values AEQ for
B, C, D sites could be underestimated.
For the EFG calculations we used the oxygen atomic positions obtained from
the refinement of the X-ray diffraction profile (table 1). To take into account the
displacement u of the Fe atoms from their ideal Cul (0, 0, 0) or Cu2(0, 0, z) sites
toward the center of the coordination polyhedra, we used a large range of values,
up to 0.4.~, in the three coordinations. The real values of these iron displacements
cannot be obtained with accuracy from neutron or X-ray diffraction refinements
since the environment of iron is different from that of copl~er. However, crystal
chemistry considerations show that the u values close to 0.4 A are realistic for iron
in Cu2 sites, but should be lower in Cul sites.
Fig. 2 presents the results of our monopolar lattice sum calculations for each of
the three iron coordinations as a function of the variation in u: calculated
Vxx, Vyy, V~z (in e .~-3), hence Vzz, rl and [AEQ[ (in mm/s) are represented. The
absolute values of AEQ give a semiquantitative agreement with the experimental
MSssbauer quadrupole splitting observed for A, B, C and D room-temperature
subspectra (table 2). Moreover, the three iron coordinations are consistent with the
available information about the sign and the direction of Vzz in A, B, C and D
MSssbauer sites:
(i) Observe (fig. 2a), that for the Cu2 pyramidal site, V= is obviously the principal component Vzz of an axial (r/= 0) EFG tensor. The gradient is always positive
and the calculated AEQ value decreases when increasing the iron displacement u
toward the apical 04 oxygen. The experimental values of AEQ, for the A subspectrum, in the range 0.6-0.9 mm/s suggest an important u displacement (,-~ 0.35 A)
toward the apex of the pyramid. This confirms the significant difference in the geometry of the pyramids between copper and iron in the Cu2 sites, observed earlier
in ref. [19]. Such a significant deviation of iron coordinates from the ideal Cu2 sites
A. Rykov et al. / Two-dimensional spinfreezing
286
~
g=z
0
Vx.~ Vyy
. . . . . . . . .
t . . . . . . . . .
i . . . . . . . . .
................................................................
~ . . . . . . . . .
,
. . . . . . . . .
i . . . . . . . . .
1 . . . . . . . . .
i . . . . . . . . .
,.
.05
JO
.15
.20
.25
,30
.35
AO
.05
,10
.15
.20
.25
Jo
J5
.,tO
.15
.20
.25
.30
DISPLACEMENT U
J$
,VO
E
N
.0
Vxx
Vzx
.05
JO
(A)
Fig. 2. Dependence of the calculated components Vx~, Vyy, V= of the EFG tensor (in e.~-3), absolute
values [AE(~}of the quadrupole splitting and of the asymmetry parameter T/on the Fe atom position
u inside of its coordination polyhedron. The distances from the ideal site to oxygen ligands were taken
starting from the atomic coordinates in the [OOLr] sample (table 1). The Cartesian axes were
x[la, ytlb, zlle for both Cu2 (a) and Cul (b) pyramids and xl][1 i0], YII[110], zlle for Cul tetrahedra (c).
Zero displacement u = 0 corresponds to iron location in an ideal copper site. In the Cul pyramids, the
oxygen atoms are located at the Cartesian coordinates (a/2,0,O);(O,a/2,0);(O,-a/2,0);
(0,0,cz(02)/2); (0,0,-cz(02)/2). In the Cul tetrahedra oxygen atoms are located at (a/2v~,a
/ 2 v ~ , 0); (a/2V~, -a/2V'2, 0); (0, 0, cz(04)/2); (0, O, -cz(04)/2). The displacements of Fe are in
crystallographic direction [00i] for Cu2 and in [100] for Cul pyramids and [1i0] for Cul tetrahedra.
is consistent with a weak sensitivity o f the chemical shift of the A subspectrum to
the hole concentration of these Cu2 sites. Thus, the attribution o f the A-subspectrum to an "interstitial" site by N a t h et al. [32] m a y be comforted if"interstitial"
means a position distinct from Cu2, inside the same coordination pyramids.
A. Rykov et al. / Two-dimensional spin freezing
287
o
(ii) For the Cul pyramidal site, with u ranging from 0 to 0.3 A, fig. 2b shows
decreasing calculated values of [AEQ], when iron moves along [100]. Observed
values of 1.0-1.2 mm/s for the B subspectrum (small clusters Fe2Og, Fe3013 made
of corner-sharing FeO5 pyramids) are consistent with the calculated curve. Owing
to the real iron displacement in Cul sites, in contrast to the Cu2 site, it is reasonable
to limit them to about 0.1 A because of the small Fe-O 1 distances in the ab-plane
(1.93 ,~). With this restriction, fig. 2b shows that either Vxx or Vzz could correspond
to the principal component Vzz of the EFG tensor, depending on the real u value.
Note, in this range, the calculated asymmetry parameter 77~ 1. High values
of ~7have been derived from single crystal [33] and grain oriented powder [34]
M6ssbauer spectra. For very small u values, Vzz coincides with the Vxx, positive,
component of EFG, in agreement with the widely accepted idea, that in pyramidal
Cul sites the EFG principal axis is directed toward the apical oxygen [34], thus parallel to the a-axis. For upper u values, Vzz is given by the negative Vzz component
of the EFG, parallel to the c-axis. Such an orientation of Vzz was used in the interpretation of M6ssbauer spectra of single crystals [33]. Note, that the change from
Vxx to V= for Vzz principal value with increasing u does not generate any discontinuity in the magnitude of AEQ, since for ~ = 1, Vyy = O, [Vxx[ = [Vzz[. So, in this
case no privileged axis exists for the EFG gradient in the ac-plane. In fact, the contradiction which appeared previously in different interpretations of the EFG sign
and direction for B sites can be attributed to different ways of extracting and interpreting this information. Indeed, two solutions for the sign and direction of Vzz
may be deduced within the scope of experimental error, if one applies for the B-site
as well general relationships for line intensities of oriented powder spectra [35] as
quadrupolar parameters in case of combined magnetic dipole and electric quadrupole interactions [36].
The experimental [AEQ[ = 1.8 mm/s corresponding to the pyramidal Cul C
site is larger than the [AEQI for the B site. This is consistent with the attribution of
the C subspectrum to FeO5 and CuO5 pyramids sharing their corners [ 19]. In such a
configuration the u displacement of Fe toward the apical oxygen is decreased with
respect to the B subspectrum configuration. This explains the increase of [AEQ[ as
shown in fig. 2b.
(iii) Fig. 2c is relative to the tetrahedral Cul site; Vzz is the negative principal
component of the EFGs. The contribution of two nearest 04 oxygens defines the
negative sign and direction of the global EFGs; this could explain why a number of
papers have been concerned with misleading assignment of the D doublet to a
two-fold coordination of iron [20,37]. The evidence of negative Vzz = Vz~ for the D
site has been obtained experimentally [33,34,38,39]. Fig. 2c shows that the
observed values of ]AEQ]of about 1.94 mm/s are very close to calculated values corresponding to very small displacements of the Fe atoms from the edge to the center
of the FeO4 tetrahedron. This is in agreement with the range 0 ~ u ~<0.16 .~ previously observed by neutron diffraction [40]. Indeed, small u values are coherent
with the rigidity of the perovskite framework formed by neighbouring BaO layers.
288
A. Rykov et al. / Two-dimensional spinfreezing
An other consequence of such a small displacement is the calculated value of asymmetry parameter rl, close to zero. This was observed for the D subspectrum of
c-axis oriented thin films [39] and grain oriented samples with 0° geometry [34].
In spite of the various approximations and uncertainties, which cannot be
avoided in the above EFG calculations, we can observe that the monopolar lattice
EFG evaluation for several coordinations around Fe in Cul and Cu2 sites supports our recent assignments of M6ssbauer subspectra [19] made on the basis of
spectral intensity redistributions caused by different thermal treatments. Consequently, it appears that our treatment has taken sufficient account of the covalency
effects between oxygen and iron in these compounds, which result rather in a rearrangement of the atoms in Fe-O polyhedra than in drastic charge density effects.
5. Magnetic hyperfine spectra
Generally, the orientation of the axis of easiest magnetization relatively to the
EFG axes is deduced from low-temperature Mrssbauer spectra using the two independent parameters Fzz and r/of the EFG tensor. On the other hand, the knowledge of the spin alignment axis established independently, e.g. by neutron
diffraction, promotes the EFG determination from M6ssbauer data. However, the
complexity of the magnetic structure for Fe and Co doped YBa2Cu3Or+y, and the
insufficient number (3-5) of magnetic Bragg peaks observed in neutron diffraction
patterns [41-43] do not allow reliable data to be obtained about the internal magnetic field direction for the Cul site. On the other hand, the results of Mrssbauer
studies have not been largely used up to now in neutron diffraction analysis of the
magnetic structure. Such a situation may be attributed to the complexity of the
magnetically split M6ssbauer spectra for the "123" phases doped with iron. From
this point of view an interesting observation made by Mirebeau et al. [44] in desoxygenated YBa2Cu3_xFexOr+ywas that there coexist two different types of magnetic
order, i.e. long-range antiferromagnetic order and spin-glass freezing. Such a coexistence, involving different spin components, cannot be accounted for by long
range magnetic order, observed in neutron diffraction.
To determine the influence of the local EFGs on the spin orientation of iron the
samples JAr] and [Airq] for x = 0.24, z = 0.24, and the samples [Ar] and [ArOLT]
for x = 0.09, z = 0.24 were studied by Mrssbauer spectroscopy at 4.2 K. The corresponding spectra are shown in figs. 3 and 4, respectively. The difference between
the magnetic behaviour of Fe in Cul and Cu2 sites can immediately be seen if
we compare the room temperature and 4.2 K spectra for desoxygenated samples
(fig. 3). For Fe ions located in Cu2 sites of the highly desoxygenated [Ar] sample the
ordering temperature TN lies slightly above room temperature. In contrast, B and
D subspectra assigned to Cul sites show a paramagnetism of Fe ions at room temperature. At 4.2 K, both Cul and Cu2 sites are involved in the magnetic ordering.
However, the Cul and Cu2 sites are well distinguished at 4.2 K by the values of the
A. Rykov et al. / Two-dimensional spin freezing
4.2 K
300 K
E
Z
289
O0
100
0
99
99
98
~ 98
<
I.~
97
97
[Airql
,,
i
M
111
~, 100
-3
-2
1
-1
I1'
96
~. 96
•
2
,,,
3
-10
-8
-6
.4
-2
0
4
6
8
,
I
10
,
90
96
80
94
tAr]
,,,
,
J
,
a
J
i
-6
-4
-2
0
2
4
VELOCITY
92
6
i,
.10
-8
-6
(mn't/s)
-4
.2
i
,
a
0
2
4
VELOCITY
-
8
i
10
(mtrffs
Fig. 3. M6ssbauer spectra at room temperature and at 4.2 K of Yo.TaCao.24Ba2Cu2.76Feo.2406+yprepared by [Ar] and [Airq] methods.
100
~
99
Z
0
98
~
97
Z
<
,.o
E-
96
~
<
,d
99
,~
98
[Ar]
97
[ArOLT]
-10
-8
.6
-4
-2
0
VELOCITY
2
4
6
Cram/s)
8
lO
Fig. 4. Magnetic hyperfine spectra at 4.2 K for Yo.76Cao.24Ba2Cu2.91Feo.0906+y,prepared by methods
[Ar] and [ArOLT].
290
A. Rykov et al. / Two-dimensional spinfreezing
saturation hyperfine fields (table 3). The subspectra B and D cannot be separated
correctly in our magnetically split spectra because o f their b r o a d e n e d shape.
Besides, such a separation is highly controversal in m a n y works due to close values
o f the hyperfine parameters for the pyramidal and tetrahedral Cul sites. The sum
o f intensities o f B and D subspectra at 300 K for all the samples is in agreement with
the total intensity involving the B + D magnetic sites and a small paramagnetic
c o m p o n e n t D' (3-10%) at 4.2 K. The intensity o f this paramagnetic line increases
with decreasing the iron population on the Cul sites and reaches the total intensity
o f D subspectrum observed at r o o m temperature for the [Ar] sample (x = 0.09, z
= 0.24). The values o f the quadrupole lineshift 2e, evaluated at 4.2 K for B + D components are in the range 0 . 3 - 0 . 4 m m / s . Taking into account that for the [Airq] sample the D-subspectrum is predominant, one can evaluate the orientation (0, q~) o f
the hyperfine field in the principal axes o f the non-axial E F G tensor f r o m the general relationship [36],
2e/laEQI =
[sign(Vzz)/2][3cos: 0 - 1 + 77 sin20 cos(2q~)].
(1)
The obvious choice o f a negative sign and of the z-direction for V z z for D sites
(as these parameters were calculated above for distorted tetrahedral iron coordination) results in 01 ~ 60 ° if r / = 0 and in 01 ~ 50 ° if r / = 1 (2q~ = 180 °, since the H direction is considered to be confined in the (110) crystallographic plane, the
crystallographic directions [001] and [1 I0] being parallel to the two m a j o r E F G
c o m p o n e n t s in the distorted tetrahedron). Thus, since the E F G principal compon e n t V z z = Vzz is fixed to be parallel to the c-axis, the direction o f spin alignment at
Table 3
Hyperfine parameters of M6ssbauer spectra measured at 4.2 K; isomer shift relative to ct-Fe(6is);
quadrupole lineshift 2~ = AEQ(3cos2 0 - 1)/2); mean hyperfine field Hhf; 0 angle between the principal EFG component and the magnetic hyperfine field direction and relative areas of observed
M6ssbauer subspectra (%).
x, z
Treatment
Subspectra
6xs(ram/s)
24 (mm/s)
Hhf (T)
0(deg)
0.24, 0.24
[Airq]
A
B÷D
D'
0.423(5)
0.18(3)
0.21(1)
-0.346(6)
0.38(3)
-
48.4(1) 73.0
28.6(2) 50-62
-
69
27
4
0.24, 0.24
[Ar]
A
B+D
D'
0.408(2)
0.11(7)
0.20(5)
-0.466(4)
0.34(4)
-
49.57(4) 75
30.1(4) 56
-
58
38
4
0.09, 0.24
[Ar]
A
D'
0.393(3)
0.43(3)
-0.366(2)
-
47.95
-
90
10
0.09,0.24
[ArOLr]
Aa
A+B+D a
0.368(6)
0.28(4)
-0.31(1)
0.34(6)
38.47(6) 90
20.8(4)
-
74.7
-
%
58
42
a A tentative representation of spectra by two components is shown in fig. 4. The results of a more
accurate treatment using an hyperfine field distribution are shown in fig. 6.
A. Rykov et al. / Two-dimensional spin freezing
291
4.2 K is neither parallel nor perpendicular to the c-axis. Both the parallel (MII)
and the perpendicular (M±) to c-axis magnetic moment components should be
involved in the antiferromagnetic structure with an absolute value of/1411 close to
IMI/2. Miceli et al. [41] reported for Co substituted YBa2Cu306+y with a similar
substitution rate (x = 0.2) the presence of ordered moments on both Cul and Cu2
sites below the freezing temperature Tf = 211 K (T~2 in their notation), while in
the range Tf < T < TN = 415 K an ordered moment was observed only on Cu2 sites.
Above Tf, the antiferromagnetic sheets of spins lying in the ab-planes are stacked
collinearly along c in the sequence " + - 0 + - 0 + - 0 " . At room temperature,
a 90 ° angle between Vzz and the hyperfine field direction is observed in the
M6ssbauer spectra [20,21,38]. Below Tf, the appearance of an ordered moment on
Cul sites leads to the doubling of the magnetic cell along c. The antisymmetric
spin contribution of stacking sequence " - ~ - + E) + - ~ - + E), appearing
below Tf, has also been assumed [41] to be perpendicular to the c-axis. However,
taking into account our result on the 01 value for Cul sites, one should allow for
such an antisymmetric stacking of magnetic sheets to be composed of moments
tilted with respect to the ab-plane. The assumption of a tilt angle ~x/2 - 01 may not
significantly modify the calculated neutron magnetic reflections intensities and
such a structure can describe equally a few magnetic peaks available in the neutron
diffraction experiments. The MII component of chain moments should perturb the
moments of the Cu2 planes leading to the appearance of small " + - " in the latter
sequence " + - ~ - + • + - @ - + E)". Such a perturbation can be observed in
M6ssbauer spectra of Fe located in Cu2 sites.
In order to evaluate the MII value induced in the Cu2 sites for the samples [Ar]
(x = 0.09, z = 0.24, and x = 0.24, z = 0.24) and [Airq] (x = 0.24, z = 0.24), the A
subspectra were fitted by Zeeman sextets of inhomogeneously broadened Lorentzian lines of full width Fi = FO "1- 7ilZNAI[ (71 m. 0.0388, 3'2 = 0.1418,"/3
= 0.2449, AH is the half width of the field distribution P(H) and #N is the nuclear
magneton). A well defined geometry of the iron coordination polyhedra in Cu2
sites helps to determine with a good precision the angle 02 between the c-axis and
the hyperfine field direction. Since the Cu2 site possesses a roughly tetragonal symmetry, the principal EFG axis is directed along c and the E F G asymmetry parameter r/is close to zero; it has also been demonstated in section 4 that Vz~> O.
Hence, the quadrupole splitting AEQ and Zeeman quadrupole lineshift e are related
with the same 82 by 2c/AEQ = (3 cos 2 02 - 1)/2. If 02 exceeds the magic angle
54.7 ° = arccos(1/v~), then e becomes negative and it reaches its maximum value
AEQ/4 for 02 = n/2. In fact, for our [Airq] sample (x = 0.24, z = 0.24) the 14elvalue
of 0.692 m m / s measured for the A subspectrum at 4.2 K (table 3) is lower than
AEQ = 0.93 mm/s, measured at room temperature (section 4). Eq. (1) gives for Cu2
site the value 02 = 73 °. For the x = 0.09, z = 0.24 [Ar]-sample 02 is 74.7 °. In a previous work, for a number of samples, we have observed 2e values at room temperature larger than those at 4.2 K (table 3). Hence, at 300 K, 02 = ~/2 indicates an
alignment of both copper and iron spins in the ab-plane. Thus, a finite value of MII
292
A. Rykov et al. / Two-dimensional spinfreezing
appears in our samples below Tf (Tr < 300 K) in both Cul and Cu2 sites. The evaluated smallvalue of MII yields a model ofnon-collinear spin arrangement. The available set of magnetic peaks in neutron diffraction might be fitted within the scope
of this model
It should be emphasized here that the increase of Fe content leads to a decrease
of 02 even at room temperature. The deviation of 02 from 7t/2 can be recognized in
the room temperature spectra shown by Felner et al. [10] and Lyubutin et al. [45],
as weI1 as in our data for high doping x = 0.36 [46]. The formation of a complex
long range magnetic structure involving MII in both Cul and Cu2 sites was
observed for such a substitution rate (x = 0.8) in neutron diffraction [43]. Thus, for
x > 0.6-0.5, the 3D long range magnetic ordering differs significantly from the 213
antiferromagnetism in YBa2Cu306. For low Fe contents (in this study x = 0.09 and
x = 0.24), the measured angle deviates slightly from n/2; consequently, below Tf
the sman value of the MII introduces a weak perturbation of the Cu2 site in-plane
anti ferromagnetism.
A ratio value 2e/AEQ = - 1 / 2 could be approximately evaluated for the main
magnetic subspectrum of[ArOLw]-treated sample (x = 0.09, z = 0.24) (tables 2 and
3). This means that the majority of the spins are oriented essentiaUy in the abplane. However, the method of fitting used for the [Ar]-sample failed for the
[ArOLw]-sample. In the latter case, sp~tral lines are worse resolved and clearly
asymmetric. Attempts to fit the spectrum with two components lead to a ratio
value of subspectra areas 40% : 60% (fig. 4 and table 3) instead of 20% : 80% (the
ratio of Fe fractions in Cul and Cu2 sites, respectively, observed at room temperature (fig. I and table 2)). Therefore, spectra measured at several values of temperature and external magnetic field have been evaluated using a histogram-type
hyperfine field analysis. These distributions concern principaUy the Cu2 sites .but
do not exclude a smallcontribution (20%) of the Cul sites.
The evolution of the MSssbauer spectra of the superconducting [ArOLw]-sample on decreasing the temperature is presented in fig. 5. The coexistence of paramagnetic and magnetically ordered fractions is observed only on a very narrow
temperature range. This results suggests that aU the ions behave similarly with the
temperature variation. Thus, there is no evidence, for some clusters, of rigidly
coupled spins, which would involve a superparamagnetic behaviour. The appearance of a broad hyperfine field distribution is related to a spin-glass transition at
Tf = 10 K, and the magnetically split spectrum becomes clearly resolved at 4.2 K.
The M6ssbauer spectrum measured in an external magnetic field of 4.28 T
(fig. 5) perpendicular to the propagation of T-rays, shows a remarkable polarization effect. The distributions of both, the orientations and the values of hyperfine
fields, are affected by the external field. The former is related to the partial spin
alignment in the field direction, while the latter is reflected in the shape of the hyperfine field distribution P(H). The dependence of the MSssbauer absorption probability on the angle between the direction of propagation ofT-rays and H results in
the full polarization in the hyperfine components intensity ratio I : 4 : 3. The
A. Rykov et al. / Two-dimensional spin freezing
293
100
95
300 K
it!
H.,,=0
90
100
98
SK
",~
96
::
H~t=O
..~
-.
I00
Z
0
99
5.5 K
;~, ~ . * ,
.'~.,'."
"v- " ,'e.,
Hext=0 |
"i,,
/
98
100
^~
<
•
99
:5
98
" :
•
4.2 K
I00
.. ~
"
~
•
".
:.
"~
"
.~
't.t
Hext=O
~'~'~
-,, .A .~,
•
, ~".\~
i .~'..
•~ : .. -.
~ . "~-
"~"
99
.:
~.
~t
98
4.2 K
.10
-8
-6
Hext= 4.28T
.4
-2
0
2
4
6
8
10
V E L O C I T Y (ram/s)
F i g . 5.57Fe M o s s b a u e r spectra o f the 49 K superconductor Y0.7~Cao.24Ba2Cu2.91Feo.0907 m e a s u r e d
at d i f f e r e n t t e m p e r a t u r e s in different e x t e r n a l fields. T h e s a m p l e w a s first a n n e a l e d a t 8 5 0 " C in Ar,
t h e n o x y g e n a t e d at 4 0 0 " C in 0 2 ([ArOLT] t r e a t m e n t ) .
induced alignment of spins in the field direction is implied by the redistribution of
the spectral intensity between the Am = 0 hyperfine components (lines 2 and 5) and
the rest of the spectrum. On the other hand, the narrowing of the spectral lines
and the decrease of absorption in the middle of the spectrum measured in an external field suggest a significant change in P(H).
The experimental spectra were fitted with a distribution of hyperfine field from
0 to 50 T, with equal width (1.5 T full width at half maximum). The line intensity
ratios were fixed to 1 : 2 : 3 for Hext = 0. For the spectrum measured in the trans-
A. Rykov et al. / Two-dimensional spinfreezing
294
verse external field of 4.28 T the distributions of hyperfine field were calculated
for two idealized intensity ratios 1 : 2 : 3 and 1 : 4 : 3. The distribution ofquadrupolar interactions was assumed to be correlated linearly with the hyperfine field of
the different components of the distribution: 2ei = 2el + 2e2(Hi/Ho).For Hcxt = 0,
the best fit was obtained for values 2el = 0.15 m m / s and 2ez = - 0 . 4 5 m m / s , which
provided the value 2e0 = - 0 . 3 mm/s, the ratio 2eo/AEfl = - 1 / 2 and 00 = Ir/2 for
the main ( H = H0) component of the hyperfine field distribution. In the spectra,
measured at 4.2 K, the main peaks are located at Ho = 40 T for Hext = 0 and at
H0 = 38 T for n e x t = 4.28 T (fig. 6). Such a shift of the P(H) maximum towards a
T=5~ K, liexlffi0
1-
f ,i . . . . . . . . . . .
0
10-
T=4.I K, Hext=0
8.
2
0 .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1412-
Tffi4.2 K, Hext= 4.28 T
10.
8,
6
4
2
0
0
4
8
12
~.6
INTERNAL
20
24
28
FIELD
32
36
40
44
48
H(T)
Fig. 6. Hypvrfmv field distributions P(H) at 4.2 K in the external fields Hcxt = 0 and Hcxt = 4.28 T
and at 5.5 K with Hcxt = 0. Yo.76Cao.24Ba2Cu2.9!FCo.o907 was prepared by the [AXOLT]method.
A. Rykov et al. / Two-dimensional spinfreezing
295
lower effective internal field is due to the negative sign of Hhf with respect to the
Fe magnetic moment, which aligns parallel to the external field.
Changes in the shape of P(H) induced by the external field were observed for
both variants of calculations with different intensity ratios (1 : 2 : 3 and 1 : 4 : 3).
The distribution represented at the bottom of fig. 6 was obtained in the fit with
fixed ratio 1 : 4 : 3. Since the 12E01value of 0.3 m m / s decreased only slightly under
Hext = 4.28 T, we can assume that the full spin polarization in the field direction
was not achieved in our experiment. Nevertheless, the disappearance of a low-field
tail in P(H) with external field (fig. 6) means that the polarization is facilitated for
the Fe spins whose contribution is in the low-field tail of the P(H) curve. However, since 2eo/AEQ= - 1 / 2 for the high-field peak of the P(H) distribution, this
peak should be related to spins aligned essentially in the ab-plane, while the lowfield tail may correspond to some randomized array of spins. Therefore, the external field produces an additional alignment of some fraction of the Fe spins in the
ab-plane. This result is indicative of the rearrangement of frustrated magnetic
bonds for a fraction of Fe atoms on the Cu2 sites. Such an effect of the external field
on the localized moments of the Cu2 sites shows that the local anisotropy for Cu2
is essentially weaker than for Cul, whose magnetic moments in the frozen state are
not influenced by the external field [47].
6. Discussion
The lack of a well-defined six-line structure in the Mrssbauer spectra with classical lines intensities ratios 1 : 2 : 3 evidences an important symptom of spin-glass
behaviour. Nevertheless, the understanding of hyperfine interactions in oxide spin
glasses is not quite satisfactory, neither on the theoretical nor on the experimental
level. A broad distribution P(H) arises in spin glasses as the result of bond disorder
in magnetic interactions. However, a conventional interpretation of broadened
Mrssbauer spectra appeals to a site disorder, appearing when Fe atoms have a
different number of magnetic neighbours [3]. In our iron-diluted system, the random distribution of Fe and Cu ions leads to a small probability for next neighbour
Fe-Fe bond (P4(1)= 4g(1 _ g ) 3 = 0.13 with the random occupation number
g = 0.035), while in the cluster hypothesis, the site disorder is much more important. In the analysis of Mrssbauer spectra of Fe-doped GdBa2Cu3Or+y, Tang et al.
[11] consider the cluster formation for Fe dopants in the Cu2 planes to be energetically unfavorable. Indeed, since the charge of Fe 3+ is larger than that of Cu z+, the
Fe clusters in Cu2 plane would lead to the local charge excess. Smith et al. [14] also
have assumed Fe atoms in Cu2 sites of Y1-zCa~Ba2Cu3_xFexOr+yto be randomly
distributed. These ideas stimulate our attempts to consider the bond disorder as the
most adequate model. Therefore, this model applied to spin-glass magnetism may
allow useful information to be obtained about local spin correlations in the superconducting state.
296
Our observed
A. Rykov et al. / Two-dimensional spinfreezing
P(H) histogramm can be compared with the distributions of
Hi = ~'~i(#j)JuSJ obtained in Monte Carlo simulations for 3D and 2D Ising models
[48], whichshow in the T < Tf region a maximum of P(H) at a finite value H0 and
a low-field tail. On the other hand, when T > Tf the internal field still persists in
these models in disagreement with our observation. Gabay and Toulouse [49] have
pointed out that the properties of magnetic systems with competition between magnetic interactions may be described more adequately by isotropic vector spins.
The infinite-range model of random magnets composed of Heisenberg-like spins
allow for the longitudinal and transverse spin components to order at distinct critical temperatures. In the Heisenberg model for two-dimensional spins with distribution of Jy-interactions [50], P(H) shows a tail for H > H0 and a sharp cutoff in the
low-field region, which does not agree with our shape of P(H). If we assume a constant module H = H0 for the magnetic field created by spins aligned in the abplane, then for a random spin orientation P(O) = 1 the density of probability P(H)
is proportional to [1 - (H/Ho)2]-1/2. Such a distribution culminates very sharply
at H0 and possesses a low-field tail.
Let us compare the magnetic transitions in the oxygen-saturated [ArOLT] and
oxygen-depleted [Ar] samples. Because of the weakness ofinterplanar coupling, the
3D long-range antiferromagnetic ordering at TN presents the two-dimensional
character with TN very close to the Txy transition temperature of the KosterlitzThouless model [51]. In the desoxygenated samples TN is affected only slightly by
iron substitution. On the other hand, the local anisotropy in Cul sites induces a
freezing of both iron and copper spins corresponding to the spin-glass transition at
Tf. Below, Tf, the antiferromagnetic order in Cu2 sites coexists with the spin glass
order, which involves both the moments in Cul sites as well as the orientational perturbations in Cu2 planes. These perturbations, estimated by the 02 tilt angle and
the Tf temperature measured by M6ssbauer spectroscopy, increase when increasing the iron substitution rate x. At x = 0.3-0.4, the crossover from 2D to 3 D antiferromagnetic long-range order takes place (Tf = TN).
In the Fe-doped oxygen-saturated samples, neutron diffraction studies [16,17]
show the absence of long-range magnetic ordering. Instead, short-range Cu-spin
correlations are induced by iron substitution [11]; one can suppose these correlations to be originated from a strong ab-coupling in Cu2-planes. These 2D Cu-spin
correlations might be frozen on the time scale of 57Fe Mfssbauer probe and they
develop in three dimensions if some magnetic moments, which enhance interplanar
coupling, reside in the Cul sites. The same type of enhancement of antiferromagnetic coupling has been observed by Miceli et al. [41]. For our [ArOLT] sample, a
saturation field value of 40 T has been observed, which might seem rather weak,
compared, for instance, with Tamaki's value of 48 T [I]. But in our samples, the
small fraction of iron atoms in Cul sites (20°/'0)generates a decrease of the coupling
between planes and chains, which can explain our depressed H0 value.
The effects of a dynamic disorder in spin alignment might be essential near the
freezing point and can be accounted for, as it has been proposed recently [52].
A. Rykov et al. / Two-dimensional spinfreezing
297
Treatments of M6ssbauer data, involving consideration on relaxation processes
in correlated spin clusters, are planned to clarify this point.
7. Concluding remarks
In
summary,
we were able to
prepare
the
superconductor
Y0.76Ca0.24Ba2Cu2.91Fe0.0907, which exhibits 79% population of iron atoms in Cu2
site. The coexistence of superconductivity (Tc = 49 K) and spin-glass freezing in
iron-copper magnetic system (Tr = 10 K) was investigated by using M6ssbauer
spectroscopy. In the glass-like state, frozen magnetically on the time scale of 57Fe
M6ssbauer probe, the localized moments are oriented essentially in the ab-plane.
Thus, an important property of spin-glass freezing in Fe-doped high-To supercond u c t o r - its two-dimensional character - is evidenced.
Another important result deals with the spin-glass transition at Tf in the oxygen-depleted low-y phase. It is shown that below Tf the magnetic moments are not
aligned perfectly in the ab-plane, neither in Cul sites nor in Cu2 sites. The coexistence of long-range antiferromagnetic ordering and spin-glass order below Tf has
been suggested from these results. Below Tf, the spin-glass order in oxygendepleted samples involves both Cul and Cu2 sites, while for x lower than 0.3 the
long-range antiferromagnetic order involves only Cu2 sites.
The calculation of the EFG tensor has been performed for different iron coordinates in Cul and Cu2 sites. These results confirm our previous assignment of the distribution of iron in the different copper sites, as well as its various coordinations.
Acknowledgement
One of the authors (AIR) gratefully acknowledges the kind attitude of Yu.T.
Pavlukhin and V.V. Boldyrev whose particular interest in performing this work
was supported by the Scientific Council on HTcSC, grant N189 of the Russian program on High-Temperature Superconductivity.
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