Melting of Orbital Ordering in KMgxCu1-xF3 Solid Solution - The

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J. Phys. Chem. B 2007, 111, 5976-5983

Melting of Orbital Ordering in KMgxCu1-xF3 Solid Solution Cesare Oliva,† Marco Scavini,† Serena Cappelli,† Claudio Bottalo,† Claudio Mazzoli,‡ and Paolo Ghigna*,§ Dipartimento di Chimica Fisica ed Elettrochimica, UniVersita` di Milano, V. Golgi 19, I-20133 Milano, Italy, European Synchrotron Radiation Facility, 6 rue Jules Horowitz, BP 220, 38043 Grenoble CEDEX 9, France, I.E.N.I.-C.N.R. and Dipartimento di Chimica Fisica, UniVersita` di PaVia, Viale Taramelli 16, I-27100 PaVia, Italy ReceiVed: NoVember 14, 2006; In Final Form: March 16, 2007

The long-range and short-range structures of KMgxCu1-xF3 (0 < x < 1) have been investigated by means of XRPD and EPR. Two different solid solutions are present, based on the structure of KMgF3 (for x > 0.42) and of KCuF3 (for x < 0.26), respectively, and they are separated by a biphasic zone. Positional disorder is induced by doping due to the different Cu and Mg environments. In fact, the EPR measurements have shown that the Cu environment is isotropic for x > 0.8. It shows axial symmetry for 0.45 < x < 0.70 and orthorhombic symmetry for x ) 0.43. For x > 0.42, the crystallographic structure is cubic, and in absence of local disorder, a fully isotropic octahedral undistorted environment is expected for Cu. In the tetragonal structure, collective magnetic interactions arise, and a progressive EPR signal symmetrization is observed due to anisotropic exchange and to Dzialoshinsky-Moriya antisymmetric exchange processes. The mixing of triplet and singlet states induced by the above exchange mechanisms leads to the conclusion that the orbital order is melt in the x ) 0.1 sample, for which the cooperative Jahn-Teller distortion is still active and the 3D magnetic order is still antiferromagnetic, as in KCuF3.

Introduction KCuF3 is a Mott-Hubbard insulator with a pseudocubic perovskite structure.1 In its most common crystalline form (the so-called “a” poly type; see below), it belongs to the I4/mcm space group. The structural distortion is due to orbital ordering associated with cooperative Jahn-Teller effect.2 CuF6 octahedra in the ab plane are elongated along the a- or b-axis in an antiferrodistortive pattern. The distortion corresponds to an alternate occupation of Cu-3dy2-z2 and Cu-3dx2-z2 hole states on the Cu(3d9) ion located in adjacent sites in the ab plane (orbital ordering).3 This orbital configuration has been proposed to explain the quasi-one-dimensional magnetic properties of this compound. It has been shown that nearest-neighbor superexchange (NN-SE) interactions are strong and antiferromagnetic (AF) along the c-axis and weak and ferromagnetic in the ab plane, resulting in a one-dimensional antiferromagnetism at high temperatures. For T e TN ) 38 K, KCuF3 shows threedimensional antiferromagnetic order. The ratio between NNSE along and perpendicular to c is |Jc|/Ja| = 100.4 In the orbital ordered structure,1 both the sign and the actual value of the exchange constants are in agreement with the GoodenoughKanamori-Anderson rules. Resonant and nonresonant magnetic scattering measurements revealed a significant orbital contribution to the total magnetic moment of the Cu ions; in addition, at T g TN, there is a drastic increase in the resonant X-ray scattering (XRS) signal. To explain this result, it has been proposed that magnetic and orbital degrees of freedom are coupled in some way;3,5 however, very * To whom correspondence should be addressed. Phone: +39 0382 987574. Fax: +39 0382 987574. E-mail: [email protected]. † Universita ` di Milano. ‡ European Synchrotron Radiation Facility. § I.E.N.I.-C.N.R. and Universita ` di Pavia.

recently, theoretical works claimed both that the orbital order parameter should be almost saturated already at room temperature and that a change in the magnetic structure is expected to have only a small influence on the Jahn-Teller distortion in the commonly accepted RT crystallographic structure of KCuF3. It has, therefore, been suggested that the XRS signal near the Ne´el temperature may be related to a low-temperature structural transformation.6 X-ray powder diffraction measurements carried out at low temperature by some of us at the ID31 beamline of the European Synchrotron Radiation Facility, however, failed to detect any structural phase transition down to 20 K. It is, therefore, highly desirable to get further insight into this intricate behavior. In particular, one of the main questions that remain open is about the relative energy scales of the magnetic, orbital, and structural degrees of freedom. Melting of orbital order in KCuF3 is expected to occur well above room temperature,2 where the cooperative structural distortion should disappear and the undistorted cubic perovskite structure (space group Pm3m) should be favored: the energy gap for destroying orbital order, calculated through local density approximation model, is about 2.5 eV.3 Therefore, to observe the melting of the orbital ordering in KCuF3, it is likely that temperatures much higher than those reachable in a suitable experimental apparatus are needed. A system in which melting of the orbital order could be possibly more easily observed is the solid solution KMgxCu1-xF3 (0 < x < 1). Indeed, the strength of the Cu-Cu interaction can be modulated by varying the Cu/Mg ratio. In this way, the interplay between structural, orbital, and magnetic degrees of freedom in KCuF3 could be better understood. The crystal structure of the solid solution is strongly influenced by the chemical composition. In fact, at room temperature, the structure of the Mg-rich part of this solid

10.1021/jp067539p CCC: $37.00 © 2007 American Chemical Society Published on Web 05/10/2007

Orbital Ordering in KMgxCu1-xF3 Solid Solution

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Figure 2. Observed (crosses) and calculated (continuous line) profile of the KMg0.6Cu0.4F3 sample. In the same Figure, the residuals are also shown (bottom).

The aim of this paper is to study these features by means of a combined X-ray powder diffraction (XRPD) and electron paramagnetic resonance (EPR). Figure 1. Structural relationship between KMgF3 and KCuF3 structures. Black full circles, K ions; empty circles, Mg and Cu ions; gray circles, F ions. (a) Undistorted perovskitic cubic cell for KMgF3 (space group Pm3m). (b) Antiferrodistortive pattern of the positional distortion of the F ions in the pseudocubic ab plane of KCuF3. (c) Pseudocubic cell of KCuF3; the orbital ordering (alternate occupation of Cu-3dy2-z2 and Cu-3dx2-z2 hole states on the Cu(3d9) ion located in adjacent sites) and the spin ordering are highlighted. (d) Tetragonal cell for the “a” poly type of KCuF3 (dotted lines, space group I4/mcm). Only a few F and Cu ions are displaced for simplicity. The metric relationships between the tetragonal and the pseudocubic cells are shown.

solution is isomorphic with KMgF3 undistorted cubic perovskite (space group Pm3m). Mg and Cu ions occupy the (0, 0, 0) site, K the (1/2, 1/2, 1/2) one, and F ion the (1/2, 0, 0) site (hereafter, Cu1/Mg1, K1, and F1 sites, respectively). The structure is shown in Figure 1, continuous lines. Conversely, the Cu-rich part of the solid solution is isomorphic with KCuF3: the space group is I4/mcm. Even in this structure, only one nonequivalent site is present for Cu/Mg ions (1/2, 0, 0) and K ions (0, 0, 1/4), whereas fluoride is present in two sites: F1 at (1/2, 0, 1/4) and F2 in (x, 1/2 + x, 0) (see Figure 1, dashed line). The transition between the two crystallographic structures is understood as a cooperative Jahn-Teller distortion that causes the CuF6 octahedra to elongate in the ab plane along the a- or b-axis in an antiferrodistortive pattern (Figure 1) and cause the lowering of the Cu/Mg site symmetry from Oh (m3hm) to D2h (mmm). In pure KCuF3, this corresponds to the orbital ordering of the hole orbitals described above. As a result, in the ab plane, each copper has two short Cu-F bonds along a (b) of the pseudocubic cell and two long Cu-F bonds along the b (a) axis. Along the c-axis, Cu-F bonds distortions in the ab plane for consecutive layers can be concordant (poly type d) or discordant (poly type a, most commonly found). In this latter case, the result is a doubling of the c-axis for the tetragonal cell with respect to the pseudocubic one. In KMgxCu1-xF3, one is easily induced to think that the progressive substitution of the magnetic, Jahn-Teller and d9 Cu(II) cation with the nonmagnetic, spherical, and closed-shell Mg(II) ion could have a different effect on the magnetic, crystal, and orbital structure. Therefore, it could be possible to disentangle the relevant degrees of freedom and their energy scales.

Experimental Details KMgxCu1-xF3 samples of composition x ) 0.00, 0.10, 0.20, 0.30, 0.35, 0.40, 0.45, 0.60, 0.70, 0.80, 0.90, and 1.00 have been prepared. KCuF3 crystals have been synthesized by the Hirakawa method.7 An aqueous solution of HF (45% in volume) and then an aqueous solution of KF at 70 °C were added to a solution of CuCO3‚Cu(OH)2‚H2O at 60 °C. The slow evaporation of the solvent at 37 °C allowed obtaining quite large and not twinned crystals of a polytype.3 KMgF3 and intermediate solid solutions have been synthesized by solid-state reactions starting from KF (Aldrich, 99%), MgF2 (Unaxis Materials, 99.99%), and CuF2 (Alfa Aesar, 99.5%). These materials were powdered and carefully mixed in a Siemens mBRAUN UNIlab dry box, which is able to keep water and oxygen concentration below 1 ppm. The samples so obtained were pelletized and put in a platinum crucible and then in a quartz capsule. The pellets were surrounded (avoiding direct contact) by sheets of metallic zirconium to capture the oxygen in the reaction chamber and kept in flowing argon (2 L/h) at 750 °C for ∼1 h. These reaction conditions were chosen to obtain a compromise between a minimization of spurious phases (mainly Cu2O and K2MgyCu1-yF4) and to bring complete reaction. After quenching to room temperature, the pellet was taken out of the capsule. Room temperature XRPD patterns were collected between 15 and 105° (2θ range, ∆2θ ) 0.02°) and at a counting rate of 10 s/step either with a Philips 1820 diffractometer (samples with x ) 0.00, 0.10, 0.20, 0.45, 0.70, 0.80, and 0.90) or with a Brucker D8 diffractometer (samples with x ) 0.30, 0.35, 0.40, 0.60, and 1.00). Both diffractometers were operating with CuKR radiation (λ ) 1.5418 Å) in Bragg Brentano reflection θ/2θ geometry with a secondary beam graphite monochromator. Rietveld refinements have been performed using the GSAS software suite8 and its graphical interface EXPGUI.9 Backgrounds have been subtracted using shifted Chebyshev polynomials. The diffraction peak profiles have been fitted with a pseudo-Voight profile function. All isotropic thermal factors have been varied during the refinement and site occupancies have been taken fixed to the values determined through the quantitative analysis of the experimental patterns (see Tables 1 and 2).

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TABLE 1: Composition, Cell Parameters, Structural Parameters, and Agreement Values of KMgxCu1-xF3 Samples in the Tetragonal and Biphasic Domains, Determined by X-ray Diffraction x nominal x actual % cubic KMgxCu1-xF3 % tetragonal KMgxCu1-xF3 % Cu2O % K2MgyCu1-yF4 % K3MEF6 a (Å) cubic a (Å) tetragonal a (Å) tetragonal xF2 Uiso (Mg/Cu) Uiso (K) Uiso (F/F1/F2) Uiso (mean) Rp WRp R(F2) a

0 0.00 100

0.1 0.101

0.2 0.204

95.19( 2) 0.63 (1)

92.16(7) 0.93 (1) 4.05 (1) 2.86 (1)

4.18 (1) 5.8660 (1) 7.8720 (1) 0.228 0.0304 (8) 0.0126 (7) 0.011 (1) 0.0192 (5) 0.0308 0.0515 0.0872

5.8232 (1) 7.8983 (3) 0.228 0.0406 (6) 0.0132 (6) 0.030 (1) 0.0306 (8) 0.0241 0.0380 0.0651

0.3 0.310 32.6 (8) 59.3 (6) 1.52 (5) 3.01 (1) 3.63 (1) 4.0276 (2) 5.7601 (4) 7.9519 (7) 0.228 0.029 (1) 0.021 (1) 0.024 (2) 0.0270 (8) 0.0629 0.0831 0.0859

5.7830 (2) 7.9314 (2) 0.228 0.0313 (7) 0.0106 (7) 0.0152 (9) 0.0215 (5) 0.0262 0.0377 0.0531

0.35 0.366 54.3 (8) 37.1 (10) 2.04 (1) 6.56 (5) 4.0276 (2) 5.7489 (5) 7.969 (1) 0.228 0.029 (1) 0.012 (1) 0.023 (2) 0.0221 (8) 0.0726 0.0931 0.2151

% indicates weight percentages. The isotropic thermal factors are expressed as (Å2). The agreement values are defined in ref 8.

TABLE 2: Composition, Cell Parameters, Structural Parameters, and Agreement Values of KMgxCu1-xF3 Samples in the Cubic Domain, Determined by X-ray Diffractiona x nominal x actual % cubic KMgxCu1-xF3 % Cu2O % CuO % K2MgyCu1-yF4 % K3MEF6 % MgF2 a (Å) cubic Uiso (Mg/Cu) Uiso (K) Uiso (F) Uiso (mean) Rp WRp R(F2) a

0.4 0.409 91.95 (6) 1.23 (5)

0.45 0.458 95.29 (2) 0.81 (1)

0.6 0.607 95.51 (3) 0.61 (1)

0.7 0.715 96.53 (1) 1.13 (1)

0.8 0.795 96.05 (2)

0.9 0.902 96.24 (2)

6.82 (10)

1.94 (1) 1.96 (1)

2.64 (2) 1.23 (1)

2.34 (1)

2.70 (1)

0.16 (2) 3.60 (4)

4.0308 (1) 0.0249 (6) 0.0117 (6) 0.0194 (7) 0.0186 (4) 0.0317 0.0485 0.0757

4.02667 (5) 0.0313 (5) 0.0172 (5) 0.0244 (6) 0.0252 (4) 0.0289 0.0441 0.0774

4.0125 (2) 0.0237 (7) 0.0159 (7) 0.0177 (8) 0.0191 (5) 0.0613 0.0783 0.0686

4.0081 (1) 0.0257 (5) 0.0132 (5) 0.0234 (5) 0.0199 (4) 0.0326 0.0476 0.0555

2.25 (1) 4.00503 (8) 0.0244 (4) 0.0166 (5) 0.0244 (4) 0.0217 (4) 0.0361 0.0487 0.0340

3.9965 (6) 0.0344 (8) 0.0044 (6) 0.0260 (6) 0.0187 (4) 0.0799 0.1110 0.0712

1 1.00 100

3.9865 (1) 0.0116 (8) 0.0182 (9) 0.0186 (9) 0.0164 (6) 0.1274 0.1945 0.1025

% indicates weight percentages. The isotropic thermal factors are expressed as Å2. The agreement values are defined in ref 8.

The EPR spectra have been recorded by a Bruker Elexsys spectrometer equipped with liquid nitrogen variable temperature device (modulation amplitude 3 G, microwave attenuation 15 dB, gain 20 dB). EPR spectra have been recorded in a wide temperature range (110 < T < 380 K). Results XRPD Results. The XRPD patterns for all the samples have been analyzed through the Rietveld method. Scale factors, cell dimension, background, and peak profile parameters have been varied in the last refinement together with Cu/Mg, K, and F isotropic thermal parameters. In the tetragonal phase, the isotropic thermal parameters for F1 and F2 have been kept equal. The x coordinate for F2 for all tetragonal samples () 0.228) has been chosen by refining the XRPD patterns at different fixed xF2 values and determining the minimum of the R(F2) parameter as a function of xF2. The determined value is very close to 0.2276(1), determined through single-crystal X-ray diffraction by Buttner et al.10 It is worth noticing that the (2 1 0) superstructure peak of the d poly type that is expected at ∼34.5° is completely absent in all the tetragonal samples. The XRPD pattern relative to the x ) 0.60 sample is shown in Figure 2 as an example. The experimental (crosses) and calculated (continuous line) X-ray patterns are reported together with the difference profile (bottom). Tables 1 and 2 report the results of the refinements.

In almost all the samples, spurious minor phases are present (see Tables 1 and 2), that is, Cu2O, K2MgyCu1-yF4, and K3MEF6, with ME ) Cu, Mg, Fe, Ni. Fe and Ni could be delivered by the K-type thermocouple that was kept near the samples during the synthesis. Mass fractions for the phases have been determined from the Rietveld refinement result according to ref 11. However, it will be shown in the following that for all the samples and for all investigated T’s, the impurities give a negligible contribution to the EPR spectra. As a consequence of this contamination, the actual Mg/Cu concentrations in KMgxCu1-xF3 phases are slightly different from the “nominal” ones (see Tables 1 and 2), that is, the ones fixed by the stoichiometry of the reactants. Hereafter, as already mentioned in the Experimental Section, we will refer to the nominal Mg content within KMgxCu1-xF3 phases, unless better specified. Selected details of experimental patterns are shown in Figure 3a. The numbers within the parentheses are the Miller indices for each reflection. In particular, those at the top of the Figure refer to the tetragonal phase; those at the bottom refer to the cubic phase. Samples with x e 0.26 are isomorphic with KCuF3 (I4/mcm space group); samples with x g 0.42 are isomorphic with KMgF3 (Pm3m space group). The phase transition is highlighted by the splitting of the cubic reflection into two peaks whose angular distance increases with decreasing x.

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Figure 4. EPR spectra of KMgxCu1-xF3 at room temperature. Nominal value of x from a to m: x ) 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

Figure 3. (Top) Selected details of experimental XRPD patterns for KMgxCu1-xF3 samples. The numbers between the parentheses are the Miller indices for each reflection. In particular, those at the top of the Figure refer to the tetragonal phase, whereas those at the bottom refer to the cubic phase. The symbols *, +, and o indicate peaks relative to the K2MgyCu1-yF4, K3MEF6, and Cu2O spurious phases, respectively. (Bottom) Pseudocubic cell constants as a function of x for the tetragonal (triangles) and the cubic (circles) phases. The two vertical dashed lines delimit the miscibility gap region.

Samples with nominal composition x ) 0.30 and 0.35 show both cubic and tetragonal phases, with the ratio increasing with increasing x. The repeatability of this observation indicates that a biphasic region is present; the actual width of the miscibility gap is 0.26 < x < 0.42. The trend of the cell parameters with x is shown in Figure 3b. In particular, the pseudocubic lattice parameters are displayed to make it easier to compare the two phases. Starting from tetragonal KCuF3, the increase in the Mg concentration is accompanied by the increase in the c-axis and by the decrease in the a-axis and, as a consequence, by the reduction of the tetragonal distortion. A monotonic decrease in the a cell parameter with increasing x appears in the cubic phase. This trend is in accord with the different ionic radii of Cu2+ and Mg2+.12

Figure 5. EPR spectrum of KMgxCu1xF3 with x ) 0, detected at 120 K. Together with the experimental curve (EXP), three simulated patterns are also shown in the figure (R, β, and γ). See text for details.

EPR Spectra. The EPR spectra collected at room temperature for all the samples are shown in Figure 4. The EPR spectrum of the powdered KCuF3 sample is mainly composed of three features at g = 2.4, 2.2, and 2.1, respectively (See Figures 4a and 5). The first of them (labeled A, in Figure 5) has the shape typical of the g// spectral region of Cu2+ ions. The second (labeled E in Figure 5) is nearly symmetric. Finally, the third feature (labeled C in Figure 5) is the most intense one, having the shape typical for the g⊥ spectral region of Cu2+ ions. The whole EPR pattern has an intensity increasing with decreasing temperature, keeping unchanged the spectral profile. When ∼10% of Mg substituted for Cu, the EPR spectrum collapsed into a single Lorentzian-shaped line characterized by a peak-to-peak width of ∆Hpp = 85 G at room temperature (Figure 4b) down to ∼150 K. However, at the lower temper-

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Figure 6. EPR spectra of KMgxCu1-xF3 with (a) x ) 10 and (b) x ) 30 (nominal values). Detection temperature, ∼120 K. Figure 8. EPR spectra of KMgxCu1-xF3 with x ) 90 (nominal values). Detection temperature, 110 K.

Figure 7. EPR spectra of KMgxCu1-xF3 with (a) x ) 40 and (b) x ) 45 (actual values). Detection temperature ∼140 K. Simulation parameters: (a) gx ) 2.096, gy ) 2.198, gz ) 2.310, and (b) g// ) 2.315, g⊥ ) 2.20.

atures, this pattern divides into two overlapping symmetric lines, with the narrower characterized by ∆Hpp = 19 G (Figure 6a). An EPR pattern of an orthorhombic system is observed at all temperatures when ∼20 or ∼30% of Mg substitutes for Cu (see Figure 4c and d). However, measurements carried out at T e ∼130 K still reveal the presence of the symmetric ∼19 G narrow line with both of these two samples (Figure 6b). About 43% of Mg substituting for Cu2+ produces an orthorhombic crystal field, characterized by the temperatureindependent parameters gx ) 2.09, gy ) 2.19, and gz ) 2.31 (Figures 4e and 7a). However, a new EPR pattern appears at still increasing amounts (∼45 and ∼60%) of Mg substituting for Cu2+ (Figure 4f; g), typical of an axial crystal field. Spectral simulation provides the temperature-independent spectral parameters g// = 2.315 and g⊥ = 2.20 (Figure 7b). The EPR spectrum collapses again into a single feature at g ) 2.274 when ∼72% of Mg substitutes for Cu, but it seems that the baseline is no more linear or that a very broad band overlaps to the narrower one (Figure 4h). However, we must indicate that very intense but unrepeatable low-field ferromagnetic features (not shown) appear with this sample only. The last, therefore, appears like in an unstable state between different situations. The very broad band overlapping the narrower one in the EPR spectrum of the sample with ∼72% of Mg definitively prevails with ∼80% of Mg (Figure 4i). Indeed, this feature appears Lorentzian-shaped with g ) 2.274 and with intensity decreasing with increasing temperature. Traces of S ) 1 triplet states and a complex hyperfine pattern recorded in the presence of Mg amounts >90% are also found. This last feature has been already noticed in literature with KMgF313,14 and attributed to F2- ions (or to Mn impurities) interacting with the other paramagnetic nuclei present in the sample. Regarding the lowintensity triplet spectrum adding to the main pattern for T e 150 K (Figure 8), we can notice that the intensity of these lines is even lower than that of the above-mentioned impurities. Therefore, the presence of these triplet states is of almost no

relevance for the interpretation of the EPR spectra in this compositional range. In the last sample, an EPR spectrum with isotropic g ) 2.0106 value and a rich hyperfine structure prevails at room temperature on any other feature (Figure 4l). This sample has been reexamined by Q-band EPR spectroscopy, and the above-reported g values for the two overlapping patterns were obtained. The same hyperfine-structured EPR spectrum is obtained with pure KMgF3 (Figure 4m). This new pattern is due to two different paramagnetic species. Indeed, the six more intense lines saturate at a lower microwave power with respect to the less intense ones. EPR Spectral Intensity vs Temperature. The spectral intensity, I, is defined as the double integral of the EPR line, in arbitrary units. The reciprocal of I shows a linear trend vs T, following the equation

1 ) a + bT I

(1)

The mean values of a = +0.13 ( 0.02 and b = (57 ( 1) × 10-4 were found with ∼10% of doping Mg. By contrast, a = -0.4 ( 0.1 and b ) (90 ( 4) × 10-4 have been obtained when Mg was ranging between ∼30 and ∼90%. Two different portions of the same batch with an intermediate value of ∼20% of Mg gave an a not significantly different from 0, being a = -0.01 ( 0.04 and -0.08 ( 0.06 with b = (65 ( 2) × 10-4 and (68 ( 2) × 10-4, respectively, in the two cases. Therefore, we can hypothesize that ∼20% of Mg is a borderline composition value between the case with a < 0 and that with a = 0, and that the transition between negative and positive values of this parameter does not occur uniformly through all the bulk of the sample. The above-reported numerical values of a and b depend, of course, also on the arbitrary units adopted for the spectral intensity, I; however, they can be compared to each other, because in all the cases, we have adopted the same units for I. Discussion The values of ∼2.4 and 2.1 measured for the g parameter of the A and C features, respectively, of the powdered KCuF3 sample (Figure 5 EXP and simulated pattern R) are close to the values g// ) 2.39 and g⊥ ) 2.15 reported in the literature15 for a single crystal of analogous composition and there attributed to the elongated axis and to a direction perpendicular to it, respectively. However, we must indicate that in ref 15, a ga ) (g// + g⊥)/2 ) 2.27 value was measured in the ab plane accompanied by a g⊥ ) 2.15 in the c direction instead of the separated g// ) 2.39 and g⊥ ) 2.15 values. In any case, the

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observation of g// * g⊥ in pure KCuF3 is a consequence of the orbitally ordered structure of this compound. The E line is by far less intense than the A and C ones. Therefore, E can be attributed to Cu ions in the neighbors of impurities, stacking faults, or local stresses having disturbing effects on the orbital order parameter. Two different interpretations can be proposed for the origin of this line. Indeed, its g ) 2.2 value coincides with (g// + 2g⊥)/3, where g// and g⊥ refer to A and C, respectively. Therefore, E could be due to the same paramagnetic species generating A and C, but affected by threedimensional exchange phenomena mediating the anisotropic values of the g tensor. As an alternative to this interpretation, E could be attributed to the intermediate component at gy ) 2.2 of an orthorhombic tensor with gx ) 2.1 and gz)2.4. The corresponding paramagnetic species, if isolated, would show the EPR spectrum reported as pattern β in Figure 5, whereas this pattern could contribute to the whole experimental spectrum, as indicated by the simulated pattern γ of Figure 5, corresponding to a contribution of 130 K . TN, as is, indeed, observed. On the other hand, the value of ∆Hpp = 85 G is similar to that reported with KMnF322, and it is of the same order of magnitude as those reported with CuX42- (XdCl and Br) ferromagnetic layers,19 but it is an order of magnitude smaller than that obtained in a KCuF3 single crystal analyzed at 24.5 GHz.18 In all these cases, the presence of both AE and DM exchange was invoked to account for this line width and for its broadening with increasing temperature.23,24 Indeed, it has been reported17-19,23 that phonon modulation of AE and DM exchange mixes the singlet and triplet states, leading to a nearly linear dependence of ∆Hpp vs T, with a slope proportional to J4. Anyway, the main broadening contribution comes from DM.24 Therefore, our interpretation of the EPR behavior of KMg0.1Cu0.9F3 is as follows: the exchange between Cu2+ ions involves both AE and DM mechanisms, producing the ∆Hpp = 85 G line. However, these two phenomena mix together only above a specific temperature, namely, T > 160 K, causing a DM line width intermediate between ∆HAE pp and ∆Hpp . At a lower temperature, that is, at T e 150 K, these two exchange mechanisms are disentangled, and the single line splits into two DM lines, ∆HAE pp and ∆Hpp broad, respectively. This supports our attribution of the ∼19 G narrow line to AE only, whereas the ∆Hpp = 85 G line could be better attributed, in this case, to the presence of both AE and DM exchange mechanisms. The mixing of singlet and triplet states induced by both exchange mechanisms implies that, at least on the time scale of EPR, the orbital ordering (OO) is possibly melt in KMg0.1Cu0.9F3. In fact, the OO parameter can be defined as the number of holes in the Cu-3dy2-z2(Cu-3dx2-z2) states normalized to the total number of holes in the d states. When the OO parameter is saturated () 1), only spin doublets are expected, and therefore, the EPR spectrum of pure KCuF3 should be detected. The fact that mixing of triplets and singlets is detected in KMg0.1Cu0.9F3 implies a decrease in the OO parameter in this sample, whereas

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the Jahn-Teller effect is still active because the crystal structure is tetragonal. We may point out that OO and crystal field distortions are different contributions to the total Hamiltonian of the system. According to the KK model,1 pure KCuF3 is an example of a system in which the exchange interaction alone results in the correct OO. The orbital ordering then drives the cooperative J-T distortion. What happens in the KMg0.1Cu0.9F3 sample is actually a different phenomenon. In this case, the degeneracy of the eg states is still removed because we still have a cooperative J-T distortion, but the hole states are not pure Cu-3dy2-z2(Cu-3dx2-z2) in character. In this case, therefore, the spin doublet ground state of Cu(II) is converted into an admixture of singlet and triplet states. In the biphasic sample (30% Mg) and at higher Mg doping levels, that is, for the cubic phases, the ∆Hpp = 85 G line is no more observable, even at low temperature, at difference with the narrower ∆Hpp = 19 G line (Figure 6b). Therefore, the DM exchange is active in the tetragonal phase only for Mg < 25%. It is well-known that the double integral I of the first derivative EPR spectrum is directly proportional to the magnetic susceptibility χ. Therefore, the following relation is expected between I and the detection temperature, T

I∝

C T+Θ

(3) Conclusions

where C is the Curie constant and Θ ) 0 in the case of isolated ions, that is, of a paramagnetic sample. Equation 3 holds in the cases of both FM and AFM interactions among ions, Θ being positive in the latter case and negative and equal to -TC in the former (TC being the Curie temperature). Here, the symbols of ref 25 have been used so that the positive sign of the Weiss constant results correct. Therefore, the following linear trend is also expected.

1 Θ T ∝ + I C C

(4)

By comparing the last equation with eq 1, we can write

a∝

Θ C

(5)

b∝

1 C

(6)

and

in which the same proportionality parameter appears in eq 5 and eq 6, so that these relations immediately lead to

Θ)

a b

and the magnetic and structural degrees of freedom appear to be the most robust. For x g 0.4, the XRD pattern is typical of the undistorted perovskite cubic cell. However, EPR detects an orthorhombic symmetry for x ) 0.4 (Figures 4e and 7a) and an axial symmetry of the crystal field at higher amounts of doping (x ) 0.45 and 0.6) (Figure 4f and g). We are, therefore, induced to conclude that for 0.4 e x e 0.7, the cooperative Jahn-Teller distortion is removed, but the local chemical environment of copper is still randomly distorted. A cubic symmetry appears in the EPR spectra only for x ) 0.8, but at T > 297 K only (Figure 4i). The Lorentzianshaped band observed at room temperature in this case and still faintly present at x ) 0.9 (Figures 4i and l) can be attributed to Cu2+ ions substituting for Mg2+ in sites characterized by cubic crystal fields. Indeed, its g ) 2.274 value is in line with that reported for the spin-flop from the [110]p axis of easy magnetization to a direction perpendicular to it in the c plane of KCuF3.26,27 The linebroadening of this Lorentzian-shaped band with increasing temperature reveals the presence of a temperaturedependent spin-spin relaxation mechanism acting among the Cu2+ ions.

(7)

The positive value Θ = +23 ( 4 K obtained with 10% of doping indicates that at this relatively low Mg doping level, the 3D magnetic order is still AFM, as in pure KCuF3. By contrast, the negative value Θ = (-40 ( 10) K obtained at Mg doping levels higher than 20% indicates that the ferromagnetic interaction among Cu2+ ions prevails in this composition interval. The intermediate value of 20% of Mg would correspond to a critical situation between these two kinds of competing interactions. Now, considering that the XRPD pattern of KMgxCu1-xF3 is indexed as tetragonal up to x ) 0.26, we can infer that the orbital degrees of freedom are the most affected by Mg substitution,

The KMgxCu1-xF3 system has been investigated in the whole x compositional range by means of XRPD and EPR measurements. XRPD experiments have revealed that two different solid solutions are present when x < 0.26 and when x > 0.42. The former is based on the structure of KCuF3 (tetragonal system, space group I4/mcm) whereas the latter is based on the structure of KMgF3 (cubic system, space group Pm3m). The two solid solutions are separated by a miscibility gap. Positional disorder is induced by doping, due to the different Cu and Mg environments. In particular, EPR measurements revealed that at low Mg2+ doping levels (x ) 0.1, 0.2), two exchange mechanisms, that is, Dzyaloshinsky-Moriya antisymmetric exchange and anisotropic exchange, are active at T e 390 K and T < ∼190 K, respectively, in the two cases. It has been reported that both these exchange mechanisms are operative in pure KCuF3. Here, we have shown that they are active also in KMgxCu1-xF3 at low enough Mg2+ doping concentrations and at low enough temperature. Both AE and DM are active but disentangled from each other when x ) 0.1 at T < ∼150 K so that the line splits into two overlapping lines with different width due to AE and to DM, respectively. The mixing of triplet and singlet states induced by the AE and DM exchange mechanisms leads to the conclusion that the orbital order is melt in the x ) 0.1 sample, for which the cooperative Jahn-Teller distortion is still active, and the 3D magnetic order is still antiferromagnetic, as in KCuF3. Therefore, the orbital degrees of freedom appears less robust than the magnetic and structural (cooperative J-T effect) ones with respect to Mg substitution. AE is active only when x ∼ 0.2 at T < ∼150 K. At x = 0.3 and T < ∼150 K, the AE mechanism is still present among Cu2+ ions, probably grouped into subsystems. The Cu environment is orthorhombic at x ) 0.43 (actual composition). By contrast, Cu2+ is in a axial crystal field when x ) 0.45 and 0.60, becoming cubic at higher (x g 0.8) Mg2+ doping levels.

Orbital Ordering in KMgxCu1-xF3 Solid Solution References and Notes (1) Kugel, K. I.; Khomskii, D. I. SoV. Phys. Usp. 1982, 25, 231. (2) Feiner, L. F.; Oles´, A. M; Zaanen, J. Phys. ReV. Lett. 1997, 78, 2799. (3) Caciuffo, R.; Paolasini, L.; Sollier, A.; Ghigna, P.; Pavarini, E.; van den Brink, J.; Altarelli, M. Phys. ReV. B: Condens. Matter Mater. Phys. 2002, 65, 174425. (4) Satija, S. K.; Axe, J. D.; Shirane, G.; Yoshizawa, H.; Kirakawa, K. Phys. ReV. B: Condens. Matter Mater. Phys. 1980, 21, 2001. (5) Paolasini, L.; Caciuffo, R.; Sollier, A.; Ghigna, P.; Altarelli, M. Phys. ReV. Lett. 2002, 88, 106403-1. (6) Binggeli, N.; Altarelli, M. Phys. ReV. B: Condens. Matter Mater. Phys. 2004, 70, 085117. (7) Hirakawa, K.; Kurogi, Y. Suppl. Prog. Theor. Chem. 1970, 46, 147. (8) Larson, A. C.; Von Dreele, R. B. GSAS, General Structure Analysis System: Los Alamos, NM, 2001. (9) Toby, B. H. J. Appl. Cryst. 2001, 34, 210-214. (10) Buttner, R. H.; Maslen, E. N.; Spadaccini, N. Acta Crystallogr., Sect. B: Struct. Sci. 1990, 46, 131. (11) See, for example: Langford, J. I.; Looue¨r, D. Rep. Prog. Phys. 1996, 59, 131. (12) Shannon, R. D.; Prewitt, C. T. Acta Crystallogr., Sect. B: Struct. Sci. 1969, 25, 925.

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