Interplay between structural and magnetic phase transitions in copper ferrite studied with high-resolution neutron diffraction

Journal of Magnetism and Magnetic Materials 374 (2015) 591–599

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Interplay between structural and magnetic phase transitions in copper ferrite studied with high-resolution neutron diffraction A.M. Balagurov a,n, I.A. Bobrikov a,n, V. Yu. Pomjakushin b, D.V. Sheptyakov b, V. Yu. Yushankhai c a

Frank Laboratory of Neutron Physics, JINR, 141980 Dubna, Russia Laboratory for Neutron Scattering, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland c Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna, Russia b

art ic l e i nf o

a b s t r a c t

Article history: Received 1 July 2014 Received in revised form 25 August 2014 Available online 1 September 2014

A detailed neutron diffraction study of copper ferrite in a broad temperature range has allowed to precisely access the peculiarities of magnetic and structural phase transitions in it. On heating from 2 to 820 K, a fully inverted tetragonal (sp. gr. I41/amd) spinel CuFe2O4 is observed up to a TC E 660 K, where a cubic phase (sp. gr. Fd3m) appears, and up to T E 700 K, both structural phases coexist. The inversion parameter of spinel structure does not change at the transition to the cubic phase. Deformation of the (Cu,Fe)O6 octahedra in the tetragonal phase corresponds to the Jahn–Teller nature of the structural phase transition. Néel ferrimagnetic structure – a ferromagnetic ordering of the magnetic moments of Fe3 þ in the tetrahedral (A) and moments of Fe3 þ and Cu2 þ in the octahedral (B) positions with opposite directions of magnetization of the sublattices – disappears at TN E 750 K. The magnetic moment in the A-positions (Fe3 þ ) and the total one in the B-positions (Fe3 þ þ Cu2 þ ) at T o30 K are equal to 4.06(6) and 4.89(8) μB, respectively. The difference between these values corresponds to a spin moment of Cu2 þ . Qualitative analysis of the magnetic interactions in the inverted mixed spinel showed that the dominant antiferromagnetic interaction between A and B sublattices, which is required to stabilize the collinear Néel order in CuFe2O4, follows naturally from the standard superexchange theory. In the co-existence range of structural phases diffraction peaks are significantly broadened. The size effects providing the main contribution to peak broadening is also superimposed with the microstrain-conditioned peak broadening. In the tetragonal phase, microstrains in the crystallites are highly anisotropic. & 2014 Elsevier B.V. All rights reserved.

Keywords: Ferrite Ferrimagnetic Inverted spinel Phase transition Superexchange theory Neutron diffraction

1. Introduction Spinel-type ferrites with the formula unit AB2O4 are a classic target for numerous neutron diffraction studies whose history can be traced back to the 1950s. The relative simplicity of the spinel structure and high informational content of neutron diffraction data allowed in the very first studies of NiFe2O4 [1] and CuFe2O4 [2] obtaining of reliable information on the main features of their atomic and magnetic structures, despite of not a very high quality of raw experimental data. Magnetic structure of spinel ferrites and the temperature of a magnetic ordering essentially depend on the nature (magnetic or non-magnetic) of cations residing on the tetrahedral (A) and octahedral (B) sites. In the subsequent studies, a cation distribution between the A and B positions and its impact

n

Corresponding authors. E-mail addresses: [email protected] (A.M. Balagurov), [email protected] (I.A. Bobrikov). http://dx.doi.org/10.1016/j.jmmm.2014.08.092 0304-8853/& 2014 Elsevier B.V. All rights reserved.

on the specific magnetic properties of different spinel ferrites are the main objects of analysis. Since many spinels are known to exist in cubic (at high temperatures) and tetragonal symmetry modifications, the analysis of the structural transition between them and its connection to the magnetic transition are also challenges for neutron experiments. Interest to the studies of spinel ferrites is still supported by their theoretical relevance and numerous technological applications. For instance, the magnetite-based compound MxFe3 xO4, with M¼Ni, Mn, Zn, etc. hold great promise for application in functional spintronic devices [3,4]. The LiMn2O4 spinel is one of the most promising cathode materials for lithium batteries (see, for example, review [5]). At the same time, fundamental questions remain associated mainly with magnetic structure of spinel ferrites and its dependence on temperature and A/B distribution of constituent cations. For a given regular distribution of magnetic cations over A and B sites, a magnetic structure is usually thought to be determined by three oxygen-mediated superexchange interactions, namely, the dominant inter-sublattice coupling JAB and somewhat weaker intra-sublattice

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couplings, JBB and JAA. According to the Néel’s two-sublattice meanfield theory [6], this hierarchy of exchange parameters suggests a collinear ferrimagnetic structure. However, if the constituent cations are randomly distributed in one or in both sublattices, a larger set of exchange parameters is required and the resulting magnetic structure is expected to be not fully collinear. The other interesting issue is connected with temperature-induced Jahn–Teller (JT) effect, which may strongly influence the exchange coupling parameters and change magnetic properties of a system. One has to address to the above-mentioned problems when dealing with the CuFe2O4 compound, which is the subject of the present study. CuFe2O4 copper ferrite crystallizes in the classical spinel structure and can be found in two symmetry modifications: cubic (Fd3m, at T4 700 K) and tetragonal (I41/amd) space groups. The structural phase transition between them is due to the JT effect, which causes the distortion of the octahedral oxygen environment around Cu2 þ ions and removal of the eg orbital degeneracy. Analysis of the crystalline field symmetry in spinel structure shows (see, for instance, [7]) that presence of a JT-cation in the tetrahedral (A) site usually results in a cooperative distortion with c/ ao1. On the contrary, presence of a JT-cation in the octahedral (B) site causes a distortion with c/a41. For CuFe2O4 in tetragonal phase, the low-T ratio γ ¼c/aE1.0641 reliably indicates occurrence of the major part of copper atoms in octahedral positions. Therefore, copper ferrite is a fully or partially inverted spinel, the structural formula of which can be written as (Cu1  xFex)[CuxFe2  x] O4, where the inversion parameter xr1. At x¼1, a half of iron atoms is in А-cation position, while B-cation position is statistically equally filled with iron and copper atoms. A systematic theoretical consideration [8] leads to the conclusion that in the inverted spinel CuFe2O4 the cubic-to-tetragonal transition has to be a first-order type, and the tetragonal distortion parameter γ is related to the inversion parameter x. In paper [9], on the basis of calorimetric measurements a conclusion was made that in the tetragonal phase the copper ferrite is always partially inverted, xo1, and the inversion parameter is related to the temperature from which the cooling was started and to the cooling rate. Studies of thin-film copper ferrite [10] demonstrated strong dependence of the tetragonal distortion parameter γ and the coercitive force on the annealing temperature, which the authors associated with the change of inversion parameter. On the contrary, according to Mössbauer data [11], at room temperature, stoichiometric copper ferrite is a fully inverted spinel, i.e. all copper cations are in octahedral positions. One can conclude that there is no definite opinion in the literature. Probably, experimental data suggest that copper ferrite at room temperature can exist in both states: as a partially or fully inverted spinel, and the inversion parameter depends on the synthesis and annealing procedures and the cooling mode. Neutron diffraction papers on copper ferrite, in which cation content and magnetic moment values in both positions and their variation with temperature would be directly determined are not yet available. It is possibly connected with an increased complexity of the task, as in copper ferrite the positions of magnetic and nuclear peaks coincide, and the contrast between cations (relative difference in coherent scattering lengths of copper and iron) is equal to  20% only. As a result, in the process of structural analysis strong correlations between structural and magnetic parameters occur, and even insignificant systematic uncertainties can dramatically affect their values. In this respect, an application of high-resolution neutron diffraction measurements to the MgCr2O4 normal spinel [12] with somewhat less complicated properties is worth mentioning. In this compound, nonmagnetic Mg2 þ ions and magnetic Cr3 þ ions are fully ordered in the A- and B-positions, respectively, in the cubic phase chromium atoms form “pyrochlore lattice”. Geometrical frustration of

the pyrochlore lattice with nearest-neighbor antiferromagnetic interactions is expected [13] to prevent any long-range ordering of Cr3 þ moments. However, as shown in Ref. [12], a 3D magnetic ordering exists in the MgCr2O4 compound below TN ¼ 12 K, which the authors attribute to the partial relief of magnetic frustration due to the structural transition to a tetragonally compressed structure. In this paper it was also shown that the magnetic and structural (between cubic and tetragonal phases) transitions coincide within a resolution of 0.1 K, the thermal variations of the tetragonal lattice strain and ordered Cr magnetic moment are identical, and the transition between the structural phases is accompanied by a very weak, but reliably identified volume discontinuity (0.05 Å3) and thermal hysteresis (0.15 K). It should be noted that the precision and comprehensiveness of these data are provided by a high quality of high resolution powder neutron diffraction data (D2B diffractometer at ILL), and the possibility to trace the changes in the nuclear and magnetic structures simultaneously in a neutron experiment. In the current paper, precision analysis of the atomic and magnetic structures of CuFe2O4 using high-resolution neutron diffraction was carried out. Preliminary results [14] acquired at the time-of-flight diffractometer allowed asserting that in the cubic phase the structure is fully inverted, while in the tetragonal phase the inversion does not exceed 5%. Moreover, it was estimated that the temperature of the magnetic ordering TN is evidently (several tens of degrees) higher than the temperature of structural transition TS. These results appeared to be unexpected and, to a large extent, contradicting the information available in the literature. Accordingly, a decision was made to carry out additional experiments at the diffractometer with a constant wavelength and with a more detailed temperature scanning. All obtained results are discussed with an emphasis on the mechanisms of structural and magnetic phase transitions and on the specific features of the magnetic structure formation in CuFe2O4.

2. Experimental details Polycrystalline sample of CuFe2O4 was synthesized from stoichiometric mixture of CuO and Fe2O3 using conventional ceramic technology. The synthesis was carried out in two stages at temperatures of  1000 and  1100 K in open air. The resulting composition was slowly cooled down to room temperature. According to X-ray and neutron diffraction data, the sample contained a small amount (about 1% of mass) of two impurity phases—tenorite (CuO) and hematite (Fe2O3), which were taken into account in data processing. In addition, neutron diffraction patterns showed magnetic peaks from hematite, which were also included in the experimental data processing. Neutron diffraction patterns were measured by HRPT [15] operating at constant wavelength at the SINQ spallation source (PSI, Switzerland). HRPT is a high-resolution diffractometer (Δd/dE0.001 in the minimum of the resolution curve), which promotes precise analysis of crystal structure parameters and peak broadening effects. Acquisitions of diffraction data were carried out with neutron wavelength λ ¼1.494 Å in the temperature range from 2 to 820 K on heating. 20 diffraction patterns were measured at fixed temperature values with high statistics (3 h for each pattern), mainly in the region of structural and magnetic phase transitions. In between these points with fixed temperatures, diffraction data were measured with lower statistics ( 20 min per pattern). 3. Data processing and results The spinel structure (AB2O4) is usually represented as a cubic close-packed arrangement of large-size (r E1.3 Å) oxygen ions

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forming a face-centered lattice. In such packing, there are two different sites—with tetrahedral and octahedral environment. Assuming full inversion for CuFe2O4, tetrahedral sites (A-positions) are filled with trivalent iron cations (Fe3 þ ), while in the octahedral sites (B-positions), equal amounts of Fe3 þ and Cu2 þ are statistically distributed. At high temperature CuFe2O4 is in the cubic phase (PC), sp. gr. Fd3m (no. 227), a E8.42 Å, Z¼ 8. In this phase, A- and B-cations are in fixed special positions, and oxygen atoms are in the 32e (x, x, x) positions. Transition to the tetragonal phase (PT) is usually regarded as compression or tension along one of the main axes of the cube, the structure becomes tetragonal with a body-centered group I41/amd (no. 141), a0 ¼a/√2E 5.82 Å, c E8.69 Å, Z ¼4. In this phase, A- and B-cations remain in fixed special positions, and the oxygen atoms are in the 16 h (0, y, z) position. It is known that CuFe2O4 is ferrimagnetic (with a propagation vector of magnetic structure k¼0) up to the temperatures slightly higher than 700 K (according to literature the magnetic transition temperature varies between 710 and 780 K), and the corresponding long-range order in the arrangement and orientation of magnetic moments makes additional contribution to the intensities of particular diffraction peaks. Conventionally, magnetic structure is described as a ferromagnetic ordering in A- and B-positions with the opposite directions of magnetization. Ferrimagnetism arises both from the difference in the magnetic moments of iron cations in the tetrahedral and octahedral oxygen environment, and from the contribution of Cu2 þ magnetic moment (nominally МCu ¼1 μB). Analysis of diffraction patterns by the Rietveld method was carried out using FullProf package [16]. The entire temperature range was divided into regions of pure existence of either tetragonal or cubic phase of CuFe2O4 (low and high temperatures, respectively), and the region of intermediate temperatures, in which both phases coexist. In the most general case 7 phases were considered: atomic and magnetic structure of CuFe2O4 in the cubic and tetragonal phases, atomic structure of CuO, atomic and magnetic structure of Fe2O3. Transition temperatures from tetragonal to cubic and from ferrimagnetic to paramagnetic phase were most reliably determined by analyzing the profiles of particular diffraction peaks in the range of scattering angles 2θ ¼ 15–451 and by considering the dependences of their intensity, position and width on the temperature. The results of this processing indicate that during heating, the indications for the cubic phase appear at TS1 E660 K, the tetragonal phase disappears at TS2 E700 K, and magnetic contribution to the intensities fades at TN E750 K. The examples of obtained dependences are shown in Fig. 1.

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to refine and may be varied without any restrictions. Its possible departures beyond the limits of the relevant range (0rxr1), to some extent, characterize the influence of systematic errors on the determination of the occupancy factors, in particular, that of neglecting the presence of a small amount of impurity phases when imposing the occupational constraints listed above. Processing of all cubic phase patterns (eight temperature points) in the temperature range of 705–820 K led to inversion parameter values close to 1 ranging from 0.987(3) to 1.021(3) for different temperatures. Thus, the fact of full inversion of CuFe2O4 spinel in the cubic phase is confirmed with an accuracy of about 2%. A similar result was obtained by the analysis of time-of-flight (TOF) diffraction data [14]. An example of refinement of the cubic phase diffraction pattern is shown in Fig. 2. The above-mentioned constraints were used for refinement of the inversion parameter in the tetragonal phase as well, which, however, did not facilitate avoiding strong correlations to the values of refined magnetic moments on iron. A certain improvement was achieved by refining at relatively large scattering angles,

Fig. 1. Temperature dependences (data obtained on heating) of integral intensities of (1 1 1) and (2 2 2) peaks with high magnetic contribution (squares and rhombs, cubic phase indices, right scale, numbers are intensity of (1 1 1) peak) and (4 0 0) peak width (triangles, left scale). Arrows TS2 and TN indicate approximate temperatures of completion of transition from tetragonal to cubic phase and disappearing of long-range magnetic order.

3.1. Copper ferrite crystal structure and inversion parameter The issue of cations distribution between A- and B-positions, i.e. of the inversion parameter value x and its possible change in course of transition between tetragonal and cubic phases, is one of special importance for the structural analysis of copper ferrite. The difference between coherent scattering lengths of iron and copper (bFe ¼0.945, bCu ¼0.772 in 10  12 cm) provides the necessary contrast (about 20%) to determine x, while the precision of its determination is actually poor. In the process of the refinement of the occupancy factors nA and nB without any constrains, the statistical error of the inversion parameter is approximately 5 times greater than the statistical errors of nA and nB, which prevents its reliable determination. The situation improves dramatically by fixing nominal amounts of atoms and nominal populations of positions according to the structural formula (Cu1 xFex)[CuxFe2 x]O4, i.e. assuming that n(Cu1)þ n (Cu2)¼1, n(Fe1)þn(Fe2)¼2, n(Cu1)þn(Fe1)¼ 1, n(Cu2)þn(Fe2)¼ 2. In this case the x value remains a single occupational parameter

Fig. 2. An example of the Rietveld refinement pattern and difference plot (in the bottom) of the neutron diffraction data measured at Т ¼720 K. Vertical bars indicate peak positions (from top to bottom) of: CuFe2O4 crystal cubic phase, CuFe2O4 ferrimagnetic phase, CuO (tenorite), Fe2O3 (magnetite) crystal phase, Fe2O3 magnetic phase.

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where magnetic contribution to the intensities virtually disappears. For example, for the pattern measured at T¼2 K, refinement in the interval of 2θ ¼ 50–1631 resulted in x¼1.013(3) and an isotropic thermal factor of cations BC ¼ 0.54(3) Å2, for the interval of 67–1631 we obtain x¼0.991(3) and BC ¼0.57(3) Å2. Refinement in the same version of patterns measured at temperatures ranging from 200 to 400 K resulted in the inversion parameter values insignificantly (by 0.01–0.02) greater than 1. In fact, it means that in tetragonal as well as in cubic phase, our sample of copper ferrite is a fully inverted spinel phase with the inversion parameter of x ¼1.00(2). Summary data on the refinement of CuFe2O4 structure in the tetragonal and cubic phases for the temperatures of 2 and 800 K are given in Table 1. 3.2. Thermal evolution of the CuFe2O4 structure Temperature evolution of neutron diffraction patterns of CuFe2O4 on heating is shown in a 2D view in Fig. 3. Coexistence of the PC and PT phases in a certain temperature range and presence of magnetic contribution above the temperature of the PT phase vanishing are clearly seen. Table 1 Structural parameters for (Cu1  xFex)[CuxFe2  x]O4 obtained at T ¼ 2 K (tetragonal phase) and T ¼800 K (cubic phase). In the tetragonal space group I41/amd (the second setting) the atoms are in positions: Fe1 (4a)—(0, 3/4, 1/8), (Cu/Fe2) (8d)— (0, 0, 1/2), O (16h)—(0, x, z). In the cubic space group Fd3m (the second setting) the atoms are in positions: Fe1 (8a)—(1/8, 1/8, 1/8), (Cu/Fe2) (16d)—(1/2, 1/2, 1/2), O (32h)—(x, x, x). The conventional experimental (Re) and weighted (Rw) R-factors and χ2-value are pointed. The inversion parameter (x), tetragonal distortion ratio (γ), and the relevant interatomic distances are also presented. Parameter

T¼2 K

T ¼ 800 K

Sp. gr. χ2 Re/Rw a (Å) c (Å) γ x BA (Å2) BB (Å2) x(O) y(O) z(O) BO (Å2) А–О (Å) B–О1 (Å) B–О2 (Å)

I41/amd 9.6 2.1/6.6 5.8054(2) 8.7058(3) 1.060 1.00(2) 0.33(3) 0.19(3) 0 0.0156(2) 0.2498(2) 0.56(3) 1.888(2) 2.174(2) 1.991(2)

Fd3m 2.6 2.7/4.4 8.4268(1) – – 1.00(1) 1.47(2) 1.32(2) 0.2558(1) 0.2558(1) 0.2558(1) 1.88(2) 1.908(1) 2.060(1) 2.060(1)

Fig. 3. Evolution of diffraction patterns of CuFe2O4 in the low angle range on heating from 660 to 800 K. Miller indices of particular diffraction peaks are indicated with Т for tetragonal phase and С for cubic phase. The temperatures of the PT phase vanishing (700 K) and disappearing of magnetic contribution to the intensities (750 K) are indicated by dashed lines.

Temperature dependences of main structural parameters are shown in Figs. 4–6, in which a region of coexistence of the PC and PT phases is also visible. Unit cell parameters do not demonstrate any specific features. In particular, vanishing of the long-range magnetic ordering at 750 K does not obviously affect the dependence aC(T). A more detailed analysis shows that the expansion coefficient becomes significantly smaller after transition to the tetragonal phase (αV E5.2  10  5 1/K just above and αV E3.4  10  5 1/K just below the transition), and no marked discontinuity in the unit cell volume is observed (Fig. 5). Fig. 6 illustrates the temperature dependence of the interatomic distances between oxygen and A- and B-cations. It can be seen that, as noted in classical paper [2], in the tetragonal phase, tetrahedra demonstrate insignificant compression, while BO6 octahedra show noticeable tension along the tetragonal axis and compression in the perpendicular plane. The ideal tetrahedral angle О–А–О (109.471) splits into 109.291 and 109.561 in the tetragonal phase. Bond angles О–B–O in the octahedra, important for the analysis of magnetic interactions, deviate from 901 by no more than 2.71 in the cubic phase, and in case of transition to the tetragonal phase, they change by no more than 711. Visible in Figs. 5 and 6, slight changes in the cell volume and interatomic distances at around the phase transition are presumably associated with the change of the diffraction data processing mode, and namely, with the including of both phases, and thus should be regarded as an artifact of data processing, and not as a real effect.

Fig. 4. Temperature dependences of unit cell parameters (a0 T ¼ √2  aT). Particular temperature points were measured twice. Statistical errors are smaller than symbol sizes.

Fig. 5. Temperature dependences of unit cell volume (crosses in cubic phase, triangles in tetragonal phase, left scale) and tetragonal distortion ratio (rhombs, right scale) for 2–820 K. For tetragonal phase double cell volume is shown. When heating to 820 K cubic phase appears at TS1 E 660 K. Statistical errors are smaller than symbol sizes.

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Fig. 8. Temperature dependences (data obtained on heating) of ordered magnetic moments in octahedral (doubled value, 2MB) and tetrahedral (MA) sites and difference between them (2MB  MA). Statistical errors are indicated. Line drawn through the difference 2MB  MA is an average value (0.81 μB) for all points in the (1.5–750) K range.

Fig. 6. Temperature dependences of cation-oxygen interatomic distances in tetrahedra (A–O) and octahedra (B–O). In PC phase (T 4700 K) AO4 tetrahedra and BO6 octahedra are regular. In the PT phase octahedra are stretched along tetragonal axis (B–O1) and compressed in perpendicular plane (B–O2), tetrahedra remain regular. Statistical errors are comparable with the symbol sizes.

Fig. 7. Neutron diffraction pattern measured at HRPT at T ¼2 K and refined using Rietveld method. Vertical bars indicate peak positions (from top to bottom) of: CuFe2O4 tetragonal phase, CuFe2O4 ferrimagnetic phase, CuO, Fe2O3, Fe2O3 magnetic phase.

3.3. Magnetic ordering An example of refinement of diffraction patterns in the tetragonal phase over the full interval of scattering angles taking into account magnetic contribution is shown in Fig. 7. Magnetic ordering was described in conventional version of Néel configuration, i.e. with collinear and oppositely aligned moments in the Aand B-positions. Calculation of magnetic contribution was done using Fe3 þ form-factor and assuming also identical nominal Fe3 þ moments per atom of iron in both octahedral and tetrahedral sites for the tetragonal phase. Temperature dependences of the magnetic moments in A- and B-positions obtained in this version of data processing are shown in Fig. 8. As well as in the case of the unit cell parameters, the dependences are entirely uniform, features clearly beyond the statistical error are not observed,

including the region of co-existence of two crystalline phases. Thus, the observed temperature dependences do not provide any ground for introduction of non-collinear components of the measured average magnetic moments, which justifies the refinement of moment values in the simplest collinear approximation. An attempt to determine the magnetic moments independently in the cubic and tetragonal phases in the region of their co-existence did not lead to any particular result due to strong correlations between the parameters. For that reason, the moment magnitudes for both phases in the temperature range of their coexistence were contained to be equal. Insignificant fluctuations in moment values at 300 K can be associated to the change of equipment for heating the sample (a furnace instead of a cryostat). All magnetic diffraction peaks could be ascribed to the propagation vector k ¼(0, 0, 0) of magnetic long-range ordering. The symmetry analysis of possible magnetic structures built up by magnetic moments located in the tetrahedral (0, 3/4, 1/8) and octahedral (0, 0, 1/2) positions of the tetragonal unit cell with I41/ amd symmetry and propagation vector k¼ (0, 0, 0) has been carried out with the program SARAh [17]. Assuming that the magnetic ordering at both sites most probably should occur with one and the same irreducible representation (IR), we are left with just two IRs, Γ3 and Γ9, in notations of SARAh. Both possibilities have been checked with Rietveld refinements, and it has been found that it is the IR Γ9, which leads to the significantly better agreement factors, and thus this has been chosen as a final model for the magnetic structure of CuFe2O4. Thus, the observed magnetic ordering is found to be compatible with the two-sublattice Néel ferrimagnetic structure. An interesting new feature is that all the moments in both sublattices are aligned perpendicular to the c-axis, which indicates the presence of presumably weak easy-plain anisotropy. At T ¼2 K, the measured magnetic moments are MA ¼ (3.96 70.05) μB and MB ¼ (2.39 70.04) μB for the cations in the tetrahedral and octahedral positions, respectively. Assuming that the magnetic moments of iron in A- and B-positions are approximately identical in their size, the dependence of absolute values MA and MB on the inversion parameter x can be written as MA ¼xMFe þ(1  x)MCu and MB ¼[xMCu þ(2  x)MFe]/2, where MCu and MFe are magnetic moments of Cu2 þ and Fe3 þ , and, since xE 1, 2MB MA EMCu. As can be seen from Fig. 8, in the entire temperature range (including the cubic phase), the difference in 2MB and MA moments is close to 0.8 μB, with an error at the level of 0.1 μB, which actually corresponds to the spin magnetic moment of Cu2 þ .

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3.4. Microstructure In order to analyze the temperature changes in the microstructure – the average size of coherently scattering blocks and microstrains in the crystallites – the diffraction data acquired both at the HRPT and the HRFD were involved. HRFD (IBR-2 pulsed neutron source, Dubna) [18] is a TOF diffractometer with a correlation method of data acquisition. It provides exceptionally high resolution (Δd/d E0.001) which is, in addition, weakly dependent on dh k l in a wide range of d-spacings. The diffraction peak broadening depends on dh k l in different way for finite size, L, and microstrain effects, ε, allowing for their separation. The HRFDmeasured widths of the diffraction peaks, Wh k l, depend on the dh k l in the following way (in Gaussian approximation for distribution functions): 2

associated size reduction of the regions occupied by the PC phase. The peaks of the PT phase are gradually narrowing, but even at room temperature, their average width is nearly two times higher than in the initial state of the cubic phase. Moreover, there is a strong dependence of the width on a specific set of Miller indices (anisotropic broadening). Fig. 11 demonstrates that the widths of all the peaks in the PT phase are evidently larger than the resolution function, the most narrow peaks correspond to the (h 0 h) indices, whereas the (h 0 l)-type peaks have the largest widths.

4. Discussion 4.1. Crystal structure of CuFe2O4

4

W 2 ¼ C 1 þ ðC 2 þ C 3 Þd þ C 4 d ; where the constants C1 and C2 are determined by the resolution function of the diffractometer, C3 is microstrain contribution, C3  (2ε)2, C4 is finite size contribution, C4  (1/L)2. Knowing resolution function and plotting the dependences W2(d2) in a sufficiently wide range of d-spacings, ε и L can be found. For the HRFD experiment the same sample of CuFe2O4 was used, however, it was carried out on cooling from 770 K and only few selected temperatures across the structural phase transition region and at room temperature. Fig. 9 shows an example of the measured dependences W2(d 2), from which it follows that at T¼ 770 K in the cubic phase, the size effect is negligible (L 43000 Å) and the crystallites display a weak, standard for oxides, level of microstrains with ε E0.001. When approaching the temperature of appearance of the tetragonal phase, the dependence W2(d 2) becomes parabolic: at T¼ 700 K, coherent block sizes are reduced to L E800 Å, and the microstrains remain at the same level. Further cooling and the occurrence of a twophase state lead to a sharp broadening of the diffraction peaks of the cubic phase accompanied by the appearance of broad peaks of the PT phase and their gradual narrowing (Fig. 10). These dependences can be explained by the manifestation of the size effect— appearance of small nuclei of PT phase, their gradual growth and

Fig. 9. Dependences of diffraction peak widths on d-spacing for CuFe2O4 cubic phase. At 770 K the linear dependence is observed, while at 700 K the dependence is parabolic, which is associated to a finite size effect ( E800 Å). Bottom line corresponds to the diffractometer resolution function measured with a standard sample.

In the fundamental book [19] on the structure and physical properties of spinel ferrites the tendency of different ions to particular oxygen coordination is discussed and the results of calculations of the corresponding energies are given. For (Cu1 xFex) [CuxFe2 x]O4 it is concluded that the spinel is to be fully inverted, but since the Cu2 þ activation energy, when changing position, is very

Fig. 10. Temperature dependences of average width of diffraction peaks in cubic and tetragonal phases defined by Rietveld processing of HRFD-measured data.

Fig. 11. Diffraction peak widths, W2(d2), measured at room temperature (PT phase) for various (h k l) sets. Widths are divided into three groups: (h,0,h), (h,0,l), (h,ka0,l), within which standard linear dependences can be drawn through the points. Different slopes of straight lines indicate a significantly different microstrain level.

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small ( 0.1 eV), the degree of x deviation from 1 strongly depends on the sample preparation procedures and the rate of its cooling after synthesis. Experimental conclusions about the inversion degree of copper ferrite are often made on the basis of indirect evidence, for example, on the assumption of a linear relation between x and the tetragonal distortion value [20], which does not necessarily reflect the reality. It was established that the examined in the current paper sample (Cu1  xFex)[CuxFe2  x]O4 is, with an accuracy of 2%, a fully inverted spinel (x E1) in both structural phases. Since in the PT phase the tetragonal distortion has a conventional value (γ ¼1.06), the models of phase transition based on the relation of γ and x alone, are unlikely to be correct. From the nature of the temperature changes in interatomic distances it follows that the basis of the transition from the PC to the PT phase is the cooperative Jahn–Teller distortion of CuO6 octahedra, while the possible (not detected) insignificant migration of copper and iron atoms (change in the inversion parameter) manifests itself simply as a weak side effect. This structural rearrangement has indications of both the first and the second kind transitions. From one hand, near the transition temperature the system separates into coexisting phases, however, no discontinuity in the sample volume was detected. It is established that in the investigated transition between tetragonal and cubic phases, both structural states coexist in a considerably wide temperature range ( 40 K, regardless of the direction of temperature change). Besides that, their co-existence is of equilibrium nature, i.e. it does not change during long exposure at a fixed temperature, and the typical size of the longrange ordered domains of the coexisting phases is large ( 1000 Å, which is usually referred to as mesoscopic phase separation). One of the causes of stabilization of such a state is the long-range internal stresses in the crystallites (see, for example, [21]), resulting from a structural phase transition, and manifesting themselves in a strong anisotropic broadening of the diffraction peaks. The corresponding energy contribution and microstrain value depend on the grain size, morphology of boundaries, density of defects and other features of the microstructure. Our experiments [22] with (LaPr)0.7Ca0.3MnO3 manganites synthesized by different methods demonstrated a remarkable influence of samples with different microstructure on their mesoscopic phase separation. 4.2. Magnetic ordering type in CuFe2O4 In general, structural and magnetic phase transitions in Jahn– Teller systems are driven by mechanisms of different nature. The cooperative JT transition accompanied with a lowering of the lattice symmetry and an orbital ordering (of the eg orbitals of copper ions in the case under consideration) is governed by electron–lattice interaction that can be eventually reduced to the Coulomb interaction [7]. In contrast, mechanisms of electron superexchange transfer within cation pairs (Fe–Fe), (Fe–Cu), and (Cu–Cu) via intermediate oxygen ions are mainly responsible for the magnetic ordering. An appearance of tetragonal structural distortions at TS2 E700 K appreciably lower than TN E 750 K indicates that the magnetic and the structural order parameters are decoupled. Moreover, the observed regular T-dependence of magnetic moments, both in A and B cation positions, at TS2 and in a narrow temperature range E 40 K below, where the lattice reconstruction occurs, shows that the magnetic degrees of freedom are only weakly influenced by the lattice ones. As discussed below, an application of concepts of superexchange theory to the inverse mixed spinel CuFe2O4 offers several sound arguments in favor of this conjecture. Methods based on the band structure calculations provide a firm ground for quantitative estimates of magnetic exchange interactions

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in transition metal oxides [23]. To our best knowledge, the only study along this way available in the literature for the inverse spinel CuFe2O4 is reported in Ref. [24]. There, the magnetic and electronic properties of copper ferrites are examined using a spin-polarized band structure calculation method. In fact, the calculations merely revealed general trends in changes of relevant magnetic couplings as a free parameter (w) controlling the strengths of exchange interaction varies in a wide range. Furthermore, the calculations were carried out with fixed lattice parameters and, hence, an analysis of possible variations of magnetic interactions under a structural transition is lacking. To fill this gap, based on the standard concepts of superexchange theory [25] we developed a semi-quantitative analysis of magnetic couplings in CuFe2O4, which allowed us to estimate relative strengths of exchange parameters for different magnetic bonds in the spinel lattice and decide about their changes under the structural phase transition. Brief summary of this analysis and several conclusions are presented below. In the inverse mixed spinel CuFe2O4 dominant magnetic interactions between neighboring cations are described by the following exchange constants: J(Fe–Fe) , J(Fe–Fe) , J(Fe–Fe) , J(Fe–Cu) , J(Fe–Cu) , AA AB BB AB BB and J(Cu–Cu) . Here, an affiliation of ions to sublattices is given in the BB subscript. In Fig. 12, a schematic view of a lattice fragment in spinel structure with representative AB and BB cation–cation linkages through intermediate oxygens can be found, except for the more distant AA one. Hereafter, these linkages are merely referred to as magnetic bonds. All other magnetic bonds can be obtained by symmetry operations of the lattice and, in this respect, they are equivalent to those presented in Fig. 12. It is assumed that in the low-temperature tetragonal phase the 4-fold axis is along c axis. For Fe3 þ ions in the high-spin state S ¼5/2 (both in A and B positions) each of five d-orbitals, eg and t2g, with formal hole occupancy nh ¼1 contributes to the superexchange coupling with neighboring cations. For pairs (Fe–Fe), an additional contribution from the antiferromagnetic (AFM) direct d–d orbital exchange has to be taken into account as well [26]. Both mechanisms result in the total AFM interaction for all different (Fe–Fe) pairs, with the shortest AB bond being dominant, J(Fe–Fe) 4J(Fe–Fe) 4J(Fe–Fe) 40. AB BB AA A transition from the cubic to the tetragonal structure does not change the occupancy of d orbitals at Fe3 þ , and the exchange in the pairs (Fe–Fe) slightly varies only due to weak variations in the lengths and angles of cation–anion–cation bonds. The strength of exchanges in pairs including Cu2 þ ion is expected to change more dramatically. In the cubic structure, two eg orbitals of Cu2 þ are degenerate (neglecting a weak trigonal distortion of the crystal field at B sites) and their hole occupancy

Fig. 12. Schematic view of a lattice fragment of CuFe2O4 with cation positions, including A, and B1,2,3,4, shown as big balls, and several oxygen (anion) positions, shown as small red balls. Superexchange along different cation–anion–cation linkages give rise to magnetic couplings for cation pairs AB and BB, as discussed in the text. For a more detailed figure, see [26].

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nh ¼1/2. Both d(x2  y2) and d(z2) orbitals participate in the indirect exchange with neighboring Fe or Cu, however, the strength of all allowed superexchanges is weakened because of a partial eg-orbital occupancy of Cu ions. In the tetragonal structure, JT distortion of oxygen octahedra stabilizes the d(z2) orbitals that becomes fully occupied (nh ¼0) and the d(x2  y2) orbitals are left half-filled (nh ¼1) each. This means that superexchange processes with d(z2) orbitals involved are now forbidden, while the strengths of those with d(x2  y2) orbitals are enhanced. For instance, in the cubic phase the magnetic coupling J(Fe–Cu) AB for three pairs Fe(A)-Cu(B1,3,4) is of the AFM character and formed by an electron transferring via the oxygen O1 between eg and t2g orbitals of Fe3 þ and partially occupied eg orbitals of Cu2 þ . In the tetragonal phase, the indirect exchange along the vertical bond Fe (A)–Cu(B1) is fully suppressed with simultaneously enhanced AFM exchange for pairs Fe(A)–Cu(B3,4). Next, for each of three pairs Cu(B1)–Fe(B2,3,4), a weak exchange J(Fe–Cu) is dictated by nearly 901 geometry of two superexchange BB paths forming these magnetic bonds. For instance, in the pair Cu(B1)–Fe(B2) two paths are B1–O3–B2 and B1–O4–B2. Interference of superexchange processes along two paths explains a weakness of resulting exchange coupling J(Fe–Cu) , which is either FM or AFM BB depending on cation–anion–cation bond’s angles that vary with structural changes. Finally, a weak exchange in pairs Cu(B1)–Cu(B2,3,4) in the cubic phase are even less intensive, i.e. |J(Cu–Cu) | o|J(Fe–Cu) |. At the transiBB BB tion to the tetragonal phase, the exchange in the pair Cu(B1)–Cu (B2) develops in a similar manner as in Cu(B1)–Fe(B2), while J(Cu–Cu) BB for Cu(B1)–Cu(B2,3,4) is suppressed. Summarizing, when comparing pairs of magnetic bonds having in spinel structure the equivalent position, but different ionic composition, one expects that the exchange intensities decrease as J(Fe–Fe) 4|J(Fe–Cu)| 4 |J(Cu–Cu)|. It should be especially emphasized those mutually compensative changes of magnetic interactions in pairs including copper ions that occur at the structural transition— some of magnetic interactions are suppressed with simultaneous enhancement of others. With the use of above arguments, the magnetic behavior experimentally observed in the inverse mixed spinel CuFe2O4 can be explained as follows. 1. The dominant AFM interaction between A and B sublattices necessary for a stabilization of the overall collinear Néel ferrimagnetic ordering is readily apparent from arguments of standard superexchange theory. 2. Among the manifestations of magnetic complexity, a random and weak non-collinearity of magnetic ordering in a nearest-neighbor length scale is expected. Actually, given a uniform statistical distribution of Cu ions over B cation positions, strong AFM Fe (B)–Fe(B) couplings are frustrated by more weak Fe(B)–Cu(B) and Cu(B)–Cu(B) couplings; the values of AFM interactions on Fe(A)–Fe (B) and Fe(A)–Cu(B) bonds are also different. As a result, in both structural phases the local exchange fields at cations and their magnetic moments acquire randomly distributed static components perpendicular to a distinguished direction unique for a given domain of the spinel sample. This unique direction is dictated by the collinear Néel ferrimagnetic configuration developed in the domain. The net transverse component of the magnetic moment obtained by averaging over the domain volume tends to zero. Thus, in the measurements, longitudinal components of magnetic moments in domains are only observable. We suggest that this mechanism, together with an effective reduction of magnetic moments due to strong cation–anion covalent bonding [27], contributes considerably to the deviation of the observed for Fe3 þ low-T magnetic moment MFe E4 μB from its nominal value 5 μB.

3. The measured effective magnetic moment per formula unit Δ ¼ (2MB  MA) takes the value E0.8 μB in the whole temperature interval 1.5oT o750 K. This value shows no perceptible temperature dependence and corresponds to the slightly reduced nominal moment of Cu2 þ , which is understood because the mechanism indicated above for Fe3 þ should lead to a reduction of the Cu2 þ magnetic moments as well. We note a reduction by 20% in the size of observed magnetic moments for both cations. 4. Frustration of exchange interactions and a compensative behavior of their alteration at the structural phase transition is suggested to be the main cause for a weak coupling between the magnetic and lattice degrees of freedom in CuFе2O4. Actually, the removal of the orbital degeneracy at Cu ions induced by the JT distortion, which appears at TS2 and develops down to TS1, is accompanied with a weakening of exchange couplings on particular bonds together with a stiffening on other magnetic bonds. Consequently, at the transition temperature TS2 ( oTN) and its near vicinity the alternating local changes of magnetic interactions tend to compensate each other without strong impact on the spin arrangement established below TN. This explains a rather smooth T-dependence of magnetization in the region of structural reconstruction, except for several weak features related probably to weak intrinsic magnetoelastic effects. The observed decoupling of magnetic and structural phase transitions in the inverse mixed spinel CuFe2O4 is in contrast to the behavior found in the normal magnetic spinel MgCr2O4, where the structural and magnetic phase transitions coincide (to within a resolution of 0.1 K). However, the physics behind this behavior is quite different. Actually, in this spinel compound all magnetic nonJT ions Cr3 þ are located at B sites forming the pyrochlore lattice with the same AFM interaction between nearest neighboring Cr ions. Due to a geometrical frustration of the pyrochlore lattice in the high-T cubic phase, all possible magnetic structures are macroscopically degenerate and the system is in a paramagnetic state. The structural transition at  12 K reduces the cubic symmetry to a lower one, the equivalence of AFM bonds is violated, and the degeneracy is removed, which makes it possible for the system to lower its magnetic free energy immediately at the same temperature.

5. Conclusions The experiments with copper ferrite (Cu1  xFex)[CuxFe2  x]O4 carried out at high-resolution neutron diffractometers have revealed several previously unknown aspects of the magnetic and structural phase transitions in this compound. A sample of copper ferrite examined in the current study is a fully inverted spinel (x ¼1 70.02) in both structural phases—cubic and tetragonal. The tetragonal phase has a conventional value of the tetragonal distortion (γ ¼1.06 at room temperature and lower), whereas the inversion parameter does not change in the phase transition. This fact challenges the models of phase transition based on the relation of γ and x. The peculiarities of temperature changes of interatomic distances indicates that the mechanism of the structural transition is driven by the cooperative Jahn–Teller distortion of CuO6 octahedra, but not a mutual migration of copper and iron atoms. The temperature of formation of long-range ferrimagnetic order is significantly higher (by  50 K) than the temperature of structural transition. This indicates a weak relation between the lattice (orbital) and magnetic (spin) subsystems and that the structural and magnetic transitions in copper ferrite are not fully coupled to each other (are performed through different

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mechanisms). Qualitative analysis showed that the inverse spinel structure of CuFe2O4 and standard concepts of the superexchange theory result in antiferromagnetic interaction of A- and B-sublattices, i.e. the condition, which is necessary for the stabilization of the long-range ferrimagnetic order. The absence of an ideal coupling between the structural and magnetic transitions in CuFe2O4 is one of the essential differences between this spinel and normal spinels with magnetic cations in B-positions only. In the latter, due to formation of “pyrochlore lattice” by magnetic atoms, the long-range magnetic order is being established as a result of the frustration weakening accompanying the structural transition. High-resolution of neutron diffractometers, at which the experiments were carried out, allowed separating strong differences in microstructural parameters of the crystal in the tetragonal and cubic phases and their evolution in the process of structural transition. While in the cubic phase the strength of microstrains in the crystallites corresponds to the typical value for oxides, tetragonal phase is characterized by a significantly higher average level of microstrains superimposed with their strong anisotropy—the widths of the diffraction peaks strongly depend on the Miller indices. Presumably, it is the long-range anisotropic internal strains within the crystallites that are the main cause of stabilization of the equilibrium two-phase state in a considerably wide temperature range ( 40 K). Recently, an increasing attention has been paid to the nanostructured spinels with typical crystallite size at the level of 10 nm. Information is available that by mechanical or mechanochemical influence on the initial material, it is possible to significantly alter the degree of its density of defects and, in particular, to influence the distribution of cations over positions [28]. As a consequence, magnetic parameters can be altered. For instance, in Ref. [29] in the course of a long-term grinding a gradual increase in the magnetization and stabilization of the cubic phase was observed. The size effect is associated, in particular, with the emergence of random local deviations of the moments from the general collinear direction (see review [30]), thus explaining the reduction of the observed average moments. Using neutron diffraction, it would be interesting to test these effects. Acknowledgments This work is supported by the grants from the Russian Foundation for Basic Research no. 12-02-00686. Neutron diffraction

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experiments were performed on the SINQ (Paul Scherrer Institut, Switzerland) and IBR-2 (JINR, Russia) neutron sources. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

[16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]

J.M. Hastings, L.M. Corliss, Rev. Mod. Phys. 25 (1953) 114. E. Prince, R.G. Treuting, Acta Crystallogr. 9 (1956) 1025. J. Takaobushi, et al., Phys. Rev. B: Condens. Matter 76 (2007) 205108. M. Bibes, A. Barthélémy, IEEE Trans. Electron Devices 54 (2007) 1003–1023. J. Cabana, L. Monconduit, D. Larcher, M.R. Palacín, Adv. Mater. 22 (2010) E170–E192. L. Néel, Ann. Phys. Paris 3 (1948) 137–198. K.I. Kugel, D.I. Khomskii, Sov. Phys. Usp. 25 (1982) 231–256. P.J. Wojtowicz, Phys. Rev. 116 (1959) 32–45. X.X. Tang, A. Manthiram, J.B. Goodenough, J. Solid State Chem. 79 (1989) 250. M. Desai, S. Prasad, N. Venkataramani, I. Samajdar, A.K. Nigam, R. Krishnan, J. Appl. Phys. 91 (2002) 2220. S.S. Ata-Allah, J. Solid State Chem. 177 (2004) 4443–4450. L. Ortega-San-Martın, A.J. Williams, C.D. Gordon, S. Klemme, J.P. Attfield, J. Phys.: Condens. Matter 20 (2008) 104238. B. Canals, C. Lacroix, Phys. Rev. B: Condens. Matter 61 (2000) 1149. A.M. Balagurov, I.A. Bobrikov, M.S. Maschenko, D. Sangaa, V.G. Simkin, Crystallogr. Rep. 58 (2013) 710–717. P. Fischer, G. Frey, M. Koch, M. Koennecke, V. Pomjakushin, J. Schefer, R. Thut, N. Schlumpf, R. Buerge, U. Greuter, S. Bondt, E. Berruyer, Physica B 276–278 (2000) 146–147. J. Rodríguez-Carvajal, Physica B 192 (1993) 55. A.S. Wills, Physica B 276 (2000) 680. A.M. Balagurov, Neutron News 16 (2005) 8. S. Krupička, P. Novák, Oxide Spinels in Ferromagnetic Materials, NorthHolland, Amsterdam, 1982. J. Darul, Z. Kristallogr. (Suppl. 30) (2009) 335–340. K.H. Ahn, T. Lookman, A.R. Bishop, Nature (London) 428 (2004) 401. V. Yu. Pomjakushin, D.V. Sheptyakov, K. Conder, E.V. Pomjakushina, A.M. Balagurov, Phys. Rev. B: Condens. Matter 75 (2007) 054410. K.M. Rabe, Annu. Rev. Condens. Matter Phys. 1 (2010) 211. X. Zuo, A. Yang, C. Vittoria, V.G. Harris, J. Appl. Phys. 99 (2006) 08M909. J.B. Goodenough, Magnetism and the Chemical Bond, , 1963. D.G. Wickham, J.B. Goodenough, Phys. Rev. 115 (1959) 1156. Min Feng, Aria Yang, X.u. Zuo, C. Vittoria, Vincent G. Harris, J. Appl. Phys. 107 (2010) 09A521. J.A. Gomes, M.H. Sousa, G.J. da Silva, F.A. Tourinho, J. Mestnik-Filho, R. Itri, G.de M. Azevedo, J. Depeyrot, J. Magn. Magn. Mater. 300 (2006) e213–e216. S.J. Stewart, M.J. Tueros, G. Cernicchiaro, R.B. Scorzelli, Solid State Commun. 129 (2004) 347–351. S. Mørup, D.E. Madsen, C. Frandsen, C.R.H. Bahl, M.F. Hansen, J. Phys.: Condens. Matter. 19 (2007) 213202.