Magnetic and Polar Properties' Optimization in the Magnetoelectric

Article pubs.acs.org/JPCC

Magnetic and Polar Properties’ Optimization in the Magnetoelectric Ga2−xFexO3 Compounds

Christophe Lefevre,*,† Francois Roulland,† Alexandre Thomasson,† Christian Meny,† Florence Porcher,‡ Gilles André,‡ and Nathalie Viart† †

Institut de Physique et Chimie des Matériaux de Strasbourg (UMR 7504 CNRS-UDS), BP 43, 23, rue du Loess, 67034 Strasbourg Cedex 2, France ‡ Laboratoire Léon Brillouin (UMR12 CEA-CNRS), Bât 563 CEA Saclay, 91191 Gif sur Yvette, France ABSTRACT: The influence of the iron content on the magnetic, polar, and magnetoelectric properties of Ga2−xFexO3 (x = 1.0; x = 1.4) polycrystalline samples was studied by a combined magnetic (SQUID) and structural (X-ray and temperature-dependent neutrons diffraction) study. As expected, the samples showed a ferrimagnetic structure, with moments aligned along the c axis. The Néel temperature increases with x, from 210 K for GaFeO3 to 360 K for Ga0.6Fe1.4O3. The magnetic moment is close to 3.8 μB per iron atom for all compositions. The structural investigations show a decrease in the distortion parameters with increasing iron content, and computation of the polarization with a pointcharge model gives a similar significant and temperature-independent value of ≈20 μC/cm2 for both compositions. This study clearly indicates that magnetic properties can be strongly enhanced by increasing the Fe content in the cell, while the nonnegligible polarization value is preserved. Because the magnetoelectric coupling is also predicted to be preserved when increasing the iron content to x = 1.4, this composition is the most appropriate for applications.

I. INTRODUCTION Materials that exhibit both magnetic and electric orderings in the same phase are very attractive, especially if these orderings are coupled, as in magnetoelectrics. Such materials open up the possibility of new applications because it is possible to consider inducing magnetization with an electric field. Magnetoelectric materials therefore receive a considerable renewal of interest for their potential use in new electronic devices.1−3 The moststudied materials are perovskite oxides such as BiFeO34 and TbMnO3.5 The majority of these materials have major drawbacks, either because of their low magnetic ordering temperature or because of their resultant zero-moment antiferromagnetic ordering. Bulk GaxFe2−xO3 (GFO) has proved to have magnetoelectric properties with a spontaneous polarization along the b axis and a ferrimagnetic ordering temperature as high as 370 K for x = 1.4.6,7 This compound crystallizes in the orthorhombic Pc21n (33) space group, with lattice constants a = 0.87512 ± 0.00008, b = 0.93993 ± 0.00003, and c = 0.50806 ± 0.00002 nm. It has four cationic sites, the tetrahedral Ga1 and the three octahedral Ga2, Fe1, and Fe2 (Figure 1). Frankel et al.8 first showed the ferrimagnetic behavior of GFO by Mössbauer spectroscopy. This behavior was later confirmed and described in detail by Bertaut et al.9 with a combined Mössbauer, magnetic measurements, and neutron diffraction study. The cationic sites Ga1 and Fe1 are antiferromagnetically coupled with Ga2 and Fe2. This should result in antiferromagnetism for x = 1.0. However, a net magnetic moment is observed for this © 2013 American Chemical Society

Figure 1. Projection of the crystal structure of Ga2−xFexO3 along the c axis.

composition below its order temperature due to the existence of a cationic site disorder. This critical issue of cationic sites occupation has been studied by Arima et al.7 with neutron Received: April 15, 2013 Revised: June 10, 2013 Published: June 12, 2013 14832

dx.doi.org/10.1021/jp403733b | J. Phys. Chem. C 2013, 117, 14832−14839

The Journal of Physical Chemistry C

Article

diffraction experiments on GFO single crystals (0.8 ≤ x ≤ 1.15) produced by various preparation methods. This study shows a strong dependence of the magnetic properties on both the Fe/ Ga ratio and the preparation method because this has a strong impact on the distribution of the cations on the four available sites. Kang et al.10 and Kim et al.11 came to the same conclusions studying gallium ferrite powders prepared by solid-state reactions using various annealing conditions with X-ray diffraction and Mössbauer spectroscopy. More recently, Mohamed et al.12,13 also showed, through a combined neutron and Mössbauer study, that polycrystalline samples prepared by sol−gel and solid-state reactions had different cationic site occupations, resulting in varying values of the ordering temperatures. This is fully consistent with the fact that the magnetic properties in GFO are governed by the superexchange interactions between neighboring Fe3+ ions14 and will therefore be strongly affected by the Fe−O−Fe bond angles, hence by the cationic ordering. In addition to the cationic site distribution, the distortion of the polyhedral and the displacements of the cations from their supposed equilibrium positions are also of high interest. While the tetrahedral Ga1 and octahedral Ga2 sites were observed to be regular by Abrahams et al., the Fe1 and Fe2 sites were observed to be distorted octahedra.15 This distortion and the displacements of the cations from their equilibrium positions are thought to be the origin of the electric polarization. Arima et al.7 evaluated the polarization of the GaFeO3 compound using a simple pointcharge calculation model to be −0.025 C/m2 from the displacements of the cations in the cell deduced from their neutron diffraction refinements. More recently, Stoeffler et al.16 and Roy et al.17 have predicted sensibly larger polarization values for GFO of −25 and 56 μC/cm2, respectively, using first principles methods and a more modern theory of polarization. The combined experimental knowledge of both the cationic displacements and the magnetic moments they carry have allowed a greater insight into the magnetoelectric properties of the material. Arima et al.7 observed that the displacements of the Fe ions from the center of the oxygen octahedron along the b axis and the spin moment along the c axis are arranged in opposite directions for Fe1 and Fe2 sites. This results in outer products of displacements and magnetic moments in the same direction for both sites and could explain the large magnetoelectric effect observed in GFO. Neutron diffraction is a privileged technique to accurately determine the positions of both the metal and oxygen ions, which are necessary to compute the polyhedral distortions and calculate the electric polarization. This technique also allows the determination of the magnetic moments on the different atoms. It provides accurate information on the cationic site occupancies resulting from important Fermi length differences between Fe and Ga (bFe = 9.450 and bGa = 7.288 fm). A temperature-dependent neutron diffraction study allows the investigation of the influence of possible temperature-dependent structural modifications on the magnetic and electric properties of the material. To our knowledge, there are only two published temperature-dependent neutron diffraction studies of GFO. Both of them concern the x = 1 composition only. One study is a combined X-ray/neutron diffraction study of polycrystalline samples performed between 5 and 300 K.18 It shows a surprising non-monotonous variation for the lattice parameters, with a minimum at ≈150 K. The other study19 shows that there is neither structural transition nor modification of the cationic sites disorder between 296 and 1368 K. The spontaneous polarization is found to only slightly decrease from 15.3 (296 K) to 14.0 μC/ cm2 (1368 K) upon increasing the temperature. We have

performed a temperature-dependent neutron diffraction study on Ga2−xFexO3 compounds with x = 1.0 and x = 1.4, in order to study the influence of the composition on potential structural transitions. The x = 1.4 composition is the most interesting one both because of its potential applications in spintronics and because its Néel temperature is well above room temperature (370 K). The lack of experimental data concerning this composition probably stems from the difficulty to produce pure samples of this composition, free from any parasitic phase. This composition is indeed the limit for the existence of the Pc21n phase, and a further increase in the iron content would lead to crystallization into an α-Fe2O3-like phase, belonging to the R3̅c space group. The temperature range chosen for the study was 2− 400 K, in order to include the magnetic phase transition. We have compared the structural distortions in both compounds and have shown that an increase in the Fe content of the GFO cell led to an enhancement of the magnetic properties of the compound, without deteriorating its electric properties. The same polarization values could be calculated for both compounds. This confirms the high potential of the Ga0.6Fe1.4O3 compound for multiferroic and magnetoelectric applications at room temperature.

II. EXPERIMENTAL PROCEDURES The polycrystalline GaFeO3 (GFO) and Ga0.6Fe1.4O3 (GFO 1.4) samples were prepared by a solid-state reaction using the experimental conditions described in a previous work.20 The stoichiometric milling of Ga2O3 (99.999%, Alfa Aesar) and αFe2O3 (>99%, Prolabo) was carried out in an attritor mill for 1 h in an ammoniacal solution (pH = 9). The solution was then placed in a drying oven until full evaporation of the liquid part. The resulting powder was manually ground. An organic binder (polyvinyl alcohol) was systematically added at approximately 3 wt % to improve the mechanical behavior of the samples. The powders were compacted into pellets and sintered in a platinum crucible at 1400 °C for 20 h under air with a heating rate of 1.7 °C/min. The powders were then reground, pelletized, and sintered at 1450 °C during 10 h under air with a heating rate of 1.7 °C/min in order to obtain the expected composition. The final products were characterized by XRD using a Bruker D8 Advance equipped with monochromatic copper radiation (Kα = 1.54056 Å) and a Sol-X detector. Neutron experiments were carried out at the LLB (Saclay, France). The powder diffraction patterns at T = 10 K and in the paramagnetic state (300 and 400 K for GFO and GFO 1.4, respectively) were performed on the 3T2 diffractometer, and the thermal evolution from 1.8 to 290 K of the diffraction patterns was recorded on the G4.1 multidetector diffractometer. For the 3T2 experiments, the wavelength was 1.22523 Å, and the angular range was 4.5° < 2θ < 121° with a step of 0.05°. For the G4.1 experiments, the wavelength was 2.423 Å, and the angular range was 15° < 2θ < 94° with a step of 0.1°. All the diffraction patterns were analyzed by the Rietveld method using the FULLPROF refinement program,21 for which a Thompson−Cox−Hasting function was chosen to generate the line shape of the diffraction peaks. The agreement indices were the usual parameters which are used for Rietveld refinement. The compositions of the samples were checked by EDX spectroscopy coupled to a JEOL 6700 scanning electron microscope (SEM). Magnetization measurements, including hysteresis loops at 5 K and thermomagnetic curves (field-cooled measurements under 50 Oe), were performed using a Quantum Design MPMS SQUID VSM dc magnetometer. The Néel temperature was determined from the maximum of |dM/dT|. 14833



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III. RESULTS AND DISCUSSION Both GFO and GFO 1.4 samples were first characterized by Xray diffraction measurements at room temperature. All the peaks could be indexed in the Pc21n orthorhombic unit cell of Ga2−xFexO3, and no impurities were evidenced. The refined cell parameters using the Le Bail fitting procedure are presented in Table 1. They are consistent with the literature,7,20 and

equal to that observed by Mohamed et al. These results are therefore within the limits of the already observed values and confirm that the cationic site occupancies are strongly dependent on the synthesis conditions. The Ga1 site is occupied predominantly by Ga [0.86(2) and 0.67(2) for GFO and GFO1.4, respectively], while the Fe1 site is occupied mainly by Fe, almost exclusively for the highest iron content [0.88(3) and 0.97(2) for GFO and GFO 1.4, respectively]. The occupation difference between GFO and GFO 1.4 demonstrates distinct iron affinities of crystallographic sites. Indeed, after the Fe1 site is fully occupied by iron atoms for GFO and GFO 1.4, both Ga2 and Fe2 sites are filled. Such behavior is consistent with the strong preference of gallium for tetrahedral coordination, which was evidenced in other iron−gallium oxide compounds like ferrite or those with garnet-type structure.23,24 Finally, the refined occupation leads to a calculated composition which perfectly corresponds to the expected value for both samples. Indeed, summation of all occupancies gives Ga2.05Fe1.95O6 ≅ GaFeO3 and Ga1.09Fe2.91O6 = Ga0.55Fe1.45O3 ≅ Ga0.6Fe1.4O3, reinforcing the idea that no parasitic phase is present. After the samples were cooled, the intensities of both the (110) and (020) peaks strongly increase. This behavior is particularly obvious in Figure 4 that shows the diffraction patterns of GFO for 2θ with a range from 15 to 45° and a temperature range between 298.0 and 1.8 K. No additional diffraction peak is evidenced when going from the paramagnetic to the ordered magnetic state. This large enhancement of both the (110) and (020) Bragg peaks suggests that the iron moment lies along the c axis. The identical positions of magnetic and nuclear peaks indicate a propagation vector k = (0, 0, 0) and therefore equivalent magnetic and chemical unit cells. This observation is in good agreement with previous work.7,8 A ferrimagnetic structure was then included in the lowtemperature refinement with the magnetic components of Fe in the four sites oriented along the c axis corresponding to Bertaut’s notation (Ax, Cy, Gz).9,25 Refinements that were made considering the three other theoretical possibilities (Gx,Fy,Az), (Fx,Gy,Cz), and (Cx,Ay,Fz) gave no satisfactory results. The neutron diffraction patterns of both GFO and GFO 1.4 recorded at 10 K using the 3T2 diffractometer are presented in Figure 3. For the different refinements, the site occupancies which were obtained in the paramagnetic state were kept constant, and the initial value of the Fe3+ moment was taken as corresponding to a high spin state. Results of the refinements are shown in Table 2. The mean Fe3+ magnetic moment at low temperature is 3.85(4) and 3.89(1) μB for GFO and GFO 1.4, respectively. These values are similar to those reported previously7,12,13 and lower than the expected values (gJJ = 5 μB). The low value of the moment should be related to the chemical disorder within the structure.26 Such a disorder involves a random disruption of the magnetic interaction paths between Fe3+ ions by the nonmagnetic Ga3+ ions. Interatomic distances and some selected M−O−M′ angles calculated according to the refined atomic positions are reported in Table 3. They show rather small temperature dependence between 10 and 300 K (400 K for GFO 1.4). It is well-known that the Néel temperature of both compounds is related to the superexchange interactions between neighboring Fe3+ ions. Because the main Fe−O−Fe bond angles do not significantly change with the increasing iron content, the increase of TN should be only ascribed to the magnetic concentration of the different sublattices. In addition, the calculated distances indicate regular Ga1O4 tetrahedra and Ga2O6 octahedra having homogeneous bond lengths, whereas the two other octahedra are characterized by distorted bonds lengths. Those are usually

Table 1. EDX Analysis and Cell Parameters of GaFeO3 and Ga0.6Fe1.4O3 Determined from X-ray Diffraction Pattern at Room Temperature Using a Le Bail Fitting. The Error Is Given for Each in Terms of 3σ Ga/Fe content a b c

GaFeO3

Ga0.6Fe1.4O3

1.02(1)/0.98(1) 8.745(1) 9.393(1) 5.082(1)

0.66(1)/1.34(1) 8.765(2) 9.422(2) 5.086(2)

referenced therein. The compositions of both samples were checked by EDX. The values given in Table 1 are an average of at least three measurements at different locations with a standard deviation inferior to 1% wt. They are in perfect agreement with the expected measurements. Figure 2 reports the thermal

Figure 2. Isofield (50 Oe) thermal variation of the magnetization of GaFeO3 and Ga0.6Fe1.4O3 bulk samples.

dependence of the magnetization for the examined bulk samples. The curves are characteristic of ferrimagnetic behavior with Néel temperatures equal to 210 and 360 K for GFO and GFO 1.4, respectively, which enables structural investigations above these given TN from neutron diffraction. The neutron powder diffraction patterns for GFO and GFO 1.4 in their paramagnetic state, which have been recorded on the 3T2 diffractometer, are presented in Figure 3. The refined atomic coordinates, occupation rate for all atoms, and cell parameters are given in Table 2. All the coordinates are consistent with previous results.7,9 The determination of the cationic distribution within the structures was performed considering, as a starting hypothesis, that both gallium and iron atoms were equally introduced in all sites (i.e., Fe/Ga = 0.5/0.5 for GFO and Fe/Ga = 0.7/0.3 for GFO 1.4 for all sites). The Fe/Ga occupations were then separately refined. The occupancy refinements are presented in Table 2. The fitted occupancy values of Ga1 and Ga2 sites for GFO are between those obtained by Mohamed et al.12 and Arima et al.,7 and they are close to those obtained by Wang et al.22 While the fitted value for the Fe1 site is close to that observed by Arima et al., the fitted value for the Fe2 site is almost 14834



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Figure 3. Observed (black squares), calculated (red full line), and difference (blue full line) neutron powder diffractions pattern of GaFeO3 and Ga0.6Fe1.4O3 in their paramagnetic state and at T = 10 K recorded on the 3T2 diffractometer (λ = 1.22523 Å). Positions of the Bragg reflections are represented by vertical bars.

metric pseudosymmetry were calculated using the code of the Bilbao crystallographic server.31 Using formula 1 with the fitted atomic coordinates listed in Table 2, calculated polarization values are −25.3(13) and −23.3(9) μC/cm2 at T = 10 K and values are −25.8(9) and −24.5(10) μC/cm2 at room temperature for GFO and at 400 K for GFO 1.4. This observation indicates that the decrease of the degree of distortion is not large enough to have a significant influence on the polarization. The observed weak thermal evolution has already been reported by Mishra et al. They observed a decrease of the calculated polarization of only 1.3 μC/cm2 between room temperature and 1368 K.18 This result indicates that while the magnetic properties are strongly enhanced by the substitution of gallium for iron, the ferroelectric properties are only slightly modified by the doping. Finally, Arima et al. and Popov et al. have pointed out in previous publications that the large magnetoelectric effect in GaFeO3 should be ascribed to both an opposite displacement of Fe1 and Fe2 ions from the center of their distorted polyhedra and an antiparallel direction of their magnetic moments.7,32 Calculations of the experimental displacements along the b axis for both Fe1 and Fe2 ions in our compounds have been performed using the refined atomic positions. For GFO at T = 10 K, displacements of Fe1 and Fe2 from the center of their octahedron along the b axis are +0.25 and −0.13 Å, respectively. For GFO 1.4, they are +0.27 and −0.14 Å. Because both compounds have the same magnetic structure characterized by magnetic moment vectors at Fe1 and Fe2 in an opposite direction, we can assume that the magnetoelectric effect still occurs with increasing iron content in the Ga2−xFexO3 compounds. The thermal variations for the unit cell volume in the temperature range between 1.8 and 300 K for both compounds, as deduced from the refinements, are shown in Figure 5. As stated above, the occupation factors of the different ions were kept fixed equal to those refined in the paramagnetic state, whereas all other parameters were varied freely. No abrupt transition is observed,

related to the valence state of the cation which can be calculated using the Brown model. This model gives a phenomenological relationship between the formal valence sum and the corresponding bond length.27,28 Table 4 lists the valences calculated for both GFO and GFO 1.4 from the distances reported in Table 3. For all sites, the bond valence sum method is in good agreement with a +3 oxidation state. The distortion parameters for the different polyhedra can be evaluated by calculating the mean square relative deviation from average bond length Δ = 1/mΣm1 [(1i − ⟨1⟩)/⟨1⟩]2 where ⟨1⟩ is the mean bond length and m the number of vertices.29 The results are listed in Table 4. Considering this approach, the computed Δ values for the Ga1O4 tetrahedron are the lowest for both compounds (Δ = 0.013 and 0.004% for GFO and GFO 1.4, respectively) reinforcing the idea that these polyhedra are less distorted and are not affected by the iron content increase. On the contrary, the Fe2 site is the most distorted (Δ = 0.76 and 0.65% for GFO and GFO 1.4, respectively). It is noticeable that Δ somehow decreases with the increasing iron content, which suggests that the polyhedra are less distorted when the chemical composition is close to the one driving a transition toward the hematite structure.30 This decrease in the degree of distortion may suggest a diminution of the polarization of the solid solution with the increasing iron content. Refined atomic coordinates at low temperature allow performing calculations of the polarization using a point-charge model. These calculations were made, and a value of −25.0 μC/cm2 has been computed for GaFeO3 presenting Arima’s atomic positions.16 This formalism states that the polarization is given by the relationship e Pz = (3(uz ,{Ga} + uz ,{Fe}) − 2uz ,{O}) (1) V where uz is the displacement of the ith atom relative to a centrosymmetric structure, and uz{X} denotes the sum over all X atoms. The coordinates of the different atoms in a centrosym14835



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Table 2. Refined Parameters of GaFeO3 and Ga0.6Fe1.4O3 from Neutron Diffraction Data on the 3T2 Diffractometer GaFeO3 site Ga1

Ga2

Fe1

Fe2

O1

O2

O3

O4

O5

O6

a (Å) b (Å) c (Å) m (μB) Rp, Rwp, Rmagn

x y z Occ(Ga/Fe) x y z Occ(Ga/Fe) x y z Occ(Ga/Fe) x y z Occ(Ga/Fe) x y z x y z x y z x y z x y z x y z

Ga0.6Fe1.4O3

T = 10 K

T = 300 K

T = 10 K

T = 400 K

0.1539(5) 0 0.1748(6)

0.1504(4) 0 0.1763(5)

0.1530(4) 0 0.1756(6)

0.1602(4) 0.3056(4) 0.8121(6)

0.1599(3) 0.3078(3) 0.8079(5)

0.1543(4) 0.5821(3) 0.1885(6)

0.1518(4) 0.5839(3) 0.1905(6)

0.0332(3) 0.7966(4) 0.6794(6)

0.0316(3) 0.7963(4) 0.6809(5)

0.3247(5) 0.4278(5) 0.9807(5) 0.4900(6) 0.4310(7) 0.5180(6) 0.0010(6) 0.2010(5) 0.6505(8) 0.1600(5) 0.1984(4) 0.1534(7) 0.1694(6) 0.6709(5) 0.8409(8) 0.1689(5) 0.9370(6) 0.5169(7) 8.7467(1) 9.3962(1) 5.0845(1)

0.3241(5) 0.4280(5) 0.9793(8) 0.4893(6) 0.4325(7) 0.5170(7) 0.9986(5) 0.1993(5) 0.6532(8) 0.1599(5) 0.1961(4) 0.1535(8) 0.1655(5) 0.6711(5) 0.8453(8) 0.1682(6) 0.9370(6) 0.5168(8) 8.7534(1) 9.4185(1) 5.0799(1) 3.89(1) 4; 7.0; 4.4

0.1523(4) 0 0.1753(6) 0.67(2)/0.33(2) 0.1593(3) 0.3087(4) 0.8096(5) 0.21(2)/0.79(2) 0.1527(4) 0.5846(3) 0.1920(6) 0.03(2)/0.97(2) 0.0333(3) 0.7986(4) 0.6782(5) 0.18(2)/0.82(2) 0.3242(5) 0.4277(5) 0.9768(5) 0.4887(6) 0.4338(5) 0.5162(5) 0.9988(5) 0.2049(4) 0.6527(8) 0.1605(6) 0.1989(5) 0.1555(9) 0.1677(5) 0.6744(5) 0.8437(8) 0.1690(7) 0.9375(6) 0.5149(8) 8.7726(1) 9.4272(1) 5.0930(1)

0.86(2)/0.14(2) 0.1601(4) 0.3078(5) 0.8089(7) 0.64(2)/0.36(2) 0.1521(5) 0.5852(4) 0.1881(6) 0.11(3)/0.88(3) 0.0309(5) 0.7993(5) 0.6788(6) 0.44(2)/0.56(2) 0.3217(5) 0.4295(7) 0.9763(8) 0.4908(8) 0.4326(7) 0.5135(8) 0.0011(7) 0.2025(8) 0.6567(8) 0.1618(6) 0.1994(6) 0.1507(8) 0.1670(6) 0.6749(7) 0.8415(8) 0.1687(8) 0.9374(7) 0.5136(8) 8.7376(1) 9.3885(1) 5.0784(1) 3.85(4) 4.9; 6.48; 7

3.55; 4.90; -

3.03; 3.94; -

indicating that the crystal structure remains the same between 300 and 1.8 K. This is in contradiction with a previous neutron diffraction study on Al1−xGaxFeO3 compounds, which reported a change in slope of the thermal variation of the cell parameters around 150 K.18 In our case, the cell volumes show a quadratic evolution with temperature and could be refined using the room pressure equation of state: V (T ) = V0

∫0

exp

T

α(T )dT

(2)

in which α(T) is a temperature-dependent thermal expansion coefficient defined by α(T ) = α0 + α1T

(3)

where α0 and α1 are the coefficients determined by a Levenberg− Marquardt analysis of the volume expansion data. The refined values of α0, α1, and V0 are given in Table 5. We can notice that those values for both GFO and GFO 1.4 are almost identical, indicating that the volumetric thermal expansivity is not affected

Figure 4. Temperature variation of the neutron diffraction pattern of GaFeO3.

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Table 3. Selected Distances (Å) and Angles (°) for Both GaFeO3 and Ga0.6Fe1.4O3 Bulk Compounds GaFeO3

Ga0.6Fe1.4O3

T = 10K Ga1O4 tetrahedra M−O2 M−O4 M−O6 M−O6 Ga2O6 octahedra M−O1 M−O1 M−O2 M−O3 M−O4 M−O4 Fe1O6 octahedra M−O1 M−O1 M−O2 M−O3 M−O5 M−O5 Fe2O6 octahedra M−O1 M−O2 M−O3 M−O4 M−O5 M−O6

T = 300K

T = 10K

1.829(5) 1.870(5) 1.823(4) 1.849(5)

1.834(5) 1.870(4) 1.837(6) 1.872(5)

1.848(4) 1.851(4) 1.837(6) 1.857(6)

1.845(5) 1.879(4) 1.833(6) 1.863(6)

2.005(4) 2.044(5) 2.047(5) 1.873(4) 2.013(5) 2.025(4)

2.031(5) 2.043(7) 2.052(5) 1.891(6) 2.007(6) 2.034(6)

2.026(5) 2.022(5) 2.050(5) 1.913(4) 2.047(5) 2.050(4)

2.021(5) 2.037(5) 2.045(7) 1.892(5) 2.044(4) 2.047(5)

2.343(5) 2.082(4) 2.098(6) 1.904(6) 1.955(4) 1.953(5)

2.332(6) 2.084(6) 2.088(5) 1.941(6) 1.959(6) 1.917(6)

2.363(5) 2.086(4) 2.083(5) 1.883(4) 1.941(6) 1.961(6)

2.379(5) 2.081(5) 2.089(6) 1.919(4) 1.970(4) 1.947(5)

2.336(5) 2.032(6) 1.951(6) 2.114(4) 1.860(6) 1.958(6)

2.347(5) 2.026(5) 1.926(6) 2.105(6) 1.868(6) 1.958(6)

2.346(5) 2.035(5) 1.946(5) 2.101(4) 1.861(5) 1.970(6)

2.337(5) 2.049(5) 1.924(4) 2.120(5) 1.862(5) 1.955(5)

Table 4. Mean Square Relative Deviation from Average Bond Length and Bond Valence Sum Computed at 10 K for GaFeO3 and Ga0.6Fe1.4O3 GaFeO3 Ga1 Ga2 Fe1 Fe2

Fe1−O1−Fe2 Fe1−O1−Ga2 Fe2−O4−Ga1 Ga2−O4−Ga1 Ga1−O6−Fe2 Ga1−O2−Ga2 Fe2−O−Ga2

BVS

Δ (%)

BVS

0.013 0.201 0.599 0.766

2.99(3) 3.01(3) 2.85(2) 2.91(3)

0.004 0.074 0.640 0.652

2.98(3) 2.96(3) 2.92(2) 2.96(3)

Ga0.6Fe1.4O3

168.6(3) 166.7(4) 112.1(3) 123.7(3) 124.1(4) 114.7(4) 86.6(3)−104.5(4)

167.4(3) 164.7(3) 113.0(3) 120.9(3) 124.7(3) 117.6(3) 86.6(3)−104.0(3)

Table 5. Refined Values of the Volume at Low Temperature and the Coefficients of Thermal Expansion for Both GaFeO3 and Ga0.6Fe1.4O3 Bulk Compounds

Ga0.6Fe1.4O3

Δ (%)

GaFeO3

T = 400K

α1 (K−1) α2 (K−2) V0 (A3)

GFO

GFO 1.4

−1.2(4) × 10−6 3.9(1) × 10−8 416.6(8)

−1.5(5) × 10−6 4.4(4) × 10−8 418.7(3)

covalent solids. This nonevolution of α(T) should therefore be ascribed to the similar nature of the Ga−O and Fe−O bonds due to the close values of Ga and Fe electronegativities (1.6 and 1.8, respectively). The temperature dependence of the ordered magnetic Fe3+ moment magnitude for both GaFeO 3 and Ga 0.6 Fe 1.4 O 3 compounds is presented in Figure 6. For GaFeO3, the magnetic moment magnitudes were fitted to the empirical equation β ⎛ ⎛ T ⎞α ⎞ ⎟ ⎜ M ( T ) = M 0 ⎜1 − ⎜ ⎟ ⎟ ⎝ TN ⎠ ⎠ ⎝

(4)

which qualitatively fits the data well at all temperatures below TN. In the limit of low temperatures, M(T) ∼ M0(1 − β(T/TN)α). The asymptotic behavior of the model function M(T) is then determined by α. At T ∼ TN, M(T) ∼ M0αβ(1 − T/TN)β. When approaching TN, the M(T) formulation is thus simplified to the usual critical exponent expression, with the asymptote being determined by β. The fitted value of β for GFO is equal to 0.46(4), which is close to that predicted by the mean field theory (β = 0.5).

Figure 5. Thermal variations of the unit cell volume for both GaFeO3 (red) and Ga0.6Fe1.4O3 (black) compounds.

by the increasing iron content. It is well known that ionic solids have a higher thermal expansion coefficient compared to 14837



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(3) Ju, S.; Cai, T. Y.; Guo, G. Y.; Li, Z. Y. Electrically Controllable Spin Filtering and Switching in Multiferroic Tunneling Junctions. Phys. Rev. B 2007, 75, 064419-1−064419-5. (4) Wojdeł, J. C.; Iniguez, J. Magnetoelectric Response of Multiferroic BiFeO3 and Related Materials from First-Principles Calculations. Phys. Rev. Lett. 2009, 103, 267205-4. (5) Kimura, T.; Goto, T.; Shintani, H.; Ishizaka, K.; Arima, T.; Tokura, Y. Magnetic Control of Ferroelectric Polarization. Nature 2003, 426, 55−58. (6) Rado, G. T. Observation and Possible Mechanisms of Magnetoelectric Effects in a Ferromagnet. Phys. Rev. Lett. 1964, 13, 335−337. (7) Arima, T.; Higashiyama, D.; Kaneko, Y.; He, J. P.; Goto, T.; Miyasaka, S.; Kimura, T.; Oikawa, K.; Kamiyama, T.; Kumai, R.; Tokura, Y. Structural and Magnetoelectric Properties of Ga2−xFexO3 Single Crystals Grown by a Floating-Zone Method. Phys. Rev. B 2004, 70, 064426-1−064426-8. (8) Frankel, R. B.; Blum, N. A.; Foner, S.; Freeman, A. J.; Schieber, M. Ferrimagnetic Structure of Magnetoelectric Ga2−xFexO3. Phys. Rev. Lett. 1965, 15, 958−960. (9) Bertaut, E. F.; Bassi, G.; Buisson, G.; Chappert, J.; Delapalme, A.; Pauthenet, R.; Rebouillet, H. P.; Aleonard, R. Study of Fe1.15Ga0.85O3 by Mössbauer Effect, X-ray and Neutron Diffraction and Magnetic Measurements. J. Phys. (Paris) 1966, 27, 433−449. (10) Kang, K. U.; Kim, S. B.; An, S. Y.; Cheong, S.-W.; Kim, C. S. Magnetic Properties of GaFeO3 Prepared by Slow Cooling and Quenched Heat Treatment Method. J. Magn. Magn. Mater. 2006, 304, e769−e771. (11) Kim, W.; We, J. H.; Kim, S. J.; Kim, C. S. Effects of Cation Distribution for AFeO3 (A = Ga, Al). J. Appl. Phys. 2007, 101, 09M5151−09M515-3. (12) Mohamed, M. B.; Senyshyn, A.; Ehrenberg, H.; Fuess, H. Structural, Magnetic, Dielectric Properties of Multiferroic GaFeO3 Prepared by Solid State Reaction and Sol−Gel Methods. J. Alloys Compd. 2010, 492, L20−L27. (13) Szymanski, K.; Dobrzynski, L.; Bakr, M.; Satula, D.; Olszewski, W.; Parzych, G.; Fuess, H. Fe Cation Occupancies in GaFeO3 Prepared by Sol−Gel and Solid State Reaction. Phase Transitions 2010, 83, 824− 835. (14) Levine, B. F.; Nowlin, C. H.; Jones, R. V. Magnetic Properties of Ga2−xFexO3. Phys. Rev. 1968, 174, 571−582. (15) Abrahams, S. C.; Reddy, J. M.; Bernstein, J. L. Crystal Structure of Piezoelectric Ferromagnetic Gallium Iron Oxide. J. Chem. Phys. 1965, 42, 3957−3968. (16) Stoeffler, D. First Principles Study of the Electric Polarization and of its Switching in the Multiferroic GaFeO3 System. J. Phys.: Condens. Matter 2012, 24, 185502-1−185502-7. (17) Roy, A.; Mukherjee, S.; Gupta, R.; Auluck, S.; Prasad, R.; Garg, A. Electronic Structure, Born Effective Charges and Spontaneous Polarization in Magnetoelectric Gallium Ferrite. J. Phys.: Condens. Matter 2011, 23, 325902-1−325902-9. (18) Saha, R.; Shireen, A.; Bera, A. K.; Shirodkar, S. N.; Sundarayya, Y.; Kalarikkal, N.; Yusuf, S. M.; Waghmare, U. V.; Sundaresan, A.; Rao, C. N. R. Structure and Magnetic Properties of the Al1−xGaxFeO3 Family of Oxides: A Combined Experimental and Theoretical Study. J. Solid State Chem. 2011, 184, 494−501. (19) Mishra, S. K.; Mittal, R.; Singh, R.; Zbiri, M.; Hansen, T.; Schrober, H. Phase Stability of Multiferroic GaFeO3 up to 1368 K from In Situ Neutron Diffraction. J. Appl. Phys. 2013, 113, 17410-1−1741025. (20) Roulland, F.; Lefevre, C.; Thomasson, A.; Viart, N. Study of Ga2−xFexO3 Solid Solution: Optimisation of the Ceramic Processing. J. Eur. Ceram. Soc. 2013, 33, 1029−1035. (21) Rodriguez-Carvajal, J. Recent Advances in Magnetic Structure Determination by Neutron Powder Diffraction. Physica B 1993, 192, 55−69. (22) Wang, N.; Wen, F. S.; Li, L.; Lü, Y. F.; Liu, S. C.; Lu, Y. F.; Liu, Z. Y.; Xu, B.; He, J. L.; Yu, D. L.; Tian, Y. J. Magnetic Frustration Effect in Polycrystalline Ga2−xFexO3. J. Magn. Magn. Mater. 2010, 322, 3595− 3600.

Figure 6. Thermal variation of the iron moment magnitude for GaFeO3 and Ga0.6Fe1.4O3 compounds.

IV. CONCLUSIONS Highly pure GaFeO3 and Ga0.6Fe1.4O3 bulk samples have been prepared by a solid-state reaction and characterized by X-ray and temperature-dependent neutron diffraction and magnetic measurements. A collinear ferrimagnetic structure along the c axis has been observed for both compounds with a magnetic moment close to 3.8 μB per iron atom. The Neél temperature is increased from 210 to 360 K upon increasing the iron content of the cell. Structural investigations show a decrease of the distortion parameter with the increasing iron content. The variation of the distortion parameter is, however, not large enough to have any significant influence on the polarization, which remains almost unchanged. This study indicates clearly that the magnetic properties of Ga2−xFexO3 can be strongly enhanced through increasing x, without deteriorating the polarization within the structure. Moreover, magnetic structure and displacements of Fe1 and Fe2 from the center of their octahedron along the b axis suggest that a magnetoelectric coupling still occurs with the increasing iron content. Finally, the value of the critical exponent β has been fitted to 0.5 for GaFeO3, indicating that magnetic interactions are described by the mean field approach in this compound.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors wish to thank the LLB for making neutron beam time available. They are also indebted to C. Piamonteze and U. Staub for preliminary measurements on the SINQ source. This research was conducted with financial support from the international ANR DFG Chemistry project GALIMEO #2011INTB-1006-01.

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REFERENCES

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Magnetic and Polar Properties' Optimization in the Magnetoelectric

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