Origin of the magnetoelectric effect in the Cs2FeCl5·D2O compound

Oscar Fabelo,1,* J. Alberto Rodríguez-Velamazán,1,2 Laura Canadillas-Delgado,1,3 Lidia Mazzuca,1 Javier Campo,2 Ángel Millán,2 Laurent C. Chapon,1 and Juan Rodríguez-Carvajal1 1Institut Laue Langevin, 71 Avenue des Martyrs, CS 20156, Cedex 9, Grenoble, 38042, France 2Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, C/ Pedro Cerbuna 12, Zaragoza, 50009, Spain 3Centro Universitario de la Defensa de Zaragoza, Carretera de Huesca s/n. 50090 Zaragoza, Spain (Received 23 May 2017; revised manuscript received 21 July 2017; published 21 September 2017)


I. INTRODUCTION
Magnetoelectric (ME) materials, in which magnetization or polarization can be induced by, respectively, an electric or magnetic field, represent an attractive class of compounds with rich fundamental physics and potential applications in memory and logic devices [1]. Basically, two groups of ME materials can be distinguished: those where the ME effect is obtained due to the combination of different building blocks, each one responsible for the electrical and magnetic properties, respectively, and those where the ME effect is obtained in a single-phase compound. Within this second group there is a category of materials with linear ME coupling properties, such as MnTiO 3 , NdCrTiO 5 , FeSb 2 O 4 , or Cr 2 O 3 , in which electric polarization is induced by a special magnetic structure and increases linearly with increasing magnetic fields [2][3][4][5]. The ME effect couples both electric and magnetic fields, so that neither time reversal nor spatial inversion can be a symmetry operation of these systems; that is, linear ME effects can only occur in systems where both the spatial and the time inversion symmetry are broken.
In a previous paper we have reported the mechanism of multiferroicity of the (ND 4 ) 2 FeCl 5 ·D 2 O compound [6], which was explained by the so-called inverse Dzyaloshinskii-Moriya (DM) effect [7] or spin current mechanism, that predicts an electric polarization, P, proportional to r ij × (S i × S j ), where r ij is the vector connecting the nearest spins, S i and S j . The exploration of other members of the A 2 FeX 5 ·H 2 O family, where A stands for an alkali metal or ammonium ion and X for a halide ion [8], has proven the occurrence of ME effects for some alkali-based compounds: K 2 FeCl 5 ·H 2 O, Rb 2 FeCl 5 ·H 2 O, and Cs 2 FeCl 5 ·H 2 O. The K-and Rb-containing compounds crystallize in the Pnma orthorhombic space group * fabelo@ill.fr [9,10], with a crystal structure at RT isomorphic to that of the ammonium-based multiferroic compound [6,11,12]. The magnetic structure of the (ND 4 ) 2 FeCl 5 ·D 2 O compound at zero field and 2 K shows an incommensurate cycloidal spin structure with a propagation vector k = (0,0,k z ), with k z = 0.2288(4) [6]. The magnetic moments are contained mostly in the ac plane with a small tilting angle of ca. 4°w ith respect to the b axis, and the cycloid propagates along the c axis. A recent work [13] shows the presence of weak second-order satellites, suggesting a non-negligible magnetostructural coupling. These results are rather different from those of the K 2 FeCl 5 ·H 2 O and Rb 2 FeCl 5 ·H 2 O compounds, which present commensurate, k = (0,0,0), antiferromagnetic structures and absence of ferroelectric signal at zero field. The magnetic structures at zero field of K 2 FeCl 5 ·H 2 O and Rb 2 FeCl 5 ·H 2 O compounds are described by the Shubnikov magnetic space group P n m a belonging to the magnetic class m m m [14]. The magnetic moments of the Fe(III) ions are antiferromagnetically coupled within the zigzag chain running along the b axis, with the magnetic moments along the a direction; all the adjacent zigzag chains are in phase forming ferromagnetic ac planes, antiferromagnetically coupled along the b axis. These results are compatible with the occurrence of a magnetoelectric tensor where only the diagonal terms are nonzero and therefore the system can be described as linear ME [8].
The case of the Cs 2 FeCl 5 ·H 2 O compound is slightly different. The macroscopic measurements show that the system presents linear ME effect [8]; however, the origin of this behavior is not clear. In order to understand deeply the magnetoelectric correlations, the determination of the magnetic structure of this compound is mandatory.
In this paper, we investigate the temperature dependence of the nuclear structure using single-crystal neutron diffraction measurements. Below T N we have determined the magnetic structure at zero magnetic field as well as the temperature evolution of the magnetic structure by combining singlecrystal and powder neutron diffraction. Finally, we present the magnetic structure determination above the magneticfield-induced spin-flop transition, with the magnetic field applied along the b axis. All the magnetic structures have been analyzed using representational analysis, proving that the linear ME effect observed on the Cs 2 FeCl 5 ·H 2 O compound is compatible with the proposed magnetic structures.

A. Materials
Deuterated reagents and solvents used in the synthesis were purchased from commercial sources and used without further purification.

B. Synthesis of the Cs 2 FeCl 5 ·D 2 O compound
Single crystals of Cs 2 FeCl 5 ·D 2 O of suitable size for neutron scattering were prepared by the slow evaporation technique under a controlled atmosphere. Stoichiometric quantities of CsCl and anhydrous FeCl 3 were dissolved in a minimum quantity of D 2 O. The solution was filtered and left in a controlled atmosphere. Large red prismatic single crystals of Cs 2 FeCl 5 ·D 2 O were collected after several weeks (see Fig. S1 in the Supplemental Material [15]). The twinned or small-size crystals were collected and milled to obtain enough product to perform neutron powder diffraction experiments

C. Neutron diffraction instruments
Neutron diffraction measurements were performed with different instruments at Institut Laue Langevin (ILL, Grenoble, France): D1B and D2B, for powder diffraction measurements, and D9 and CYCLOPS for single-crystal diffraction studies.
Neutron powder diffraction experiments were carried out on the medium-resolution and high-flux D1B diffractometer and on the high-resolution D2B diffractometer, both equipped with variable temperature environment. The sample was contained in a Ø 5-mm cylindrical vanadium can and placed inside an Orange Cryostat or a closed-cycle cryostat device for D1B and D2B, respectively. High-resolution neutron diffraction patterns were acquired at room temperature (RT) and 45 K in D2B (wavelength 1.595Å) in the 2θ range 0°-159.95°with a step size of 0.05°. The D1B instrument was operated with a wavelength of 2.521Å, produced by its pyrolytic graphite monochromator. Graphite filters between the monochromator and the sample reduce the higher-order wavelength contamination, the proportion of λ/2 contamination being ca. 0.03%, which in the present case is in the limit of observation. Two high-flux neutron patterns were collected at 1.8 and 10 K, in the ordered and paramagnetic phases, respectively. The temperature evolution of the neutron diffraction pattern was followed from 1.8 to 10 K, with a heating rate of 0.04 K/min. Data reduction was carried out using LAMP software [16].
The single-crystal measurements (D9 and CYCLOPS) were carried out in a sample of 3 × 4 × 4 mm 3 , approximately, which was mounted on a standard aluminum pin. The D9 instrument was equipped with a closed-cycle cryostat for low-temperature measurements. The instrument was operated in the four-circle configuration with a wavelength of 0.8409Å for data collections at zero magnetic field at RT, 20 K (paramagnetic phase) and in the magnetically ordered phase (ca. 1.8 K). The measurements under external magnetic field were performed in D9 operating in "normal beam" geometry, working with the same wavelength and equipped with a vertical-field cryomagnet, which allows applying magnetic fields ranging from 0 to 6 T. The magnetic field was only applied along the b crystallographic direction (corresponding to the a axis of the high-temperature phase; see the crystal structure section). The crystal alignment was previously done using D9 working in a four-circle configuration.
The data collections in D9 consist of ω scans or ω-2θ scans. The program RACER [17] was used to integrate these scans and to correct them for the Lorentz factor. The crystal absorption corrections were made with the DATAP program [18], using an estimated absorption coefficient of 0.608 cm −1 , for a wavelength of 0.8409Å, essentially due to the absorption cross section of the chlorine atoms [19].
The CYCLOPS measurements consisted of an exploration of the Laue patterns, at a specific orientation, as a function of the temperature. One hundred fifteen Laue diffraction patterns were collected during 15 min each with a difference of temperature of 1 K. Two different patterns after and before the nuclear structure transformation can be seen in Fig. S2 in the Supplemental Material [15].
The refinement of the nuclear and the magnetic structures was performed using the program FULLPROF. [20]. Due to the structural phase transition, the occurrence of two twin domains has been observed. These were included in the data reduction, and the ratio between both domains was refined giving rise to a proportion of 53%:47%. The models for the magnetic structure were deduced from the output of the program BASIREPS [21] included in the FULLPROF suite [20].

D. Neutron diffraction measurements
In order to determine an accurate structural model of the Cs 2 FeCl 5 ·D 2 O compound, in particular the deuterium positions, which are not easily determined from the x-ray experiments due to the low scattering power of these light atoms, neutron diffraction experiments were necessary [22]. Room temperature (RT) single-crystal neutron diffraction measurement was carried out at the D9 diffractometer. The obtained model was used as starting point to fit the lowtemperature powder diffraction data collected on the D1B diffractometer. The fit of the data in the paramagnetic phase at low temperature with the room temperature model was not satisfactory, suggesting the occurrence of a nuclear phase transition, similar to that observed in the (ND 4 ) 2 FeCl 5 ·D 2 O compound [6]. This option was explored initially using the Laue diffractometer CYCLOPS [23] as a function of temperature and later on, with high-resolution powder neutron diffraction (see Figs. S2 and S3 in the Supplemental Material [15]). The comparison between different Laue images shows the appearance of new Bragg reflections below ca. 175 K, which is a fingerprint of the occurrence of a phase transition. The occurrence of this phase transition was corroborated through specific heat measurements, where a weak lambda peak was observed at 173 K (see Fig. S4 in the Supplemental Material [15]). After the successful indexing of the lowtemperature neutron powder diffraction, a full data set was collected at ca. 20 K on the D9 diffractometer in order to solve the crystal structure at low temperature in the paramagnetic phase. The magnetic structure determination at zero magnetic field and 1.8 K was carried out combining D1B and D9 data in a joint refinement.

A. Crystal structure at high temperature (HT)
The title compound crystallizes in the orthorhombic Cmcm space group with the following unit cell parameters: a = 7.412302 (3), b = 17.3011 (7), c = 8.0742 (3)Å, and α = β = γ = 90.0 • . The nuclear structure is built up from [FeCl 5 ·D 2 O] 2− ionic units and Cs + counterions in a ratio of 1:2. The crystal structure can be seen as chains of [FeCl 5 ·D 2 O] 2− units connected along the c axis through an extensive network of H bonds. Each chain is surrounded by six other chains following a stacking sequence ABAB along the b axis. The empty space between chains is filled by the Cs + counterions (see Fig. 1). The crystallographic details of the two phases (above and below the structural phase transition), including space groups and lattice parameters as well as some details of the data refinement, are shown in Table I. The atomic positions and thermal displacement parameter can be consulted in Table S1 or in the CIF files, data available in the Supplemental Material [15].
The Fe(III) atom is located in the intersection of two mirror planes, the first one perpendicular to the a axis and the second one perpendicular to the c axis. Moreover, a twofold axis is present along the b direction. The Fe(III) environment is filled by five chlorine ions and one coordination water molecule, which is disordered into two different positions, with an occupancy of 0.5. All the hydrogen atoms of this water molecule are involved in hydrogen bonds, giving rise to the mentioned chains along the c axis. The [FeCl 5 ·D 2 O] 2− units form slightly distorted octahedra. The shortest Fe-Cl bond distances correspond to Cl(1), which is coordinated in transconformation with respect to the water molecule (see Table II).
The Fe-O(1w) bond distance is slightly elongated compared with the value previously reported for (ND 4 ) 2 FeCl 5 ·D 2 O compound and the trans-Fe-Cl(1) bond distance is slightly shorter. However, no significant difference has been observed for the bond distances in the equatorial plane. These deviations are related with the strength of the different hydrogen bonds at play. In this compound, the only hydrogen bonds are those related with the coordination water molecule [O(1w)-D · · · Cl(2)], with a D · · · Cl distance of 2.517(3)Å, notably longer compared with that previously reported for (ND 4 ) 2 FeCl 5 ·D 2 O [2.217(2)Å]. A detailed list with the geometrical parameters of all the possible H bonds can be consulted in Table III. (8) Fe (1)· · · Fe(1a 2 ) 5.790 (5) Fe (1)· · · Fe(1b 2 ) 6.954 (4) There are two crystallographically independent Cs + counterions, both located in 4c Wyckoff positions. However, from the crystal point of view, both behave very differently. The Cs(1), which is located at (0, 0.47044, 0.2500) and symmetry related positions, forms a zigzag chain with the adjacent Cs(1) along the c axis, while the Cs(2), located at (0, 0.75458, 0.2500) and symmetry related positions, lies in an almost perfect plane (see Fig. S5 in the Supplemental Material [15]).

B. Crystal structure at low temperature (LT)
The neutron diffraction data below the phase transition temperature (ca. 175 K) reveal a nuclear phase transition from the Cmcm space group to C2/c. Although C2/c is the standard space group, along this section, for the sake of the comparison, we are going to describe the crystal structure using the nonstandard I 2/c space group. Keeping invariant the origin of the unit cell at high temperature, the orthorhombic unit cell can be transformed into the monoclinic one by means of a simple axis permutation plus an axis doubling; then V LT  Fig. 2). The symmetry breaking from orthorhombic to monoclinic produces instead notable changes in the Fe(III) site environment: The two mirror planes and the twofold axis that were located on Fe(III) in the orthorhombic phase are not present in the low-temperature phase. Therefore, the Fe(III) environment is now built up from five crystallographically independent chlorine ions and one coordination water molecule. A remarkable consequence of this symmetry breaking is the loss of the disorder in the coordination water molecule that was observed in the orthorhombic phase. This feature, together with the doubling of the c axis, causes the water molecules to follow a + − + − sequence along the c axis. The + and − signs have been used to represent the tilting angle of the water molecule, with + if it is tilted up and-if it is tilted down with respect to the ac plane (see Fig. 2). As in the orthorhombic phase, all the hydrogen atoms are involved in hydrogen bonds.

C. Magnetic structure at zero magnetic field
The neutron diffraction measurements at 1.8 K (below T N ) and zero magnetic field were carried out in D1B (powder) and D9 (single-crystal) instruments and analyzed in a joint refinement. The observed magnetic contribution, on top of nuclear reflections in the powder pattern, suggests that the magnetic reflections can be indexed with the propagation vector k = (0,0,0). This was confirmed by the survey of the reciprocal space in the single-crystal experiment, proving that the only compatible propagation vector is k = (0,0,0). A total of 1120 independent reflections were collected in D9 at 1.8 K (the same temperature of the data obtained in D1B). The temperature evolution of the sample was collected on D1B in the temperature range from 1.8 to 10 K (see Fig. 3). The onset of the appearance of magnetic reflections below ca. 6.6 K is in good agreement with T N determined from the magnetometry measurements [8] and with the signal observed in the specific heat curve (Fig. S4 in the Supplemental Material [15]). In order to study the entropy related with the magnetic transition, we carried out a background correction by subtracting the phonon contribution (AT 3 term). The value of A was fixed to give no magnetic contribution well above the magnetic transition (above 20 K, T > 3T N ). The magnetic entropy was derived by integration of the Cp/T versus T plot up to 20 K, once the AT 3 contribution was subtracted. The value of the entropy associated to the magnetic transition approaches 14.7 J mol −1 K −1 (per Fe atom), remarkably close to 14.9 J mol −1 K −1 , the calculated value for Rln(2s + 1) if s = 5/2, as is expected for a Fe(III) ion.
The representational analysis technique described by Bertaut was used to determine the possible magnetic structures compatible with the (nonstandard setting) I 2/c space group and propagation vector k = (0,0,0) [24]. Four irreducible representations (irreps) of the group G k ,( 1 ,− 4 ) and the corresponding set of basis vectors for each irreducible representation were determined using the program BASIREPS [21]. The magnetic representation M for the magnetic site  = (0,0,0). The symmetry elements are written according to Seitz's notation. Magnetic moment components of the four irreps are also given. Atoms related by the centering translation I ( 1 2 , 1 2 , 1 2 ) are omitted.
principle all the irreps are possible solutions.
A summary of the four possible irreps together with a detailed description of the basis vectors for the four possible irreps is shown in Table IV. The magnetic moments for the 8f Wyckoff position are obtained from the basis vectors as m 8f (1) = (u,v,w); therefore there are three degrees of freedom for the four possible magnetic structures. The Shubnikov group of each magnetic structure is written in the last column of Table IV.
The only irreducible representation that provides a satisfactory agreement between the calculated and the experimental diffraction data collected below T N is 4 . From the joint powder/single-crystal refinement (see Fig. 4) we are able to obtain the relative orientation of the magnetic moments of the magnetic sites. The magnetic structure corresponds to a collinear antiferromagnetic (AF) arrangement, with the magnetic moments lying along the b axis. The refined magnetic moment is ±4.39 μ B , value which is in agreement with previously reported Fe(III)-based compounds [14], and with the entropy value derived from heat capacity. Although the magnetic moments are not symmetry restricted to be along the b axis the refined components along the other directions are zero within the experimental error and were fixed in the last refinement (see Fig. 5). The refined magnetic structure gives rise to a magnetic model (I 2 /c) which is a subgroup of the orthorhombic magnetic structure Cmcm predicted by Ackerman et al. [8]. However, this prediction did not take into account the occurrence of the structural phase transition at ca. 175 K that produces a breaking of symmetry from the orthorhombic Cmcm to the monoclinic I 2/c space group, and  therefore the magnetic space group must be, more specifically, a subgroup of the paramagnetic group I 2/c1 . The evolution of the integrated intensity of the magnetic (0 0 2) reflection as a function of the temperature is shown in Fig. 3(b), while the evolution of the refined magnetic moment is shown in Fig. S6 in the Supplemental Material [15]. The integrated intensity of the (0 0 2) reflection was fitted in the critical region (|T − T N |/T N < 0.1) using a power law I = I 0 |T − T N | 2β [solid line in Fig. 3(b)] giving rise to a critical exponent β of 0.38 (2). This number should be taken with care, due to the low number of experimental points to fit in the critical region, but is in agreement with a 3D Heisenberg model, as expected for a Fe(III)-based compound. This result points to a non-negligible interaction between the adjacent zigzag chains running along the c axis (see Fig. 5).
The magnetic structure can be described as supramolecular Fe(III) chains connected through hydrogen bonds. The Fe · · · Fe chains connect iron atoms along the c axis following a zigzag sequence. The magnetic moment along these chains follows an antiferromagnetic arrangement. Each one of these chains is surrounded by six other chains, all of them magnetically equivalent (see Fig. 5). Alternatively, the magnetic structure can be described as a layered structure, the magnetic moments within the bc plane being ferromagnetically coupled, with the magnetic moments contained in the b axis. These layers are antiferromagnetically coupled along the a axis following an ABAB sequence (see Fig. 5).

D. Magnetic structure as a function of the magnetic field
The application of a weak magnetic field (below ca. 1.2 T) at temperatures below T N along the b axis (a axis in the RT phase) produces an electric polarization along the a axis, while if the magnetic field is applied along the a axis, the electric polarization is observed along the b axis. The polarization along the a axis (magnetic field applied along the b axis), decreases noticeably when the external magnetic field approaches a critical field of ca. 1.2 T, while the components along the b and c axes arise. A detailed study of the electric polarization as a function of the applied external field in different crystal orientations can be consulted in Ref. [8].
The neutron diffraction measurements under magnetic field consisted firstly of an exploration of the reciprocal space at  Fig. S7 in the Supplemental Material [15]. The variation of intensity from 0 to 1.2 T is not significant, although it deserves to be noted that even if the variation of intensity is not noticeable after applying an external magnetic field, the occurrence of electric polarization involves an underlying breaking of symmetry (structural and magnetic). After the spin-flop transition, above 1.2 T, the intensity of the magnetic reflections changes drastically, indicating a further breaking of the magnetic symmetry. Hereafter, we are going to evaluate the possible magnetic structures based on the symmetry analysis. This analysis can be extended to the nuclear structure, although, due to the low number of observations, we have described this last one in the parent I 2/c space group.
In the low-magnetic-field region (from 0 to 1.2 T), the changes in the magnetic intensities are subtle, which precludes an accurate determination in this region of a magnetic structure different from the one at zero field. However, the magnetic space group in this phase can be obtained from symmetry analysis. Taking into account the magnetic models at zero magnetic field, the four magnetic space groups corresponding to 1 [25]. However, none of these magnetic space groups is compatible with the electric polarization observed in the macroscopic measurements. Therefore, a combination of irreducible representations is needed to explain the magnetoelectric effect observed in this phase. As the electric polarization occurs even at low magnetic fields, the magnetic structure in this phase should be a combination of the magnetic structure described at zero field with a second irreducible representation, allowing the occurrence of polarization. From the representational analysis described in the previous section, we can combine the 4 irreducible representation (which describes the magnetic structure at zero magnetic field) with 1 , which is the only irreducible representation that allows a ferromagnetic component along the b axis, the direction of the external magnetic field. The magnetic structure in this region should be represented by the combination of 1 and 4 , giving rise to the I c space group (or Cc in standard notation), which is compatible with the macroscopic electric-polarization measurement.
In order to determine the magnetic structure above the spinflop transition, 413 reflections were collected at 1.8 K and 4.5 T. The representational analysis described in the previous section is also valid for the current phase since the propagation vector remains k = (0,0,0). However, in this phase the system displays magnetoelectric behavior [8], and therefore neither time reversal nor spatial inversion can be symmetry operations of the system, which means that none of the zero-field irreps is able to generate individually the experimentally observed macroscopic electric polarization, as was described for the low-magnetic-field phase.
In order to allow for the occurrence of electric polarization, a combination of magnetic models is again necessary. The list of subgroups of the paramagnetic I 2/c1 space group compatible with the macroscopic electric polarization is as follows: I c (N. 9.39), I c (N. 9.37), I 2 (N. 5.15), I 2 (N. 5.13), and P 1 (N. 1.1). Moreover, the only irreducible representation allowing a ferromagnetic signal along the b axis is 1 : hence only the monoclinic space groups compatible with a field-induced component due to the application of an external field are the I c and I 2 space groups. Both magnetic space groups were used to refine the single-crystal data, although the best refinement was obtained using a combination of magnetic models belonging to the 1 and 2 irreducible representations (see Fig. S8 in the Supplemental Material [15]), described by the I 2 (N. 5.13) magnetic space group. This means that a supplementary symmetry breaking occurs, due to the high field, with respect to the low-field phase that cannot be explained by a group-subgroup relation. The magnetic structure obtained can be described as a layered structure with the magnetic moments pillared along the c axis. The magnetic moments are shifted with respect to the zero-magnetic-field phase from the b axis to mainly the c axis (see Fig. 6). Different from the zero-field model, the magnetic structure under magnetic field has a non-negligible contribution along the other directions [a (ca. 1.07 μ B ) and b axis (ca. 2.2 μ B )]. The components along the a and c axes are symmetry constrained to be antiferromagnetically coupled, but the contribution along the b axis is not compensated due to the application of the external magnetic field along this direction (see Fig. 6). Moreover, the comparison of the magnetic moment component along b in the two possible magnetic structures (I c and I 2) gives rise to 3.2(2) and 2.2(2) μ B for the I c and I 2 magnetic space groups, respectively. For the I c magnetic structure this value is far from the 1.9 μ B expected from the magnetometry measurements, and therefore the I c model can be discarded. Based on the refined magnetic model we can conclude that the crystal structure should also be described in the I 2 space group but, since there are not enough observations to refine it, we have kept the parent I 2/c space group for the description of the crystal structure.

IV. CONCLUSIONS
In this work we have analyzed the nuclear and magnetic structures of the Cs 2 FeCl 5 ·D 2 O magnetoelectric compound by combining different neutron diffraction techniques. The occurrence of a structural phase transition has been determined using temperature-variable Laue diffraction and confirmed through specific heat measurements. The nuclear structure above and below the structural phase transition has been determined using monochromatic single-crystal neutron diffraction. The transformation of the space group from the orthorhombic Cmcm to the monoclinic C2/c (the nonstandard I 2/c space group has been used throughout the manuscript for the sake of easy comparison) was described. This transformation implies a doubling of the c axis associated with the ordering of the crystallization water molecules, which are disordered into two different orientations above the phase transition (ca. 175 K).
The accurate localization of the hydrogen (deuterium) atoms allows explaining the order-disorder phase transition as a consequence of the hydrogen bond network: The hydrogen bond distance thorough two [FeCl 5 ·D 2 O] 2− units along the c axis is notably shorter in the monoclinic phase, giving rise to an ordered structure.
The determination of the magnetic structure at zero field has been done combining powder and single-crystal neutron diffraction data. The obtained magnetic space group is I 2 /c, which has the spatial inversion as a symmetry operator but it is associated with time inversion in the action on spins. Therefore, the obtained magnetic model is compatible with the absence of electric polarization, as was observed in the macroscopic electric-polarization measurements; however, the presence of the1 operator ensures that it is linear magnetoelectric. The application of an external magnetic field, along the b axis, produces a field-induced ferromagnetic component. This produces a symmetry breaking, which is the responsible of the macroscopic electric polarization. However, the intensity of the magnetic reflections is not significantly modified with respect to the zero-field phase. This suggests that the magnetic model is not drastically changed with respect to the zero-field model. Symmetry analysis techniques have been used to propose a magnetic structure in the low-magnetic-field region (below 1.2 T). This analysis points to a phase transition from the nonpolar I 2 /c magnetic space group to the polar I c.
The evolution of the magnetic reflections as a function of the external magnetic field proves that a spin-flop transition occurs at ca. 1.2 T at 1.8 K. This transition involves a reorientation of the magnetic moments from parallel to the b axis at zero field to mainly along the c axis at high field, with nonzero components along the a and b axes. The magnetic structure was refined in the I 2 space group, which is compatible with both electric-polarization and magnetometry measurements.
The symmetry lowering below T N confirms that the ferroelectricity observed in this compound is a direct consequence of the different magnetic structures as a function of the external magnetic field. The symmetry breakings resulting from these magnetic structures imply small shifts in the atoms' positions, which are the final responsible of the electric polarization. Therefore, from a crystallographic point of view, both the magnetic and crystal structures are concerned by the symmetry lowering, explaining the linear magnetoelectric behavior of the title compound above and below the spin-flop transition.