Abstract Magnetoelectric multiferroics have attracted enormous attention in the past years because of their high potential for applications in electronic devices, which arises from the intrinsic coupling between magnetic and ferroelectric ordering parameters. The initial finding in TbMnO 3 has triggered the search for other multiferroics with higher ordering temperatures and strong magnetoelectric coupling for applications. To date, spin-driven multiferroicity is found mainly in oxides, as well as in a few halogenides. We report multiferroic properties for synthetic melanothallite Cu 2 OCl 2 , which is the first discovery of multiferroicity in a transition metal oxyhalide. Measurements of pyrocurrent and the dielectric constant in Cu 2 OCl 2 reveal ferroelectricity below the Néel temperature of ~70 K. Thus, melanothallite belongs to a new class of multiferroic materials with an exceptionally high critical temperature. Powder neutron diffraction measurements reveal an incommensurate magnetic structure below T N , and all magnetic reflections can be indexed with a propagation vector [0.827(7), 0, 0], thus discarding the claimed pyrochlore-like “all-in–all-out” spin structure for Cu 2 OCl 2 , and indicating that this transition metal oxyhalide is, indeed, a spin-induced multiferroic material.

Keywords

multiferroics

spin-induced multiferroicity

magnetoelectric

magnetism

ferroelectricity

oxyhalide

dielectric measurements

neutron scattering

INTRODUCTION Magnetoelectric multiferroics with spiral magnetic structures are one of the central topics in contemporary condensed matter physics, inorganic chemistry, and materials science (1–8). These recently found multiferroics are expected to be the key ingredients for future magnetoelectrical or magneto-optic memory devices with enhanced efficiency. Generally, multiferroic materials simultaneously exhibit at least two ferroic ordering parameters. The simultaneous appearance of magnetic order and ferroelectricity is especially of interest for applications (9, 10). In multiferroics with a spiral magnetic structure, ferroelectricity is induced by the spin structure itself. Thus, large magnetoelectric effects can be expected for these novel multiferroics, which would allow for an efficient tuning of the ferroelectric polarization by applying an external magnetic field and, vice versa, the control of the magnetization with an applied electric field. These promising findings have triggered the search for new high-performance multiferroic materials in the past years. Besides a small induced electric polarization, the low transition temperatures (usually less than 40 K) especially hamper the use of multiferroics for applications. A spiral magnetic structure appears when a competition of (next) nearest neighboring exchange interactions can be observed in the system. This effect is also called frustration. The lack of inversion symmetry of noncentrosymmetric spiral spin structures also alters the charge distribution via spin-orbit interactions. Thus, a ferroelectric polarization is created, which is proportional to e i,j × (S i × S j ) in systems with a cycloidal magnetic structure according to the inverse Dzyaloshinskii-Moriya interaction mechanism (11–13) or proportional to (S i · e i,j )S i − (S j · e i,j )S j in systems with a helical spin structure according to the Arima model (14, 15), with S i being the spin at site i and e i,j being the vector between sites i and j. Transition metal (TM) oxychlorides MOCl (M = Sc, Ti, V, Cr, Fe) are quasi–two-dimensional (2D) systems that exhibit interesting electronic and magnetic properties (16–22). Up to M = Fe, these 3d TM oxychlorides crystallize in the layered FeOCl structure with space group Pmmn. In the FeOCl structure, the trivalent TM ions are octahedrally coordinated by four oxygen atoms and two chlorine ions and arranged into bilayers that are separated by the large Cl ions. For M = Cu, on the other hand, the TM oxychlorides crystallize in a different melanothallite structure with space group Fddd (see Fig. 1). As in the FeOCl structure, the copper ions are octahedrally coordinated by oxygen and chlorine ions. Yet, in the melanothallite structure, the TM ion is divalent and coordinated by four chlorine and two oxygen ions with two Cl ions located in the apical positions and with two Cl and two O ions in basal positions. Moreover, the structure is not quasi-2D anymore. Instead, edge-sharing CuO 2 Cl 2 squares form chains running in the [1 1 0] and [±1 ∓1 0] directions that are interconnected via a common O ion in the c direction as well (see Fig. 1). Thus, the O ions are tetrahedrally coordinated by four Cu ions forming a corner-sharing 3D network, and the Cl ions are located in the free space between these OCu 4 tetrahedra. Fig. 1 The crystal structure of Cu 2 OCl 2 . Green, yellow, and blue atoms denote Cu, Cl, and O ions, respectively. The structure consists of CuO 2 Cl 2 square chains running in the [1 1 0] and [±1 ∓1 0] directions (left). The squares are the basal planes of strongly distorted CuO 2 Cl 4 octahedra (green) with apical Cl ions that are farther away from the Cu ions (middle). Alternatively, the structure can be described as a network of OCu 4 tetrahedra (right). Cu 2 OCl 2 exhibits long-range antiferromagnetic order below T N ~70 K, as observed in muon spin rotation/relaxation (μSR) experiments (23). Recently, a nuclear magnetic resonance (NMR) study claimed that melanothallite is a pyrochlore-like antiferromagnet with the so-called “all-in–all-out” spin structure (24). Above room temperature, an anomalous negative thermal expansion of the b lattice constant, has been reported (25). This anomalous thermal expansion above room temperature is induced by a change of the angle between the chains of edge-sharing CuO 2 Cl 2 squares running in the [1 1 0] and [−1 1 0] directions. At room temperature, this angle amounts to 76°, and upon heating, it increases towards 90° (25).

RESULTS Magnetism and magnetoelastic coupling Figure 2A shows the magnetic susceptibility of our synthetic melanothallite single crystals. As can be seen, the magnetic ordering temperature T N amounts to ~70 K in our Cu 2 OCl 2 samples, which is in agreement with previous studies (26). The derivative of χ is shown in the Supplementary Materials. Figure 2B shows the lattice parameters of Cu 2 OCl 2 as a function of temperature. At the lowest temperatures, the b and c lattice parameters become identical (within the error bars). This indicates that the OCu 4 tetrahedra become more symmetric roughly below T N . Either this could be caused by magnetoelastic coupling or the system could start to order magnetically once the OCu 4 tetrahedra are more symmetric. Fig. 2 Magnetism and magnetoelastic coupling in Cu 2 OCl 2 . (A) Magnetic susceptibility of Cu 2 OCl 2 with T N ~70 K. A field of 1 T was applied perpendicular to the c direction (blue) and parallel to the c direction. (B) Temperature dependence of the lattice parameters of Cu 2 OCl 2 . Dielectric properties and magnetodielectric effect The temperature dependence of the zero-field dielectric constant ε and the dielectric loss tanδ measured in the c direction are shown in Fig. 3 (A to D). For all measurement frequencies (1 to 20 kHz), an anomalous λ-like peak can be observed in ε and tanδ at T N , which is indicative of a ferroelectric transition. Artificial signals can be excluded as a result of the frequency invariance in our observations (see Fig. 3, C and D). These findings were also reproducible for several different single crystals that we measured as well as for our polycrystalline pellets. Furthermore, our pyrocurrent measurements on Cu 2 OCl 2 single crystals reveal a ferroelectric polarization P in the c direction that appears below T N (see Fig. 3E), which amounts to roughly 40 μC/m2 at the lowest temperature. A measurement on polycrystalline pellets yields values that are one order of magnitude smaller, which confirms the ferroelectric polarization in the c direction. Moreover, P can be inverted by opposite poling, thus unambiguously confirming the ferroelectric nature of Cu 2 OCl 2 . Therefore, the TM oxyhalide Cu 2 OCl 2 is multiferroic, and oxyhalides with a melanothallite structure turn out to be a new class of multiferroic materials. Fig. 3 Evidence of multiferroicity in Cu 2 OCl 2 . (A to D) Dielectric constant ε(T) and dielectric loss tanδ(T) of Cu 2 OCl 2 single crystals measured in the c direction at different frequencies in zero field and also at 9 T. (E) The temperature dependence of the zero-field electric polarization in Cu 2 OCl 2 , measured with applied positive and negative poling electric fields. The dotted curves are the corresponding values for a polycrystalline (pellet) sample. (F) The coefficient (ε(H) − ε(H = 0))/ε(H = 0) as a function of magnetic field shows the magnetodielectric effect in Cu 2 OCl 2 for different temperatures (measured with 10 kHz). To study the magnetoelectric coupling in Cu 2 OCl 2 , we measured the magnetodielectric effect. In Fig. 3F, the coefficient (ε(H) − ε(H = 0))/ε(H = 0) is shown as a function of external magnetic field for different temperatures. As can be seen, a sizeable magnetodielectric effect is only found in the multiferroic phase below T N . The field dependence observable in the magnetically ordered phase is also indicative of a magnetic origin for ferroelectricity in Cu 2 OCl 2 . Spin structure For an understanding of the origin of the magnetoelectric coupling and multiferroicity in Cu 2 OCl 2 , knowledge of its magnetic structure is required. To date, only μSR studies report long-range magnetic orders below T N with first indications for frustration effects in the system (23). Furthermore, an NMR study suggested an all-in–all-out spin structure for Cu 2 OCl 2 (24). Here, we studied the magnetic structure of synthetic melanothallite by means of powder neutron diffraction measurements using the D1B diffractometer. Below T N , three incommensurate magnetic reflections appear (see Fig. 4A). These reflections can all be indexed with the propagation vector [0.827(7), 0, 0]. Hence, we can exclude the claimed pyrochlore-like k = 0 all-in–all-out spin structure (24). According to the symmetry analysis performed with the FullProf program package, there are four possible irreducible representations Irep 1 -Irep 4 . A successful magnetic structure refinement of our powder neutron diffraction data is possible with a spin structure based on the irreducible representation Irep 2 and moments within the ac plane (see Fig. 4B). The ordered magnetic moment amounts to 1.0(2) μ B and points in the direction of Cu-O-Cu chains formed by the OCu 4 tetrahedra running in the [±1 0 1] direction (see also Fig. 1, right). Also, our susceptibility measurements on oriented single crystals, shown in Fig. 2A, would be in agreement with the Irep 2 spin structure shown in Fig. 4 (right). Considering the fact that we are dealing with a local moment magnetic Mott insulator, our neutron results point toward the presence of a spiral magnetic structure in synthetic melanothallite rather than a spin structure where the moment sizes are modulated. These observations, together with the coincidence of the magnetic and ferroelectric transition temperatures in Cu 2 OCl 2 , indicates spin-driven ferroelectricity in melanothallite—either via the Arima model or via the inverse Dzyaloshinskii-Moriya interaction mechanism. Fig. 4 Incommensurate magnetic structure of Cu 2 OCl 2 . Powder neutron diffraction measurements of Cu 2 OCl 2 . Below T N , three magnetic peaks appear (magenta arrows). The red line represents the refinement with a spin structure according to the irreducible representation Irep 2 . The right bottom panel depicts the spin structure. For clarity, we show the corresponding OCu 4 tetrahedral chains (orange) in the upper right panel. Within each OCu 4 tetrahedral chain, the magnetic moments point in the chain direction. a.u., arbitrary units.

DISCUSSION To date, multiferroic properties have been observed in binary copper oxide CuO, also known as tenorite (27), as well as in binary copper halogenides such as CuBr 2 (28). Multiferroicity occurs below 73.5 K in CuBr 2 (28), whereas it occurs only within a very narrow temperature range of ~17 K in CuO (27), where noncollinear spiral spin order occurs. The size of the ferroelectric polarization amounts to about 8 μC/m2 in CuBr 2 (28) and 160 μC/m2 in CuO (27). In TM oxyhalides, no observation of multiferroicity has been reported before. Here, we find multiferroic properties in Cu 2 OCl 2 below ~70 K with a polarization that amounts to roughly 40 μC/m2. The coincidence of magnetic and ferroelectric transition temperatures in Cu 2 OCl 2 and the presence of incommensurate magnetism indicate a magnetic origin of ferroelectricity in Cu 2 OCl 2 . Thus, TM oxyhalides with a melanothallite structure are a new class of multiferroic materials with potentially promising properties because of the emergence of spin-induced ferroelectricity. Our finding gives rise to the search for new high-performance multiferroic materials because various substitutions are possible in this ternary melanothallite system, which is an advantage compared to binary copper oxide CuO and binary copper halogenides. For example, the substitution of Cl ions by other halogen ions, such as Br, seems promising with regard to the change of the critical temperature from 23.9 K in CuCl 2 (29, 30) to 73.5 K in CuBr 2 (28). Note that the physical properties do not change qualitatively when transitioning from CuCl 2 to CuBr 2 (28–30); the same is true for other oxychlorides, such as TiOCl and TiOBr (31). In Cu 2 OCl 2 , the TM ion could be substituted as well, for example, by Ni or Co, thus altering the magnetoelectric properties like in the series MTeO 6 , with M = Mn, Co, and Ni (32–39). Thus, our findings open new ways of discovering materials with potentially interesting magnetoelectric properties and of investigating the systematics of multiferroics. Furthermore, our finding of multiferroicity in Cu 2 OCl 2 shows that divalent copper compounds have the potential to be high-T C multiferroic materials. This systematic observation of high-T C multiferroicity in divalent copper compounds might arise from the presence of comparably large exchange interactions J in these materials. The importance of exchange interactions for multiferroicity in CuO has been pointed out by theoretical calculations (40, 41). A high J value is responsible for a high magnetic ordering temperature despite the presence of frustration in these systems, but this frustration is the prerequisite for incommensurate magnetism, which is responsible for spin-induced ferroelectricity and, thus, for the desirable magnetoelectric properties. This might also be a common phenomenon in high-T C multiferroics and high-T C superconductors, which are based on copper compounds (42–44), thus linking some of the most active research fields in contemporary condensed matter physics.

MATERIALS AND METHODS Cu 2 OCl 2 single crystals were synthesized by chemical vapor transport techniques using copper(II) chloride and oxide as starting materials in stoichiometric ratios (CuCl 2 /CuO = 1:1). The starting materials were pressed to pellets and sealed in quartz ampoules. Afterward, the pellets were sintered at 350°C for 24 hours. These polycrystalline starting materials were sealed together with a tiny excess of 20 mg of CuCl 2 in quartz ampoules and heated at 455°C for 14 days in the hot zone (T source ) of a two-zone furnace. Single crystals with a plate-like shape crystallized in the cold zone at 355°C (T sink ). Single-crystal x-ray diffraction measurements performed with a Bruker D8 VENTURE single-crystal x-ray diffractometer (Mo Kα) indicate that all our tested single crystals (including larger pieces with a size of several millimeters) are free from any impurity phase and are twinned with two twin domains marked as A and B. The twinning occurs in the ab plane, which is also the plane of the plate-like grown single crystals. At room temperature, the b axis of twin domain B is rotated by about 75.5° away from the corresponding axis of twin domain A. This angle is identical to the angle between the chains of edge-sharing CuO 2 Cl 2 squares running in the [1 1 0] A and [−1 1 0] A directions and, thus, explains the origin of twin formation with the underlying twin law matrix (−1/4 −5/4 0, −1/4 3/4 0, 0 0 –1): in twin domain B, the direction of one of the edge-sharing CuO 2 Cl 2 square chains is mirrored (or rotated by 180°) across the other square chain. Details of the crystal structure can be obtained from the cif file in the Supplementary Materials. For the powder neutron diffraction measurements, Cu 2 OCl 2 powder samples were synthesized in a similar way in sealed quartz glass ampoules. Because Cu 2 OCl 2 is hygroscopic and any exposure to air should be avoided, a minor impurity phase appears in our powder samples. Magnetic properties were measured in a SQUID (superconducting quantum interference device) magnetometer (MPMS, Quantum Design) (see the Supplementary Materials). The magnetic ordering temperature T N amounts to ~70 K in our Cu 2 OCl 2 samples, which is in agreement with previous studies (26). The plate-like single crystals were coated on both sides with silver paint as electrodes to measure the dielectric properties of Cu 2 OCl 2 . Thus, the dielectric properties of Cu 2 OCl 2 could be measured in the c direction, where twinning plays no role. The dielectric constant was measured within a Quantum Design PPMS (Physical Property Measurement System) using a homemade sample holder and an Andeen-Hagerling capacitance bridge. For pyroelectric current measurements, we polarized the samples upon cooling with a static electric field of roughly 500 kV/m. The pyroelectric current was, then, measured upon heating. Powder neutron diffraction measurements were performed using the D1B and D2B diffractometers at the Institut Laue-Langevin in Grenoble, France. The incident neutron wavelength amounts to 2.52 Å (D1B) and 1.59 Å (D2B). Powder x-ray diffraction measurements were performed with a Bruker D8 Discover A25 powder x-ray diffractometer using Cu Kα 1 radiation (Johansson monochromator) and an Oxford PheniX helium cryostat.

SUPPLEMENTARY MATERIALS Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/5/e1600353/DC1 Powder x-ray diffraction Magnetization measurements Single crystal x-ray diffraction Pyroelectric coefficient measurements fig. S1. Powder x-ray diffraction pattern of Cu 2 OCl 2 . fig. S2. Magnetic susceptibility of our polycrystalline Cu 2 OCl 2 samples. fig. S3. First temperature derivative of the magnetic susceptibility of Cu 2 OCl 2 single crystals indicating T N . fig. S4. Specific heat of a Cu 2 OCl 2 single crystal indicating a value of T N that is consistent with our magnetization. CIF-file: Cu2OCL2_Fddd_v3_s.cif

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.