Symmetry in crystal structures plays a pivotal role in determining emergent phenomena in condensed matter systems, including unique electronic band structures with robust spin-momentum locking1,2,3, time-reversal symmetry broken states4,5, and topological swirling spin textures known as magnetic skyrmions6. Skyrmions have garnered significant attention for their potential applications in spintronic devices. Their helicity is highly dependent on the symmetry of their host material7. Known bulk skyrmion hosts include MnSi8, FeGe9, Fe1−xCoxSi10, and Cu2OSeO311,12, which crystallize in the cubic P2₁3 space group, as well as GaV4(S/Se)8 in R3m13,14 and VOSe2O5 in P4cc 15. In these systems, the stabilization of the multiple-q skyrmion lattice (SkL) phase originates from the Dzyaloshinskii-Moriya interaction (DMI) within the helimagnetic ground state, a consequence of the relativistic spin–orbit coupling16,17. Notably, skyrmions in P213 systems are of the Bloch type, whereas in hosts with R3m symmetry, Néel-type skyrmions are observed.
Among these hosts, Cu2OSeO3 stands out as the first insulating material in which skyrmions were experimentally discovered. Its insulating nature enables electric-field manipulation of the SkL phase18,19,20,21,22, a property complemented by other phenomena such as the stabilization of an independent SkL phase at low temperature23,24 and novel magnetic and functional behaviors25,26,27,28. Under high pressure, Cu2OSeO3 undergoes a series of structural phase transitions: first to an orthorhombic P212121 phase, then to a monoclinic P21 structure, and finally to a triclinic P1 polymorph29,30. Remarkably, pressure has been shown to extend the stability range of the SkL phase up to room temperature30. These attributes make Cu2OSeO3 a model system for advancing skyrmion physics. Recent studies have also demonstrated that when skyrmion hosts are confined in nanoparticles, approaching the size of a single skyrmion, the magnetic phase diagram is significantly altered, leading to modifications of the topological spin textures existing in bulk crystals and even lead to the emergence of novel ones31,32,33,34. However, due to the finite spin–lattice coupling in the aforementioned SkL hosts, it is imperative to discuss the underlying crystal structure, especially while the particle size approaches the diameter of a single isolated skyrmion.
In this work, we present the discovery of a new polymorph of Cu2OSeO3. Through detailed crystallographic studies and density functional theory calculations, we show that this novel polymorph crystallizes in the trigonal space group R3m, belonging to the same C3v point group symmetry than the Néel-type skyrmions hosts GaV₄(S/Se)₈. This structural change suggests that size effects could potentially drive a transformation from Bloch-type to Néel-type skyrmions in Cu2OSeO3. Our findings offer a possible alternate explanation for the unexpected observations of Néel-type skyrmions at the surfaces of bulk Cu2OSeO3 crystals35.
For this study, bulk and few hundred micron sized single crystals were grown by chemical vapor transport. They were characterized using X-ray diffraction (XRD). Fifty single crystals exhibited a chiral enantiopure structure, with equal distribution between “right-handed” (denoted as I) and “left-handed” (denoted as I’) enantiomorphs. Both conform to the chiral space group P2₁3, with structure I matching prior reports on Cu2OSeO3 structure7,36. No new polymorph was found in single crystals with size down to few tens of microns. Cu2OSeO3 nanoparticles were synthesized via a wet chemical process. Their crystal structure was determined using electron diffraction (ED) (Fig. 1a).
Structural Interrelations and Symmetry Adaptations in Cu2OSeO3 Crystals and Nanoparticles. (a) Representative electron microscopy image of the analyzed particles. In (b) and (c), projection of the electron diffraction patterns along the cubic axis. The absence of extinctions rules in (b) points to P-centered cubic unit cell characteristic of the crystal structure of both I and I’ enantiomorphs. In (c), the reflection extinctions satisfy the condition h + l = 2n revealing an F-centered cubic unit cell characteristic for the type-II structure. In d, e and f, representative structural fragments for I (I’), II, and the proposed prototype, showing all independent atoms. All atoms with the exception of O2, O3 (pink) and Cu2 (blue) are located in the threefold axes. The substructure Cu2OSe remains identical in all structures. In the prototype (space group F-43m), the additional oxygen atoms (the half-filled pink circles), required to complete the Cu2OSeO3 structure occupy half-filled positions, resulting in unacceptably long Se–O distances of 2.23 Å. Lowering the symmetry to P2₁3 for the two enantiomorphic structures I, I’ or to R3m (non-standard F3m) for the structure II allows the Se atoms to shift from the (000) position reducing the Se–O distances to approximately 1.70 Å. Concurrently both O2 and O3 occupied sites are increased to full occupancy.
Of the ten analyzed nanoparticles, eight consisted of twins combining both enantiomorphs, typically comprising ~ 80% of I and ~ 20% of I’ (Fig. 1b). Two nanoparticles displayed F-centered cubic unit cell (Fig. 1c), with lattice parameters a = 8.893(5)Å (Table 1). The corresponding structure (denoted as II) was refined in the trigonal space group R3m (nonstandard F3m) with twinning along the twofold axes (100), (010), and (001) of the cubic basis (Fig. 1e). Refinement yielded R1obs = 0.0862 and wRall = 0.0656. To assess the stability of the trigonal structure II, density functional theory (DFT) calculations were performed within the generalized gradient approximation (GGA). The results yielded relatively small Hellmann–Feynman forces, suggesting that the structure is close to a local energy minimum. This was further validated by a direct structural optimization, using the experimental unit cell parameters and internal atomic coordinates as input. The total GGA energy of the optimized R3m phase was found to be approximately 0.8 eV/f.u. higher than that of the cubic P2₁3 phase. However, surface effects, prominent in nanoparticles, cannot be accounted in the DFT calculations but could significantly alter the energy balance and stabilize the R3m phase. Detailed refinement parameters and characteristics of structure II are provided in Tables S1, S2 and S3. Atomic positions and interatomic parameters of the trigonal phase II obtained by refinement of the ED data and by DFT are compared in Table 2 and Table S4, respectively.
All three structures I, I’ and II contain a similar substructure unit with Cu2OSe composition and which has a cubic symmetry with the F-43m space group. Cu2OSeO3 is obtained by adding two O sites with half occupancy (half-filled pink circles in Fig. 1f). Based on this structural similarity, a prototype model of the ambient-pressure Cu2OSeO3 structure is proposed. The prototype is constructed from the substructure unit and the two additional O-sites (Fig. 1f and Table S5). However, this leads to unacceptably long Se-O distances of 2.23 Å (Table S3). These structure anomalies may be resolved by reducing the structure symmetry in two ways: (i) from F-43m to P213 characteristic of I and I’ (Fig. 1d) or (ii) from F-43m to R3mtrigonal = F3mcubic characteristic of II (Fig. 1e). During the refinement, the Se–O distances decrease to an acceptable 1.70 ± 0.01 Å in both cases (Table S3). We attribute the difference in the crystal structure to the size of the nanoparticles. Indeed, the crystals showing the I–I’ twinned structure are well-formed nanoparticles as indicated by the rather bright experimental reflections with a low background (Fig. 1b). The crystals exhibiting the structure II are characterized by weaker and split experimental reflections with a much lower intensity (Fig. 1c), indicating smaller attached nanoparticles. Unlike the pure enantiomorph bulk crystals grown from a single nucleus, multiple nucleation centers form during the synthesis process after selenious acid leaching from CuSeO3·2H2O precursor. This leads to nanoparticles with multiple twinning. The smaller particle size observed in the R3m polymorph suggests the existence of a critical size threshold below which the cubic form of Cu₂OSeO₃ cannot be stabilized. This hypothesis warrants further investigation.
Figure 2 illustrates both the similarities and differences among the three structural forms of Cu2OSeO3. The fundamental building unit consists of two corner-sharing oxygen-centered tetrahedrons, forming structural [O2Cu7] dimers 7. Across all structures, the interatomic distances and Cu–O–Cu bond angles remain comparable (see Table S3 in the Supplementary Information). In the cubic structure, these [O2Cu7] dimers exhibit ferrimagnetic ordering, with Cu1 and Cu2 carrying opposing magnetic moments. In all structures, including the prototype (Fig. 2b), the structural dimers are arranged in hexagonal rings oriented perpendicular to the threefold axis along the four diagonals of the cubic lattice (Figs. 2c-d). Similar hexagonal arrangements appear in the trigonal lattice along the (001) plane, as well as the (021), (-221), and (2–21) planes (Fig. 2e). However, the arrangement of the [O2Cu7] dimers within these hexagonal rings differs between the cubic and trigonal structures. In the cubic structure, hexagons consist of alternating O1-Cu1-O3 and O3-Cu2-O1 bonds (Figs. 2c-d), whereas in the trigonal structure, they are built with six O1-Cu2-O4 bonds, with O4-Cu1-O1 acting as bridges along the threefold symmetry axis (Fig. 2e). The distinct arrangement of dimers in the trigonal structure, as compared to the cubic phase, suggests a different magnetic ordering and hierarchy of energy scales, which may give rise to fundamentally different magnetic structures in the trigonal polymorph.
Structural variations in Cu2OSeO3. (a) View of the [O2Cu7] dimer, fundamental structural unit of the Cu2OSeO3 structures. (b–e) Comparison of hexagonal fragments in the prototype structure (b), enantiomorphic structures I (c) and I’ (d), and the trigonal polymorph II (e). In all panels, copper atoms are shown in blue. Cu1 and Cu2 are respectively located inside and outside the threefold axes. The green and purple tetrahedra [OCu4] contain respectively O1 and O4 which are also located inside the threefold axes. The light purple arrows and triangles indicate some of the threefold axes that distinguish the structures shown. The figure was made using the software Diamond v5.0.2.
In the cation-centered polyhedral representation (Fig. 3), Cu1 and Cu2 are positioned within a trigonal bipyramid and a tetragonal pyramid, respectively. The Cu2-centered tetragonal pyramids differ between the two structures in terms of Cu–O interatomic distances: in the cubic structure, the apical Cu–O bond is longer than the equatorial ones, whereas in the trigonal structure, all five Cu–O distances are similar. Although the Cu1- and Cu2-containing polyhedra share edges and follow a similar arrangement (Fig. 3a), the connectivity of Cu2-centered polyhedra varies due to differences in the positioning of SeO3 groups. In the cubic lattice, these tetragonal pyramids contribute to a three-dimensional framework, while in the trigonal structure, they form a flat triangular arrangement (Fig. 3b). Consequently, the trigonal polymorph of Cu2OSeO3 exhibits a layered-like structural organization (Fig. 3b).
Cation-centered polyhedral representation of cubic (I, I’) and trigonal (II) Cu2OSeO3 structures. (a) Coordination environments of Cu1 and Cu2 within their respective polyhedra. (b) Connectivity of Cu2-centered tetragonal pyramids in the two structures. (c) Three-dimensional visualization of the cubic and trigonal frameworks. Selenium atoms are represented as cyan circles. The figure was made using the software Diamond v5.0.2.
This structural distinction may help explain a previously unpredicted observation reported by Zhang et al35. who used resonant elastic X-ray scattering (REXS) at the Cu–L₂ absorption edge. At this energy, the X-ray penetration depth is limited to only a few tens of nanometers which is the size range of the Cu2OSeO3 nanoparticles studied here. The unexpected Néel-type swirls observed at the surface of bulk Cu2OSeO3 could be attributed to a local symmetry lowering, potentially reflecting the trigonal structure similar to the one discussed in this work. While our single-crystal XRD results rule out the presence of the R3m polymorph in the bulk, they do not preclude the possibility of this lower-symmetry phase existing at the surface.
In conclusion, this study reveals the discovery of a new polymorph of Cu2OSeO3, observed exclusively in nanoparticles. Electron diffraction based crystallographic analysis and DFT calculations confirm its R3m space group. While both trigonal and cubic polymorphs share a [O₂Cu₇] dimer-based framework, differences in SeO3 positioning result in distinct connectivity between Cu-centered polyhedra, leading to a layered-like structure in the trigonal phase. The trigonal polymorph exhibits C3v symmetry, like Néel-type skyrmion hosts, suggesting that size effects may drive a transformation from Bloch-type to Néel-type skyrmions in Cu2OSeO3. This discovery opens several promising directions for future research. First and foremost is the development of synthesis methods or deposition protocols capable of producing phase-pure trigonal nanoparticles or thin films. Such samples would allow precise determination of the stoichiometry of the trigonal phase, either confirming the composition deduced from structural analysis or revealing an off-stoichiometry required to stabilize this polymorph. They would also enable the investigation of skyrmion behavior under C3v symmetry in Cu2OSeO3. If successful, this would open the door to a range of studies, including the identification of a cycloidal magnetic ground state, the emergence of a field-induced Néel-type skyrmion lattice, potential magnetoelectric coupling, electric-field-driven skyrmion dynamics, and the collective behavior of magnon modes in the microwave regime.