New insight about the magnetic order in peculiar multiferroic Ba2CoGe2O7 by revealing the sign of the Dzyaloshinskii-Moriya Interaction by Polarized Neutron Diffraction.

Abstract

The antiferromagnetic Ba2CoGe2O7 has aroused great interest in current condensed matter research over the last decade, starting in 2008 when the appearance of ferroelectricity below the magnetic ordering temperature and a strong in-plane anisotropy were first reported [1]. Since the observed unique behaviour of the electric polarization with changing magnetic field in Ba2CoGe2O7 could not be explained by existing models, they accounted these effects to the presence of Dzyaloshinskii-Moriya interaction (DMI) [2,3], which is allowed by its non-centrosymmetric space group P-421m. Subsequently, to better explain this unconventional phenomena, a novel spin-dependent p-d hybridization mechanism of multiferroicity [4] and a spontaneous toroidic effect mechanism [5] were proposed. Also spin-nematic interactions were suggested as origin for the experimentally observed peculiar behaviour of the induced polarization [6]. This large variety of new models instigated further detailed studies of Ba2CoGe2O7, including a detailed determination of the crystal structure [7] and a theoretical symmetry analysis, identifying most of the observed peculiar effects as symmetry-forced results of the weak ferromagnetic (WF) canting, resulting from DMI [8]. This further endorses the DMI as a fundamental basis for the emergence and understanding of the unconventional multiferroic behavior observed in Ba2CoGe2O7. Therefore, not only the magnitude of the DMI exchange constant, but also its sign is of particular interest. In general, polarized neutron diffraction (PND) was proposed as one of the most suitable methods to determine this absolute DMI-sign in WF materials [9]. PND provides a direct access to the scattering contribution from nuclear-magnetic interference and thus reveals the phase difference between the nuclear and magnetic structure. This permits to determine the absolute direction of the individual magnetic moments with respect to the atomic arrangement, distinguishing between two equivalent AFM arrangements.In our study we performed PND measurements on a high quality Ba2CoGe2O7 single crystal at the polarized diffractometer VIP at the Orphée reactor of LLB (Saclay, France) [10]. The crystal was placed in a high magnetic field of 6 T along the [100] direction to obtain a single domain state with the WF moments aligned along and the AFM structure perpendicular to the applied field direction. The asymmetry values A=(I+-I-)/( I++I-) for 545 Bragg reflections were measured. Here, I± is the measured intensity for the two antiparallel spin orientations of the incoming neutron beam. Using these values and the crystal structure reported previously [7], we could refine the precise orientation of the AFM moments in Ba2CoGe2O7 at 2 K (Fig. 1). Overall, we observed a good fit agreement between the calculated and experimentally measured asymmetry values (Fig. 2). The resulting magnetic moment value of around 2.6 μB/Co2+ is in good agreement with previous non-polarized neutron and macroscopic studies [11].Performing a detailed symmetry analysis of the magnetic structure, including the symmetry averaging of the DMI vector, we deduced its restriction along the z-axis. Depending on the absolute sign of the Dz component, two symmetry-equivalent AFM spin configurations could be realized. By comparison with the experimentally observed magnetic moment directions in regard to the quantization field (Fig. 1), we can finally and unambiguously determine the negative sign of Dz in Ba2CoGe2O7.To further emphasize the power of the presented PND method, we additionally relate the Dz-sign to the expected asymmetry-sign of the single exemplary (210) reflection. By evaluating the nuclear and magnetic scattering factors, we obtain an opposite signed asymmetry value A(210) and mb (the AFM moment in b-direction for the central Co atom in Fig. 1). Moreover, utilizing the general equation for the DMI energy, the sign of Dz must be opposite to mb to be energetically favored, leading finally to same signed A(210) and Dz values. Thus, the experimentally determined negative asymmetry value for just one reflection allows one to conclude about the negative sign of Dz in the whole compound. In fact, all the asymmetry points shown in Fig. 2 within the two white areas support the negative sign of Dz, whereas asymmetry points in the gray areas would support an inverted sign. All experimental asymmetries lie in the white areas proving that PND allows to determine such a fundamental information as the sign of the DMI from the measurement of a single reflection. This is especially powerful for difficult samples or/and technically challenging experiments (e.g. high pressure) where the collection of large datasets is impossible.Within this study, we could for the first time experimentally determine the absolute sign of the DMI in the peculiar non-centrosymmetric multiferroic Ba2CoGe2O7. The precise spin arrangement and its evolution with applied in-plane magnetic field up to 6 T could be established. On one side, our results provide new input for theoretical modeling on this intriguing material. On the other side, they demonstrate the capability of PND to straightforwardly determine the DMI-sign in the large class of WF materials with zero propagation vector. **