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@INPROCEEDINGS{Thoma:897120,
      author       = {Thoma, Henrik and Hutanu, Vladimir and Angst, Manuel and
                      Roth, Georg},
      title        = {{T}he {A}bsolute {S}ign of the {D}zyaloshinskii-{M}oriya
                      {I}nteraction in {M}ultiferroic {B}a2{C}o{G}e2{O}7 disclosed
                      by {P}olarized {N}eutron {D}iffraction},
      reportid     = {FZJ-2021-03618},
      year         = {2021},
      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.
                      Overall, we observed a good fit agreement between the
                      calculated and experimentally measured asymmetry values. 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, 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 the AFM
                      moment in b-direction for the central Co atom. 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. It is shown, 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. [1] H. T. Yi, Y. J. Choi, S.
                      Lee et al., Appl. Phys. Lett. 92(21), 212904 (2008); [2] I.
                      E. Dzyaloshinskii, Sov. Phys. – JETP 5, 1259 (1957); [3]
                      T. Moriya, Phys. Rev. 120, 91 (1960); [4] H. Murakawa, Y.
                      Onose, S. Miyahara et al., Phys. Rev. Lett. 105(13), 137202
                      (2010); [5] P. Toledano, D. D. Khalyavin, L. C. Chapon,
                      Phys. Rev. B 84, 094421 (2011); [6] M. Soda, M. Matsumoto,
                      M. Månsson et al., Phys. Rev. Lett. 112(12), 127205 (2014);
                      [7] V. Hutanu, A. Sazonov, H. Murakawa et al., Phys. Rev. B
                      84, 212101 (2011); [8] J. M. Perez-Mato, J. L. Ribeiro, Acta
                      Crystallogr., Sect. A: Found. Crystallogr. 67(3), 264–268
                      (2011); [9] V. E. Dmitrienko, E. N. Ovchinnikova, S. P.
                      Collins et al., Nat. Phys. 10, 202 (2014); [10] A. Gukasov,
                      S. Rodrigues, J.-L. Meuriot et al., Physics Procedia 42, 150
                      (2013); [11] V. Hutanu, A. Sazonov, M. Meven et al., Phys.
                      Rev. B 86, 104401 (2012)},
      month         = {Apr},
      date          = {2021-04-26},
      organization  = {INTERMAG 2021, online event (France),
                       26 Apr 2021 - 30 Apr 2021},
      subtyp        = {After Call},
      cin          = {JCNS-FRM-II / JARA-FIT / JCNS-2 / JCNS-4 / MLZ},
      cid          = {I:(DE-Juel1)JCNS-FRM-II-20110218 /
                      $I:(DE-82)080009_20140620$ / I:(DE-Juel1)JCNS-2-20110106 /
                      I:(DE-Juel1)JCNS-4-20201012 / I:(DE-588b)4597118-3},
      pnm          = {6G4 - Jülich Centre for Neutron Research (JCNS) (FZJ)
                      (POF4-6G4) / 632 - Materials – Quantum, Complex and
                      Functional Materials (POF4-632)},
      pid          = {G:(DE-HGF)POF4-6G4 / G:(DE-HGF)POF4-632},
      experiment   = {EXP:(DE-MLZ)POLI-HEIDI-20140101},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://juser.fz-juelich.de/record/897120},
}