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Incommensurate spin ordering and excitations in multiferroic SrMnGe2O6

Claire V. Colin, Lei Ding, Eric Ressouche, Julien Robert, Noriki Terada, Frederic Gay, Pascal Lejay, Virginie Simonet, Céline Darie, Pierre Bordet, and Sylvain Petit
Phys. Rev. B 101, 235109 – Published 2 June 2020
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  • INTRODUCTION
  • EXPERIMENTAL DETAILS
  • RESULTS
  • DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    Anisotropic multiferroic properties of SrMnGe2O6 pyroxene single crystals were systematically investigated by means of magnetization, heat capacity, pyroelectric current measurement, and elastic and inelastic neutron-scattering experiments. Single-crystal neutron diffraction allows us to unambiguously reveal the presence of two incommensurate magnetic orderings: a nonpolar amplitude-modulated collinear sinusoidal magnetic structure emerges at TN1=4.36(2)K followed by a polar elliptical cycloidal spin structure below TN2=4.05(2)K. Pyroelectric current measurements on single crystal confirm the appearance of a spontaneous polarization within the (ac) plane below TN2 associated with the latter magnetic symmetry through the extended Dzyaloshinskii-Moriya mechanism. The magnetic phase diagram was calculated considering the three isotropic exchange couplings relevant in this system. The magnetic excitations spectra of SrMnGe2O6 measured by inelastic neutron scattering were successfully modeled using a set of exchange interactions consistent with this phase diagram.

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    • Received 23 December 2019
    • Accepted 17 April 2020

    DOI:https://doi.org/10.1103/PhysRevB.101.235109

    ©2020 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    AntiferromagnetismElectric polarizationExchange interactionFerroelectricityMagnetic phase transitionsMagnetoelectric effectMagnons
    1. Physical Systems
    Crystal structuresInorganic compoundsMultiferroicsSingle crystal materials
    1. Techniques
    CrystallographyDC susceptibility measurementsInelastic neutron scatteringNeutron diffractionSpecific heat measurements
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Claire V. Colin1,*, Lei Ding2, Eric Ressouche3, Julien Robert1, Noriki Terada4, Frederic Gay1, Pascal Lejay1, Virginie Simonet1, Céline Darie1, Pierre Bordet1, and Sylvain Petit5

    • 1Université Grenoble Alpes, CNRS, Institut Néel, 38000 Grenoble, France
    • 2ISIS Facility, Rutherford Appleton Laboratory, Harwell Oxford, Didcot OX11 0QX, United Kingdom
    • 3Université Grenoble Alpes, CEA, IRIG, MEM, MDN, F-38000 Grenoble, France
    • 4National Institute for Materials Science, Sengen 1-2-1, Tsukuba, Ibaraki 305-0047, Japan
    • 5Laboratoire Léon Brillouin, Université Paris-Saclay, CNRS, CEA, CEA-Saclay, Gif-sur-Yvette F-91191, France

    • *claire.colin@neel.cnrs.fr

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    Issue

    Vol. 101, Iss. 23 — 15 June 2020

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    Images

    • Figure 1
      Figure 1

      (a) Crystal structure of SrMnGe2O6 (C2/c) projected along two different directions. Atoms are represented by colored spheres: Sr in gold, Mn in purple, Ge in green, and O in red. Right: Sketch of the three main exchange interactions. (b) Photograph and (c) x-ray Laue image of the single crystal of SrMnGe2O6 grown by floating zone method.

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    • Figure 2
      Figure 2

      (a) Temperature dependence of magnetic susceptibility measured under a magnetic field of 0.1 T applied along the a, b, and c* axis. (b) Temperature dependence of heat capacity and magnetic susceptibility measured under a magnetic field of 0.01 T applied along the b axis. The dashed lines indicate magnetic phase transitions.

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    • Figure 3
      Figure 3

      Temperature dependence of the electric polarization of SrMnGe2O6 measured with the electric field parallel to the a, b, and c* axis.

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    • Figure 4
      Figure 4

      Temperature dependence of the ky component of the magnetic propagation vector k=(0,ky,0) (top) and the integrated intensity of the (1,1−ky,1) magnetic reflection (bottom).

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    • Figure 5
      Figure 5

      Illustration of the determined magnetic structures: (a) ICM1 amplitude-modulated collinear sinusoidal structure with moments along the direction defined by the α angle (b) ICM2 elliptical cycloidal spin structure with the moments rotating within the ab plane (c) α angle give the direction of the easy magnetic axis located at about 18.5° from the a axis towards the c axis.

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    • Figure 6
      Figure 6

      The MnO6 zigzag chains connected through GeO4 tetrahedra in SrMnGe2O6. The bold solid, thin solid, and dotted lines correspond to exchange paths J, J1, and J2.

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    • Figure 7
      Figure 7

      Magnetic phase diagram for an antiferromagnetic intrachain interaction J < 0, representing the stability of different magnetic ground states in function of on relative values of the exchange parameters, J1/|J| and J2/|J|. Phase boundaries are represented by the plain black lines while the dashed one shows the iso−ky=0.424. The black point is the sets of parameters obtained for SrMnGe2O6 (see text). The color scale represents the ky value: the red region shows the magnetic phase characterized by k=(0,1,0), while the region in blue corresponds to the k=0 phase.

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    • Figure 8
      Figure 8

      Energy scans measured at selected positions Q=(0K1) (a) and Q=(0kyL) (b) to determine the magnon dispersion in the ferroelectric elliptical cycloidal phase at T=1.5K. (c), (d) Representative Q scans at constant energy transfer in the [0K1] (c) and [0kyL] (d) directions crossing the spin-wave excitations.

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    • Figure 9
      Figure 9

      Measured (top) and calculated (bottom) intensity mapping of the inelastic intensity for T=2K along Q=(0ky1) and (0k1) direction; black circles mark the fitted magnon energies. The calculations were performed with J=0.11meV, J1=0.086meV and J2=0.031meV and planar single-ion anisotropy =0.12meV.

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    • Figure 10
      Figure 10

      Schematic illustration representing the elliptical cycloid running along the b axis and the electric polarization directions in the (a, c) plane, Pexp being the experimental one, P1 and P2 corresponding to the extended inverse DM mechanism [6].

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    • Figure 11
      Figure 11

      Neutron intensity calculated along (0,q0,1) for various J while B20=0. The bottom right panel shows the experimental data. Black dot correspond to the fitted positions of the different modes.

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    • Figure 12
      Figure 12

      Neutron intensity calculated along (0,q0,1) for various J and B20.

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    • Figure 13
      Figure 13

      Neutron intensity calculated along (0,q0,1) for various J and B20.

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    • Figure 14
      Figure 14

      Neutron intensity calculated along (0, k, 1) for various J and B20=0.09 meV. The bottom right panel shows the experimental data.

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    • Figure 15
      Figure 15

      Curie-Weiss temperature (in K; see the color scale on the right of the figure). The dashed ellipse shows the range of parameters determined by comparison with INS data. Since the experimental Curie-Weiss temperature is 20 K, this cross-check calculation favors the strongest values of J.

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