Chirality of matter shows up via spin excitations

Journal name:
Nature Physics
Volume:
8,
Pages:
734–738
Year published:
DOI:
doi:10.1038/nphys2387
Received
Accepted
Published online

An object is considered chiral if its mirror image cannot be brought to coincide with itself by any sequence of simple rotations and translations1. Chirality on a microscopic scale—in molecules2, 3, clusters4, crystals5 and metamaterials6, 7—can be detected by differences in the optical response of a substance to right- and left-handed circularly polarized light2, 3. Such ‘optical activity’ is generally considered to be a consequence of the specific distribution of electronic charge within chiral materials. Here, we demonstrate that a similar response can also arise as a result of spin excitations in a magnetic material. Besides this spin-mediated optical activity (SOA), we observe notable differences in the response of Ba2CoGe2O7—a square-lattice antiferromagnet that undergoes a magnetic-field driven transition to a chiral form—to terahertz radiation travelling parallel or antiparallel to an applied magnetic field. At certain frequencies the strength of this magneto-chiral effect8, 9, 10 is almost complete, with the difference between parallel and antiparallel absorption of the material approaching 100%. We attribute these phenomena to the magnetoelectric 11, 12 nature of spin excitations as they interact with the electric and magnetic components of light.

At a glance

Figures

  1. Chiroptical spectroscopy: an efficient probe of chirality both via charge and spin excitations.
    Figure 1: Chiroptical spectroscopy: an efficient probe of chirality both via charge and spin excitations.

    Depending on the wavelength, λ, light interacts with various degrees of freedom and detects the handedness of matter at different levels. The soft X-ray natural circular dichroism (SXNCD) picks up chirality via the core-electron excitations, whereas the circular dichroism in the ultraviolet and visible region (UV/VIS CD) probes it through transitions of valence electrons. Molecular vibrations are also sensitive to the handedness, which is manifested in the vibrational circular dichroism (VCD) or the Raman optical activity (ROA). We predict that besides the charge excitations above, spin-wave excitations in the gigahertz–terahertz region (λ~100μm–10mm) of the electromagnetic spectrum can also probe the chirality of magnetic materials and show SOA.

  2. Main aspects of magnetically induced chirality.
    Figure 2: Main aspects of magnetically induced chirality.

    a, The crystal structure of Ba2CoGe2O7belongs to the tetragonal space group . The corresponding point group can be represented by a single tetrahedron compressed in the [001] direction. Its two longer edges are indicated with blue lines. b, When the external magnetic field points along the [100] or [010] axis, the antiferromagnetic spin pattern with field-induced canting (blue arrows) breaks all mirror-plane symmetries of the lattice, hence, it makes the crystal chiral with the point symmetry of 222 or 222, respectively. Switching between the left-handed (L) and right-handed (R) enantiomers can be carried out by rotation of the magnetic field from the [100] to the [010] direction, being equivalent to the m(110) mirror reflection (dashed line). c, The magnetically induced chirality of the material and the corresponding point symmetries can be schematized by the compressed tetrahedron together with a magnetic moment connecting midpoints of two opposite shorter edges (representing the lattice symmetry and the spin system, respectively). In the mirror image obtained by m(110) reflection, the tetrahedron remains unchanged, while the magnetic moment (axial vector) is rotated by π/2. Image and mirror image are enantiomeric pairs as they cannot be brought into coincidence with each other by pure rotations and translations even when combined with time-reversal operation.

  3. Absorption ([alpha]), polarization rotation ([theta]) and ellipticity ([eta]) spectra of the spin-wave modes for light propagation along the [001] axis as measured by time-domain terahertz spectroscopy and calculated theoretically.
    Figure 3: Absorption (α), polarization rotation (θ) and ellipticity (η) spectra of the spin-wave modes for light propagation along the [001] axis as measured by time-domain terahertz spectroscopy and calculated theoretically.

    a, The modes observed at 0.5THz and 1THz in zero field show clear splittings in high magnetic fields parallel to the [010] axis, as indicated by arrows. The ‘Goldstone mode’ (G) is centred around 0.27THz. The large polarization rotation and ellipticity are even functions of the magnetic field. b, When the external magnetic field direction is rotated from the [100] to the [010] axis, both θ and η change sign, whereas they are zero within the experimental accuracy when the magnetic field points along the [110] direction and the m(110) mirror-plane symmetry is restored. Thus, these polarization phenomena can be identified as SOA in a chiral media.

  4. Magneto-chiral effect in the field-induced chiral state.
    Figure 4: Magneto-chiral effect in the field-induced chiral state.

    Absorption is studied when light propagates along the [010] axis parallel (+Bdc) and antiparallel (−Bdc) to the external magnetic field. a,b, Absorption spectra for light polarizations Eω[100] (a) and Eω[001] (b), measured as a function of the magnetic field, are shifted in proportion to the corresponding Bdc values. Red and blue curves indicate the case of +Bdc and −Bdc, respectively. Between the spin resonances the material is transparent, as α0. The magneto-chiral dichroism, corresponding to the difference of the absorption coefficients for counter-propagating beams, is huge both for the ‘Goldstone mode’ (highlighted green) and the low-frequency branch of the resonance at ~ 1THz (highlighted orange). Δα/αmax70% in the highlighted regions. c,d, The sign and magnitude of the experimentally observed MChD effect (coloured curves) are reproduced by our theoretical model (black curves) for two polarizations Eω[100] and Eω[100] as in c and d, respectively.

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Author information

Affiliations

  1. Department of Physics, Budapest University of Technology and Economics and Condensed Matter Research Group of the Hungarian Academy of Sciences, 1111 Budapest, Hungary

    • S. Bordács,
    • I. Kézsmárki,
    • D. Szaller &
    • L. Demkó
  2. Multiferroics Project, ERATO, Japan Science and Technology Agency (JST), Japan c/o The University of Tokyo, Tokyo 113-8656, Japan

    • S. Bordács,
    • I. Kézsmárki,
    • L. Demkó,
    • N. Kida,
    • H. Murakawa,
    • Y. Onose,
    • R. Shimano,
    • S. Miyahara,
    • N. Furukawa &
    • Y. Tokura
  3. Department of Advanced Materials Science, The University of Tokyo, 5-1-5 Kashiwanoha, Chiba 277-8561, Japan

    • N. Kida
  4. Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan

    • Y. Onose &
    • Y. Tokura
  5. Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan

    • R. Shimano
  6. National Institute of Chemical Physics and Biophysics, Tallinn 12618, Estonia

    • T. Rõõm &
    • U. Nagel
  7. Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara, Kanagawa 252-5258, Japan

    • N. Furukawa
  8. Cross-correlated Materials Group (CMRG) and Correlated Electron Research Group (CERG), RIKEN Advanced Science Institute, Wako 351-0198, Japan

    • Y. Tokura

Contributions

S.B., I.K., T.R., U.N., D.S. and L.D. performed the measurements and analysed the data; H.M. and Y.O. contributed to the sample preparation; N.K., R.S., T.R. and U.N. developed the experimental set-up; S.M. and N.F. developed the theory; S.B. and I.K. wrote the manuscript; and Y.T. and I.K. planned the project.

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The authors declare no competing financial interests.

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