Nonreciprocity of spin waves in the conical helix state

N. Ogawa; L. Köhler; M. Garst; S. Toyoda; S. Seki; Y. Tokura

doi:10.1073/pnas.2022927118

New Research In

Edited by Angel Rubio, Max Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany, and approved January 15, 2021 (received for review November 2, 2020)

Significance

While spin waves in conventional ferromagnets are well understood, those in more complicated magnets hosting spatially textured magnetization, such as helical/conical and skyrmion/hedgehog configurations, are less explored. We investigate experimentally and theoretically the spin waves of the conical spin helix in a chiral magnet with the help of Brillouin light scattering. We discovered that the dynamics of the conical spin helix is characterized by a distinct nonreciprocity with spin waves preferentially propagating in a specific direction controlled by the orientation of the magnetic field. Our work therefore demonstrates that all the spin phases of bulk chiral magnets allow, in principle, the realization of a switchable spin wave diode functionality.

Abstract

Nonreciprocity emerges in nature and in artificial objects from various physical origins, being widely utilized in contemporary technologies as exemplified by diode elements in electronics. While most of the nonreciprocal phenomena are realized by employing interfaces where the inversion symmetry is trivially lifted, nonreciprocal transport of photons, electrons, magnons, and possibly phonons also emerge in bulk crystals with broken space inversion and time reversal symmetries. Among them, directional propagation of bulk magnons (i.e., quanta of spin wave excitation) is attracting much attention nowadays for its potentially large nonreciprocity suitable for spintronic and spin-caloritronic applications. Here, we demonstrate nonreciprocal propagation of spin waves for the conical spin helix state in Cu₂OSeO₃ due to a combination of dipole and Dzyaloshinskii–Moriya interactions. The observed nonreciprocal spin dispersion smoothly connects to the hitherto known magnetochiral nonreciprocity in the field-induced collinear spin state; thus, all the spin phases show diode characteristics in this chiral insulator.

Footnotes

↵¹To whom correspondence may be addressed. Email: naoki.ogawa{at}riken.jp or markus.garst{at}kit.edu.

Author contributions: N.O., S.T., S.S., and Y.T. designed research; N.O., M.G., S.T., and S.S. performed research; L.K. and M.G. contributed new reagents/analytic tools; N.O., L.K., and M.G. analyzed data; and N.O., L.K., M.G., S.T., S.S., and Y.T. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at https://www.pnas.org/lookup/suppl/doi:10.1073/pnas.2022927118/-/DCSupplemental.

Data Availability

All study data are included in the article and/or SI Appendix.

Published under the PNAS license.

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References

↵
1. L. Onsager
, Reciprocal relations in irreversible processes. I. Phys. Rev. 34, 405 (1931).
OpenUrl
↵
1. C. Caloz et al
., Electromagnetic nonreciprocity. Phys. Rev. Appl. 10, 047001 (2018).
OpenUrl
↵
1. L. D. Barron,
2. J. Vrbancich
, Magneto-chiral birefringence and dichroism. Mol. Phys. 51, 715 (1984).
OpenUrl CrossRef
↵
1. Y. Tokura,
2. N. Nagaosa
, Nonreciprocal responses from non-centrosymmetric quantum materials. Nat. Commun. 9, 3740 (2018).
OpenUrl
↵
1. S. Toyoda et al.
, One-way transparency of light in multiferroic CuB₂O₄. Phys. Rev. Lett. 115, 267207 (2015).
OpenUrl
↵
1. R. W. Damon,
2. J. R. Eshbach
, Magnetostatic modes of a ferromagnet slab. J. Phys. Chem. Solids 19, 308–320 (1961).
OpenUrl CrossRef
↵
1. T. An et al
., Unidirectional spin-wave heat conveyer. Nat. Mater. 12, 549–553 (2013).
OpenUrl
↵
1. R. L. Melcher
, Linear contribution to spatial dispersion in the spin-wave spectrum of ferromagnets. Phys. Rev. Lett. 30, 125 (1973).
OpenUrl
↵
1. M. Kataoka
, Spin waves in systems with long period helical spin density waves due to the antisymmetric and symmetric exchange interactions. J. Phys. Soc. Jpn. 56, 3635–3647 (1987).
OpenUrl
↵
1. S. Seki et al
., Magnetochiral nonreciprocity of volume spin wave propagation in chiral-lattice ferromagnets. Phys. Rev. B 93, 235131 (2016).
OpenUrl
↵
1. S. Seki et al
., Propagation dynamics of spin excitations along skyrmion strings. Nat. Commun. 11, 256 (2020).
OpenUrl
↵
1. Y. Iguchi,
2. S. Uemura,
3. K. Ueno,
4. Y. Onose
, Nonreciprocal magnon propagation in a noncentrosymmetric ferromagnet LiFe₅O₈. Phys. Rev. B Condens. Matter Mater. Phys. 92, 184419 (2015).
OpenUrl
↵
1. S. Seki,
2. X. Z. Yu,
3. S. Ishiwata,
4. Y. Tokura
, Observation of skyrmions in a multiferroic material. Science 336, 198–201 (2012).
OpenUrl Abstract/FREE Full Text
↵
1. T. Adams et al
., Long-wavelength helimagnetic order and skyrmion lattice phase in Cu₂OSeO₃. Phys. Rev. Lett. 108, 237204 (2012).
OpenUrl CrossRef PubMed
↵
1. O. Janson et al
., The quantum nature of skyrmions and half-skyrmions in Cu₂OSeO₃. Nat. Commun. 5, 5376 (2014).
OpenUrl
↵
1. Y. Onose,
2. Y. Okamura,
3. S. Seki,
4. S. Ishiwata,
5. Y. Tokura
, Observation of magnetic excitations of Skyrmion crystal in a helimagnetic insulator Cu₂OSeO₃. Phys. Rev. Lett. 109, 037603 (2012).
OpenUrl PubMed
↵
1. Y. Okamura et al
., Microwave magnetoelectric effect via skyrmion resonance modes in a helimagnetic multiferroic. Nat. Commun. 4, 2391 (2013).
OpenUrl
↵
1. N. Ogawa,
2. S. Seki,
3. Y. Tokura
, Ultrafast optical excitation of magnetic skyrmions. Sci. Rep. 5, 9552 (2015).
OpenUrl
↵
1. T. Schwarze et al
., Universal helimagnon and skyrmion excitations in metallic, semiconducting and insulating chiral magnets. Nat. Mater. 14, 478–483 (2015).
OpenUrl
↵
1. M. Kugler et al
., Band structure of helimagnons in MnSi resolved by inelastic neutron scattering. Phys. Rev. Lett. 115, 097203 (2015).
OpenUrl
↵
1. P. Y. Portnichenko et al.
, Magnon spectrum of the helimagnetic insulator Cu₂OSeO₃. Nat. Commun. 7, 10725 (2016).
OpenUrl
↵
1. I. Stasinopoulos et al
., Low spin wave damping in the insulating chiral magnet Cu₂OSeO₃. Appl. Phys. Lett. 111, 032408 (2017).
OpenUrl
↵
1. M. Weiler et al
., Helimagnon resonances in an intrinsic chiral magnonic crystal. Phys. Rev. Lett. 119, 237204 (2017).
OpenUrl
↵
1. T. J. Sato et al
., Magnon dispersion shift in the induced ferromagnetic phase of noncentrosymmetric MnSi. Phys. Rev. B 94, 144420 (2016).
OpenUrl
↵
1. T. Weber et al
., Field dependence of nonreciprocal magnons in chiral MnSi. Phys. Rev. B 97, 224403 (2018).
OpenUrl
↵
1. T. Weber et al
., Polarized inelastic neutron scattering of nonreciprocal spin waves in MnSi. Phys. Rev. B 100, 060404 (2019).
OpenUrl
↵
1. T. Sebastian,
2. K. Schultheiss,
3. B. Obry,
4. B. Hillebrands,
5. H. Schultheiss
, Micro-focused Brillouin light scattering: Imaging spin waves at the nanoscale. Front. Phys. 3, 35 (2015).
OpenUrl
↵
1. Kh. Zakeri et al
., Asymmetric spin-wave dispersion on Fe(110): Direct evidence of the Dzyaloshinskii-Moriya interaction. Phys. Rev. Lett. 104, 137203 (2010).
OpenUrl PubMed
↵
1. H. T. Nembach,
2. J. M. Shaw,
3. M. Weiler,
4. E. Jue,
5. T. J. Silva
, Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii–Moriya interaction in metal films. Nat. Phys. 11, 825–829 (2015).
OpenUrl
↵
1. J. Cho et al
., Thickness dependence of the interfacial Dzyaloshinskii-Moriya interaction in inversion symmetry broken systems. Nat. Commun. 6, 7635 (2015).
OpenUrl PubMed
↵
1. K. Di et al
., Direct observation of the Dzyaloshinskii-Moriya interaction in a Pt/Co/Ni film. Phys. Rev. Lett. 114, 047201 (2015).
OpenUrl PubMed
↵
1. A. Chacon et al
., Observation of two independent skyrmion phases in a chiral magnetic material. Nat. Phys. 14, 936–941 (2018).
OpenUrl
↵
1. M. Garst,
2. J. Waizner,
3. D. Grundler
, Collective spin excitations of helices and magnetic skyrmions: Review and perspectives of magnonics in non-centrosymmetric magnets. J. Phys. D Appl. Phys. 50, 293002 (2017).
OpenUrl
↵
1. C. Herring,
2. C. Kittel
, On the theory of spin waves in ferromagnetic media. Phys. Rev. 81, 869 (1951).
OpenUrl
↵
1. W. Wettling,
2. M. G. Cottam,
3. J. R. Sandercock
, The relation between one-magnon light scattering and the complex magneto-optic effects in YIG. J. Phys. C Solid State Phys. 8, 211–228 (1975).
OpenUrl
↵
1. R. B. Versteeg et al
., Optically probed symmetry breaking in the chiral magnet Cu₂OSeO₃. Phys. Rev. B 94, 094409 (2016).
OpenUrl

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Proceedings of the National Academy of Sciences: 118 (8)

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Submit

Article Classifications

Physical Sciences
Physics

[1] ↵
L. Onsager
, Reciprocal relations in irreversible processes. I. Phys. Rev. 34, 405 (1931).
OpenUrl

[2] L. Onsager

[3] ↵
C. Caloz et al
., Electromagnetic nonreciprocity. Phys. Rev. Appl. 10, 047001 (2018).
OpenUrl

[4] C. Caloz et al

[5] ↵
L. D. Barron,
J. Vrbancich
, Magneto-chiral birefringence and dichroism. Mol. Phys. 51, 715 (1984).
OpenUrl CrossRef

[6] L. D. Barron,

[7] J. Vrbancich

[8] ↵
Y. Tokura,
N. Nagaosa
, Nonreciprocal responses from non-centrosymmetric quantum materials. Nat. Commun. 9, 3740 (2018).
OpenUrl

[9] Y. Tokura,

[10] N. Nagaosa

[11] ↵
S. Toyoda et al.
, One-way transparency of light in multiferroic CuB₂O₄. Phys. Rev. Lett. 115, 267207 (2015).
OpenUrl

[12] S. Toyoda et al.

[13] ↵
R. W. Damon,
J. R. Eshbach
, Magnetostatic modes of a ferromagnet slab. J. Phys. Chem. Solids 19, 308–320 (1961).
OpenUrl CrossRef

[14] R. W. Damon,

[15] J. R. Eshbach

[16] ↵
T. An et al
., Unidirectional spin-wave heat conveyer. Nat. Mater. 12, 549–553 (2013).
OpenUrl

[17] T. An et al

[18] ↵
R. L. Melcher
, Linear contribution to spatial dispersion in the spin-wave spectrum of ferromagnets. Phys. Rev. Lett. 30, 125 (1973).
OpenUrl

[19] R. L. Melcher

[20] ↵
M. Kataoka
, Spin waves in systems with long period helical spin density waves due to the antisymmetric and symmetric exchange interactions. J. Phys. Soc. Jpn. 56, 3635–3647 (1987).
OpenUrl

[21] M. Kataoka

[22] ↵
S. Seki et al
., Magnetochiral nonreciprocity of volume spin wave propagation in chiral-lattice ferromagnets. Phys. Rev. B 93, 235131 (2016).
OpenUrl

[23] S. Seki et al

[24] ↵
S. Seki et al
., Propagation dynamics of spin excitations along skyrmion strings. Nat. Commun. 11, 256 (2020).
OpenUrl

[25] S. Seki et al

[26] ↵
Y. Iguchi,
S. Uemura,
K. Ueno,
Y. Onose
, Nonreciprocal magnon propagation in a noncentrosymmetric ferromagnet LiFe₅O₈. Phys. Rev. B Condens. Matter Mater. Phys. 92, 184419 (2015).
OpenUrl

[27] Y. Iguchi,

[28] S. Uemura,

[29] K. Ueno,

[30] Y. Onose

[31] ↵
S. Seki,
X. Z. Yu,
S. Ishiwata,
Y. Tokura
, Observation of skyrmions in a multiferroic material. Science 336, 198–201 (2012).
OpenUrl Abstract/FREE Full Text

[32] S. Seki,

[33] X. Z. Yu,

[34] S. Ishiwata,

[35] Y. Tokura

[36] ↵
T. Adams et al
., Long-wavelength helimagnetic order and skyrmion lattice phase in Cu₂OSeO₃. Phys. Rev. Lett. 108, 237204 (2012).
OpenUrl CrossRef PubMed

[37] T. Adams et al

[38] ↵
O. Janson et al
., The quantum nature of skyrmions and half-skyrmions in Cu₂OSeO₃. Nat. Commun. 5, 5376 (2014).
OpenUrl

[39] O. Janson et al

[40] ↵
Y. Onose,
Y. Okamura,
S. Seki,
S. Ishiwata,
Y. Tokura
, Observation of magnetic excitations of Skyrmion crystal in a helimagnetic insulator Cu₂OSeO₃. Phys. Rev. Lett. 109, 037603 (2012).
OpenUrl PubMed

[41] Y. Onose,

[42] Y. Okamura,

[43] S. Seki,

[44] S. Ishiwata,

[45] Y. Tokura

[46] ↵
Y. Okamura et al
., Microwave magnetoelectric effect via skyrmion resonance modes in a helimagnetic multiferroic. Nat. Commun. 4, 2391 (2013).
OpenUrl

[47] Y. Okamura et al

[48] ↵
N. Ogawa,
S. Seki,
Y. Tokura
, Ultrafast optical excitation of magnetic skyrmions. Sci. Rep. 5, 9552 (2015).
OpenUrl

[49] N. Ogawa,

[50] S. Seki,

[51] Y. Tokura

[52] ↵
T. Schwarze et al
., Universal helimagnon and skyrmion excitations in metallic, semiconducting and insulating chiral magnets. Nat. Mater. 14, 478–483 (2015).
OpenUrl

[53] T. Schwarze et al

[54] ↵
M. Kugler et al
., Band structure of helimagnons in MnSi resolved by inelastic neutron scattering. Phys. Rev. Lett. 115, 097203 (2015).
OpenUrl

[55] M. Kugler et al

[56] ↵
P. Y. Portnichenko et al.
, Magnon spectrum of the helimagnetic insulator Cu₂OSeO₃. Nat. Commun. 7, 10725 (2016).
OpenUrl

[57] P. Y. Portnichenko et al.

[58] ↵
I. Stasinopoulos et al
., Low spin wave damping in the insulating chiral magnet Cu₂OSeO₃. Appl. Phys. Lett. 111, 032408 (2017).
OpenUrl

[59] I. Stasinopoulos et al

[60] ↵
M. Weiler et al
., Helimagnon resonances in an intrinsic chiral magnonic crystal. Phys. Rev. Lett. 119, 237204 (2017).
OpenUrl

[61] M. Weiler et al

[62] ↵
T. J. Sato et al
., Magnon dispersion shift in the induced ferromagnetic phase of noncentrosymmetric MnSi. Phys. Rev. B 94, 144420 (2016).
OpenUrl

[63] T. J. Sato et al

[64] ↵
T. Weber et al
., Field dependence of nonreciprocal magnons in chiral MnSi. Phys. Rev. B 97, 224403 (2018).
OpenUrl

[65] T. Weber et al

[66] ↵
T. Weber et al
., Polarized inelastic neutron scattering of nonreciprocal spin waves in MnSi. Phys. Rev. B 100, 060404 (2019).
OpenUrl

[67] T. Weber et al

[68] ↵
T. Sebastian,
K. Schultheiss,
B. Obry,
B. Hillebrands,
H. Schultheiss
, Micro-focused Brillouin light scattering: Imaging spin waves at the nanoscale. Front. Phys. 3, 35 (2015).
OpenUrl

[69] T. Sebastian,

[70] K. Schultheiss,

[71] B. Obry,

[72] B. Hillebrands,

[73] H. Schultheiss

[74] ↵
Kh. Zakeri et al
., Asymmetric spin-wave dispersion on Fe(110): Direct evidence of the Dzyaloshinskii-Moriya interaction. Phys. Rev. Lett. 104, 137203 (2010).
OpenUrl PubMed

[75] Kh. Zakeri et al

[76] ↵
H. T. Nembach,
J. M. Shaw,
M. Weiler,
E. Jue,
T. J. Silva
, Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii–Moriya interaction in metal films. Nat. Phys. 11, 825–829 (2015).
OpenUrl

[77] H. T. Nembach,

[78] J. M. Shaw,

[79] M. Weiler,

[80] E. Jue,

[81] T. J. Silva

[82] ↵
J. Cho et al
., Thickness dependence of the interfacial Dzyaloshinskii-Moriya interaction in inversion symmetry broken systems. Nat. Commun. 6, 7635 (2015).
OpenUrl PubMed

[83] J. Cho et al

[84] ↵
K. Di et al
., Direct observation of the Dzyaloshinskii-Moriya interaction in a Pt/Co/Ni film. Phys. Rev. Lett. 114, 047201 (2015).
OpenUrl PubMed

[85] K. Di et al

[86] ↵
A. Chacon et al
., Observation of two independent skyrmion phases in a chiral magnetic material. Nat. Phys. 14, 936–941 (2018).
OpenUrl

[87] A. Chacon et al

[88] ↵
M. Garst,
J. Waizner,
D. Grundler
, Collective spin excitations of helices and magnetic skyrmions: Review and perspectives of magnonics in non-centrosymmetric magnets. J. Phys. D Appl. Phys. 50, 293002 (2017).
OpenUrl

[89] M. Garst,

[90] J. Waizner,

[91] D. Grundler

[92] ↵
C. Herring,
C. Kittel
, On the theory of spin waves in ferromagnetic media. Phys. Rev. 81, 869 (1951).
OpenUrl

[93] C. Herring,

[94] C. Kittel

[95] ↵
W. Wettling,
M. G. Cottam,
J. R. Sandercock
, The relation between one-magnon light scattering and the complex magneto-optic effects in YIG. J. Phys. C Solid State Phys. 8, 211–228 (1975).
OpenUrl

[96] W. Wettling,

[97] M. G. Cottam,

[98] J. R. Sandercock

[99] ↵
R. B. Versteeg et al
., Optically probed symmetry breaking in the chiral magnet Cu₂OSeO₃. Phys. Rev. B 94, 094409 (2016).
OpenUrl

[100] R. B. Versteeg et al

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