magnetosomes. Both authors acknowledge financial fund-
ing by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation), BZ: Project-ID 405553726—TRR
270, MW: Project-ID 395940726—SFB 1372.

Data availability statement

All data is made available by the authors upon reasonable
request.

ORCID iDs

Anjan Barman https://orcid.org/0000-0002-4106-5658

Gianluca Gubbiotti https://orcid.org/0000-0002-7006-0370

S Ladak https://orcid.org/0000-0002-0275-0927

A O Adeyeye https://orcid.org/0000-0001-9724-2468

M Krawczyk https://orcid.org/0000-0002-0870-717X

J Gräfe https://orcid.org/0000-0002-4597-5923

C Adelmann https://orcid.org/0000-0002-4831-3159

S Cotofana https://orcid.org/0000-0001-7132-2291

A Naeemi https://orcid.org/0000-0003-4774-9046

V I Vasyuchka https://orcid.org/0000-0002-5077-7059

B Hillebrands https://orcid.org/0000-0001-8910-0355

S A Nikitov https://orcid.org/0000-0002-2413-7218

H Yu https://orcid.org/0000-0002-3291-6713

D Grundler https://orcid.org/0000-0002-4966-9712

A V Sadovnikov https://orcid.org/0000-0002-8847-2621

A A Grachev https://orcid.org/0000-0003-2023-910X

S E Sheshukova https://orcid.org/0000-0001-5732-0038

J-Y Duquesne https://orcid.org/0000-0001-9156-8758

M Marangolo https://orcid.org/0000-0001-6211-8168

G Csaba https://orcid.org/0000-0001-7592-0256

W Porod https://orcid.org/0000-0002-9854-6540

V E Demidov https://orcid.org/0000-0002-7840-5679

S Urazhdin https://orcid.org/0000-0002-6972-0300

S O Demokritov https://orcid.org/0000-0003-4422-4201

E Albisetti https://orcid.org/0000-0002-8134-0482

D Petti https://orcid.org/0000-0002-9273-1884

R Bertacco https://orcid.org/0000-0002-8109-9166

H Schultheiss https://orcid.org/0000-0002-6727-5098

V V Kruglyak https://orcid.org/0000-0001-6607-0886

V D Poimanov https://orcid.org/0000-0003-3078-2480

S Sahoo https://orcid.org/0000-0003-0207-5682

J Sinha https://orcid.org/0000-0003-3208-0570

H Yang https://orcid.org/0000-0003-0907-2898

M Münzenberg https://orcid.org/0000-0002-1332-5678

T Moriyama https://orcid.org/0000-0001-7071-0823

S Mizukami https://orcid.org/0000-0001-9913-1833

P Landeros https://orcid.org/0000-0002-0927-1419

R A Gallardo https://orcid.org/0000-0002-4495-5592

G Carlotti https://orcid.org/0000-0002-1511-7987

J-V Kim https://orcid.org/0000-0002-3849-649X

R L Stamps https://orcid.org/0000-0003-0713-4864

B Rana https://orcid.org/0000-0002-1076-4165

Y Otani https://orcid.org/0000-0001-8008-1493

W Yu https://orcid.org/0000-0001-6675-5535

T Yu https://orcid.org/0000-0001-7020-2204

G E W Bauer https://orcid.org/0000-0002-3615-8673

C Back https://orcid.org/0000-0003-3840-0993

G S Uhrig https://orcid.org/0000-0003-1961-0346

O V Dobrovolskiy https://orcid.org/0000-0002-7895-8265

B Budinska https://orcid.org/0000-0001-7640-5213

H Qin https://orcid.org/0000-0002-6894-3967

S van Dijken https://orcid.org/0000-0001-6372-2252

A V Chumak https://orcid.org/0000-0001-5515-0848

A Khitun https://orcid.org/0000-0003-4501-4687

D E Nikonov https://orcid.org/0000-0002-1436-1267

I A Young https://orcid.org/0000-0002-4017-5265

B W Zingsem https://orcid.org/0000-0002-9899-2700

M Winklhofer https://orcid.org/0000-0003-1352-9723

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[223] Zhang X, Bauer G E W and Yu T 2020 Nonreciprocal pumping of phonon spin by magnetization dynamics *Phys. Rev. Lett.* **125** 077203

[224] Papasimakis N, Fedotov V A, Savinov V, Raybould T A and Zheludev N I 2016 Electromagnetic toroidal excitations in matter and free space *Nat. Mater.* **15** 263–71

[225] Elyasi M, Blanter Y M and Bauer G E W 2020 Resources of nonlinear cavity magnonics for quantum information *Phys. Rev. B* **101** 054402

[226] Wang X S, Zhang H W and Wang X R 2018 Topological magnonics: a paradigm for spin-wave manipulation and device design *Phys. Rev. Appl.* **9** 024029

[227] Malki M and Uhrig G S 2020 Topological magnetic excitations *Europhys. Lett.* **132** 20003

[228] Onose Y, Ideue T, Katsura H, Shiomi Y, Nagaosa N and Tokura Y 2010 Observation of the magnon Hall effect *Science* **329** 297

[229] Hirschberger M, Krizan J W, Cava R J and Ong N P 2015 Large thermal Hall conductivity of neutral spin excitations in a frustrated quantum magnet *Science* **348** 106

[230] Tanabe K, Matsumoto R, Ohe J-I, Murakami S, Moriyama T, Chiba D, Kobayashi K and Ono T 2016 Observation of magnon Hall-like effect for sample-edge scattering in unsaturated YIG *Phys. Status Solidi* B **253** 783

[231] Chisnell R, Helton J S, Freedman D E, Singh D K, Bewley R I, Nocera D G and Lee Y S 2015 Topological magnon bands in a kagome lattice ferromagnet *Phys. Rev. Lett.* **115** 147201

[232] Yao W *et al* 2018 Topological spin excitations in a three-dimensional antiferromagnet *Nat. Phys.* **14** 1011

[233] Li R, Ohe J-i, Matsumoto R, Murakami S and Saitoh E 2013 Chiral spin-wave edge modes in dipolar magnetic thin films *Phys. Rev. B* **87** 174402

[234] Malki M and Uhrig G S 2019 Topological magnon band for magnonics *Phys. Rev. B* **99** 174412

[235] Ghader D 2020 Magnon magic angles and tunable Hall conductivity in 2D twisted ferromagnetic bilayers *Sci. Rep.* **10** 15069

[236] Nakata K, Kim S K, Klinovaja J and Loss D 2017 Magnonic topological insulators in antiferromagnets *Phys. Rev. B* **96** 224414

[237] Díaz S A, Klinovaja J and Loss D 2019 Topological magnons and edge states in antiferromagnetic skyrmion crystals *Phys. Rev. Lett.* **122** 187203

[238] McClarty P A, Krüger F, Guidi T, Parker S F, Refson K, Parker A W, Prabhakaran D and Coldea R 2017 Topological triplon modes and bound states in a Shastry–Sutherland magnet *Nat. Phys.* **13** 736

[239] Coldea M, Belotelov V I, Akimov I A, Savochkin I V, Yakovlev D R, Zvezdin A K and Bayer M 2017 Magnon accumulation by clocked laser excitation as source of long-range spin waves in transparent magnetic films *Phys. Rev. X* **7** 021009

[240] Lachance-Quirion D, Tabuchi Y, Gloppe A, Usami K and Nakamura Y 2019 Hybrid quantum systems based on magnonics. *Appl. Phys. Express* **12** 070101

[241] Li Y, Zhang W, Tyberkevych V, Kwok W-K, Hoffmann A and Novosad V 2020 Hybrid magnonics: physics, circuits, and applications for coherent information processing *J. Appl. Phys.* **128** 130902

[242] Dobrovolskiy O V *et al* 2019 Magnon–fluxon interaction in a ferromagnet/superconductor heterostructure *Nat. Phys.* **15** 477

[243] Bozhko D A, Vasyuchka V I, Chumak A V and Serga A A 2020 Magnon–phonon interactions in magnon spintronics (review article) *Low Temp. Phys.* **46** 383

[244] Jeon K-R *et al* 2019 Effect of meissner screening and trapped magnetic flux on magnetization dynamics in thick Nb/Ni₈₀Fe₂₀/Nb trilayers *Phys. Rev. Appl.* **11** 014061

[245] Golovchanskiy I A, Abramov N N, Stolyarov V S, Bolginov V V, Ryazanov V V, Golubov A A and Ustinov A V 2018 Ferromagnet/superconductor hybridization for magnonic applications *Adv. Funct. Mater.* **28** 1802375

[246] Shekhter A, Bulaevskii L N and Batista C D 2011 Vortex viscosity in magnetic superconductors due to radiation of spin waves. *Phys. Rev. Lett.* **106** 037001

[247] Hu J-M, Chen L-Q and Nan C-W 2016 Multiferroic heterostructures integrating ferroelectric and magnetic materials *Adv. Mater.* **28** 15

[248] Chu Y-H *et al* 2008 Electric-field control of local ferromagnetism using a magnetoelectric multiferroic *Nat. Mater.* **7** 478

[249] Lahtinen T H E, Tuomi J O and van Dijken S 2011 Pattern transfer and electric-field-induced magnetic domain formation in multiferroic heterostructures *Adv. Mater.* **23** 3187

[250] Hämäläinen S J, Brandl F, Franke K J A, Grundler D and van Dijken S 2017 Tunable short-wavelength spin-wave emission and confinement in anisotropy-modulated multiferroic heterostructures *Phys. Rev. Appl.* **8** 014020

[251] Van de Wiele B, Hämäläinen S J, Baláž P, Montoncello F and van Dijken S 2016 Tunable short-wavelength spin wave excitation from pinned magnetic domain walls *Sci. Rep.* **6** 21330

[252] Dobrovolskiy O V, Vodolazov D Y, Porrati F, Sachser R, Bevz V M, Mikhailov M Y, Chumak A V and Huth M 2020 Ultrafast vortex motion in a direct-write Nb–C superconductor *Nat. Commun.* **11** 3291

[253] Pósfai M, Lefèvre C T, Trubitsyn D, Bazylinski D A and Frankel R B 2013 Phylogenetic significance of composition and crystal morphology of magnetosome minerals *Front. Microbiol.* **4** 344

[254] Zingsem B W, Feggeler T, Terwey A, Ghaisari S, Spoddig D, Faivre D, Meckenstock R, Farle M and Winklhofer M 2019 Biologically encoded magnonics *Nat. Commun.* **10** 4345

[255] Wang Q *et al* 2019 Spin pinning and spin-wave dispersion in nanoscopic ferromagnetic waveguides *Phys. Rev. Lett.* **122** 247202

[256] Toro-Nahuelpan M, Giacomelli G, Raschdorf O, Borg S, Plitzko J M, Schüler D, Müller F-D and Müller F-D 2019 MamY is a membrane-bound protein that aligns magnetosomes and the motility axis of helical magnetotactic bacteria *Nat. Microbiol.* **4** 1978–89

[257] Shcherbakov V P, Winklhofer M, Hanzlik M and Petersen N 1997 Elastic stability of chains of magnetosomes in magnetotactic bacteria *Eur. Biophys. J.* **26** 319–26

[258] Prozorov T *et al* 2014 Manganese incorporation into the magnetosome magnetite: magnetic signature of doping *Eur. J. Mineral.* **26** 457–71

[259] Scheffel A, Gärdes A, Grünberg K, Wanner G and Schüler D 2008 The major magnetosome proteins MamGFDC are not essential for magnetite biomineralization in Magnetospirillum gryphiswaldense but regulate the size of magnetosome crystals *J. Bacteriol.* **190** 377–86

[260] Kent A D and Worledge D C 2015 A new spin on magnetic memories *Nat. Nanotechnol.* **10** 187–91

[261] Sankey J C, Braganca P M, Garcia A G F, Krivorotov I N, Buhrman R A and Ralph D C 2006 Spin-transfer-driven ferromagnetic resonance of individual nanomagnets *Phys. Rev. Lett.* **96** 227601

[262] Vansteenkiste A, Leliaert J, Dvornik M, Helsen M, Garcia-Sanchez F and Van Waeyenberge B 2014 The design and verification of MuMax3 AIP Adv. **4** 107133
[223] Zhang X, Bauer G E W and Yu T 2020 Nonreciprocal pumping of phonon spin by magnetization dynamics *Phys. Rev. Lett.* **125** 077203

[224] Papasimakis N, Fedotov V A, Savinov V, Raybould T A and Zheludev N I 2016 Electromagnetic toroidal excitations in matter and free space *Nat. Mater.* **15** 263–71

[225] Elyasi M, Blanter Y M and Bauer G E W 2020 Resources of nonlinear cavity magnonics for quantum information *Phys. Rev. B* **101** 054402

[226] Wang X S, Zhang H W and Wang X R 2018 Topological magnonics: a paradigm for spin-wave manipulation and device design *Phys. Rev. Appl.* **9** 024029

[227] Malki M and Uhrig G S 2020 Topological magnetic excitations *Europhys. Lett.* **132** 20003

[228] Onose Y, Ideue T, Katsura H, Shiomi Y, Nagaosa N and Tokura Y 2010 Observation of the magnon Hall effect *Science* **329** 297

[229] Hirschberger M, Krizan J W, Cava R J and Ong N P 2015 Large thermal Hall conductivity of neutral spin excitations in a frustrated quantum magnet *Science* **348** 106

[230] Tanabe K, Matsumoto R, Ohe J-I, Murakami S, Moriyama T, Chiba D, Kobayashi K and Ono T 2016 Observation of magnon Hall-like effect for sample-edge scattering in unsaturated YIG *Phys. Status Solidi* B **253** 783

[231] Chisnell R, Helton J S, Freedman D E, Singh D K, Bewley R I, Nocera D G and Lee Y S 2015 Topological magnon bands in a kagome lattice ferromagnet *Phys. Rev. Lett.* **115** 147201

[232] Yao W *et al* 2018 Topological spin excitations in a three-dimensional antiferromagnet *Nat. Phys.* **14** 1011

[233] Li R, Ohe J-i, Matsumoto R, Murakami S and Saitoh E 2013 Chiral spin-wave edge modes in dipolar magnetic thin films *Phys. Rev. B* **87** 174402

[234] Malki M and Uhrig G S 2019 Topological magnon band for magnonics *Phys. Rev. B* **99** 174412

[235] Ghader D 2020 Magnon magic angles and tunable Hall conductivity in 2D twisted ferromagnetic bilayers *Sci. Rep.* **10** 15069

[236] Nakata K, Kim S K, Klinovaja J and Loss D 2017 Magnonic topological insulators in antiferromagnets *Phys. Rev. B* **96** 224414

[237] Díaz S A, Klinovaja J and Loss D 2019 Topological magnons and edge states in antiferromagnetic skyrmion crystals *Phys. Rev. Lett.* **122** 187203

[238] McClarty P A, Krüger F, Guidi T, Parker S F, Refson K, Parker A W, Prabhakaran D and Coldea R 2017 Topological triplon modes and bound states in a Shastry–Sutherland magnet *Nat. Phys.* **13** 736

[239] Coldea M, Belotelov V I, Akimov I A, Savochkin I V, Yakovlev D R, Zvezdin A K and Bayer M 2017 Magnon accumulation by clocked laser excitation as source of long-range spin waves in transparent magnetic films *Phys. Rev. X* **7** 021009

[240] Lachance-Quirion D, Tabuchi Y, Gloppe A, Usami K and Nakamura Y 2019 Hybrid quantum systems based on magnonics. *Appl. Phys. Express* **12** 070101

[241] Li Y, Zhang W, Tyberkevych V, Kwok W-K, Hoffmann A and Novosad V 2020 Hybrid magnonics: physics, circuits, and applications for coherent information processing *J. Appl. Phys.* **128** 130902

[242] Dobrovolskiy O V *et al* 2019 Magnon–fluxon interaction in a ferromagnet/superconductor heterostructure *Nat. Phys.* **15** 477

[243] Bozhko D A, Vasyuchka V I, Chumak A V and Serga A A 2020 Magnon–phonon interactions in magnon spintronics (review article) *Low Temp. Phys.* **46** 383

[244] Jeon K-R *et al* 2019 Effect of meissner screening and trapped magnetic flux on magnetization dynamics in thick Nb/Ni₈₀Fe₂₀/Nb trilayers *Phys. Rev. Appl.* **11** 014061

[245] Golovchanskiy I A, Abramov N N, Stolyarov V S, Bolginov V V, Ryazanov V V, Golubov A A and Ustinov A V 2018 Ferromagnet/superconductor hybridization for magnonic applications *Adv. Funct. Mater.* **28** 1802375

[246] Shekhter A, Bulaevskii L N and Batista C D 2011 Vortex viscosity in magnetic superconductors due to radiation of spin waves. *Phys. Rev. Lett.* **106** 037001

[247] Hu J-M, Chen L-Q and Nan C-W 2016 Multiferroic heterostructures integrating ferroelectric and magnetic materials *Adv. Mater.* **28** 15

[248] Chu Y-H *et al* 2008 Electric-field control of local ferromagnetism using a magnetoelectric multiferroic *Nat. Mater.* **7** 478

[249] Lahtinen T H E, Tuomi J O and van Dijken S 2011 Pattern transfer and electric-field-induced magnetic domain formation in multiferroic heterostructures *Adv. Mater.* **23** 3187

[250] Hämäläinen S J, Brandl F, Franke K J A, Grundler D and van Dijken S 2017 Tunable short-wavelength spin-wave emission and confinement in anisotropy-modulated multiferroic heterostructures *Phys. Rev. Appl.* **8** 014020

[251] Van de Wiele B, Hämäläinen S J, Baláž P, Montoncello F and van Dijken S 2016 Tunable short-wavelength spin wave excitation from pinned magnetic domain walls *Sci. Rep.* **6** 21330

[252] Dobrovolskiy O V, Vodolazov D Y, Porrati F, Sachser R, Bevz V M, Mikhailov M Y, Chumak A V and Huth M 2020 Ultrafast vortex motion in a direct-write Nb–C superconductor *Nat. Commun.* **11** 3291

[253] Pósfai M, Lefèvre C T, Trubitsyn D, Bazylinski D A and Frankel R B 2013 Phylogenetic significance of composition and crystal morphology of magnetosome minerals *Front. Microbiol.* **4** 344

[254] Zingsem B W, Feggeler T, Terwey A, Ghaisari S, Spoddig D, Faivre D, Meckenstock R, Farle M and Winklhofer M 2019 Biologically encoded magnonics *Nat. Commun.* **10** 4345

[255] Wang Q *et al* 2019 Spin pinning and spin-wave dispersion in nanoscopic ferromagnetic waveguides *Phys. Rev. Lett.* **122** 247202

[256] Toro-Nahuelpan M, Giacomelli G, Raschdorf O, Borg S, Plitzko J M, Schüler D, Müller F-D and Müller F-D 2019 MamY is a membrane-bound protein that aligns magnetosomes and the motility axis of helical magnetotactic bacteria *Nat. Microbiol.* **4** 1978–89

[257] Shcherbakov V P, Winklhofer M, Hanzlik M and Petersen N 1997 Elastic stability of chains of magnetosomes in magnetotactic bacteria *Eur. Biophys. J.* **26** 319–26

[258] Prozorov T *et al* 2014 Manganese incorporation into the magnetosome magnetite: magnetic signature of doping *Eur. J. Mineral.* **26** 457–71

[259] Scheffel A, Gärdes A, Grünberg K, Wanner G and Schüler D 2008 The major magnetosome proteins MamGFDC are not essential for magnetite biomineralization in Magnetospirillum gryphiswaldense but regulate the size of magnetosome crystals *J. Bacteriol.* **190** 377–86

[260] Kent A D and Worledge D C 2015 A new spin on magnetic memories *Nat. Nanotechnol.* **10** 187–91

[261] Sankey J C, Braganca P M, Garcia A G F, Krivorotov I N, Buhrman R A and Ralph D C 2006 Spin-transfer-driven ferromagnetic resonance of individual nanomagnets *Phys. Rev. Lett.* **96** 227601

[262] Vansteenkiste A, Leliaert J, Dvornik M, Helsen M, Garcia-Sanchez F and Van Waeyenberge B 2014 The design and verification of MuMax3 AIP Adv. **4** 107133