The authors thank A. M. Balbashov for bulk crystals of orthoferrites of an exceptionally high quality, I. Gronwald for assistance with electron-beam lithography, J. Fabian and M. S. Sherwin for fruitful discussions and T. Rasing for continuous support. The work in Regensburg was supported by the DFG through grant number HU 1598/2 and SFB 1277 (Project A05) as well as by the European Research Council through grant no. 305003 (QUANTUMsubCYCLE). The work in Nijmegen was supported by the European Research Council ERC Grant Agreement number 339813 (Exchange) and NWO (The Netherlands Organization for Scientific Research). The work in Moscow was supported by RSF grant number 17-12-01333. D.C.V. acknowledges the support of NSF DMR 1710639.

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Nature thanks Uwe Bovensiepen, Jakob Walowski and Guo Ping Zhang for their contribution to the peer review of this work.