{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T02:20:34Z","timestamp":1781576434015,"version":"3.54.5"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T00:00:00Z","timestamp":1713312000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T00:00:00Z","timestamp":1713312000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100010446","name":"Institute for Basic Science","doi-asserted-by":"publisher","award":["IBS-R011-D1"],"award-info":[{"award-number":["IBS-R011-D1"]}],"id":[{"id":"10.13039\/501100010446","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2019R1A6A301096112"],"award-info":[{"award-number":["NRF-2019R1A6A301096112"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2022R1A2C1006740"],"award-info":[{"award-number":["NRF-2022R1A2C1006740"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nat Commun"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Phase diagrams of materials are typically based on a static order parameter, but it faces challenges when distinguishing subtle phase changes, such as re-ordering. Here, we report a dynamic nonequilibrium order parameter termed re-order parameter to determine subtle phases and their transitions in interacting magnets. The dynamical precession of magnetization, so-called magnon, premises as a reliable re-order parameter of strong spin-orbit coupled magnets. We employ orthoferrites YFeO<jats:sub>3<\/jats:sub> and its Mn-doped variations, where diverse magnetic phases, including canted antiferromagnetic (\u0393<jats:sub>4<\/jats:sub>) and collinear antiferromagnetic (\u0393<jats:sub>1<\/jats:sub>) states, have been well-established. Low-energy magnon uncovers the spin-orbit coupling-induced subtle magnetic structures, resulting in distinct terahertz emissions. The temporal and spectral parameters of magnon emission exhibit characteristics akin to BCS-type order parameters, constructing the magnetic phase diagram of Mn-doped YFeO<jats:sub>3<\/jats:sub>. This approach further reveals a concealed ferrimagnetic phase within the \u0393<jats:sub>1<\/jats:sub> state, underscoring its potential to search for hidden phases of materials, completing their phase diagrams.<\/jats:p>","DOI":"10.1038\/s41467-024-47637-2","type":"journal-article","created":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T09:04:12Z","timestamp":1713344652000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Re-order parameter of interacting thermodynamic magnets"],"prefix":"10.1038","volume":"15","author":[{"given":"Byung Cheol","family":"Park","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Howon","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sang Hyup","family":"Oh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1510-2857","authenticated-orcid":false,"given":"Hyun Jun","family":"Shin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1711-0607","authenticated-orcid":false,"given":"Young Jai","family":"Choi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4089-1982","authenticated-orcid":false,"given":"Taewoo","family":"Ha","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,4,17]]},"reference":[{"key":"47637_CR1","doi-asserted-by":"crossref","unstructured":"Lewis, G. N. & Merle, R. Thermodynamics, 2nd edn, Ch. 27 (McGraw-Hill, 1961).","DOI":"10.1149\/1.2427918"},{"key":"47637_CR2","unstructured":"Greiner, W., Neise, L. & St\u00f6cker, H. Thermodynamics and Statistical Mechanics, 1st edn, Ch. 17 (Springer, 2012)."},{"key":"47637_CR3","unstructured":"Ashcroft, N. W. & Mermin, N. D. Solid State Physics, Ch. 33 (Saunders College Publishing, 1976)."},{"key":"47637_CR4","unstructured":"Kittle, C. Introduction to Solid State Physics, 5th edn, Ch. 10 & Ch. 16 (Wiley, New York, 1976)."},{"key":"47637_CR5","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1016\/0022-3697(58)90076-3","volume":"4","author":"I Dzyaloshinsky","year":"1958","unstructured":"Dzyaloshinsky, I. A thermodynamic theory of \u201cweak\u201d ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241\u2013255 (1958).","journal-title":"J. Phys. Chem. Solids"},{"key":"47637_CR6","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1103\/PhysRev.120.91","volume":"120","author":"T Moriya","year":"1960","unstructured":"Moriya, T. Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91\u201398 (1960).","journal-title":"Phys. Rev."},{"key":"47637_CR7","doi-asserted-by":"publisher","first-page":"237201","DOI":"10.1103\/PhysRevLett.105.237201","volume":"105","author":"K Yamaguchi","year":"2010","unstructured":"Yamaguchi, K., Nakajima, M. & Suemoto, T. Coherent control of spin precession motion with impulsive magnetic fields of half-cycle terahertz radiation. Phys. Rev. Lett. 105, 237201 (2010).","journal-title":"Phys. Rev. Lett."},{"key":"47637_CR8","doi-asserted-by":"publisher","first-page":"207204","DOI":"10.1103\/PhysRevLett.118.207204","volume":"118","author":"J Lu","year":"2017","unstructured":"Lu, J. et al. Coherent two-dimensional terahertz magnetic resonance spectroscopy of collective spin waves. Phys. Rev. Lett. 118, 207204 (2017).","journal-title":"Phys. Rev. Lett."},{"key":"47637_CR9","doi-asserted-by":"publisher","first-page":"137204","DOI":"10.1103\/PhysRevLett.110.137204","volume":"110","author":"K Yamaguchi","year":"2013","unstructured":"Yamaguchi, K. et al. Terahertz time-domain observation of spin reorientation in orthoferrite ErFeO3 through magnetic free induction decay. Phys. Rev. Lett. 110, 137204 (2013).","journal-title":"Phys. Rev. Lett."},{"key":"47637_CR10","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-23159-z","volume":"12","author":"T Makihara","year":"2021","unstructured":"Makihara, T. et al. Ultrastrong magnon\u2013magnon coupling dominated by antiresonant interactions. Nat. Commun. 12, 3115 (2021).","journal-title":"Nat. Commun."},{"key":"47637_CR11","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1038\/s41567-021-01290-4","volume":"17","author":"JR Hortensius","year":"2021","unstructured":"Hortensius, J. R. et al. Coherent spin-wave transport in an antiferromagnet. Nat. Phys. 17, 1001\u20131006 (2021).","journal-title":"Nat. Phys."},{"key":"47637_CR12","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1016\/0031-9163(66)90649-4","volume":"22","author":"VM Judin","year":"1966","unstructured":"Judin, V. M., Sherman, A. B. & Myl\u2019Nikova, I. E. Magnetic properties of YFeO3. Phys. Lett. 22, 554\u2013555 (1966).","journal-title":"Phys. Lett."},{"key":"47637_CR13","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/0304-8853(80)90475-8","volume":"21","author":"H L\u00fctgemeier","year":"1980","unstructured":"L\u00fctgemeier, H., Bohn, H. G. & Brajczewska, M. NMR observation of the spin structure and field induced spin reorientation in YFeO3. J. Magn. Magn. Mater. 21, 289\u2013296 (1980).","journal-title":"J. Magn. Magn. Mater."},{"key":"47637_CR14","doi-asserted-by":"publisher","first-page":"3051","DOI":"10.1088\/0022-3719\/8\/18\/024","volume":"8","author":"GW Durbin","year":"1975","unstructured":"Durbin, G. W., Johnson, C. E. & Thomas, M. F. Direct observation of field-induced spin reorientation in YFeO3 by the Mossbauer effect. J. Phys. C: Solid State Phys. 8, 3051 (1975).","journal-title":"J. Phys. C: Solid State Phys."},{"key":"47637_CR15","doi-asserted-by":"publisher","first-page":"062903","DOI":"10.1063\/1.4791697","volume":"102","author":"M Shang","year":"2013","unstructured":"Shang, M. et al. The multiferroic perovskite YFeO3. Appl. Phys. Lett. 102, 062903 (2013).","journal-title":"Appl. Phys. Lett."},{"key":"47637_CR16","doi-asserted-by":"publisher","first-page":"092403","DOI":"10.1063\/1.4913998","volume":"106","author":"X Lin","year":"2015","unstructured":"Lin, X. et al. Terahertz probes of magnetic field induced spin reorientation in YFeO3 single crystal. Appl. Phys. Lett. 106, 092403 (2015).","journal-title":"Appl. Phys. Lett."},{"key":"47637_CR17","doi-asserted-by":"publisher","first-page":"137202","DOI":"10.1103\/PhysRevLett.107.137202","volume":"107","author":"P Mandal","year":"2011","unstructured":"Mandal, P. et al. Spin-reorientation, ferroelectricity, and magnetodielectric effect in YFe1-xMnxO3 (0.1\u2264 x \u2264 0.40). Phys. Rev. Lett. 107, 137202 (2011).","journal-title":"Phys. Rev. Lett."},{"key":"47637_CR18","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1016\/j.jssc.2012.09.005","volume":"197","author":"P Mandal","year":"2013","unstructured":"Mandal, P. et al. Spin reorientation and magnetization reversal in the perovskite oxides, YFe1-xMnxO3 (0\u2264 x\u2264 0.45): a neutron diffraction study. J. Solid State Chem. 197, 408 (2013).","journal-title":"J. Solid State Chem."},{"key":"47637_CR19","doi-asserted-by":"publisher","first-page":"094403","DOI":"10.1103\/PhysRevB.93.094403","volume":"93","author":"TN Stanislavchuk","year":"2016","unstructured":"Stanislavchuk, T. N. et al. Magnon and electromagnon excitations in multiferroic DyFeO3. Phys. Rev. B 93, 094403 (2016).","journal-title":"Phys. Rev. B"},{"key":"47637_CR20","doi-asserted-by":"publisher","first-page":"192903","DOI":"10.1063\/5.0070952","volume":"119","author":"H Lee","year":"2021","unstructured":"Lee, H. et al. Terahertz spectroscopy of antiferromagnetic resonances in YFe1\u2212xMnxO3\u2008(0 \u2264 x \u2264 0.4) across a spin reorientation transition. Appl. Phys. Lett. 119, 192903 (2021).","journal-title":"Appl. Phys. Lett."},{"key":"47637_CR21","unstructured":"Aharoni, A. Introduction to the Theory of Ferromagnetism, 2nd edn, Ch. 8 (Oxford University Press, New York, 2007)."},{"key":"47637_CR22","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-022-33520-5","volume":"13","author":"S Das","year":"2022","unstructured":"Das, S. et al. Anisotropic long-range spin transport in canted antiferromagnetic orthoferrite YFeO3. Nat. Commun. 13, 6140 (2022).","journal-title":"Nat. Commun."},{"key":"47637_CR23","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1021\/ic950703v","volume":"35","author":"C Mathoni\u00e8re","year":"1996","unstructured":"Mathoni\u00e8re, C. et al. Ferrimagnetic mixed-valency and mixed-metal tris(oxalato) iron (III) compounds: synthesis, structure and magnetism. Inorg. Chem. 35, 1201\u20131206 (1996).","journal-title":"Inorg. Chem."},{"key":"47637_CR24","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1126\/science.abd2774","volume":"371","author":"T Danz","year":"2021","unstructured":"Danz, T., Domr\u00f6se, T. & Ropers, C. Ultrafast nanoimaging of the order parameter in a structural phase transition. Science 371, 371\u2013374 (2021).","journal-title":"Science"},{"key":"47637_CR25","doi-asserted-by":"publisher","first-page":"208301","DOI":"10.1103\/PhysRevLett.113.208301","volume":"113","author":"V Chikkadi","year":"2014","unstructured":"Chikkadi, V., Miedema, D. M., Dang, M. T., Nienhuis, B. & Schall, P. Shear banding of colloidal glasses: observation of a dynamic first-order transition. Phys. Rev. Lett. 113, 208301 (2014).","journal-title":"Phys. Rev. Lett."},{"key":"47637_CR26","doi-asserted-by":"publisher","first-page":"849","DOI":"10.1038\/nmat3116","volume":"10","author":"K Senapati","year":"2011","unstructured":"Senapati, K., Blamire, M. G. & Barber, Z. H. Spin-filter josephson junctions. Nat. Mater. 10, 849\u2013852 (2011).","journal-title":"Nat. Mater."}],"container-title":["Nature Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41467-024-47637-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41467-024-47637-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41467-024-47637-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,17]],"date-time":"2024-04-17T09:10:47Z","timestamp":1713345047000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41467-024-47637-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,17]]},"references-count":26,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["47637"],"URL":"https:\/\/doi.org\/10.1038\/s41467-024-47637-2","relation":{},"ISSN":["2041-1723"],"issn-type":[{"value":"2041-1723","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,17]]},"assertion":[{"value":"17 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 April 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 April 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"3294"}}