{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T01:13:57Z","timestamp":1783991637318,"version":"3.55.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,11,24]],"date-time":"2016-11-24T00:00:00Z","timestamp":1479945600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2016,11,24]],"date-time":"2016-11-24T00:00:00Z","timestamp":1479945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The properties of natural and artificial assemblies of interacting elements, ranging from Quarks to Galaxies, are at the heart of Physics. The collective response and dynamics of such assemblies are dictated by the intrinsic dynamical properties of the building blocks, the nature of their interactions and topological constraints. Here we report on the relaxation dynamics of the magnetization of artificial assemblies of mesoscopic spins. In our model nano-magnetic system - square artificial spin ice \u2013 we are able to control the geometrical arrangement and interaction strength between the magnetically interacting building blocks by means of nano-lithography. Using time resolved magnetometry we show that the relaxation process can be described using the Kohlrausch law and that the extracted temperature dependent relaxation times of the assemblies follow the Vogel-Fulcher law. The results provide insight into the relaxation dynamics of mesoscopic nano-magnetic model systems, with adjustable energy and time scales, and demonstrates that these can serve as an ideal playground for the studies of collective dynamics and relaxations.<\/jats:p>","DOI":"10.1038\/srep37097","type":"journal-article","created":{"date-parts":[[2016,11,24]],"date-time":"2016-11-24T10:34:02Z","timestamp":1479983642000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Thermally induced magnetic relaxation in square artificial spin ice"],"prefix":"10.1038","volume":"6","author":[{"given":"M. S.","family":"Andersson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S. D.","family":"Pappas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H.","family":"Stopfel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"E.","family":"\u00d6stman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A.","family":"Stein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Nordblad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"R.","family":"Mathieu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"B.","family":"Hj\u00f6rvarsson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"V.","family":"Kapaklis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,11,24]]},"reference":[{"key":"BFsrep37097_CR1","first-page":"393","volume":"12","author":"R Kohlrausch","year":"1847","unstructured":"Kohlrausch, R. Theorie des elektrischen r\u00fcckstandes in der leidener flasche. Ann. Phys. (Leipzig) 12, 393 (1847).","journal-title":"Ann. Phys. (Leipzig)"},{"key":"BFsrep37097_CR2","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1039\/tf9706600080","volume":"66","author":"G Williams","year":"1970","unstructured":"Williams, G. & Watts, D. C. Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function. Transactions of the Faraday Society 66, 80\u201385 (1970).","journal-title":"Transactions of the Faraday Society"},{"key":"BFsrep37097_CR3","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1038\/267673a0","volume":"267","author":"AK Jonscher","year":"1977","unstructured":"Jonscher, A. K. The universal dielectric response. Nature 267, 673\u2013679 (1977).","journal-title":"Nature"},{"key":"BFsrep37097_CR4","doi-asserted-by":"publisher","first-page":"958","DOI":"10.1103\/PhysRevLett.53.958","volume":"53","author":"RG Palmer","year":"1984","unstructured":"Palmer, R. G., Stein, D. L., Abrahams, E. & Anderson, P. W. Models of Hierarchically Constrained Dynamics for Glassy Relaxation. Physical Review Letters 53, 958\u2013961 (1984).","journal-title":"Physical Review Letters"},{"key":"BFsrep37097_CR5","doi-asserted-by":"publisher","first-page":"4201","DOI":"10.1063\/1.466117","volume":"99","author":"R B\u00f6hmer","year":"1993","unstructured":"B\u00f6hmer, R., Ngai, K. L., Angell, C. A. & Plazek, D. J. Nonexponential relaxations in strong and fragile glass formers. The Journal of Chemical Physics 99, 4201\u20134209 (1993).","journal-title":"The Journal of Chemical Physics"},{"key":"BFsrep37097_CR6","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1038\/nphys3644","volume":"12","author":"SS Schoenholz","year":"2016","unstructured":"Schoenholz, S. S., Cubuk, E. D., Sussman, D. M., Kaxiras, E. & Liu, A. J. A structural approach to relaxation in glassy liquids. Nature Physics 12, 469\u2013471 (2016).","journal-title":"Nature Physics"},{"key":"BFsrep37097_CR7","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1126\/science.287.5453.627","volume":"287","author":"ER Weeks","year":"2000","unstructured":"Weeks, E. R., Crocker, J. C., Levitt, A. C., Schofield, A. & Weitz, D. A. Three-Dimensional Direct Imaging of Structural Relaxation Near the Colloidal Glass Transition. Science 287, 627\u2013631 (2000).","journal-title":"Science"},{"key":"BFsrep37097_CR8","doi-asserted-by":"publisher","first-page":"17004","DOI":"10.1209\/0295-5075\/108\/17004","volume":"108","author":"MS Andersson","year":"2014","unstructured":"Andersson, M. S., Toro, J. A. D., Lee, S. S., Mathieu, R. & Nordblad, P. Ageing dynamics of a superspin glass. EPL (Europhysics Letters) 108, 17004 (2014).","journal-title":"EPL (Europhysics Letters)"},{"key":"BFsrep37097_CR9","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1016\/0022-3093(91)90329-5","volume":"131","author":"F Parak","year":"1991","unstructured":"Parak, F. & Nienhaus, G. U. Glass-like behaviour of proteins as seen by M\u00f6ssbauer spectroscopy. Journal of Non-Crystalline Solids 131, 362\u2013368 (1991).","journal-title":"Journal of Non-Crystalline Solids"},{"key":"BFsrep37097_CR10","series-title":"Partially Ordered Systems","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-7649-9","volume-title":"Relaxation and Diffusion in Complex Systems","author":"K.L. Ngai","year":"2011","unstructured":"Ngai, K. L. Relaxation and Diffusion in Complex Systems (Springer-Verlag: New York,, 2011)."},{"key":"BFsrep37097_CR11","first-page":"1495","volume":"294","author":"ST Bramwell","year":"2001","unstructured":"Bramwell, S. T. & Gingras, M. J. P. Spin Ice State in Frustrated Magnetic Pyrochlore Materials. Science 294, 1495\u20131501 (2001).","journal-title":"Materials. Science"},{"key":"BFsrep37097_CR12","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1038\/nphys1896","volume":"7","author":"SR Giblin","year":"2011","unstructured":"Giblin, S. R., Bramwell, S. T., Holdsworth, P. C. W., Prabhakaran, D. & Terry, I. Creation and measurement of long-lived magnetic monopole currents in spin ice. Nature Physics 7, 252 (2011).","journal-title":"Nature Physics"},{"key":"BFsrep37097_CR13","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1038\/nphys2466","volume":"9","author":"HM Revell","year":"2012","unstructured":"Revell, H. M. et al. Evidence of impurity and boundary effects on magnetic monopole dynamics in spin ice. Nature Physics 9, 34\u201337 (2012).","journal-title":"Nature Physics"},{"key":"BFsrep37097_CR14","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1038\/nature04447","volume":"439","author":"RF Wang","year":"2006","unstructured":"Wang, R. F. et al. Artificial \u2018spin ice\u2019 in a geometrically frustrated lattice of nanoscale ferromagnetic islands. Nature 439, 303 (2006).","journal-title":"Nature"},{"key":"BFsrep37097_CR15","first-page":"363201","volume":"25","author":"LJ Heyderman","year":"2013","unstructured":"Heyderman, L. J. & Stamps, R. L. Artificial ferroic systems: novel functionality from structure, interactions and dynamics. Journal of Physics: Condensed Matter 25, 363201 (2013).","journal-title":"Journal of Physics: Condensed Matter"},{"key":"BFsrep37097_CR16","doi-asserted-by":"publisher","first-page":"057204","DOI":"10.1103\/PhysRevLett.111.057204","volume":"111","author":"A Farhan","year":"2013","unstructured":"Farhan, A. et al. Direct Observation of Thermal Relaxation in Artificial Spin Ice. Physical Review Letters 111, 057204 (2013).","journal-title":"Physical Review Letters"},{"key":"BFsrep37097_CR17","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1038\/nnano.2014.104","volume":"9","author":"V Kapaklis","year":"2014","unstructured":"Kapaklis, V. et al. Thermal fluctuations in artificial spin ice. Nat. Nanotechnol. 9, 514\u2013519 (2014).","journal-title":"Nat. Nanotechnol"},{"key":"BFsrep37097_CR18","doi-asserted-by":"publisher","first-page":"153","DOI":"10.5963\/BER0204001","volume":"2","author":"RK June","year":"2013","unstructured":"June, R. K., Cunningham, J. P. & Fyhrie, D. P. A Novel Method for Curvefitting the Stretched Exponential Function to Experimental Data. Biomed. Eng. Res. 2, 153\u2013158 (2013).","journal-title":"Biomed. Eng. Res"},{"key":"BFsrep37097_CR19","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1016\/0375-9601(81)90441-2","volume":"85","author":"S Shtrikman","year":"1981","unstructured":"Shtrikman, S. & Wohlfarth, E. P. The theory of the vogel-fulcher law of spin glasses. Phys. Lett. A 85, 467\u2013470 (1981).","journal-title":"Phys. Lett. A"},{"key":"BFsrep37097_CR20","doi-asserted-by":"publisher","first-page":"852","DOI":"10.1109\/TMAG.2009.2032240","volume":"46","author":"VL Calero-Diaz Del Castillo","year":"2010","unstructured":"Calero-Diaz Del Castillo, V. L. & Rinaldi, C. Effect of sample concentration on the determination of the anisotropy constant of magnetic nanoparticles. IEEE Trans. Magn. 46, 852\u2013859 (2010).","journal-title":"IEEE Trans. Magn."},{"key":"BFsrep37097_CR21","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1103\/PhysRev.67.351","volume":"67","author":"JA Osborn","year":"1945","unstructured":"Osborn, J. A. Demagnetizing factors of the general ellipsoid. Phys. Rev. 67, 351\u2013357 (1945).","journal-title":"Phys. Rev"},{"key":"BFsrep37097_CR22","doi-asserted-by":"publisher","first-page":"12635","DOI":"10.1038\/ncomms12635","volume":"7","author":"A Farhan","year":"2016","unstructured":"Farhan, A. et al. Thermodynamics of emergent magnetic charge screening in artificial spin ice. Nature Communications 7, 12635 (2016).","journal-title":"Nature Communications"},{"key":"BFsrep37097_CR23","doi-asserted-by":"publisher","first-page":"8278","DOI":"10.1038\/ncomms9278","volume":"6","author":"L Anghinolfi","year":"2015","unstructured":"Anghinolfi, L. et al. Thermodynamic phase transitions in a frustrated magnetic metamaterial. Nature Communications 6, 8278 (2015).","journal-title":"Nature Communications"},{"key":"BFsrep37097_CR24","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1038\/nphys3520","volume":"12","author":"I Gilbert","year":"2016","unstructured":"Gilbert, I. et al. Emergent reduced dimensionality by vertex frustration in artificial spin ice. Nature Physics 12, 162\u2013165 (2016).","journal-title":"Nature Physics"},{"key":"BFsrep37097_CR25","doi-asserted-by":"publisher","first-page":"134420","DOI":"10.1103\/PhysRevB.93.134420","volume":"93","author":"E Iacocca","year":"2016","unstructured":"Iacocca, E., Gliga, S., Stamps, R. L. & Heinonen, O. Reconfigurable wave band structure of an artificial square ice. Physical Review B 93, 134420 (2016).","journal-title":"Physical Review B"},{"key":"BFsrep37097_CR26","doi-asserted-by":"publisher","first-page":"117205","DOI":"10.1103\/PhysRevLett.110.117205","volume":"110","author":"S Gliga","year":"2013","unstructured":"Gliga, S., K\u00e1kay, A., Hertel, R. & Heinonen, O. G. Spectral Analysis of Topological Defects in an Artificial Spin-Ice Lattice. Physical Review Letters 110, 117205 (2013).","journal-title":"Physical Review Letters"},{"key":"BFsrep37097_CR27","doi-asserted-by":"publisher","first-page":"100401","DOI":"10.1103\/PhysRevB.93.100401","volume":"93","author":"MB Jungfleisch","year":"2016","unstructured":"Jungfleisch, M. B. et al. Dynamic response of an artificial square spin ice. Physical Review B 93, 100401 (2016).","journal-title":"Physical Review B"},{"key":"BFsrep37097_CR28","doi-asserted-by":"publisher","first-page":"246213","DOI":"10.1088\/0953-8984\/19\/24\/246213","volume":"19","author":"M P\u00e4rnaste","year":"2007","unstructured":"P\u00e4rnaste, M. et al. Dimensionality crossover in the induced magnetization of Pd layers. J. Phys. Condens. Matter 19, 246213 (2007).","journal-title":"J. Phys. Condens. Matter"},{"key":"BFsrep37097_CR29","doi-asserted-by":"publisher","first-page":"3761","DOI":"10.1063\/1.1148023","volume":"68","author":"J Magnusson","year":"1997","unstructured":"Magnusson, J., Djurberg, C., Granberg, P. & Nordblad, P. A low field superconducting quantum interference device magnetometer for dynamic measurements. Review of Scientific Instruments 68, 3761 (1997).","journal-title":"Review of Scientific Instruments"}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/srep37097.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/srep37097","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/srep37097.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,5]],"date-time":"2023-01-05T02:45:01Z","timestamp":1672886701000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/srep37097"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,24]]},"references-count":29,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,12,23]]}},"alternative-id":["BFsrep37097"],"URL":"https:\/\/doi.org\/10.1038\/srep37097","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,24]]},"assertion":[{"value":"26 July 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 November 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 February 2017","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Update","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The version of this paper was updated after publication, following a technical error that resulted in the link to the Supplementary Information file being omitted. This has now been corrected in the PDF and HTML versions of the paper.","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing financial interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"37097"}}