{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T15:49:39Z","timestamp":1770133779844,"version":"3.49.0"},"reference-count":63,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,5,15]],"date-time":"2017-05-15T00:00:00Z","timestamp":1494806400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2017,5,15]],"date-time":"2017-05-15T00:00:00Z","timestamp":1494806400000},"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":["npj Comput Mater"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We construct a Landau\u2013Ginzburg thermodynamic potential, and the corresponding phase diagram for pristine and slightly doped bismuth ferrite, a ferroelectric antiferromagnet at room temperature. The potential is developed based on new X-ray and neutron diffraction experiments complementing available data. We demonstrate that a strong biquadratic antiferrodistortive-type coupling is the key to a quantitative description of Bi<jats:sub>1\u2212<jats:italic>x<\/jats:italic>\n                        <\/jats:sub>La<jats:sub>\n                  <jats:italic>x<\/jats:italic>\n                <\/jats:sub>FeO<jats:sub>3<\/jats:sub> multiferroic phase diagram including the temperature stability of the antiferromagnetic, ferroelectric, and antiferrodistortive phases, as well as for the prediction of novel intermediate structural phases. Furthermore, we show that \u201crotomagnetic\u201d antiferrodistortive\u2013antiferromagnetic coupling is very important to describe the ferroelectric polarization and antiferrodistortive tilt behavior in the <jats:italic>R3c<\/jats:italic> phase of BiFeO<jats:sub>3<\/jats:sub>. The Landau\u2013Ginzburg thermodynamic potential is able to describe the sequence of serial and trigger-type phase transitions, the temperature-dependent behavior of the order parameters, and the corresponding susceptibilities to external stimuli. It can also be employed to predict the corresponding ferroelectric and antiferrodistortive properties of Bi<jats:sub>1\u2212<jats:italic>x<\/jats:italic>\n                        <\/jats:sub>La<jats:sub>\n                  <jats:italic>x<\/jats:italic>\n                <\/jats:sub>FeO<jats:sub>3<\/jats:sub> thin films and nanoparticles by incorporating the gradient and surface energy terms that are strongly dependent on the shape, size, and preparation method.<\/jats:p>","DOI":"10.1038\/s41524-017-0021-3","type":"journal-article","created":{"date-parts":[[2017,5,5]],"date-time":"2017-05-05T08:36:56Z","timestamp":1493973416000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":83,"title":["Thermodynamic potential and phase diagram for multiferroic bismuth ferrite (BiFeO\n                3\n              )"],"prefix":"10.1038","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1046-543X","authenticated-orcid":false,"given":"Dmitry V.","family":"Karpinsky","sequence":"first","affiliation":[]},{"given":"Eugene A.","family":"Eliseev","sequence":"additional","affiliation":[]},{"given":"Fei","family":"Xue","sequence":"additional","affiliation":[]},{"given":"Maxim V.","family":"Silibin","sequence":"additional","affiliation":[]},{"given":"Alexandra","family":"Franz","sequence":"additional","affiliation":[]},{"given":"Maya D.","family":"Glinchuk","sequence":"additional","affiliation":[]},{"given":"Igor O.","family":"Troyanchuk","sequence":"additional","affiliation":[]},{"given":"Sergey A.","family":"Gavrilov","sequence":"additional","affiliation":[]},{"given":"Venkatraman","family":"Gopalan","sequence":"additional","affiliation":[]},{"given":"Long-Qing","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Anna N.","family":"Morozovska","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,5,15]]},"reference":[{"key":"21_CR1","doi-asserted-by":"publisher","first-page":"R123","DOI":"10.1088\/0022-3727\/38\/8\/R01","volume":"38","author":"M Fiebig","year":"2005","unstructured":"Fiebig, M. 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