{"id":1349,"date":"2015-06-25T21:36:11","date_gmt":"2015-06-25T21:36:11","guid":{"rendered":"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/?p=1349"},"modified":"2015-06-25T21:42:19","modified_gmt":"2015-06-25T21:42:19","slug":"quantum-mechanics-of-magnetic-moments-in-spin-ice","status":"publish","type":"post","link":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/","title":{"rendered":"Quantum mechanics of magnetic moments in spin ice"},"content":{"rendered":"<ul class=\"kent-social-links\"><li><a href='http:\/\/www.facebook.com\/sharer.php?u=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/&amp;t=Quantum mechanics of magnetic moments in spin ice' target='_blank'><i class='ksocial-facebook' title='Share via Facebook'><\/i><\/a><\/li><li><a href='http:\/\/twitter.com\/home?status=Quantum mechanics of magnetic moments in spin ice%20https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/' target='_blank'><i class='ksocial-twitter' title='Share via Twitter'><\/i><\/a><\/li><li><a href='https:\/\/plus.google.com\/share?url=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/' target='_blank'><i class='ksocial-google-plus' title='Share via Google Plus'><\/i><\/a><\/li><li><a href='http:\/\/linkedin.com\/shareArticle?mini=true&amp;url=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/&amp;title=Quantum mechanics of magnetic moments in spin ice' target='_blank'><i class='ksocial-linkedin' title='Share via Linked In'><\/i><\/a><\/li><li><a href='mailto:content=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/&amp;title=Quantum mechanics of magnetic moments in spin ice' target='_blank'><i class='ksocial-email' title='Share via Email'><\/i><\/a><\/li><\/ul><p><a href=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/people\/brunos-research\/\">Bruno<\/a> recently posted the first paper resulting from <a href=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/01\/16\/bruno-tomasello\/\">his PhD thesis<\/a> to the preprint archive. In it we take the first steps towards a micr<a href=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2015\/06\/Screenshot-from-2015-06-25-223734.png\"><img loading=\"lazy\" class=\"size-medium wp-image-1353 alignright\" src=\"http:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2015\/06\/Screenshot-from-2015-06-25-223734-300x181.png\" alt=\"Crystal structure\" width=\"300\" height=\"181\" srcset=\"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2015\/06\/Screenshot-from-2015-06-25-223734-300x181.png 300w, https:\/\/blogs.kent.ac.uk\/strongcorrelations\/files\/2015\/06\/Screenshot-from-2015-06-25-223734.png 371w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a>oscopic view of the magnetic rare earth ions in spin ice, specifically taking into account their quantum-mechanical nature and the effect of crystal electric and magnetic fields. We thus depart from the simplified description of spin ice as a classical Ising system which has served the field so well in the past. This departure is an essential ingredient in the description of spin-flip dynamics and, therefore, of monopole propagation in these systems. Interestingly, the richer description has other consequences, including some curious magnetic anisotropies that might be experimentally observable.<\/p>\n<h1 class=\"title mathjax\">Single-ion anisotropy and magnetic field response in spin ice materials Ho<span id=\"MathJax-Element-1-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"msubsup\"><span id=\"MathJax-Span-4\" class=\"mi\"><\/span><span id=\"MathJax-Span-5\" class=\"texatom\"><span id=\"MathJax-Span-6\" class=\"mrow\"><span id=\"MathJax-Span-7\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>Ti<span id=\"MathJax-Element-2-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-8\" class=\"math\"><span id=\"MathJax-Span-9\" class=\"mrow\"><span id=\"MathJax-Span-10\" class=\"msubsup\"><span id=\"MathJax-Span-11\" class=\"mi\"><\/span><span id=\"MathJax-Span-12\" class=\"texatom\"><span id=\"MathJax-Span-13\" class=\"mrow\"><span id=\"MathJax-Span-14\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>O<span id=\"MathJax-Element-3-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-15\" class=\"math\"><span id=\"MathJax-Span-16\" class=\"mrow\"><span id=\"MathJax-Span-17\" class=\"msubsup\"><span id=\"MathJax-Span-18\" class=\"mi\"><\/span><span id=\"MathJax-Span-19\" class=\"texatom\"><span id=\"MathJax-Span-20\" class=\"mrow\"><span id=\"MathJax-Span-21\" class=\"mn\">7<\/span><\/span><\/span><\/span><\/span><\/span><\/span> and Dy<span id=\"MathJax-Element-4-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-22\" class=\"math\"><span id=\"MathJax-Span-23\" class=\"mrow\"><span id=\"MathJax-Span-24\" class=\"msubsup\"><span id=\"MathJax-Span-25\" class=\"mi\"><\/span><span id=\"MathJax-Span-26\" class=\"texatom\"><span id=\"MathJax-Span-27\" class=\"mrow\"><span id=\"MathJax-Span-28\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>Ti<span id=\"MathJax-Element-5-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-29\" class=\"math\"><span id=\"MathJax-Span-30\" class=\"mrow\"><span id=\"MathJax-Span-31\" class=\"msubsup\"><span id=\"MathJax-Span-32\" class=\"mi\"><\/span><span id=\"MathJax-Span-33\" class=\"texatom\"><span id=\"MathJax-Span-34\" class=\"mrow\"><span id=\"MathJax-Span-35\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>O<span id=\"MathJax-Element-6-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-36\" class=\"math\"><span id=\"MathJax-Span-37\" class=\"mrow\"><span id=\"MathJax-Span-38\" class=\"msubsup\"><span id=\"MathJax-Span-39\" class=\"mi\"><\/span><span id=\"MathJax-Span-40\" class=\"texatom\"><span id=\"MathJax-Span-41\" class=\"mrow\"><span id=\"MathJax-Span-42\" class=\"mn\">7<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h1>\n<div class=\"authors\"><a href=\"http:\/\/arxiv.org\/find\/cond-mat\/1\/au:+Tomasello_B\/0\/1\/0\/all\/0\/1\">Bruno Tomasello<\/a>, <a href=\"http:\/\/arxiv.org\/find\/cond-mat\/1\/au:+Castelnovo_C\/0\/1\/0\/all\/0\/1\">Claudio Castelnovo<\/a>, <a href=\"http:\/\/arxiv.org\/find\/cond-mat\/1\/au:+Moessner_R\/0\/1\/0\/all\/0\/1\">Roderich Moessner<\/a>, <a href=\"http:\/\/arxiv.org\/find\/cond-mat\/1\/au:+Quintanilla_J\/0\/1\/0\/all\/0\/1\">Jorge Quintanilla<\/a><\/div>\n<div class=\"dateline\">(Submitted on 8 Jun 2015)<\/div>\n<blockquote class=\"abstract mathjax\"><p>Motivated by its role as a central pillar of current theories of dynamics of spin ice in and out of equilibrium, we study the single-ion dynamics of the magnetic rare earth ions in their local environments, subject to the effective fields set up by the magnetic moments they interact with. This effective field has a transverse component with respect to the local easy-axis of the crystal electric field, which can induce quantum tunnelling. We go beyond the projective spin-1\/2 picture and use instead the full crystal-field Hamiltonian. We find that the Kramers vs non-Kramers nature, as well as the symmetries of the crystal-field Hamiltonian, result in different perturbative behaviour at small fields (<span id=\"MathJax-Element-7-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-43\" class=\"math\"><span id=\"MathJax-Span-44\" class=\"mrow\"><span id=\"MathJax-Span-45\" class=\"mo\">\u2272<\/span><span id=\"MathJax-Span-46\" class=\"mn\">1<\/span><\/span><\/span><\/span> T), with transverse field effects being more pronounced in Ho<span id=\"MathJax-Element-8-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-47\" class=\"math\"><span id=\"MathJax-Span-48\" class=\"mrow\"><span id=\"MathJax-Span-49\" class=\"msubsup\"><span id=\"MathJax-Span-50\" class=\"mi\"><\/span><span id=\"MathJax-Span-51\" class=\"texatom\"><span id=\"MathJax-Span-52\" class=\"mrow\"><span id=\"MathJax-Span-53\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>Ti<span id=\"MathJax-Element-9-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-54\" class=\"math\"><span id=\"MathJax-Span-55\" class=\"mrow\"><span id=\"MathJax-Span-56\" class=\"msubsup\"><span id=\"MathJax-Span-57\" class=\"mi\"><\/span><span id=\"MathJax-Span-58\" class=\"texatom\"><span id=\"MathJax-Span-59\" class=\"mrow\"><span id=\"MathJax-Span-60\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>O<span id=\"MathJax-Element-10-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-61\" class=\"math\"><span id=\"MathJax-Span-62\" class=\"mrow\"><span id=\"MathJax-Span-63\" class=\"msubsup\"><span id=\"MathJax-Span-64\" class=\"mi\"><\/span><span id=\"MathJax-Span-65\" class=\"texatom\"><span id=\"MathJax-Span-66\" class=\"mrow\"><span id=\"MathJax-Span-67\" class=\"mn\">7<\/span><\/span><\/span><\/span><\/span><\/span><\/span> than in Dy<span id=\"MathJax-Element-11-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-68\" class=\"math\"><span id=\"MathJax-Span-69\" class=\"mrow\"><span id=\"MathJax-Span-70\" class=\"msubsup\"><span id=\"MathJax-Span-71\" class=\"mi\"><\/span><span id=\"MathJax-Span-72\" class=\"texatom\"><span id=\"MathJax-Span-73\" class=\"mrow\"><span id=\"MathJax-Span-74\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>Ti<span id=\"MathJax-Element-12-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-75\" class=\"math\"><span id=\"MathJax-Span-76\" class=\"mrow\"><span id=\"MathJax-Span-77\" class=\"msubsup\"><span id=\"MathJax-Span-78\" class=\"mi\"><\/span><span id=\"MathJax-Span-79\" class=\"texatom\"><span id=\"MathJax-Span-80\" class=\"mrow\"><span id=\"MathJax-Span-81\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>O<span id=\"MathJax-Element-13-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-82\" class=\"math\"><span id=\"MathJax-Span-83\" class=\"mrow\"><span id=\"MathJax-Span-84\" class=\"msubsup\"><span id=\"MathJax-Span-85\" class=\"mi\"><\/span><span id=\"MathJax-Span-86\" class=\"texatom\"><span id=\"MathJax-Span-87\" class=\"mrow\"><span id=\"MathJax-Span-88\" class=\"mn\">7<\/span><\/span><\/span><\/span><\/span><\/span><\/span>. Remarkably, the energy splitting range we find is consistent with time scales extracted from experiments. We also present a study of the static magnetic response which highlights the anisotropy of the system in the form of an off-diagonal <span id=\"MathJax-Element-14-Frame\" class=\"MathJax\"><span id=\"MathJax-Span-89\" class=\"math\"><span id=\"MathJax-Span-90\" class=\"mrow\"><span id=\"MathJax-Span-91\" class=\"mi\">g<\/span><\/span><\/span><\/span> tensor and we investigate the effects of thermal fluctuations in the temperature regime of relevance to experiments. We show that there is a narrow yet accessible window of experimental parameters where the anisotropic response can be observed.<\/p><\/blockquote>\n<div class=\"metatable\">\n<table summary=\"Additional metadata\">\n<tbody>\n<tr>\n<td class=\"tablecell label\">Comments:<\/td>\n<td class=\"tablecell comments\">17 pages, 8 figures<\/td>\n<\/tr>\n<tr>\n<td class=\"tablecell label\">Subjects:<\/td>\n<td class=\"tablecell subjects\"><span class=\"primary-subject\">Strongly Correlated Electrons (cond-mat.str-el)<\/span><\/td>\n<\/tr>\n<tr>\n<td class=\"tablecell label\">Cite\u00a0as:<\/td>\n<td class=\"tablecell arxivid\"><a href=\"http:\/\/arxiv.org\/abs\/1506.02672\">arXiv:1506.02672<\/a> [cond-mat.str-el]<\/td>\n<\/tr>\n<tr>\n<td class=\"tablecell label\"><\/td>\n<td class=\"tablecell arxividv\">(or <span class=\"arxivid\"><a href=\"http:\/\/arxiv.org\/abs\/1506.02672v1\">arXiv:1506.02672v1<\/a> [cond-mat.str-el]<\/span> for this version)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<ul class=\"kent-social-links\"><li><a href='http:\/\/www.facebook.com\/sharer.php?u=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/&amp;t=Quantum mechanics of magnetic moments in spin ice' target='_blank'><i class='ksocial-facebook' title='Share via Facebook'><\/i><\/a><\/li><li><a href='http:\/\/twitter.com\/home?status=Quantum mechanics of magnetic moments in spin ice%20https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/' target='_blank'><i class='ksocial-twitter' title='Share via Twitter'><\/i><\/a><\/li><li><a href='https:\/\/plus.google.com\/share?url=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/' target='_blank'><i class='ksocial-google-plus' title='Share via Google Plus'><\/i><\/a><\/li><li><a href='http:\/\/linkedin.com\/shareArticle?mini=true&amp;url=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/&amp;title=Quantum mechanics of magnetic moments in spin ice' target='_blank'><i class='ksocial-linkedin' title='Share via Linked In'><\/i><\/a><\/li><li><a href='mailto:content=https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/&amp;title=Quantum mechanics of magnetic moments in spin ice' target='_blank'><i class='ksocial-email' title='Share via Email'><\/i><\/a><\/li><\/ul>","protected":false},"excerpt":{"rendered":"<p>Bruno recently posted the first paper resulting from his PhD thesis to the preprint archive. In it we take the first steps towards a microscopic &hellip; <a href=\"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/2015\/06\/25\/quantum-mechanics-of-magnetic-moments-in-spin-ice\/\">Read&nbsp;more<\/a><\/p>\n","protected":false},"author":976,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[597],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/posts\/1349"}],"collection":[{"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/users\/976"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/comments?post=1349"}],"version-history":[{"count":4,"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/posts\/1349\/revisions"}],"predecessor-version":[{"id":1354,"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/posts\/1349\/revisions\/1354"}],"wp:attachment":[{"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/media?parent=1349"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/categories?post=1349"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.kent.ac.uk\/strongcorrelations\/wp-json\/wp\/v2\/tags?post=1349"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}