Dirty frustrated magnets: order from disorder and disorder by disorder. Mike Zhitomirsky (CEA-Grenoble)
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1 Drty frustrated magnets: order from dsorder and dsorder by dsorder Mke Zhtomrsky (CEA-Grenoble)
2 Outlne collaborators: Order from dsorder V. Maryasn (UJF & CEA) vacances n trangular AF: lftng degeneracy n magnetc feld unfed theory of thermal/quantum and quenched fluctuatons Dsorder by dsorder H. Tsunetsugu (IP) frustrated ferro/antferromagnetc chan: feld-nduced spn glass
3 Introducton Magnetc frustraton: competng nteractons classcal degeneracy Dsorder: fluctuatons n regular spn models thermal effects tuned by T quantum effects turned by ħ or Dsorder: structural dsorder bond dsorder (magnetoelastc, chemcal, ) ste dsorder (vacances, nonmagnetc mpurtes, )
4 Impurtes n magnetc solds: nusance or useful epermental tool? ultmate probe for unconventonal C local spn polaraton probed by NMR, Zn-Cu substtuton n hgh-t c cuprates mpurty-nduced tetures n spn lquds, QC states achdev et al; en et al; Vota et al. r 2 RuO 4 eample of new states n frustrated magnets
5 Part I Order from structural dsorder
6 Frustrated lattces trangular (2D) kagomé (2D) pyrochlore (3D) garnet or hyper-kagomé (3D) and many more
7 Order from dsorder n a nutshell Vllan et al (1980), hender (1982) spontaneous symmetry breakng (Mecan hat potental) accdental degeneracy: by A. Tsvelk quantum fluctuatons: 1 E k 2 k thermal fluctuatons: F T ln k k
8 Impurty n J 1 -J 2 AFM J 1 ground states for : 2 2 J1 (,0) ( 0, ) degeneracy between and states vacancy n one sublattce creates uncompensated moment and a local feld on the other sublattce orthogonal or antcollnear sublattce orentaton Henley (1989), Weber & Mla (2012) local-feld approach s not unversal Z 2 symmetry s preserved
9 Effectve Hamltonan: thermal and quantum dsorder Hˆ transformaton to the rotatng local frame J J y y cos ( ) sn ( ) real-space perturbaton theory (lnked-cluster epanson) ˆ 0 H h loc Vˆ J y y cos thermal fluctuatons quantum fluctuatons 2 2 (2) T 2 (2) J 2 F (1 cos ) E (1 cos ) 2h loc 8 h loc Heff ~ ( 2 ) negatve bquadratc echange most collnear states
10 Hesenberg trangular AF n eternal feld classcal degeneracy, H 3J 1 3 Hs = = Monte Carlo phase dagram: effect of thermal fluctuatons: < < Kawamura & Myashta (1985), Gvodkova et al (2011)
11 Effectve Hamltonan: structural dsorder Hˆ transformaton to the rotatng local frame J J y y cos ( ) sn ( ) o bond dsorder: E 2 J 2 2h loc J J J o ste dsorder: wth p 0 or 1; sn then J p ( 1p ) 2 p p ( p ) n mp Heff ~ ( 2 ) postve bquadratc echange least collnear states
12 Dluted trangular AF n eternal feld Monte Carlo phase dagram: > > 5% of vacances vs Maryasn & MZ (2013)
13 Order versus dsorder antferromagnetc OP M Q concal M Q e Q r c ; coplanar M Q T = 0 versus spn-glass OP q EA 2 c spn-glass?
14 Part II dsorder n frustrated spn chan
15 Hgh-feld nematc state n frustrated spn chan bound magnon pars out of competng ferro/antferromagnetc echanges spn-nematc phase n LCuVO 4? 2 f Chubukov (1991), Tsunetsugu & MZ (2010) vstov et al (2011)
16 Bound magnon state on a vacancy: 1D Tsunetsugu & MZ, unpublshed 1-magnon chroednger equaton
17 Bound magnon state on a vacancy: D > 1 2D array of J 1 -J 2 chans 3D model for LCuVO 4
18 Mke Zhtomrsky Impurtes Localed magnons and M(H) spn-glass M step for solated vacances, M g Bn mp shoulder for mpurty band Buettgen et al, unpublshed spn-nematc? H H s mp H s
19 Outlook structural dsorder n frustrated magnets nduces an opposte OBDO compared to thermal/quantum fluctuatons. nterstng phase dagrams, controled mpurty dopng for swtchng chralty, beyond 2 nd order: pyrochlore Er 2 T 2 O 7 (no magnetc feld s needed) feld-nduced spn glass state n ferro/antferromagnetc chan, other models? but, spn-nematc n LCuVO 4 stll got a chance
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