Structural glasses are usually formed by cooling a viscous

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1 Mgnetic imging of supercooling glss trnsition in wekly disordered ferromgnet WEIDA WU,, CASEY ISRAEL, NAMJUNG HUR *, SOONYONG PARK, SANG-WOOK CHEONG AND ALEX DE LOZANNE Deprtment of Physics, University of Texs, Austin, Texs 787, USA Deprtment of Physics nd Astronomy nd Rutgers Center for Emergent Mterils, Rutgers University, Pisctwy, New Jersey 8854, USA *Present ddress: Deprtment of Physics, Inh University, Incheon 475, South Kore e-mil: Pulished online: 8 Octoer 6; doi:.8/nmt74 Spin glsses re founded in the frustrtion nd rndomness of microscopic mgnetic interctions. They re non-ergodic systems where replic symmetry is roken. Although mgnetic glssy ehviour hs een oserved in mny colossl mgnetoresistive mngnites, there is no consensus tht they re spin glsses. Here, n intriguing glss trnsition in (L,Pr,C)MnO is imged using vrile-temperture mgnetic force microscope. In contrst to the speculted spin-glss picture, our results show tht the oserved sttic mgnetic configurtion seen elow the glss-trnsition temperture rises from the coopertive freezing of the first-order ntiferromgnetic (chrge ordered) to ferromgnetic trnsition. Our dt lso suggest tht ccommodtion strin is importnt in the kinetics of the phse trnsition. This coopertive freezing ide hs een pplied to structurl glsses including window glsses nd supercooled liquids, nd my e pplicle cross mny systems to ny first-order phse trnsition occurring on complex free-energy lndscpe. Structurl glsses re usully formed y cooling viscous liquid fst enough to void crystlliztion t the liquid solid phse trnsition. Although this phenomenon hs een used for mny centuries, quntittive understnding of the glss trnsition is still mjor scientific chllenge. Recently, n nlogy hs een estlished etween the dynmics of structurl glsses nd tht of discontinuous spin glsses.however,itisstillnopen question whether structurl glsses nd spin glsses elong in the sme fmily. Spin glsses re disordered systems with frustrted mgnetic interctions tht result in the sence of conventionl long-rnge order 4,5. The spin-glss trnsition is one of the most intriguing prolems in condensed-mtter physics, where new type of order rises from reking n unusul symmetry: the replic symmetry. The spin-glss trnsition is signified y the devition of the zero-field-cooled (ZFC) susceptiility χ(t) from the field-cooled (FC) χ(t) t the glss-trnsition temperture, T G (refs 4,5). Historiclly, wider clss of hevily doped ferromgnets, for exmple, trnsition-metl lloys (CuMn, AuFe, FeAl nd so on) hve een termed cluster glsses or reentrnt spin glsses ecuse they show similr ehviour in χ(t) elow the ferromgnetic () trnsition 4 7. It is elieved tht the mgnetiztion of clusters freeze in rndom fshion elow the glss trnsition nd tht the mgnetiztion of ech cluster cts like n individul spin in spin glss, tht is, the mgnetiztion of ech cluster is free to rotte ove the glss temperture. Fundmentlly, cluster glss is type of spin glss 4. The most intriguing spect of these systems is the fct tht the stte ppers t higher temperture thn the glss stte, indicting tht the stte hs lrger entropy thn the glss stte. Mny colossl mgnetoresistive (CMR) mngnites, especilly those exhiiting phse seprtion, re considered to e disordered ferromgnets. In fct, spin-glss-like ehviour hs een found in mny CMR mngnites 8. It hs often een ssumed tht the isolted regions in phse-seprted mngnites ehve like the mgnetic clusters in cluster glsses, leding to oth CMR effects nd glssy ehviour 4,5. For exmple, recent experiments nture mterils VOL 5 NOVEMBER Nture Pulishing Group

2 Figure Zero-field imges of the sme re of the smple (8 8 μm ) tken t 6K., Topogrphy., M. The colour scle is nm for nd 5 mhz for. Severl smll droplets cn e seen emedded in the non-mgnetic ckground. The droplets rnge in size from roughly nm to μm. Although the mjority of the smller droplets re single domin, some of the lrger droplets rek up into multi-domin sttes (one is highlighted y the white dotted ox). The mgnetiztion of ech droplet is oriented rndomly. The droplets re rndomly distriuted on the surfce, lthough some of them seem to correlte with twin oundries (one is mrked y the lck dotted line) identified y polrized opticl microscopy. show tht L 5/8 y Pr y C /8 MnO (LPCMO) (y.4) hs clusterglss-like ehviour t low temperture,. However, relspce microscopic investigtion of the glss stte hs not een crried out to confirm the cluster-glss picture. Here, we crry out vrile-temperture mgnetic force microscope (VT-M) studies on single-crystl LPCMO (y = /8), composition in which micrometre-scle phse seprtion hs een oserved 6. The glssy ehviours of our smple hve een confirmed y trnsport nd mgnetiztion mesurements (see Supplementry Informtion, Figs S nd S). In contrst to the speculted cluster-glss picture, where rndomly distriuted clusters re expected to e seen, we found tht the smple hs very smll volume frction fter ZFC from room temperture to elow the glss-trnsition temperture, T G (Fig. ). The M imges lso show tht the volume frction does not chnge much even with the ppliction of T field (Fig. ). As the temperture pproches T G during T field-wrming (FW), more nd more non-mgnetic regions re converted to domins mostly long orthorhomic twin oundries (Fig. e). Ner nd just ove T G, the regions grow into n extensive stripe-like pttern, correlting with the shrp rise in ulk mgnetiztion nd the shrp decrese of resistivity. As the temperture is incresed further, the phse distriution pttern remins reltively constnt with some frction of the smple remining non-mgnetic (presumly the chrge-ordered () phse, which is ntiferromgnetic (A) elow 8 K (ref. )) over wide rnge of temperture, greeing with mgnetiztion nd resistivity dt. In contrst, during the FC FW process the locl phse configurtion nd therefore mgnetiztion nd resistivity re reltively sttic elow the trnsition (Fig. g,h). These M results nd the mgnetiztion dt (Fig. 4c) suggest tht the lowtemperture (T < T G ) phse-seprted sttes prepred y different thermodynmic pths rise from the coopertive, dynmic freezing of the first-order A() trnsition (Fig. 4). Figure shows typicl topogrphic imge nd the corresponding M imge t 6 K fter ZFC. The in situ resistnce is too lrge to mesure t 6 K. The mgnetic interction etween the M tip nd the smple cuses shift of the resonnt frequency of the M cntilever. The vrition of the frequency shift s the tip is scnned cross the smple forms the M imge, s descried in the Methods section. Fetures in the M imges come from the non-uniform field distriution ove the smple surfce generted y domins. There re severl smll droplets rnging in size from out nm to μm scttered in non-mgnetic mtrix, presumly the phse. Most of the droplets hve no correltion with surfce defects nd orthorhomic twin oundries (identified y polrized opticl microscopy). On the other hnd, the twin oundries ct s cler nucletion sites for the A() phse chnge, s shown elow. The mgnetiztion of the droplets is oriented rndomly. Some ig droplets hve multi-domin structure to lower their mgnetosttic energy. The smll frction of the phse grees well with the in situ resistnce mesurement nd ex situ oth superconducting quntum interference device (SQUID) nd resistivity mesurements. At low temperture fter ZFC, the phse persists unless field lrger thn the melting field is pplied 7. In Fig., we show series of M imges tken during n isotherml mgnetic field sweep t 6.8 K fter ZFC. During the initil upsweep of the field, no significnt increse of the frction is seen elow the melting field μ H m T. For fields ove.5 T, the mgnetiztion of ll the droplets is ligned with the externl field, n oservtion in greement with the low mgnetic nisotropy nd coercive field of three-dimensionl mngnites 8. As moderte field is lso enough to lign the M-tip moment with the externl field (s descried in the Methods section), the drk colour (negtive resonnt-frequency shift) in the M imges corresponds to n ttrctive interction etween the regions nd the M tip. At μ H m, the regions grow into stripe-like structures ligned prllel to the twin oundries s the mgnetiztion jumps up (Fig. c) nd the smple resistnce drops to mesurle vlue (see Supplementry Informtion, movie S). The phse recedes in stripe-like fshion t fields up to.5 T (see Supplementry Informtion, movie S), then disppers fter field increse to T (Fig. e). The fct tht the right colour is swept out of the M imges round μ H m gives further credence to our identifiction of the right colour s the phse. At T the smple is fully, with the exception of few smll regions proly pinned y defects. The smple then ehves like conventionl isotropic with sturtion field of roughly.5 T; susequent M imge tken t T (see Supplementry Informtion, movie S) shows no chnges in the stte of the smple. Figure shows two sets of M imges tken t two loctions on the smple during T FW fter ZFC nd T FC. For the ZFC FW process, imges tken from 5 to 6 K show no significnt chnges nd re omitted. Figure f shows the temperture dependences of the mgnetiztion of the smple in T field during FW fter ZFC nd FC. Compring M imges (see Fig. e nd g,h, nd Supplementry Informtion, movies S nd S, respectively) with mgnetiztion dt (Fig. f), we conclude tht the ulk mgnetiztion is good mesure of the volume frction of the phse t T. The ZFC dt in Fig. f show shrp rise in mgnetiztion from 5 to 5 K s M imges confirm significnt increse in the frction nd the in situ resistnce drops to finite vlue. The regions tend to grow into stripelike structures during the trnsition. For this choice of field ( T), some regions persist ove T G (right colour t the top centre of the frme in Fig. d nd e). In contrst to the M imges tken during ZFC FW, the FC-FW imges (Fig. g,h) spnning the sme temperture rnge show tht the locl phse configurtion is reltively sttic, greeing with the mgnetiztion dt in Fig. f. One common feture in oth the melting trnsition (Fig. ) nd the glss trnsition (Fig. ) is tht the domins form stripe-like fetures long orthorhomic twin oundries where lrge strin vrition is expected. It hs een suggested tht the micrometre-scle phse seprtion is cused y the 88 nture mterils VOL 5 NOVEMBER Nture Pulishing Group

3 c d e f 4 5 K d e M (μ B per f.u.) c 6.8 K μ H (T) Figure Isotherml mgnetic field dependence of M imges nd SQUID mgnetiztion. e, M imges of one re of the smple (7 7 μm ) t vrious mgnetic fields (out-of-plne) t 6.8 K fter ZFC. The dshed line in mrks the orthorhomic twin oundry seen in polrized opticl imges (see Supplementry Informtion, movie S). The field vlues (colour scles) of the imges re:,.t(8hz);,.6t(8hz);c,. T (5 Hz); d,. T (5 Hz); e,. T (5 Hz). f, Field dependence of the mgnetiztion (M versus μ H ) t 5 K. The filled circles re plced t the field vlues where the M imges were tken. The melting field is round T. As the melting field is pproched nd pssed, the M imges show regions (drk) ppering nd growing t the expense of the phse (right). regions form stripe-like structures prllel to twin oundries. With the ppliction of T field (e), ll of the phse in the M imge frme is converted to the phse, with the exception of few smll regions proly pinned y surfce defects. As the field is further lowered to T (see Supplementry Informtion, movie S), the smple stys mgneticlly sturted nd (lmost) fully. This grees with the mgnetiztion dt in f. c d e f 4 g T T G T ** h M (μ B per Mn) ZFC FC g d e h c T (K) T Figure M imges nd mgnetiztion. e,g,h, M imges tken t two loctions during FW ( T ) round T G fter ZFC ( e,6 6 μm )ndfc(g,h,7 7 μm ), respectively. The dshed lines in nd g mrk the orthorhomic twin oundries seen in polrized opticl imges (see Supplementry Informtion, movies S nd S). The mgnetic field is out-of-plne. The tempertures (colour scles) of the imges re:,6k(hz),, 9.4 K (7 Hz), c, K (7 Hz), d, 5.5 K (7 Hz), e, 8 K (4 Hz), g, 9 K ( Hz), nd h, 5 K ( Hz). f, Temperture dependence of the mgnetiztion (M versus T ) during FW fter ZFC (open circles) nd FC (open squres). The filled symols mrk the temperture of the corresponding M imges. The glss trnsition occurs round T G 5 K where the ZFC-FW curve rises shrply to pproch the FC-FW curve. The M imges tken cross the glss trnsition during FC-FW show reltively sttic phse pttern with lrge volume frction (which develops during FC). Some domins (right contrst) on the smple surfce re visile in these imges, indicting n incomplete trnsformtion to the stte. nture mterils VOL 5 NOVEMBER Nture Pulishing Group

4 4 T ( ρ) T **( ρ) T G ( ρ) T *(M) H H (T) μ T **(M) T G (M) PM H m Glss T (K) PM T * T G T C T ** T c 4.4 T d. T M (μ B per f.u.).75 T 5 K H H T.5 T 4 μ H (T) T * T G Figure 4 H T phse digrms nd M(H ) curves fter FC., Semi-logrithmic plot of H T phse digrm. See text for definitions of T C, T, T, T G nd H m. This phse digrm is constructed with the trnsport ρ(t ) nd SQUID mgnetiztion M(T ) dt in Supplementry Informtion, Figs S nd S. Here the filled symols re phse oundries defined y the mximum dρ/dt. The crossed open symols re oundries defined y the mximum dm/dt (the 5 K point is tken from the mximum of dm/dh of M(H ) in Fig. f). The dshed line is guide for the eye to extrpolte the supercooling line T (H ) to higher temperture.,aschemtich T phse digrm of LPCMO. The smooth red line from H m to T G ounds the frozen stte. The comintion of T G (H )ndt (H ) gives rise to non-monotonic hysteretic oundry. This oundry nd T define the hysteretic phse spce s mpped y isotherml field sweeps. The smll rrows crossing the hysteretic phse oundries indicte the direction of the vrition of T or H needed for oserving the corresponding phse oundry. The lue dshed line lelled () represents the therml pths of the isotherml field sweep (ZFC FW temperture sweep) shown in Fig. (Fig. ). c, M(H ) hysteresis fter cooling with vrious field vlues:,.5,.75,. nd.4 T. The strting mgnetiztion vlues increse systemticlly with cooling field vlues. This illustrtes tht the supercooling trnsition (T (H )) is interrupted systemticlly y the glss trnsition (T G (H )), s shown in d. d, Zoom-in of the phse digrm (mrked y pink dshed ox in )wheret G (H )ndt (H ) intercept. The htched re round T (H ) represents the finite trnsition width of the supercooling trnsition. The dshed pink lines represent the therml pths with different cooling fields (H > H > ). The supercooling trnsitions t different fields re interrupted y T G (H ) systemticlly so tht the system ends up with different volume frctions, tht is, different mgnetiztion vlues. ccommodtion strin rising from the lttice mismtch etween the metllic phse (pseudo-cuic) nd the insulting phse (orthorhomic) 9. This point of view is supported y oth experiments nd simultions,,. The correltion etween the nucletion nd growth of domins nd orthorhomic twin oundries suggests tht the ccommodtion strin is importnt in the kinetics of the phse trnsition. The nisotropic pttern of the formtion of the phse cn lso e understood y the nisotropic nture of the strin interction. It hs een shown tht the long-rnge nd nisotropic nture of the strin interction could generte complex lttice distortion texture spontneously, leding to complex free-energy lndscpe. It is likely tht the coopertive strin interctions frustrte the first-order phse trnsition in LPCMO. Figure 4 shows n H T phse digrm for LPCMO constructed from the trnsport nd mgnetiztion dt (see Supplementry Informtion, Figs S nd S). Figure 4 is proposed schemtic phse digrm sed on M studies nd Fig. 4. The thermodynmic first-order A() to phse trnsition t T C hs positive slope (dh/dt > ). The supercooling (superheting) trnsition tempertures re represented y T (T ). It is worth noting the hysteretic nture of T (T ); its definition/oservtion is only vlid during cooling (wrming). Between T nd T there is hysteretic region where two phses cn coexist. The ssumed glss-trnsition temperture T G is slightly ove T t zero field. Below T G, the relxtion is significntly slowed down nd eventully stopped, (see Supplementry Informtion, Fig. S), tht is, the phse trnsition is frozen, creting non-ergodic low-temperture stte. This metstle stte collpses with the ppliction of lrge enough mgnetic field μ H m. The comintion of T G (H) nd T (H) produces non-monotonic oundry of hysteretic phse spce. 884 nture mterils VOL 5 NOVEMBER Nture Pulishing Group

5 To illustrte the frozen sttes, we mesured the mgnetiztion M(H) (Fig. 4c) fter cooling in vrious fields to 5 K. The initil mgnetiztion of the smple increses systemticlly with the cooling field vlues, indicting n incomplete A() to trnsition interrupted y the glss trnsition s illustrted in Fig. 4d. For ech vlue of the cooling field, the metstle stte collpses to the phse t the sme μ H m s indicted y the shrp rise of the mgnetiztion round T (ref. 7). These nonergodic sttes in LPCMO re orn from the kinetic freezing of the first-order supercooling trnsition, implying tht the glss trnsition in LPCMO is supercooling glss trnsition tht is proly similr to tht of structurl glsses. Structurl glss trnsitions hve een studied in viscous liquids, polymers nd colloidl systems. Despite intensive studies, it is not cler whether this glss trnsition is true phse trnsition lurred y dynmicl effects, or just dynmic trnsition. In this work, we show tht kineticlly driven glss trnsition cn lso exist in the phse-seprted mngnite LPCMO. An emerging theme in the mngnite community is tht oth competing phses nd quenched disorder re needed to generte oth the CMR effect 5 nd mgnetic glssy ehviour 5. Yet it is under dete whether the CMR mngnites re spin glsses 4. Our M results show tht the glss stte in LPCMO is not spin-glss stte. Insted, it is tightly ssocited with the supercooled stte of the first-order A() to phse trnsition, where the kinetics of the phse trnsition is strongly influenced y the ccommodtion strin. Becuse the ionic sizes of L,Pr nd C re very similr, LPCMO is wekly disordered. It is likely tht in this wekly disordered system the ccommodtion strin, insted of quenched disorder, is responsile for the formtion of the complex free-energy lndscpe, where n extensive numer of metstle sttes re seprted y effectively infinite rriers. This self-generted complex free-energy lndscpe is one chrcteristic of structurl glsses. Recently, mgnetic glss stte hs een oserved in the doped ferromgnet CeFe,in which the kinetic rrest of the first-order to A trnsition gives rise to non-ergodic mgnetic stte 6. In principle, it is likely tht ny system with first-order phse trnsition occurring on complex free-energy lndscpe cn e quenched into nonergodic, presumly glssy stte. Our results suggest tht wekly disordered CMR mngnites re not conventionl spin glsses where quenched disorder is necessry. The dynmics of this type of mgnetic glsses my not e fundmentlly different from tht of structurl glsses. METHODS Single-crystl smples of LPCMO (y = /8) were synthesized in n opticl floting-zone furnce. One smple ws mechniclly cut, polished with. μm pper with wter, nd nneled in n O tmosphere t, C for h. The surfce orienttion is [] in orthorhomic nottion, or () in cuic nottion. The originl smple ws cleved into two pieces, one for SQUID mesurements nd one for VT-M nd trnsport mesurements. All the M imges were tken in our homemde instrument, which is inserted into superconducting mgnet efore scnning 7. The VT-M is interfced with Nnoscope III controller from Digitl Instruments. M imges were tken in frequency-modulted lift mode, in which the topogrphy nd M scn lines re interleved. The lift height rnged from to 4 nm. We used the sme lift height within ech set of M imges. It vries little etween different dt sets. For imges t different temperture, we mintined the sme lift height y compensting for the temperture dependence of the piezoelectric coefficients of the scnner tue. The M tip is coted with 5 nm Co 85 Cr 5, μ H C.5 T. The M tip is mgnetized so tht the tip moment is norml to the cntilever. The mgnetic interction etween the M tip nd the locl mgnetiztion of the smple cuses shift of the resonnt frequency of the M cntilever, which is recorded s the contrst in the M imges 7. Gold wires were ttched to the smple y silver pint for resistnce mesurements tken simultneously with the M dt. The M contrst mechnism is set forth in refs 8,9. Briefly, n ttrctive (repulsive) force on the M tip tht decys with distnce from the smple gives rise to negtive (positive) frequency shift. In the ZFC cse of Fig., the locl moments of ech of the regions hve reltively rndom orienttion so tht there re oth ttrctive (drk) nd repulsive (right) plces, depending on the specific mgnetiztion direction in ech region. In moderte mgnetic field, for exmple, T, the mgnetiztion of oth the regions in the smple nd the M tip re ligned with the externl mgnetic field. Therefore, the only force etween them is ttrctive; the drkest plces correspond to regions with the highest effective mgnetiztion, verging over volume eneth the surfce. The solute vlue of the resonnt frequency depends on temperture, so we generlly only show the vrition of the resonnt frequency in the M imges. At room temperture, LPCMO possesses n orthorhomic distortion wy from cuic symmetry nd forms so-clled orthorhomic twins. The opticl nisotropy of the orthorhomic lttice cn e used to identify different twin domins nd the twin oundries. By mtching lndmrks in opticl imges nd lrge re (normlly μm or lrger) topogrphic scns tken t room temperture, which contin the topogrphic regions tken simultneously with the M imges t low temperture, we re le to lign the M imges with polrized opticl imges, s shown in the ckground of the movies in the Supplementry Informtion. The twin oundries re mrked y the white dshed lines in the polrized opticl imges. 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Motome, Y., Furukw, N. & Ngos, N. Competing orders nd disorder-induced insultor to metl trnsition in mngnites. Phys.Rev.Lett.9, 674 (). 6. Chttopdhyy, M. K., Roy, S. B. & Chddh, P. Kinetic rrest of the first order ferromgnetic-to-ntiferromgnetic trnsition in Ce(Fe.96Ru.4) : formtion of mgnetic glss. Phys.Rev.B7, 84(R) (5). 7. Isrel, C., Hyun, C., de Loznne, A. L., Phrk, S. & Khim, Z. G. Compct vrile-temperture mgnetic force microscope with opticl ccess nd lterl cntilever positioning. Rev. Sci. Instrum. 77, 74 (6). 8. Alrecht, T. R., Grütter, P., Horne, D. & Rugr, D. Frequency modultion detection using high-q cntilevers for enhnced force microscope sensitivity. J. Appl. Phys. 69, (99). 9. Rugr, D. et l. Mgnetic force microscopy: Generl principle nd ppliction to longitudinl recording medi. J. Appl. Phys. 68, 69 8 (99). nture mterils VOL 5 NOVEMBER Nture Pulishing Group

6 . Isrel, C., Wu, W. & de Loznne, A. High-field mgnetic force microscopy s susceptiility imging. Appl. Phys. Lett. 89, 5 (6). Acknowledgements We thnk J. Mrkert for the use of his SQUID nd commercil SPM. We enefited from discussions with Q. Niu, P. Chikin, A. McDonld, P. Chndr nd P. Chddh. This work is supported y NSF DMR-8575 (A.dL.) nd NSF DMR-4568 (S.W.C.). Correspondence nd requests for mterils should e ddressed to A.dL. Supplementry Informtion ccompnies this pper on Author contriutions Crystl synthesis nd chrcteriztion: N.H., S.P. nd S.-W.C. VT M design nd construction: A.dL. nd C.I. Experiment design nd plnning: W.W., S.-W.C, C.I. nd A.dL. Dt cquisition nd nlysis: C.I. nd W.W. Competing finncil interests The uthors declre tht they hve no competing finncil interests. Reprints nd permission informtion is ville online t nture mterils VOL 5 NOVEMBER Nture Pulishing Group