Direct Imaging of Dynamic Glassy Behavior in a Strained Manganite Film
Worasom Kundhikanjana, Zhigao Sheng, Yongliang Yang, Keji Lai, Yue Ma, Yong-Tao Cui Michael A. Kelly, Masao Nakamura, Masashi Kawasaki, Yoshinori Tokura, Qiaochu Tang, Kun Zhang, Xinxin Li, Zhi-Xun Shen
DDirect Imaging of Dynamic Glassy Behavior in a Strained Manganite Film
Worasom Kundhikanjana,
1, 2
Zhigao Sheng,
3, 4
Yongliang Yang, Keji Lai, Eric YueMa, Yong-Tao Cui, Michael A. Kelly, Masao Nakamura, Masashi Kawasaki,
3, 6
Yoshinori Tokura3,
3, 6
Qiaochu Tang, Kun Zhang, Xinxin Li, and Zhi-Xun Shen Department of Applied Physics and Geballe Laboratory for Advanced Materials,Stanford University, Stanford, California 94305, USA School of Physics, Institute of Science, Suranaree University of Technology, Nakron Ratchasima, Thailand RIKEN Center for Emergent Matter Science (CEMS), Wako 251-0198, Japan High Magnetic Field Laboratory of Chinese Academy of Science, Hefei 230031,P.R. China and Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, P.R. China Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA Department of Applied Physics and Quantum Phase ElectronicsResearch Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan. State Key Lab of Transducer Technology, Shanghai Institute of Microsystem and Information Technology,Chinese Academy of Sciences, Shanghai 200050, China (Dated: September 4, 2018)Complex many-body interaction in perovskite manganites gives rise to a strong competition be-tween ferromagnetic metallic and charge ordered phases with nanoscale electronic inhomogeneityand glassy behaviors. Investigating this glassy state requires high resolution imaging techniqueswith sufficient sensitivity and stability. Here, we present the results of a near-field microwave micro-scope imaging on the strain driven glassy state in a manganite film. The high contrast between thetwo electrically distinct phases allows direct visualization of the phase separation. The low temper-ature microscopic configurations differ upon cooling with different thermal histories. At sufficientlyhigh temperatures, we observe switching between the two phases in either direction. The dynamicswitching, however, stops below the glass transition temperature. Compared with the magnetizationdata, the phase separation was microscopically frozen, while spin relaxation was found in a shortperiod of time.
A glass is formed by rapid cooling of a viscous liquid,resulting in a supercooled liquid with no crystallinity[1].Generally, such supercooled state can occur in manysystems with first-order phase transition. In these sys-tems, there are multiple competing states separated bya thermal barrier near the transition temperature. Byrapid cooling, the system can be trapped in the non-favorable state, resulting in slow relaxation and cool-ing rate dependent behaviors. Furthermore, the exis-tence of complex energy landscapes often leads to differ-ent low-temperature states even under the same coolingprocess, known as non-ergodicity. Perovskite mangan-ites are a good example of systems with such dynam-ics. In half-doped manganites, the transition from thecharge-ordered insulating state (CO-I) to the ferromag-netic metallic state (FM-M) is first-order in nature, whilethe energetic proximity between the two crystalline statesoften results a phase-separation[2, 3] with one of statesbeing metastable. The metastability gives rise to relax-ation behaviors [4, 5] and dependences on cooling his-tories [6–8]. Aspects of spin-glass-like behaviors are alsofound, such as frequency dependent AC susceptibility [9].The phase-separated (PS) state is also highly susceptibleto local parameters such as strain [10] and disorder [9].Many models for manganite glass were constructedusing macroscopic measurements[11]. However, the PSstate is necessary for understanding the physics of man-ganites [2]. Transport measurements, therefore, haveclear drawbacks. For example, macroscopic magneti- zation cannot distinguish intra domain relaxation fromphase switching [12]. Although the dynamics of PS statemay be inferred from the transports through a mangan-ite nanowire [13], but these measurements are limited toa narrow temperature range with sufficient conductiv-ity. To date, the PS state with distinct physical proper-ties has been visualized by various microscopy techniquessuch as scanning tunneling microscopy [14], electron mi-croscopy [15], photoemission spectroscopy [16], magneticforce microscopy [17, 18], and recently near-field mi-crowave impedance microscopy (MIM) [19]. However,most of these studies focus on the static phase-separation.Direct visualization of the dynamic behaviors in the PSmanganites is yet to be addressed.In this paper, we present the results of a MIM studyon a Pr . (Ca . Sr . (PCSMO) film. The high con-trast between the two electrically distinct phases allowsdetailed study of the PS states. The large field of viewand the high measurement stability enable tracking ofthe dynamic behavior of several FM-M domains in a widetemperature range and after different thermal histories.The strong dependence on cooling history and measure-ment time for the microscopic configurations of this PSfilm showed the non-ergodicity and relaxation behavior.Moreover, the dynamics of glassy behavior, driven andstrongly influenced by strain, stop evolving below thefreezing temperature.The sample is a 40 nm thick PCSMO [20–23] filmgrown on a (110) (LaAlO ) . (SrAl . Ta . O ) . (LSAT) a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n a b c d -0.53 -0.52 -0.51 -0.50 Q [ r . u . l .] -0.375 -0.370 -0.365 -0.360 -0.355 Q001 [r.u.l.] Q1-10 [r.u.l.]
LSAT 222 LSAT 310
12 K 50 K 130 K R ( Ω ) B per B’ per FM-M CO-Ips-glass ρ ( Ω c m ) film on LSAT (strained) film on CTO/STO (lattice-matched) ZFC-FW 1T T g B ( T ) PM-I (110) (110)(110)
200 nm
FIG. 1: (a) Reciprocal space map of the PCSMO film grownon LSAT. (b) Resistivity of the strained PCSMO/LSAT film(dotted-red) and a relaxed film on the CTO/STO substrate(dash-blue). The solid-black line was taken during field warm-ing after ZFC with B = 1 T. (c) Magnetoresistance afterZFC to 12 K, 50 K and 130 K. The full and empty circlesindicate B per /B ? per for the forward and backward sweeps,respectively. (d) B-T phase diagram constructed from B per and B ? per at various temperature. The insets show schematicviews of the film on LSAT (110) in each phase. Both PM-Iand FM-M phases have cubic structures, while the CO-I phaseis distorted orthorhombic. substrate by pulse laser deposition. In the X-ray recip-rocal maps, the (222) and (310) peaks of the film alignwith those of the LSAT substrate, indicating a coherentgrowth (FIG. 1 (a)). Atomic force microscopy image ofthe film shows a flat surface with atomic steps (inset ofFIG. 1(a)) and sporadic Mn O precipitates. At zeromagnetic ( B ) field, the resistivity measurement showsan insulating behavior at all temperatures (dotted-redcurve in FIG. 1(b)), with a transition from PM-I to CO-I at T co = 200 K (see the Supplemental Materials [24]for details). The FM-M state, on the other hand, canbe easily recovered by application of a small B ≈ /SrTiO (CTO/STO) with alattice constant of 3.826 ˚ A closer to the bulk PCSMO filmthan LSAT (3.869 ˚ A ) [25], the film becomes metallic atlow temperature (FIG. 1(b), dash-blue). The transportbehavior of PCSMO/LSAT is similar to bulk LPCMO[6–8, 17], where glassy PS state is found. Unlike bulkmanganites with accommodation strains [17], the PS inepitaxial films is strongly influenced by the strain from the substrate.In order to identify the glassy PS state, we constructedthe B − T phase diagram of the PCSMO film on LSATusing isothermal magnetoresistive curves obtained afterZFC to various temperatures. Examples of such curvesat 12, 50 and 130 K are given in FIG. 1(c). For T < B -fieldsshow a sharp transition to the metallic phase (percolationtransition), while the opposite is not seen when sweep-ing back to zero field (dotted-red and dash-blue curvesin FIG. 1(c)). At temperatures higher than 50 K, thetransition is smooth and the resistance returns back tothe original value with a hysteresis after sweeping backof the fields (solid-green curve). The B -field at the per-colation point during the forward sweeping ( B per ) grad-ually reduces from 12 K to 50 K and increases again athigher temperature. At T >
100 K, the backward sweep-ing curve shows a return to the high resistance state at B ? per . The B per and B ? per data points at various tem-peratures enclose the glass-like region (orange shaded re-gion) on the B-T phase diagram in FIG. 1(d). Outsidethis region, either the FM-M or CO-I states dominatethe system; while inside, a glassy mixture of the FM-Mand supercooled CO-I states is expected. In addition,the minimum Bper at 50 K indicates the freezing pointof the PS glass [8], i.e., the glass transition temperature, T g .Microscopic PS of manganites can be readily observedby MIM [19], which functions by sending a 1 GHz mi-crowave signal into a coaxial cantilever probe [26] andmeasuring the nanoscale sample impedance. FIG. 2(a)shows a schematic of the cryogenic MIM measurement[27] (top) and the equivalent lumped-element circuit(bottom). The real and imaginary parts of the MIM out-puts contain local conductivity information of the sam-ple, with a spatial resolution down to 50 nm. Mn O precipitates[28], which are always insulating within ourtemperature and field ranges, are present on the samplesurface and conveniently serve as landmarks. For thisstudy, the MIM response in the imaginary channel, whichis proportional to the tip-sample capacitance [29], is suf-ficient to identify the Mn O , CO-I and FM-M regions.We use false color map to label each region as black, red,and yellow, respectively [ ? ].We investigated the low temperature states after cool-ing at different rates. A fast cool down (FCD) at 8 K/minand a slow cool down (SCD) at 0.3 K/min, were employedto reach specific temperatures at which the images weretaken. FIG. 2b and 2c show representative images at12 K for FCD and SCD, respectively. The substantialFM-M fraction in the nominally insulating film is strik-ing. Indeed, careful image analysis (FIG. 2(g)) showsthat the FM-M states can occupy up to 40% of the sam-ple when cooling at zero field. This result indicates astrong competition between the two states even at zeroB-field. Interestingly, the presence of these FM-M clus-ters is not measurable in either the resistivity (FIG. 1(b))or the magnetization (Supplemental Materials [24]). The [001] [ ] fast slow10403020 FM-M Fraction %
T(K) e
12 K fast 12 K slow I b c g
12 K slow IIoverlap both only I only II f auto correlation da (110) LSAT PCSMO CO-I MIM tipFM-MCO-IMn O C LSAT R PCSMO C PCSMO C Mn3O4
FM-MCO-IMn O MIM output c oup l e r mixer FIG. 2: (top) Schematic of the MIM setup and (bottom) the equivalent circuit of the tip-PCSMO film interaction. The MIMresponses on the Mn3O4, CO-I and FM-M regions are colored in black, red, and yellow, respectively. (b) ? (d) From left toright, MIM images at 12 K after FCD, and after two SCDs. (e) Autocorrelation analysis of the SCD-I image, illustrating thepreferred alignment of FM-M domains along the [1-10] axis of the substrate. (f) Overlay of the domains from the two SCDs.All scale bars are 2 µ m. (g) FM-M fractions of the two processes as a function of temperature. former is expected for an FM-M faction below the perco-lation threshold [ ? ], and the latter is due to the randomorientation of macro-spins from the FM-M clusters [ ? ].By considering the crystal structure of each phase(FIG. 1(d)), we can explain how a slow cooling rateleads to fewer FM-M domains. At 200 K, the transi-tion from PM-I to CO-I is accompanied by a structuralphase transition [22, 30]. This process is likely to behighly viscous, and some PM-I regions may directly en-ter the FM-M rather than the CO-I phase; thus moreFM-M domains are found at low temperature under afast cooling process. Furthermore, in FIG. 2e, the au-tocorrelation analysis of the SCD images shows the ten-dency of FM-M domains to elongate along the [1¯10] axisof the substrate, suggesting stronge influences from thelocal domain structure [10, 19]. In addition, comparedto the metallic behavior in the unstrained film on theCTO/STO substrate, we believe that the PS glassy statein the strained film on a LSAT substrate is mainly in-duced by substrate elastic strain.The SCD state has noticeably fewer FM-M domainsthan that after FCD. Interestingly, while the percentageof area occupied by the FM-M domains are about thesame for the two identical SCDs, the MIM images showdifferent FM-M domain configurations. In FIG. 2(f), twoSCD images are overlaid for comparison, with about 50% of the FM-M domains appearing at different locations.The overlapped domains are likely pinned by intrinsicdefects [ ? ], while the random appearance of the rest isa clear evidence of the non-ergodicity.The observed PS states are far from being static, asshown in the relaxation of the PS state after zero-fieldcooling (ZFC) [4, 5, 12]. Before each cooling, the sam-ple was warmed up to 250 K, above the charge-ordertemperature T co , to remove the impact of any prior his-tory. The cooling rate was kept at 8 K/min. FIG. 3(a)shows images after ZFC to various temperatures aboveand below T g . Repeated scans on the same area showdrastic changes in the PS at T >
20 K (FIG. 3(b)). Af-ter a waiting time of 4 hours at 50 K, the FM-M domainsgrew from 40% to 50%. More importantly, many FM-Mdomains appeared at different locations even though thechange in FM-M percentage was small. In other words, asimple measure of the areal fraction (FIG. 3(c) inset) can-not capture the dynamics here. Such dynamical behaviorcan be illustrated by overlapping the FM-M domains be-fore and after the holding period at 70 K, as shown inFIG. 3(d). On the other hand, the images taken at 12K show no change after 18 hours. The microscopic rear-rangement can be numerically studied by calculating thecross-correlation coefficient r xy between the images be-fore and after the 4-hour interval. As shown in the inset
12 K18 hours a
50 K 70 K4 hours 4 hours frozen o v e r l ap K both only before only after b dynamic r xy c T(K)
FM %0.60.40.20.0 12080400 d FIG. 3: (a) and (b) MIM images after FCD and waiting for several hours at 12, 50 and 70 K, respectively. (c) Cross-correlationcoefficient r xy as a function of temperature, showing a sharp jump of r xy at T g
20 K. The inset summarizes the FM-M fractionsbefore (solid) and after (empty circle) a holding time of 4 hours. (d) Overlap of the two images at 70 K, showing the emergenceof a number of new FM domains, and the disappearance of previously existing domains. All scale bars are 2 µ m. of FIG. 3(c), r xy is small ( ≈ B -field [5] (FIG.4(a)). The sample was again prepared by ZFC to thedesired T before turning on the B -field. A field of 2.4T induced a significant portion of FM-M phases at alltemperatures. Immediately after its removal, however,very different behaviors occurred at different tempera-tures. For T < T g , the PS was frozen with virtually nochange in its configuration 18 hours after switching offthe field. In contrast, dynamic behavior was observed athigher temperatures. At 50 K, no obvious change wasobserved right after turning off B , while the insulatingregions expanded after one day. The relaxation was muchfaster at 70 K, where large changes happened right afterfield removal and continued for several hours. For highenough T = 120 K, the relaxation back to the zero-fieldstate was faster than our imaging time, so little varia-tion can be seen after another hour of waiting. FIG. 4(b) summarizes the measured FM-M fraction through-out this process. Using the FM-M fraction as a functionof time (FIG. 4(c) inset) and assuming a logarithmic timedependence [4], we can extract the relaxation time as afunction of temperature (Supplemental Materials [24]).As seen in FIG. 3(c), the relaxation time, on the orderof several hours, diverges when approaching T g . On theother hand, the magnetization dropped by almost half(FIG. 4(d)) immediately upon field removal even at 12K.In other words, a sizeable amount of spins in the FM-M clusters are still able to randomize even though thecluster itself is frozen.In summary, microwave microscopy study of PCSMOfilm on LSAT reveals a PS texture with non-ergodicityand relaxation behavior, which are the key hallmarks ofa glassy state. The glassiness is driven by phase compe-tition and strongly influenced by the tensile strain fromthe substrate, resulting in preferential alignment of theFM-M domains. The microscopic configurations of PSstates highly depend on the cooling history and differeven after the same cooling process. The PS exhibitsdynamic behavior such as growing and shrinking of theFM-M domains, but the relaxation virtually stops below B e f o r e B = . T B = T , A f t e r A f t e r + T i m e
12 K
18 hrs
50 K
22 hrs
70 K
120 K a F M %
12 K 50 K70 K100 K120 K τ ( hou r)
840 12080400T(K) frozenPS c
12 K50 K70 K100 K120 K
Time(hr) b F M - M F r a c t i on % M ( µ B / M n ) d
12 K
B off B on B off
FIG. 4: (a) MIM images taken at B = 0 T (before), B = 2.4 T, B = 0 T (after) and after several hours at the same condition(After + Time) at T = 12, 50, 70, and 120 K, respectively.All scale bars are 2 µ m (b) FM-M vs time showing the fractionbefore, at B =2.4 T, turning of the B -field at different T. (c) Relaxation time as a function of temperature calculated from anexponential fit of FM-M vs time (d) Magnetization as a function of time. The B field is applied at time zero and removed after4 hours. The arrows indicate where the MIM images were taken.. the freezing temperature. The freezing behavior is seenin the rapid growth in cross correlation coefficient fromthe time dependence images and the relaxation time con-stant from the ferromagnetic domain areal fraction. Bydemonstrating a route to visualize and quantify quantumglassy states, this work should facilitate further investi-gation of electronic phase separation systems. Acknowledgements
We thank Daniel S. Fisher for stimulating discussions.The measurement work done at Stanford University is supported by NSF grants DMR-0906027, the probe de-velopment is supported by the Center of Probing theNanoscale NSF PHY-0425897 and the Gordon and BettyMoore Foundation through Grant GBMF3133 to ZXS.The work done in RIKEN was supported by JSPS FIRSTprogram. [1] P. G. Debenedetti and F. H. Stillinger, Nature (6825), 259 (2001), ISSN 0028-0836.[2] E. Dagotto, T. Hotta, and A. Moreo, Physics Reports (1-3), 1 (2001), ISSN 0370-1573.[3] E. Dagotto, J. Burgy, and A. Moreo, Solid State Commu-nications (1-2), 9 (2003), ISSN 00381098, 0209689.[4] M. Sirena, L. B. Steren, and J. Guimpel, Physical ReviewB (10), 104409 (2001), ISSN 0163-1829.[5] J. L´opez, P. Lisboa-Filho, W. Passos, W. Ortiz, F. Araujo-Moreira, O. de Lima, D. Schaniel, andK. Ghosh, Physical Review B (22), 224422 (2001),ISSN 0163-1829.[6] L. Ghivelder and F. Parisi, Physical Review B (18),184425 (2005), ISSN 1098-0121.[7] P. Sharma, S. Kim, T. Koo, S. Guha, and S.-W. Cheong,Physical Review B (22), 224416 (2005), ISSN 1098-0121.[8] P. a. Sharma, S. El-Khatib, I. Mihut, J. B. Betts, a. Migliori, S. B. Kim, S. Guha, and S.-W. W. Cheong,Physical Review B (13), 134205 (2008), ISSN 1098-0121.[9] Y. Tomioka and Y. Tokura, Physical Review B (1), 1(2004), ISSN 1098-0121.[10] K. H. Ahn, T. Lookman, and A. R. Bishop (December 2003), 401 (2004).[11] J. Sacanell, F. Parisi, J. Campoy, and L. Ghivelder, Phys-ical Review B (1), 014403 (2006), ISSN 1098-0121.[12] I. Deac, S. Diaz, B. Kim, S.-W. Cheong, and P. Schiffer,Physical Review B (17), 174426 (2002), ISSN 0163-1829.[13] T. Z. Ward, Z. Gai, H. W. Guo, L. F. Yin, and J. Shen,Physical Review B - Condensed Matter and MaterialsPhysics (12), 1 (2011), ISSN 10980121.[14] M. F¨ath, S. Freisem, A. A. Menovsky, Y. Tomioka,J. Aarts, and J. A. Mydosh, Science (5433), 1540(1999).[15] J. Q. He, V. V. Volkov, T. Asaka, S. Chaudhuri, R. C.Budhani, and Y. Zhu, Physical Review B (22), 224404(2010).[16] M. Burkhardt, M. Hossain, S. Sarkar, Y.-D. Chuang,A. Cruz Gonzalez, A. Doran, A. Scholl, A. Young,N. Tahir, Y. Choi, S.-W. Cheong, H. D¨urr, et al. , PhysicalReview Letters (23), 237202 (2012), ISSN 0031-9007.[17] W. Wu, C. Israel, N. Hur, S. Park, S.-W. Cheong, andA. de Lozanne, Nat Mater (11), 881 (2006), ISSN 1476-1122.[18] R. Rawat, P. Kushwaha, D. K. Mishra, and V. G. Sathe,Physical Review B (6), 064412 (2013), ISSN 1098-0121.[19] K. Lai, M. Nakamura, W. Kundhikanjana, M. Kawasaki,Y. Tokura, M. A. Kelly, and Z.-X. Shen, Science (5988), 190 (2010).[20] N. Takubo, Y. Ogimoto, M. Nakamura, H. Tamaru,M. Izumi, and K. Miyano, Physical Review Letters (1),017404 (2005), ISSN 0031-9007.[21] Z. Sheng, M. Nakamura, F. Kagawa, M. Kawasaki, andY. Tokura, Nature communications (May), 944 (2012),ISSN 2041-1723.[22] Y. Wakabayashi, H. Sagayama, T. Arima, M. Nakamura,Y. Ogimoto, Y. Kubo, K. Miyano, and H. Sawa, PhysicalReview B (22), 2 (2009), ISSN 1098-0121.[23] D. Okuyama, M. Nakamura, Y. Wakabayashi, H. Itoh,R. Kumai, H. Yamada, Y. Taguchi, T. Arima,M. Kawasaki, and Y. Tokura, Applied Physics Letters (15), 152502 (2009), ISSN 00036951.[24] Supplemental Materials (????).[25] Y. Tomioka and Y. Tokura, Physical Review B (10),104416 (2002), ISSN 0163-1829.[26] Y. Yang, K. Lai, Q. Tang, W. Kundhikanjana, M. A.Kelly, K. Zhang, Z.-x. X. Shen, and X. Li, Journal ofMicromechanics and Microengineering (11), 115040(2012).[27] W. Kundhikanjana, K. Lai, M. A. Kelly, and Z.-X. Shen,Review of Scientific Instruments (3), 033705 (2011),ISSN 00346748.[28] T. Higuchi, T. Yajima, L. F. Kourkoutis, Y. Hikita,N. Nakagawa, D. a. Muller, and H. Y. Hwang, AppliedPhysics Letters (4), 043112 (2009), ISSN 00036951.[29] K. Lai, W. Kundhikanjana, M. A. Kelly, and Z. X.Shen, The Review of Scientific Instruments (6), 063703(2008), ISSN 0034-6748.[30] Y. Wakabayashi, H. Sawa, N. Takubo, M. Nakamura, Y. Ogimoto, and K. Miyano (????). Supplemental MaterialsS1. PCSMO films on LSAT (110) and CTO/STO(110) Comparision
Two high qualities Pr0.55(Ca1-ySry)0.45MnO3 (PC-SMO) with y = 0.25 films growth on LSAT andCTO/STO substrates are characterizing by X-ray recip-rocal mapping, resistivity and magnetization measure-ments. FIG. S1(a) is reciprocal space map of the PCSMOfilm on LSAT. The (222) and (310) peaks of the filmalign with the LSAT substrate. The widths of diffrac-tion peaks of film along lateral direction, correspondingto the omega scan of crystal, are comparable to those ofsubstrates suggesting a coherent growth and high qual-ity film. In FIG. S1(b), the ZFC-FW resistivity curvesin different magnetic fields show the reentrance of the in-sulating state, similar to another bi-critical phase man-ganite (La,Pr) . Ca . MnO (For example, PRB ,224416(2005)). S1(c), magnetization as a function oftemperature for ZFC-FW (black), FC (green) and, FC-FW (red) at 0.01 T. The magnetization was negligibleduring the ZFC, but could go up to 3.5 µ B /Mn dur-ing the FW if magnetic field of 5 T was used. PCSMOfilm on LSAT substrate is quite different from a film onCTO/STO and a bulk sample.The PCSMO film on CTO/STO substrate behavesrather similar to the bulk sample. FIG. S1(d) shows re-ciprocal space map of the PCSMO film on CTO/STOshows the large deviation from that on the LSAT sub-strate. Further analysis indicates that the film onCTO/STO is almost relaxed and lattice parameter isquite close to that of bulk case. The resistivity mea-surements in FIG. S1(e) indicate that the film on theCTO/STO substrate is metallic at low temperature.FIG. S1(f), Magnetization curve taken during ZFC-FW,FC, FC-FW are the same and no reentrance behavior isobserved. The absence of the insulating behavior in theCTO/STO film indicates the influence of the substrateon the properties. The lattice constant of CTO in a cu-bic convention is 3.826 ˚ A , closer to that of the PCSMOlattice (PRB , 104416 (2002)), while the lattice con-stant of LSAT is larger, 3.869 ˚ A . We called the film onCTO/STO a relaxed film and on LSAT a strained film.The results shown above imply that the tensile strainfrom the LSAT substrate favors the formation of CO-Iphase in PCSMO films with FM-M matrix. The coexis-tence and competition of and the CO-I and FM-M phasesin strained film might be responsible for the existence ofglassy behavior. FIG. S1: Characterization of PCSMO films on LSAT andCTO/STO (110) substrates
S2. Properties of PCSMO film on LSAT
This section focuses on the properties of the PCSMOfilm on LSAT. FIG. S2(a) shows resistivity( ρ ) as a func-tion of temperature taken during the FC-FW cycle atB = 0, 3, and 9 T. Cooling the sample under the mag-netic field induced the FM-M states at low temperature. FIG. S2: (a) Temperature dependence of resistivity ( ρ ) invarious magnetic fields for the PCSMO film on LSAT. (b)∆( lnρ ) / ∆(1 /T ) is plotted as a function of temperature. FIG. S3: PCSMO films on LSAT substrates showing atomicstep terrace between the Mn3O4 particles.
Transition from PM-I to CO-I at high temperature is lessobvious in the PCSMO film than in the bulk. To iden-tify the transition point, we plot ∆( lnρ ) / ∆(1 /T ) as afunction of temperature (APL ,152502 (2009)) in FIG.S2(b). The anomaly at the PM-I to CO-I transition isseen around 200 K.FIG. S3 shows AFM images of the strained PCSMOfilm. There are Mn O precipitates on the film sur-face and the regions between the precipitates are flatwith clear step and terrace structures. Similar precip-itates were also seen in the film on CTO/STO substrate.The presence of Mn O particles implies neither off-stoichiometry films nor different stoichiometry betweenthe films on different substrates. As shown in FIG. S1(a),the PCSMO films are well clamped onto the LSAT sub-strate and the narrow diffraction point indicates the highcrystalline quality of our films. Moreover, the flat surfacewith clear step and terrace structures between the pre-cipitates also suggests the high crystal quality of strainfilms (FIG. S3). The PCSMO films on both LSAT andCTO/STO were grown with same conditions with simi-lar topographical features. The relaxed PCSMO film onCTO/STO substrate, despite some precipitates, behavessimilarly to the bulk indicating correct stoichiometry. S3. Image analysis
This section explains the procedure for extracting theareal fraction of the FM-M domains, performing the au-tocorrelation analysis, overlaying two MIM images, andcalculating the cross correlation coefficient.The areal fraction of the FM-M domains was obtainedby the following procedure.1. Divide the MIM image into 10 ×
10 pixels images.2. Find a local maximum corresponding to the do-mains of each images.3. Put the images back together to obtain the imagein S4(b).
FIG. S4: Method for extracting the FM-M fraction.FIG. S5: Method for autocorrelation analysis.
4. Domains smaller than 20 pixels in size were consid-ered noise and were removed resulting in the imagein S4c.5. Using the same procedure, we extract the areacover by Mn O particles S4(d), where states un-derneath are unknown.6. The FM-M fraction was obtained by counting thenumber of the white pixels in c, and divided bynumber of the black pixels in S4(d).In order to show the preferential orientation of the FM-M domain, we performed autocorrelation analysis. Theautocorrelation analysis presented in the main text wasobtained with the following method. The metallic do-mains were extracted from FIG. S5(a) (a MIM image at12 K after a slow cool down) using a crude thresholdvalue, resulting in the black-white image in FIG. S5 (b).Autocorrelation image is shown in FIG. S5 (c). FIG.S5 (d), Plot of the linecuts along the vertical (blue) andhorizontal (red) lines of the autocorrelation. The char- FIG. S6: Overlap of the FM domains, and cross correlationcoefficient at 12 K. acteristic length along the [1¯10] and [001] axes were ob-tained by fitting exponential functions to the vertical andhorizontal linecuts.To illustrate the change of the FM-M domains beforeand after waiting, we overlaid two MIM images usingthe following procedure. Using FIG. S6(a), MIM imagesat 12 K after the two slow cool downs, as an example,the images were first aligned by optimizing the standardcross-correlation coefficient of the raw images. We thenextracted the black-and-white images showing only theFM-M domains before overlaying them on top of eachother. White, blue and red colors are assigned to theregion appeared in both images, only the first and onlythe second images accordingly. The overlaying methodis also useful for observing the relaxation of the FM-Mdomains.To further quantify the similarity of two MIM images,we calculated the cross correlation coefficient ( r xy ). The r xy calculation also employed the black-and-white imagesto prevent artifact from the MIM signal variation in theactual images. The white region is assigned the value 1and the black region the value -1. The r xy is computedfrom the sum of the dot product of these two images,divided by the number of pixels in the image. FIG. S7: Time dependence FM-M fraction and relaxationtime.
S4. Relaxation time
FIG. (a) plots the FM-M fraction as a function of time(+) where the lines are exponential fits using (a) plotsthe FM-M fraction as a function of time (+) where thelines are exponential fits using M ( t ) = M + Ae − ( t − t /τ (1)Although most transport studies ( for example PRB , 104409 (2001)) prefer fitting magnetziation data withan logaritmic function, we choose a exponential func-tionin our fit. This is because the data points from ourscans were taken at an hour apart, which is a coarse timescale compared to the transport data. The scanning datacaptures a slow relaxation process and is suitable for anexponential fit. The relxation time τ is plotted as a func-tion of temperature in FIG. (b). The purple line is justa guide to the eyes. Fitting temperature dependent re-laxation times with either the Vogel-Fulcher law or thepower law causes large error due to few data points; andthus is omitted here.0 S5. Gradual Colorscale Images1