Kinetically arrested long-range magnetic ordered phase. Alok Banerjee

Transcription

1 Kinetically arrested long-range magnetic ordered phase Alok Banerjee UGC-DAE Consortium for Scientific Research (CSR) (Formerly: Inter University Consortium for DAE Facilities) University Campus, Khandwa Road Indore-457, India. Acknowledgements: Praveen Chaddah S. B. Roy R. Rawat, Archana Lakhani Kranti Kumar, K. Mukherjee, A. K. Pramanik, S. N. Dash.

2 Outline :! Ideal Field- emperature induced magnetic first-order transitions! Disorder broadened first-order transitions in real systems.! Case study: broadened first-order transitions in manganites.! Anomaly in Field-emperature induced first-order transitions.! Coexisting phases at low temperature.! unable fractions of arrested phase with equilibrium phase at low-! Identification of low- equilibrium phase by CUF protocol.! Evidence of glass-like behaviour of the kinetically arrested phase.! Functionality arising from the glass-like phase! Remaining questions

3 Field-emperature induced first-order Phase ransition [Antiferromagnetic-Insulating (AF-I) to Ferromagnetic-Metallic (FM-M)] C * ** * * C ** AF-I FM-M FM-M AF-I C M FM-M M FM-M R AF-I AF-I ** R AF-I AF-I FM-M FM-M

4 Field and temperature induced First-order transition in Intermetallic doped CeFe Micro-all probe (scanning) S. B. Roy et al., Phys. Rev. Lett. 9, 47 ()

5 First-order magnetic transition in manganite Mesoscopic probe With spatial resolution Magnetic Force Microscopy Variation of ferromagnetic and antiferromagnetic phases + Metallic and insulating La. Pr.4 Ca. MnO L. Zhang et al., Science 98, 85 ()

6 Ideal - induced First-order phase transition Observed - induced First-order phase transition * C ** ** AF-I FM-M * * C ** C < C > C M FM-M * ** AF-I M. K. Chattopadhyay et al., Phys. Rev. B 68, 7444 ()

7 Broad first order AF-I to FM-M transition (* *) ( C, C ) (** **) (* *) ( C, C ) (** **) AF-I FM-M FM-M AF-I Disorder introduces spatial distribution in C which broadens the ( C, C ) line into a band consequently the (*, *) and (**, **) lines broadens into bands. Each region in the sample is represented by a line in the respective bands Y. Imry and M.Wortis, Phys. Rev. B 9, 58 (979).

8 (R -x A x )MnO Perovskite Manganites Where R + is the rare earth element and A + is alkaline earth element. MnO 6 Octahedron (R,A)-atom Perovskite (R/A)MnO

9 alf doped manganites R.5 A.5 MnO 5% Mn + & 5% Mn 4+ Pr.5 Sr.5 MnO, Nd.5 Sr.5 MnO, La.5 Ca.5 MnO, Pr.5 Ca.5 MnO etc. All are antiferromagntic (AF) - insulators (I). Magnetic Field induced Antiferromagnetic-insulating (AF-I) to Ferromagnetic-metallic (FM-M) transition

10 Pr.5 Sr.5 MnO Nd.5 Sr.5 MnO La.5 Ca.5 MnO Pr.5 Ca.5 MnO R. Kajimoto et al. Phys. Rev. B, 66, R84 (). Manganites around half-doping Field induced Antiferromagnetic-insulating (AF-I) to Ferromagnetic-metallic (FM-M) transition An increase in bulk magnetization of the sample can be interpreted as either increase of moment in FM-M phase, or as part transformation of AF-I to FM-M. A simultaneous measurement of magnetization and conductivity provides a clear choice between the two alternatives because of the orders of magnitude resistivity changes associated with the metal (M) to insulator (I) transition in the latter case. Relating to phase fractions

11 Pr.5 Ca.5 MnO Narrow bandwidth prototype charge ordered antiferromagnetic insulator system (About koe field is required transform the AF-I state to FM-M state through st order process) M. okunaga et al., Phys. Rev. B 57, 559 (998).

12 Pr.5 Ca.5 MnO Disorder in MnO 6 octahedron Mn site substitution Ionic size (structure) Non-Magnetic (no d-orbital) Pr.5 Ca.5 Mn.975 Al.5 O J. Phys.: Condens. Matter 6, 85 (4). Phys. Rev. Lett. 9, 74 (4). / f.u.) 4 ZFC 5K 5k ZFC - ρ ( k ohm cm ) 4 8 (koe) 6 9 (k Oe)

13 / f.u.) ρ ( k ohm cm) Pr.5 Ca.5 Mn.975 Al.5 O FCC 4 koe FCW FCC FCW 4 koe ( K ) /Mn) ρ (Ω-cm) Nd.5 Sr.5 MnO.8.4 = 5 Oe..6. = Oe 5 5 (K) Broad first order AF-I to FM-M transition 4. /f.u.) 5 K R (Ω). 5 K 4 8 (koe) (koe) Pr.5 Sr.5 MnO Field emperature induced broad first-order phase transition

14 Anomaly in st order AF-I to FM-M transformation / Mn) FCC FCW ZFC (K) koe / f.u.) FCW ZFC FCC 4 koe ( K ) Nd.5 Sr.5 MnO Pr.5 Ca.5 Mn.975 Al.5 O ρ (Ω cm).4. 4 ZFC FCW FCC 5 5 (K) koe ρ ( k ohm cm) - 4 koe ZFC FCC FCW ( K ).6 /f.u.) II Virgin (I) III 5 K 4 8 (koe) Pr.5 Sr.5 MnO R (Ω).4 Virgin (I). III 5 K. II (koe) Phys. Rev. B 74, 445 (6); J. Phys.: Condens. Matter 8, L65 (6);J. Phys.: Condens. Matter 9, 56 (7).

15 Anomaly in st order AF-I to FM-M transformation.4 FCW ZFC Nd.5 Sr.5 MnO (a).6 4 [a] Nd.5 Sr.5 MnO. ρ (Ω cm) / Mn). 4 ZFC ZFC ZFC FCW FCW FCC FCW FCC FCC FCC esla esla esla (K) esla (b).4. - / Mn) [b] 5 K K K 4 K 6 K 6 K 7 K 85 K K (esla) Not a Spin-Glass Not usual ferromagnet J. Phys.: Condens. Matter 9, 56 (7).

16 Anomaly in Field-emperature induced FOP alf doped manganites Nd.5 Sr.5 MnO (Single Crystal) Magetic Field (esla). Kuwahara, Y. omioka, A. Asamitsu, Y. Moritomo and Y. okura, Science 7, 96 (995)

17 Pr.5 Ca.5 Mn.975 Al.5 O /f.u.) K Initial (ZFC) Return cycle Next increasing cycle (esla) 5K 6 9 (k Oe) - ρ ( k ohm cm ) he half-doped CMR manganites have an important advantage that the conductivity changes drastically along with magnetic order (i.e. FM-M and AF-I) While a decrease of global magnetization in the sample can be interpreted as either a reduction of moment in the FM M phase, or as part transformation of FM M to an AF-I, a simultaneous measurement of conductivity provided a clear choice between the two alternatives because of the orders of magnitude resistivity changes associated with the metal (M) to insulator (I) transition in the latter case. Relating to phase fractions

18 Pr.5 Ca.5 Mn.975 Al.5 O /f.u.) K Initial (ZFC) Return cycle Next increasing cycle (esla) Soft ferromagnet /f.u.) (K) Incomplete first-order Magnetic transition R (kω.cm) (K)

19 Broad first order AF-I to FM-M transition (* *) ( C, C ) (** **) (* *) ( C, C ) (** **) AF-I FM-M FM-M AF-I Disorder introduces spatial distribution in C which broadens the ( C, C ) line into a band consequently the (*, *) and (**, **) lines broadens into bands. Each region in the sample is represented by a line in the respective bands Y. Imry and M.Wortis, Phys. Rev. B 9, 58 (979).

20 Pr.5 Ca.5 Mn.975 Al.5 O M ( µ B / f.u. ) Measured in 4 KOe While warming 5 5 ( K ) Cooling field in koe (ZFC) ρ ( k ohm cm ) - Measured in 4 koe While warming 5 5 ( K ) Cooling field in koe ZFC Coexistence of different fractions of AF-I and FM-M phases at 5K in 4 koe. Which one is the equilibrium phase at 5K in 4 koe? What is the ground state of such a system?

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22 Asymptotic approach to FM-M ground-state? Pr.5 Ca.5 Mn.975 Al.5 O. 8 koe K.5 =5 K M (µ Β / f.u).9 Reduced to 4 koe M (µ Β / f.u). Reduced to 4 koe.95.8 ime (minutes) 4 5 ime (minutes). ( b ) ρ(t)/ρ() koe K K 4K 8K 5K 55K 7K ime (minutes) Coexisting phase is far from equilibrium!

23 La.5 Ca.5 MnO /f.u.) K Initial (ZFC) Return cycle Next Increasing cycle (esla) / Mn) ZFC (K) / Mn) 6* 4* * ZFC Measured while warming in esla (K) ρ (k Ω.cm) ZFC 6 Resistivity in zero field While warming (K)

24 La.5 Ca.5 MnO 8 K 9 ρ(t)/ρ()..6 K 6 K K 4 6 t (sec.) 6 ρ (kω.cm) 8K 6 K K τ as < 8K τ as > K. K 4 6 t (sec.) A supercooled state will undergo metastable to stable transformation on lowering he relaxation time decreases with decrease in for a supercooled state. Whereas relaxation time increases with decrease in for a glass. P. Chaddah, Kranti Kumar, and A. Banerjee, Phys. Rev. B 77, 4(R) (8)

25 (** **) ( K K ) (* *) AF-I FM-M Y (*, *) (** **) (* *) (K K ) FM-M AF-I ( g, g ) X W AFI FMM B A Y Z Z X W C

26 Coexistence of tunable AFI and FMM phase fraction Functionality in half doped Manganites Pr.5 Ca.5 Mn.975 Al.5 O Pr.5 Sr.5 MnO M ( µ B / f.u.) / f.u.) 4 5 K 6 koe 4 koe 4 8 Cooling Field (koe) 4 5 K 4 koe koe Cooling Field (koe) σ (Ω - ) σ(~ - Ω - ) 5 K koe koe 4 8 Cooling Field (koe) 5 K 4 koe koe Cooling Field (koe) 5 Equilibrium Phase FM-M Equilibrium Phase AF-I Each curve is result of measurement at same (, ) But follows different paths of reaching that (, ). A. Banerjee, K. Mukherjee, Kranti Kumar and P. Chaddah, Phys. Rev. B 74, 445 (6). A. Banerjee, A. K. Pramanik, Kranti Kumar and P. Chaddah, J. Phys.: Condens. Matter 8, L65 (6)

27 Pr.5 Ca.5 Mn.975 Al.5 O Pr.5 Sr.5 MnO ( K K ) (* *) (** **) (* *) ( K K ) (** **) Arrested kinetics yields coexisting phases. Coexistence even in = if * and k bands cross AF-I FM-M /f.u) 6 KOe KOe 4 KOe Measuring Field 4 KOe (K) /f.u) KOe KOe KOe Measuring Field KOe (K) Starting with higher fraction of arrested (metastable) state will first get dearrested (crystal) while warming and then transform to the igh- phase (liquid). While starting with lower fraction of arrested state will not show de-arrest in the measurement time scale. It will show transformation to the high- phase on approaching the (**, **) band while warming. Cooling and eating in Unequal Fields (CUF) Identify the ground-state

28 Pr.5 Ca.5 Mn.975 Al.5 O Nd.5 Sr.5 MnO /f.u.) /f.u.) (a) ZFC (K) Warmed in 4 Warmed in Cooled in Warmed in (K) Cooled in.5.5 ZFC CUF M(µ B /Mn) M(µ B /Mn) (K) Warming in.5 Cooled in K..5 K..5 (a) Warming in.5 Cooled in. 7 K.5 K. (b).5 (K) (K) Warming in Cooled in K Warming in Cooled in K (c) (d) (K) M(µ B /Mn) M(µ B /Mn) Reentrant transition when cool < warm FM Ground state Reentrant transition when cool > warm AFM Ground state A Banerjee, Kranti Kumar and P Chaddah J. Phys.: Condens. Matter, 6 (9). S. Dash, A. Banerjee and P. Chaddah Solid State Commun. 48, 6 (8).

29 /f.u.) /f.u.) Soft ferromagnet 5 K Initial (ZFC) Return cycle Next increasing cycle (esla) 5 K Initial (ZFC) Return cycle Next Increasing cycle (esla) Pr.5 Ca.5 Mn.975 Al.5 O Ground state FM-M La.5 Ca.5 MnO Ground state AF-I Phys. Rev. B 74, 445 (6). Phys. Rev. B 77, 4(R) (8)

30 . A. Banerjee, K. Mukherjee, K. Kumar, and P. Chaddah, Phys. Rev. B 74, 4445 (6).

31 FM-ground state AFM-ground state ( K K ) (* *) (** **) (* *) (** **) ( K K ) FM-M AF-I AF-I FM-M Cooling in higher fields reduces the AFM glass fraction Cooling in higher fields increases the FM glass fraction

32 Pr.5 Ca.5 Mn.975 Al.5 O Pr.5 Sr.5 MnO C p / (mj / mol K 4 )..8.4 (, ) (5, ) (8, ) 4 C p / (mj / mol K 4 ).4.. (, ) (5, ) (5, 5) 4 (K) (K) eat capacity (C P ) is measured in PCMAO in zero field while warming after cooling in different fields (, 5 & 8) denoted by (,); (,5); (,8) Glass-like AF-I phase fraction varies in these states as: (,) > (5,) > (8,) C P is measured in PSMO while warming in zero field after cooling in & 5 and also while warming in 5 after cooling in 5 denoted by (,); (5,); (5,5) Glass-like FM-M phase fraction varies in these states as: (5,5) > (5,) > (,) C P show non-debye behavior and at the same temperature sp.ht. is higher for higher glassy fraction though the magnetic order or conductivity is opposite in the glassy phases of two samples.

33 he difference in C P of between the states with largest fraction of glass to the smaller fraction of glass ( C P ) Excess sp.ht. varies linearly with temperature wo-level system C p (J/molK).6.4. (a) PCM A O (, -8,) (5,5 -,) (, -5,) (5,5-5,) (K) (b) PSM O (K).8.4 C p (J/molK) S G (J/mol-K) (a) PCM A O (b) PSM O R ln R ln... (, -8,) (5,5 -,). 4 4 (K) (K) S G (J/mol-K) Evidence of zero point entropy in magnetic glassy state of half-doped manganites Excess specific heat and evidence of zero point entropy in magnetic glassy state of half-doped manganites. A. Banerjee, R. Rawat, K. Mukherjee and P. Chaddah. Phys. Rev. B, 79, 4 (9).

34 Long-range Structural and Spin order (not spin-glass) AF-I FM-M Pr.5 Ca.5 Mn.975 Al.5 O Pr.5 Sr.5 MnO Nd.5 Sr.5 MnO La.5 Ca.5 MnO

35 Pr.5 Ca.5 Mn.975 Al.5 O.5. 6 Cooled in.5 5 MFM image taken in 7 while warming after the sample is cooled 5K in zero field. /f.u.).5..5 g /f.u.) 4 ** 6 4 (K). 6 9 (K) ( K K ) (* *) (** **) FM-M AF-I emperature induced devitrification of the glasslike AF-I phase to equilibrium FM-M phase and then melting to AF-I phase.

36 Pr.5 Ca.5 Mn.975 Al.5 O MFM image at 6K after the sample is cooled in zero field / f.u.) Field Cycling at 6K (esla) ( K K ) (* *) (** **) Field induced devitrification of the glass-like AF-I phase to equilibrium FM-M phase. FM-M AF-I

37 IOP Select A change in one of the variables that describe a system at equilibrium produces a shift in the position of the equilibrium that counteract the effect of this change.

38 Gigantic change in Resistivity (at the same ) without magnetic field La.5 Ca.5 MnO Single annealing 4 ρ (k Ω.cm) 5 Zero field (K) ρ (k Ω.cm) () () Zero field () 5 5 (K) (4) Coexisting phase fractions tuned by thermal annealing Functionality! P. Chaddah, Kranti Kumar, and A. Banerjee, Phys. Rev. B 77, 4(R) (8)

39 Coexisting phase fractions tuned by thermal annealing La.5 Ca.5 MnO AF-I Ground State ρ (k Ω.cm) 4 Annealing emperatures 6K K K K K 4K 5K 6K ρ (k Ω.cm) Return From Warm 6K 8K K K K K 4K 5K 6K 7K 8K (K).. Cooled to 5K in 6 Measured in (K) Successive annealing A. Banerjee, Kranti Kumar and P. Chaddah. J. Phys.: Condens. Mater, 5545 (8). A Banerjee, Kranti Kumar and P Chaddah. J. Phys.: Condens. Matter, 6 (9).

40 FM-M Ground State Pr.5 Ca.5 Mn.975 Al.5 O R (k Ω.cm) 4 -W -C -W 4-C 5-W 6-C Cooled and measured in. 7-W Warming 5-4K Cooling from 4K Warming 5-6K Cooling from 6K Warming 5-8K Cooling from 8K Warming 5 (K)

41 Coexistence of tunable fractions of equilibrium and higher entropy phases with both structural and magnetic long-range order in half-doped manganites Different fractions of coexisting AF-I and FM-M phase at same & Cooling in different fields hermal annealing Recrystallization Functionality

42 ρ (kω.cm) ρ (kω.cm) ρ (~ * kω.cm) a (K) 6 c 4 Measured in Zero field Cooled in esla from K Measured in Zero field Cooled in 6 esla from K Cooled in Cooled in 6 Initial warming in Warming after return from 4K in (K) b Initial warming in Warming after return from 4K in 5 5 Annealing (K) La.5 Ca.5 MnO / Mn).5..5 (i) (ii) (iii) (iv) (v) More glass gives better crystal!! (K) M- while warming in. Sample is prepared at 5K through (i) FCC in, (ii) ZFC in, (iii) Annealed at K after FCC in, (iv) FCC 6 and annealed once at K in zero field, (v) FCC 6 and annealed successively to K. ot water can freeze faster than cold?!? --- M. Jeng, Am. J. Phys., 74, 55 (6)

43 More Glass " More crystal?? Pr.5 Ca.5 Mn.975 Al.5 O. Cooled in At 5K & 5 Annealing (K) /f.u.).9 Cooled in 5 /f.u.).6..8 Cooled in At 5K & Annealing (K)

44 Relation between supercooling and kinetic arrest (glass formation) (*, *) x y z ( K, K ) x y z (*, *) x y z ( K, K ) z y x m,, m M AFM (b) M (c) FM M AFM (b) O M (c) FM M (emu) M (emu) M (emu) (a) K 9. 4K Field Cooled in 7 koe koe koe Field Cooled in 7 koe koe koe Field Cooled in 7 koe koe K koe 4 6 (KOe) O Ce(Fe, % OS) Anti-correlation M (emu) M (emu) M (emu) O (b) Field Cooling in 5 koe koe 5 koe koe Measuring Field koe Field cooled in koe 5 koe koe 5 koe Measuring Field 4 koe Field Cooled in koe 5 koe koe Measuring Field 8 koe (K)

45 ( K, K ) x 4 y Relation between supercooling and kinetic arrest (glass formation) z 4 z (*, *) y x 4 M M 4 4 M M 4 4 FM O AFM O O M 4 /f.u.) 4 (b) Anti-correlation Field cooled in 4 koe koe 7.5 koe 5 koe ZFC = 5 K (koe) M 4 La-Pr-Ca-Mn-O Μ (µ B /f.u.) 4 (d) Field Cooled in koe 7.5 koe 6.5 koe 5. koe.5 koe ZFC Measuring Field koe (K)

46 References :. J. Phys.: Condens. Mater, (). Archana Lakhani, Pallavi Kushwaha, R. Rawat, Kranti Kumar, A. Banerjee and P. Chaddah. Phys. Rev. B, 79, 4 (9). A. Banerjee, R. Rawat, K. Mukherjee and P. Chaddah.. Phys. Rev. B, 79, 4 (9). Pallavi Kushwaha, Archana Lakhani, R. Rawat, A. Banerjee, and P. Chaddah. 4. J. Phys.: Condens. Mater, 6 (9). A Banerjee, Kranti Kumar and P Chaddah. 5. Solid State Commun., 48, 6 (8). S. Dash, A. Banerjee and P. Chaddah. 6. J. Phys.: Condens. Mater, 5545 (8). A. Banerjee, Kranti Kumar and P. Chaddah. 7. Phys. Rev. B, 77, 4(R) (8). P. Chaddah, Kranti Kumar, and A. Banerjee. 8. Pramana - J. Phys., 7, 9 (8). P. Chaddah and A. Banerjee. 9. J. Phys.: Condens. Mater 9, 56 (7). R. Rawat, K. Mukherjee, Kranti Kumar, A. Banerjee, and P. Chaddah.. Phys. Rev. B, 75, 844 (7). S. B. Roy, M. K. Chattopadhyay, A. Banerjee, P. Chaddah, J. D. Moore, G. K. Perkins, L. F. Cohen, K. A. Gschneidner, Jr., and V. K. Pecharsky.. Phys. Rev. B, 74, 4445 (6). A. Banerjee, K. Mukherjee, Kranti Kumar, P. Chaddah.. J. Phys.: Condens. Matter, 8, L65 (6). A. Banerjee, A. K. Pramanik, Kranti Kumar and P. Chaddah.. Phys. Rev. B, 7, 8445 (6). Kranti Kumar, A. K. Pramanik, A. Banerjee, P. Chaddah, S. B. Roy, S. Park, C. L. Zhang, S-W. Cheong.

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48 Devitrification & heterogeneous nucleation * < g * < < C Glass (FMM) () Equilibrium () (AFI) () ( ) < ( ) < () < (4 ) < (5) Metastable (FMM) (5) Equilibrium (AFI) (4) AFI (*, *) W Y X Z Z Y ( g, g ) X W FMM ρ(t)/ρ()..6 La.5 Ca.5 MnO 8 K 9 K 6 K K 4 6 t (sec.) 6 ρ (kω.cm) 8K 6 K C B A. K K Devitrification and recrystallization of magnetic glass La.5 Ca.5 MnO. P. Chaddah, Kranti Kumar, and A. Banerjee. Phys. Rev. B, 77, 4(R) (8). 4 6 t (sec.)