Kinetically arrested long-range magnetic ordered phase

UGC-DAE Consortium for Scientific Research (CSR)(Formerly: Inter University Consortium for DAE Facilities)

http://www.csr.ernet.in/

University Campus, Khandwa Road

Indore-452017, India.

Acknowledgements: Praveen ChaddahS. B. RoyR. Rawat, Archana LakhaniKranti Kumar, K. Mukherjee,A. K. Pramanik, S. N. Dash.

Alok Banerjee(alok@csr.ernet.in)

Outline :

! Ideal Field- Temperature induced magnetic first-order transitions

! Disorder broadened first-order transitions in real systems.

! Case study: broadened first-order transitions in manganites.

! Anomaly in Field-Temperature induced first-order transitions.

! Coexisting phases at low temperature.

! Tunable fractions of arrested phase with equilibrium phase at low-T

! Identification of low-T equilibrium phase by CHUF protocol.

! Evidence of glass-like behaviour of the kinetically arrested phase.

! Functionality arising from the glass-like phase

! Remaining questions

Field-Temperature induced first-order Phase Transition[Antiferromagnetic-Insulating (AF-I) to Ferromagnetic-Metallic (FM-M)]

H

T

FM-M AF-I

TCT* T**

M

TAF-I

FM-M

R

T

FM-M

AF-I

T

H

T

FM-MAF-I

TCT* T**

M

T

FM-M

AF-I

R AF-I

FM-M

TC

T*

T**

Field and temperature induced First-order transition in Intermetallic doped CeFe2

Micro-Hall probe (scanning)

S. B. Roy et al., Phys. Rev. Lett. 92, 147203 (2002)

L. Zhang et al., Science 298, 805 (2002)

Variation of ferromagnetic and antiferromagnetic phases

+Metallic and insulating

La0.33Pr0.34Ca0.33MnO3

Mesoscopic probe – With spatial resolution

First-order magnetic transition in manganite

Magnetic Force Microscopy

M. K. Chattopadhyay et al., Phys. Rev. B 68, 174404 (2003)

H

T

FM-MAF-I

TCT* T**

M

T

FM-M

AF-I

T**TCT*

T**

T*

T**

T*

TC T<TC T>TC

Ideal H-T induced First-order phase transition

Observed H-T induced First-order phase transition

(H* T*)(H** T**)

T

H

AF-I

(HC, T

C)

FM-M

(H* T*)

(H** T**)H

T

FM-M

(HC, TC)

AF-I

Broad first order AF-I to FM-M transition

Disorder introduces spatial distribution in TC which broadens the (HC, TC) line into a bandconsequently the (H*, T*) and (H**, T**) 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 19, 3580 (1979).

Perovskite (R/A)MnO3

MnO 6Octa

hedron

(R,A)-atom

(R1-xAx)MnO3 Perovskite ManganitesWhere R3+ is the rare earth element and A2+ is alkaline earth element.

Pr0.5Sr0.5MnO3, Nd0.5Sr0.5MnO3, La0.5Ca0.5MnO3, Pr0.5Ca0.5MnO3 etc.

All are antiferromagntic (AF) - insulators (I).

Magnetic Field inducedAntiferromagnetic-insulating (AF-I) to Ferromagnetic-metallic (FM-M) transition

R0.5A0.5MnO3

50% Mn3+ & 50% Mn4+

Half doped manganites

R. Kajimoto et al. Phys. Rev. B, 66, R180402 (2002).

Manganites around half-doping Field inducedAntiferromagnetic-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.

Pr0.5Sr0.5MnO3

Nd0.5Sr0.5MnO3

La0.5Ca0.5MnO3

Pr0.5Ca0.5MnO3

Relating to phase fractions

Pr0.5Ca0.5MnO3

M. Tokunaga et al., Phys. Rev. B 57, 5259 (1998).

Narrow bandwidth prototype charge ordered antiferromagnetic insulator system(About 300 kOe field is required transform the AF-I state to FM-M state through 1st order process)

Pr0.5Ca0.5MnO3

Disorder in MnO6 octahedron Mn site substitutionIonic size (structure)

Non-Magnetic(no d-orbital)

Pr0.5Ca0.5Mn0.975Al0.025O3

0 30 60 90

10-1

101

103

ρρ ρρ (

k o

hm c

m )

5k

H (k Oe)

ZFC

0 40 80 1200

1

2

2

3

4

ZFC

M (

µµ µµ B /

f.u.)

H (kOe)

5K

J. Phys.: Condens. Matter 16, 8335 (2004).Phys. Rev. Lett. 93, 117204 (2004).

0 .5

1 .0

1 .5

2 .0

FC W

FC C

40 kO eM

(µµ µµ B

/ f.u

.)

Pr0.5Ca0.5Mn0.975Al0.025O3

0 100 20010 -2

10 -1

10 0

10 1

10 2

FCC FCW

40 kO e

T ( K )

ρρ ρρ (

k oh

m c

m)

Broad first order AF-I to FM-M transition

0 50 100 150 200

0.3

0.6

T (K)

ρ

(Ω-c

m)

H = 0 Oe

0.0

0.4

0.8

M

(µB/M

n)

H = 500 Oe

Nd0.5Sr0.5MnO3

0 40 80 120

0

1

2

3

4

5 K

M (µ

B/f.

u.)

H (kOe)0 20 40 60 80 100

0.0

0.2

5 KR

(Ω)

H (kOe)Pr0.5Sr0.5MnO3

Field – Temperature induced broad first-order phase transition

0 100 200 3000

1

2

3

M (µ

B /

Mn)

FCW

ZFC

FCC

T (K)

10 kOe

50 100 150 200

0.2

0.4

FCC

FCW

ZFC

ρ (Ω

cm

)

T (K)

10 kOe

0 100 200

0.5

1.0

1.5

2.0

FCW

FCCZFC

40 kOe

M (

µµ µµ B /

f.u.)

T ( K )

0 100 20010-2

100

102

ZFC FCC FCW

40 kOe

T ( K )

ρρ ρρ (

k oh

m c

m)

0 40 80 120

0

1

2

3

4

Virgin (I)

5 K

M (µ

B/f.

u.)

H (kOe)

III

II

0 20 40 60 80 1000.0

0.2

0.4

0.6

Virgin (I)

5 K

R (Ω

)H (kOe)

III

II

Nd0.5Sr0.5MnO3 Pr0.5Ca0.5Mn0.975Al0.025O3

Pr0.5Sr0.5MnO3

Anomaly in 1st order AF-I to FM-M transformation

Phys. Rev. B 74, 22445 (2006); J. Phys.: Condens. Matter 18, L605 (2006);J. Phys.: Condens. Matter 19, 256211 (2007).

Anomaly in 1st order AF-I to FM-M transformation

0 100 200 3000

1

2

3

4

-1

0

1

2

3

0.0

0.2

0.4

FCW

FCC

ZFC

FCC

FCW

ZFC

ρ (Ω

cm

)

0.2

0.4

0.6

1 Tesla

(a)

2 Tesla

Nd0.5Sr0.5MnO3

2 Tesla

M (µ

B /

Mn)

FCW

ZFC

FCC

T (K)

(b)

1 Tesla

ZFC

FCC

FCW

1

2

3

4

0 2 4 6 8 100

1

2

3

[a]

5 K 20 K 30 K 40 K 60 K

Nd0.5Sr0.5MnO3

M (µ

B /

Mn)

[b]

60 K 70 K 85 K 100 K

H(Tesla)

Not a Spin-Glass Not usual ferromagnet

J. Phys.: Condens. Matter 19, 256211 (2007).

Magetic Field (Tesla)

Nd0.5Sr0.5MnO3 (Single Crystal)

H. Kuwahara, Y. Tomioka, A. Asamitsu, Y. Moritomo and Y. Tokura, Science 270, 961 (1995)

Anomaly in Field-Temperature induced FOPT – Half doped manganites

Pr0.5Ca0.5Mn0.975Al0.025O3

-12 -8 -4 0 4 8 12-3-2-10123

M (µ

B /f

.u.)

H (Tesla)

Initial (ZFC) Return cycle Next increasing

cycle

5 K

0 30 60 90

10-1

101

103

ρ (

k o

hm c

m ) 5K

H (k Oe)

The 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

0 100 200 3000

1

2

3

1T

3T

4T

6T

8T

M (µ

B /f.u

.)

T(K)

0 50 100 15010-1

100

101

102

103

4 T

3.5T

3.25T

3T

R (k

Ω.c

m)

T(K)

Incomplete first-orderMagnetic transition

Pr0.5Ca0.5Mn0.975Al0.025O3

-12 -8 -4 0 4 8 12-3-2-10123

M (µ

B /f

.u.)

H (Tesla)

Initial (ZFC) Return cycle Next increasing

cycle

5 KSoft ferromagnet

(H* T*)(H** T**)

H1

H2

T

H

AF-I

(HC, T

C)

FM-M

(H* T*)

(H** T**)

H1

H2

H

T

FM-M

(HC, TC)

AF-I

Broad first order AF-I to FM-M transition

Disorder introduces spatial distribution in TC which broadens the (HC, TC) line into a bandconsequently the (H*, T*) and (H**, T**) 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 19, 3580 (1979).

Coexistence of different fractions of AF-I and FM-M phases at 5K in 40 kOe.

Which one is the equilibrium phase at 5K in 40 kOe ?

What is the ground state of such a system ?

0 50 100 150

1

2

3

M (

µµ µµ B /

f.u. )

Cooling field in kOe 0 (ZFC) 2.5 25 27.5 30 32.5 35 40 50 60 80

T ( K )

Measured in 40 KOeWhile warming

0 50 100 150 200

10-1

100

101

ρρ ρρ

( k o

hm c

m )

Measured in 40 kOeWhile warming

T ( K )

Cooling field in kOe ZFC 30 35 40 50 60 80

Pr0.5Ca0.5Mn0.975Al0.025O3

0 100 200 3002.8

2.9

3.080 kOe

Reduced to 40 kOe

M ( µµ µµ

ΒΒ ΒΒ /

f.u)

Time (minutes)

12K

300 400 500

1.95

2.00

2.05

H=5T

Reduced to 40 kOeM ( µµ µµ

ΒΒ ΒΒ /

f.u)

Time (minutes)

12 K

Asymptotic approach to FM-M ground-state ?

Pr0.5Ca0.5Mn0.975Al0.025O3

0 20 40 60 80

0.93

0.96

0.99

1.02 ( b )

40 kOe

ρρ ρρ(t)/

ρρ ρρ(0)

Time (minutes)

10K 20K 24K 28K 35K 55K 70K

Coexisting phase is far from equilibrium !

0 100 200

1

2

3 Measured while warmingin 1 Tesla

M ( µµ µµ

B /

Mn)

T(K)

6T*

4T*

1 T*ZFC 0 100 200

0

4

8

12

16

ρρ ρρ (k

ΩΩ ΩΩ.c

m)

T(K)

Resistivity in zero fieldWhile warmingZFC

1 T

6 T

La0.5Ca0.5MnO3

-12 -8 -4 0 4 8 12-3-2-10123

M (µ

B /f

.u.)

H (Tesla)

Initial (ZFC) Return cycle Next Increasing

cycle

5 K

0 100 200 3000

2

ZFC

3T

M (µ

B /

Mn)

T(K)

0 2000 4000 6000

1.2

1.6

2.0

110K

100K

80K

t (sec.)

ρ(t)/

ρ(0) 60 K0 2000 4000 6000

3

6

9

ρ (k

Ω.c

m)

t (sec.)

110 K

100 K

80 K

60 K

La0.5Ca0.5MnO3

A supercooled state will undergo metastable to stable transformation on lowering T ⇒

The relaxation time decreases with decrease in T for a supercooled state.

Whereas relaxation time increases with decrease in T for a glass.

τ ↑ as T ↓ < 80K

τ ↑ as T ↑ > 100K

P. Chaddah, Kranti Kumar, and A. Banerjee, Phys. Rev. B 77, 100402(R) (2008)

(HK T

K )

(H* T*)(H** T**)

H1

H2

H

T

FM-MAF-I

(HKTK

) (H* T*)(H** T**)

H1

H2

T

H

AF-IFM-M

(H*,

T*)H

T

(Hg , T

g )

FMMAFI

W

X

Y

ZZ

Y

X

W

ABC

0 40 80 120

1

2

3

45 K

40 kOe

60 kOe

0 20 40 60 80

1

2

3

45 K

M (

µ B /

f.u.

)

10 kOe

40 kOe

Cooling Field (kOe)

M (µ

B /

f.u.)

0 40 80 120

0

1

2

35 K

0 kOe

40 kOe

Cooling Field (kOe)

σσ σσ (Ω

-1)

σσ σσ(~

10-2 Ω

-1 )

Cooling Field (kOe)

0 40 80 1200

5

10

15

205 K

0 kOe

40 kOe

Cooling Field (kOe)

0

20

40

60

80

Each curve is result of measurement at same (T, H)

But follows different paths of reaching that (T, H).

A. Banerjee, K. Mukherjee, Kranti Kumar and P. Chaddah, Phys. Rev. B 74, 22445 (2006).A. Banerjee, A. K. Pramanik, Kranti Kumar and P. Chaddah, J. Phys.: Condens. Matter 18, L605 (2006)

Coexistence of tunable AFI and FMM phase fraction

Functionality in half doped Manganites

Equilibrium PhaseFM-M

Equilibrium PhaseAF-I

Pr0.5Ca0.5Mn0.975Al0.025O3

Pr0.5Sr0.5MnO3

0 80 160 240 3200

1

2

3

Measuring Field 40 KOe

40 KOe

60 KOe

30 KOe

M (µ

B/f.

u)

M (µ

B/f.

u)

T (K)0 80 160 240 320

0

1

2

3

Measuring Field 20 KOe

20 KOe

10 KOe

30 KOe

T (K)

(HKTK) (H* T*)

(H** T**)

H1

H2

T

H

(HK T

K )

(H* T*)

(H** T**)

H1

H2

H

T

AF-I FM-M

Pr0.5Ca0.5Mn0.975Al0.025O3 Pr0.5Sr0.5MnO3

Starting with higher fraction of arrested (metastable) state will first get de-arrested (crystal) while warming and then transform to the High-T 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-T phase on approaching the (H**, T**) band whilewarming.

Arrested kinetics yields coexisting phases.

Coexistence even in H=0 if T* and Tk bands cross

Cooling and Heating in Unequal Fields — (CHUF) Identify the ground-state

0.5

1.0

1.5

2.0

2.5

0 100 200

Cooled in 3T11 K

110 K

M(µ

B/M

n)

Warming in 1T

(a)

0 100 200

0.5

1.0

1.5

2.0

2.5Warming in 1T

110 K

T (K)

M(µ

B/M

n)

Cooled in 1T(c)

0 100 2000.5

1.0

1.5

2.0

2.5

Warming in 1T

17 K

T (K)T (K)

M(µ

B/M

n)

110 K

Cooled in 2T

(b)0 100 200

0.5

1.0

1.5

2.0

2.5Warming in 1T

110 K

M(µ

B/M

n)

Cooled in 0 T

T (K)

(d)

Nd0.5Sr0.5MnO3

Reentrant transition when Hcool > HwarmAFM Ground state

S. Dash, A. Banerjee and P. ChaddahSolid State Commun. 148, 336 (2008).

0 50 100 150 200 250 300

0.3

0.6

0.9

1.2

1.5

Cooled in 3TM (µ

B/f.

u.)

T(K)

Warmed in 4T Warmed in 2T

(a)

Reentrant transition when Hcool < HwarmFM Ground state

Pr0.5Ca0.5Mn0.975Al0.025O3

A Banerjee, Kranti Kumar and P ChaddahJ. Phys.: Condens. Matter 21, 026002 (2009).

0 50 100 150 200 250 3000.2

0.4

0.6

0.8

1.0

1.2

ZFC

2.5T

3.5T

Warmed in 3 TM (µ

B/f.

u.)

T(K)

Cooled in 3.5 T 2.5 T ZFC

CHUF

-12 -8 -4 0 4 8 12-3-2-10123

M (µ

B /f

.u.)

H (Tesla)

Initial (ZFC) Return cycle Next increasing

cycle

5 K

-12 -8 -4 0 4 8 12-3-2-10123

M (µ

B /f

.u.)

H (Tesla)

Initial (ZFC) Return cycle Next Increasing

cycle

5 K

Pr0.5Ca0.5Mn0.975Al0.025O3

La0.5Ca0.5MnO3

Ground state – FM-M

Ground state – AF-I

Phys. Rev. B 74, 22445 (2006).

Phys. Rev. B 77, 100402(R) (2008)

Soft ferromagnet

20. A. Banerjee, K. Mukherjee, K. Kumar, and P. Chaddah, Phys. Rev. B 74, 224445 (2006).

(HK T

K )

(H* T*)

(H** T**)

H1

H2

H

T

FM-MAF-I

(HKTK)

(H* T*)

(H** T**)

H1

H2

T

H

AF-IFM-M

FM-ground state AFM-ground state

Cooling in higher fields reducesthe AFM glass fraction

Cooling in higher fields increasesthe FM glass fraction

Heat capacity (CP) is measured in PCMAO in zero field while warming after cooling in different fields

(0, 5T & 8T) denoted by (0,0); (0,5); (0,8) →→→→Glass-like AF-I phase fraction varies in these 3 states as: (0,0) > (5,0) > (8,0)

CP is measured in PSMO while warming in zero field after cooling in 0 & 5T and also while warming in

5T after cooling in 5T denoted by (0,0); (5,0); (5,5) →→→→Glass-like FM-M phase fraction varies in these 3 states as: (5,5) > (5,0) > (0,0)

CP 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 inthe glassy phases of two samples .

Pr0.5Ca0.5Mn0.975Al0.025O3Pr0.5Sr0.5MnO3

10 20 30 40

0.4

0.8

1.2

10 20 30 40

0.2

0.3

0.4

Cp/T

3 (mJ /

mol

K4 ) (0 , 0)

(5 , 0) (8 , 0)

T (K )

Cp/T

3 (mJ /

mol

K4 )

(0 , 0) (5 , 0) (5 , 5)

T (K )

4 8 12 160.0

0.2

0.4

0.6

4 8 12 16

0.04

0.08

(a)

PCM AO∆C

p (J/mol K)

T (K)

(0, 0 - 8, 0) (0, 0 - 5, 0)

(b)

PSM O

(5, 5 - 0, 0) (5, 5 - 5, 0)

T (K)

∆Cp (J/mol K)

The difference in CP of between the states with largest fraction of glass to the smaller fraction of glass (∆CP) → Excess sp.ht. varies linearly with temperature

Two-level system

0 10 20 30 40

0.01

0.1

1

10 20 30 40

0.01

0.1

1(a)

R ln 2PCM AO

SG (J/mol-K)

T (K)

(0, 0 - 8, 0)

(b)

T (K)SG (J/mol-K)

R ln 2

PSM O

(5, 5 - 0, 0)

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, 212403 (2009).

Long-range Structural and Spin order (not spin-glass)

Pr0.5Ca0.5Mn0.975Al0.025O3AF-I

Pr0.5Sr0.5MnO3

Nd0.5Sr0.5MnO3

La0.5Ca0.5MnO3

FM-M

0 30 60 90 1200.0

0.5

1.0

1.5

2.0

2.5

T**

Tg

4T

5T6T Cooled in 3.25T

M (µ

B/f.

u.)

T (K)

100 200 3000

1

2

4T

6T

M (µ

B/f.

u.)

T(K)

Pr0.5Ca0.5Mn0.975Al0.025O3

MFM image taken in 7 T while warming after the sample is cooled 5K in zero field.

(H KTK

) (H* T*)(H** T**)

H1

H2

T

H

AF-IFM-M

Temperature induced devitrification of the glass-like AF-I phase to equilibrium FM-M phase and then melting to AF-I phase.

0 2 4 6 8 100

1

2

3

Field Cycling at 6K

M (µ

B /

f.u.)

H (Tesla)

Pr0.5Ca0.5Mn0.975Al0.025O3

MFM image at 6K after the sample is cooled in zero field

(HKTK

) (H* T*)(H** T**)

H1

H2

T

H

AF-IFM-M

Field induced devitrification of the glass-like AF-Iphase to equilibrium FM-M phase.

“A change in one of the variables that describe a system at equilibrium producesa shift in the position of the equilibrium that counteract the effect of this change.”

IOP Select

0 100 200 3000

5

10

ρ (k

Ω.c

m)

T(K)

Zero field

La0.5Ca0.5MnO3

0 50 100 1500

10

20

30

40

T(K)

ρ (k

Ω.c

m)

(1)

(2)

(3)

(4)

Zero field

Gigantic change in Resistivity (at the same T) without magnetic field

Single annealing

Coexisting phase fractions tuned by thermal annealing Functionality !

P. Chaddah, Kranti Kumar, and A. Banerjee, Phys. Rev. B 77, 100402(R) (2008)

0 40 80 120 160

0

200

400

ρ (k

Ω.c

m)

T(K)

Annealing Temperatures 60K 100K 110K 120K 130K 140K 150K 160K

La0.5Ca0.5MnO3

Successive annealing

AF-I Ground State

A. Banerjee, Kranti Kumar and P. Chaddah. J. Phys.: Condens. Mater 20, 255245 (2008).A Banerjee, Kranti Kumar and P Chaddah. J. Phys.: Condens. Matter 21, 026002 (2009).

Coexisting phase fractions tuned by thermal annealing

0 20 40 60 80 100 120 140 160 180 200

0.01

0.1

1

10

100

1000

Cooled to 5K in 6TMeasured in 0T

Return From 0T Warm 60K 80K 100K 110K 120K 130K 140K 150K 160K 170K 180Kρ

(k Ω

.cm

)

T (K)

Pr0.5Ca0.5Mn0.975Al0.025O3

FM-M Ground State

0 50 1000

1000

2000

3000

4000

R (k

Ω.c

m)

T(K)

Warming 5-40K Cooling from 40K Warming 5-60K Cooling from 60K Warming 5-80K Cooling from 80K Warming

1-W

2-C

3-W 4-C

5-W 6-C

7-WCooled and measured in 2.1 T

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 T & H

Cooling in different fields Thermal annealing – Recrystallization

Functionality

0 50 100 150 2000

2

4

6

c

ρ (k

Ω.c

m)

ρ (~

103 *

kΩ

.cm

)

Annealing T(K)

Cooled in 1T Cooled in 6T

0 100 200 300

10-2

100

102

104

Cooled in 6 Tesla from 320KMeasured in Zero field

Initial warming in 0T Warming after return

from 140K in 0T

b

Initial warming in 0T Warming after return

from 140K in 0T

T (K)

0 100 200 300

10-2

100

102 a ρ

(kΩ

.cm

)

T (K)

Cooled in 1 Tesla from 320KMeasured in Zero field

0 100 200

0.5

1.0

1.5

(i)

1T

M (µ

B /

Mn)

T(K)

(ii)(iii)

(v)(iv)

M-T while warming in 1T. Sample is prepared at 5K through (i) FCC in 1T, (ii) ZFC in 1T, (iii) Annealed at 130K after FCC in 1T, (iv)FCC 6T and annealed once at 130K in zero field, (v) FCC 6T and annealed successively to 130K.

More glass gives better crystal !!More glass gives better crystal !!

“Hot water can freeze faster than cold?!?” --- M. Jeng, Am. J. Phys., 74, 515 (2006)

La0.5Ca0.5MnO3

0 20 40 60 801.8

1.9

2.0

At 5K & 5T

Cooled in 5T

Cooled in 2T

Annealing T (K)

M (µ

B /f

.u.)

0.8

1.2

1.6

2.0

0 20 40 60 80

Cooled in 2T

At 5K & 5T

Annealing T (K)

M (µ

B /f

.u.)

More Glass """"More crystal ??

Pr0.5Ca0.5Mn0.975Al0.025O3

(H*,

T*)

1

2

H

3

T

(HK , T

K )

FMAFM 1

3

2

xyzzy

x

TO

H m

M

H

(b)

1

23

T

M (c)

1

2

3

TO

(H*,

T*)

23

H

1

T

(HK , T

K )

FMAFM

1, 2, 3

zyx

x

zy

Hm

M

H

(b)

1

2

3

T

M (c)

1

2

3

TO

0

1

2

3

1 .2

1 5 .5

20K

2 K

4K

F ie ld C o oled in 7 0 k O e 3 0 k O e 1 0 k O e

0

1

2

3

2 .2

1 9 .3

F ie ld C o o led in 7 0 k O e 3 0 k O e 1 0 k O e

M (e

mu)

M (e

mu)

0 20 40 6 00

1

2

3

(a )

1 0

3 0

F ie ld C o o led in 7 0 k O e 3 0 k O e 1 0 k O e

M (e

mu)

H (K O e)

0.3

0.4

0.5

0.6

Field Cooling in 15 kOe 10 kOe 5 kOe 2 kOeMeasuring Field 1 kOe

0.6

0.9

M (e

mu)

Field cooled in 20 kOe 15 kOe 10 kOe 5 kOeMeasuring Field 4 kOe

M (e

mu)

2 4 6 8 10 12 140.8

1.0

1.2

(b)

Field Cooled in 20 kOe 15 kOe 10 kOe

T (K)

Measuring Field 8 kOe

M (e

mu)

Ce(Fe, 2% OS)2

Relation between supercooling and kinetic arrest (glass formation)

Anti-correlation

(HK

, TK

)

1

2

3

H

4

T

1

2

3

(H*, T*)

FM AFM

321

TO

xy

zzy

x

4

H4H

M

12

3

4

1

2

3

M

H

1

2

3

4

T

M

1

2

3

4

TO

1

2

3

M

T

1

2

3

4

TO

H

M

12

3

M

T12

3

4

4

0 10 20 300

1

2

3

4

H (kOe)

(b)

M (µ

B /f.u

.)

Field cooled in 14 kOe 10 kOe 7.5 kOe 5 kOe ZFC

T = 5 K

0 5 10 15 20 25 30 350

1

2

3

4

T (K)

Measuring Field 10 kOe

(d)Field Cooled in

10 kOe 7.5 kOe 6.5 kOe 5.0 kOe 2.5 kOe ZFC

Μ

Μ

Μ

Μ (µ

B/f.u.

)

La-Pr-Ca-Mn-O

Relation between supercooling and kinetic arrest (glass formation)

Anti-correlation

References :

1. J. Phys.: Condens. Mater 22, 032101 (2010). Archana Lakhani, Pallavi Kushwaha, R. Rawat, Kranti Kumar, A. Banerjee and P. Chaddah

2. Phys. Rev. B , 79, 212403 (2009). A. Banerjee, R. Rawat, K. Mukherjee and P. Chaddah.

3. Phys. Rev. B , 79, 132402 (2009). Pallavi Kushwaha, Archana Lakhani, R. Rawat, A. Banerjee, and P. Chaddah.

4. J. Phys.: Condens. Mater 21, 026002 (2009). A Banerjee, Kranti Kumar and P Chaddah.

5. Solid State Commun., 148, 336 (2008). S. Dash, A. Banerjee and P. Chaddah.

6. J. Phys.: Condens. Mater 20, 255245 (2008). A. Banerjee, Kranti Kumar and P. Chaddah.

7. Phys. Rev. B , 77, 100402(R) (2008). P. Chaddah, Kranti Kumar, and A. Banerjee.

8. Pramana - J. Phys., 70, 193 (2008). P. Chaddah and A. Banerjee.

9. J. Phys.: Condens. Mater 19, 256211 (2007). R. Rawat, K. Mukherjee, Kranti Kumar, A. Banerjee, and P.Chaddah.

10. Phys. Rev. B , 75, 184410 (2007). 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.

11. Phys. Rev. B , 74, 224445 (2006). A. Banerjee, K. Mukherjee, Kranti Kumar, P. Chaddah.

12. J. Phys.: Condens. Matter, 18, L605 (2006). A. Banerjee, A. K. Pramanik, Kranti Kumar and P. Chaddah.

13. Phys. Rev. B , 73, 184435 (2006). Kranti Kumar, A. K. Pramanik, A. Banerjee, P. Chaddah, S. B. Roy, S. Park, C. L. Zhang, S-W. Cheong.

Glass(FMM)

T ≤≤≤≤ T* <Tg

Equilibrium (AFI) (1)

(2)

(3)

T* <T < TC

Metastable (FMM)

Equilibrium (AFI) (4)

(5)

TT(1 ) < T(2 ) < T(3) < T(4 ) < T(5)

(H*,

T*)

H

T

(Hg , T

g )

FMMAFI

W

XY

ZZ

Y

XW

ABC

0 2000 4000 6000

1.2

1.6

2.0

110K

100K

80K

t (sec.)

ρ(t)/

ρ(0) 60 K0 2000 4000 6000

3

6

9

ρ (k

Ω.c

m)

t (sec.)

110 K

100 K

80 K

60 K

Devitrification & heterogeneous nucleation

La0.5Ca0.5MnO3

Devitrification and recrystallization of magnetic glass La0.5Ca0.5MnO3.P. Chaddah, Kranti Kumar, and A. Banerjee.Phys. Rev. B , 77, 100402(R) (2008).