Some experimental approaches to study the aging phenomena in spin glasses Tetsuya Sato Keio...

Some experimental approaches to study the aging phenomena in

spin glasses

Some experimental approaches to study the aging phenomena in

spin glasses

Tetsuya Sato Keio University 　Yokohama, Japan

Tetsuya Sato Keio University 　Yokohama, Japan

OutlineOutline

Aging behavior of spin glass under bond perturbationAging behavior of spin glass under bond perturbation

· What is bond perturbation· Experimental procedure· Experimental result


Behavior of spin glass nanoparticle in magnetic fieldBehavior of spin glass nanoparticle in magnetic field

· Why is spin glass nanoparticle necessary· Experimental procedure· Experimental result

· Why is spin glass nanoparticle necessary· Experimental procedure· Experimental result

Concluding remarksConcluding remarks

OutlineOutline




Behavior of spin glass nanoparticle magnetic fieldBehavior of spin glass nanoparticle magnetic field

· Why is spin glass nanoparticle necessary· Experimental procedure· Behavior of spin glass nanoparticle magnetic field


concluding remarksconcluding remarks

Aging behavior of spin glass under bond perturbation

1. What is bond perturbation

Aging behavior of spin glass under bond perturbation

1. What is bond perturbation

t w

tt = 0

TTHm

.

90

80

70

60

50

100 101 102 103 104

time (sec)

NiMn60.0 K

tw = 100 sec

tw = 1000 sec

tw = 10000 sec

.

8

6

4

2

0100 101 102 103 104

time (sec)

tw = 100 sec

tw = 1000 sec

tw = 10000 secNiMn60.0 K

· Wait time dependence· Wait time dependence

L(τ) = L0[k

BT ln(τ/τ

0)/Δ(T)]

1/Ψ

average size of excited droplet average size of excited droplet

· Temperature perturbation Temperature perturbations, e.g., temperature cycle has been extensively used to study slow dynamics of spin glasses.

· Temperature perturbation Temperature perturbations, e.g., temperature cycle has been extensively used to study slow dynamics of spin glasses.

t

3000 s

ΔTTm

1000 s

TH10 s

t=00.35

0.30

0.25

0.20

0.15

0.10

0.05

0.0010

010

110

210

310

4

t (sec)

ΔT =0

ΔT =+ 2 KΔT =+ 4 K

ΔT =+ 8 K

NiMn

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.0010

010

110

210

310

4

ΔT =0

ΔT =- 2 K

ΔT =- 4 K

ΔT =- 8 K

NiMn

t (sec)

tt = 0

ΔTTm

1000 sTH10 s

10 s

Temperature chaos Temperature chaos

· Temperature perturbation · Temperature perturbation

1. temperature perturbation change in thermal excitation of droplet separation of time scale

1. temperature perturbation change in thermal excitation of droplet separation of time scale

tp(T

m+ΔT) = τ

0 [t

eff(T

m)/τ

0 ]

Tm

/(Tm

+ΔT)

ex)

When Tm

= 7 K, ΔT = 1K, τ0 = 10-13 s

8 K : 75 s 7 K : 10000 s

difference of 1K more than 100 times difference of time scale

2. temperature perturbation indirect change in bond interaction2. temperature perturbation indirect change in bond interaction

· Bond perturbation · Bond perturbation

bond perturbation bond perturbation

Aging behavior of spin glass can be studied without separation of time scale.Aging behavior of spin glass can be studied without separation of time scale.

magnetic ionmagnetic ion




Aging behavior of spin glass can be studied without separation of time scale.Aging behavior of spin glass can be studied without separation of time scale.




· method for bond perturbation · method for bond perturbation

carrier excitation in semicondcutor change in interactioncarrier excitation in semicondcutor change in interaction

photo illuminationphoto illumination

2. Experimental procedure2. Experimental procedure

A. Bond and temperature perturbationsA. Bond and temperature perturbations

Sample

SQUID system

Optical fiber

ND filter

He-Ne laser

(543.5 nm, hν = 2.27 eV)

Optical fiber

straw

Cd0.63Mn0.37 (Te Eg = 2.18 eV)

1 mm

φ 3 mm

ΔT+ΔJ ΔT

Carbon coat

Sample

(ΔT perturbation + ΔJ perturbation) - (ΔT perturbation)(ΔT perturbation + ΔJ perturbation) - (ΔT perturbation)

= ΔJ perturbation = ΔJ perturbation


B. Bond perturbationB. Bond perturbation

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Δ T

[ ]K

15001000500

[ ]time sec

sample temperature

lumination

SQUID

semiconductor lasersemiconductor laser

polarizerpolarizerPC control polarizer PC control polarizer

optical fiberoptical fiber

Photo intensity is changed synchronously with temperature controller so as to decrease change in sample temperature.

Photo intensity is changed synchronously with temperature controller so as to decrease change in sample temperature.

Deviation of temperature < 0.02 KDeviation of temperature < 0.02 K


H

t

Tm

tw tp

0

ΔT=0

ts

LIGHTT

H

t

Tm

tw

tp

0

ΔTts

LIGHTT

1. bond and temperature perturbations1. bond and temperature perturbations

2. bond perturbation2. bond perturbation

660

640

620

600

5801210864

T [K]

Tg = 10.7 K

ZFC

FC

6

5

4

3

2

1

010008006004002000

H [Oe]

Sample temperatureSample temperature

Field cooled magnetization Field cooled magnetization

3. Experimental result3. Experimental result

1.0

0.8

0.6

0.4

0.2

no illuminationteff=125sec teff=380secteff=1100sec teff=1900secteff=3800sec teff=13000sec

(a) ΔT=0.26KΔT

noilluminationteff=125sec teff=380secteff=1100sec teff=1900secteff=3800sec teff=13000sec

(b) ΔT=0.26KΔT+ΔJ

1.0

0.8

0.6

0.4

0.2

102 103 104t [sec]


(c) ΔT=1.05KΔT

102 103 104t [sec]


(d) ΔT=1.05KΔT+ΔJ

tp(T

m+ΔT) = τ

0 [t

eff(T

m)/τ

0 ]

T/(T+ΔT)

A. bond and temperature perturbationsA. bond and temperature perturbations

1.0

0.8

0.6

0.4

0.2


(a) ΔT=0.26KΔT



1.0

0.8

0.6

0.4

0.2

102 103 104t [sec]


(c) ΔT=1.05KΔT

102 103 104t [sec]



tpeak

tp(T

m+ΔT) = τ

0 [t

eff(T

m)/τ

0 ]

T/(T+ΔT)3. Experimental result3. Experimental resultA. bond and temperature perturbationA. bond and temperature perturbation

tp(T

m+ΔT) = τ

0 [t

eff(T

m)/τ

0 ]

T/(T+ΔT)

1.0

0.8

0.6

0.4

0.2


(a) ΔT=0.26KΔT



1.0

0.8

0.6

0.4

0.2

102 103 104t [sec]


(c) ΔT=1.05KΔT

102 103 104t [sec]



sub peak

tpeak

sub peak

3. Experimental result3. Experimental resultA. bond and temperature perturbationA. bond and temperature perturbation

· tpeak

· tpeak

103

104

teff + tw [sec]

ΔTΔT+ ΔJ

(d) ΔT =1.05K

ΔTΔT+ΔJ

(b) ΔT =0.40K

103

104

ΔTΔT+ΔJ

(a) ΔT =0.26K

103

104

103 104

teff+ tw [sec]

ΔTΔT+ΔJ

(c) ΔT =0.69K

· tpeak

· tpeak

103

104

teff + tw [sec]

ΔTΔT+ ΔJ

(d) ΔT =1.05K

ΔTΔT+ΔJ

(b) ΔT =0.40K

103

104

ΔTΔT+ΔJ

(a) ΔT =0.26K

103

104

103 104

teff+ tw [sec]

ΔTΔT+ΔJ

(c) ΔT =0.69K

isothermal aging : tpeak

= teff

+ tw


= teff

+ tw

· tpeak

· tpeak

103

104

teff + tw [sec]

ΔTΔT+ ΔJ

(d) ΔT =1.05K

ΔTΔT+ΔJ

(b) ΔT =0.40K

103

104

ΔTΔT+ΔJ

(a) ΔT =0.26K

103

104

103 104

teff+ tw [sec]

ΔTΔT+ΔJ

(c) ΔT =0.69K


= teff

+ tw


= teff

+ tw

6

8100

2

4

103

104

teff [sec]

sub peaksub peak

· relative peak hight r· relative peak hight r

1.0

0.9

0.8

0.7

0.6

102

103

104

teff

[sec]

ΔT=0.26K

ΔT=0.40K

Filled:Open: ΔT+ΔJ

102 103 104

teff [sec]

ΔT=0.69K

ΔT=1.05K

Filled: ΔTOpen: ΔT+ΔJ


1.0

0.9

0.8

0.7

0.6

102

103

104

teff

[sec]

ΔT=0.26K

ΔT=0.40K


102 103 104

teff [sec]

ΔT=0.69K

ΔT=1.05K


r is intrinsically equal to 1.r is intrinsically equal to 1.

r deviates from 1.r deviates from 1.


1.0

0.9

0.8

0.7

0.6

102

103

104

teff

[sec]

ΔT=0.26K

ΔT=0.40K


102 103 104

teff [sec]

ΔT=0.69K

ΔT=1.05K


Difference between ΔT and ΔT+ΔJ perturbation disappears.Difference between ΔT and ΔT+ΔJ perturbation disappears.

r is intrinsically equal to 1.r is intrinsically equal to 1.



1.0

0.9

0.8

0.7

0.6

102

103

104

teff

[sec]

ΔT=0.26K

ΔT=0.40K


102 103 104

teff [sec]

ΔT=0.69K

ΔT=1.05K


0.6

0.5

0.4

103

104

sub peaksub peakr is intrinsically equal to 1.r is intrinsically equal to 1.


Difference between ΔT and ΔT+ΔJ perturbation disappears.Difference between ΔT and ΔT+ΔJ perturbation disappears.

· Classification of aging behavior· Classification of aging behavior

P.E.Jönsson. R. Mathieu, P. Nordblad, H. Yoshino, H. Aruga Katori and A. Ito:Phys. Rev. B 70, 174402(2004).P.E.Jönsson. R. Mathieu, P. Nordblad, H. Yoshino, H. Aruga Katori and A. Ito:Phys. Rev. B 70, 174402(2004).

· Overlap length : L

ΔX = L

0|ΔX/J|

-1/ζ· Overlap length

: L

ΔX = L

0|ΔX/J|

-1/ζ

Non-perturbed state and ΔX-perturbed state are completely different on

large scale much beyond LΔX

.

Non-perturbed state and ΔX-perturbed state are completely different on

large scale much beyond LΔX

.

· Domain size after wait time tw : L

i(t

w) (initial stage)· Domain size after wait time t

w : L

i(t

w) (initial stage)

· Domain size under ΔX-perturbation after time tp :

Lp(t

eff) (perturbation stage)

· Domain size under ΔX-perturbation after time tp :

Lp(t

eff) (perturbation stage)

· Domain size without perturbation after time t : Lh(t)

(healing stage)

· Domain size without perturbation after time t : Lh(t)

(healing stage)


· Lp(t

eff) << L

ΔX Weakly perturbed regime

· L

p(t

eff) << L

ΔX Weakly perturbed regime

Accumulative aging 　　　　　 tpeak

= teff

+ tw

Recovery of order parameter in healing stage

Accumulative aging 　　　　　 tpeak

= teff

+ tw

Recovery of order parameter in healing stage

· Li(t

w), L

p(t

eff), L

h(t) >> L

ΔX Strongly perturbed regime

· L

i(t

w), L

p(t

eff), L

h(t) >> L

ΔX Strongly perturbed regime

Chaotic behavior 　　　　　　 t

peak < t

eff + t

wDecrease in order parameter in healing stage

Appearance of sub peak

Chaotic behavior 　　　　　　 tpeak

< teff

+ tw

Decrease in order parameter in healing stage

Appearance of sub peak

· Li(t

w), L

p(t

eff), L

h(t) ~ L

ΔX Crossover regime

· L

i(t

w), L

p(t

eff), L

h(t) ~ L

ΔX Crossover regime

Intermediate behavior between weakly and strongly perturbed regimesIntermediate behavior between weakly and strongly perturbed regimes

r ~ 1r ~ 1

r < 1r < 1


1.2

1.0

0.8

0.6

0.4

0.2

0.0

102

103

104

teff

[sec]

ΔT+ΔJ

W

WC

SCS

W

WC

SCS

1.2

1.0

0.8

0.6

0.4

0.2

0.0

ΔT

S : Strongly perturbed regime

SC : Crossover regime near strongly perturbed regime

WC : Crossover regime near weakly perturbed regime

W : Weakly perturbed regime





1.2

1.0

0.8

0.6

0.4

0.2

0.0

102

103

104

teff

[sec]

ΔT+ΔJ

W

WC

SCS

W

WC

SCS

1.2

1.0

0.8

0.6

0.4

0.2

0.0

ΔT









Shift of boundary curve Shift of boundary curve


· Contribution of ΔJ· Contribution of ΔJ

Shift of boundary curveShift of boundary curve

decrease in overlap lengthdecrease in overlap length

LΔT+ΔJ

< LΔT

LΔT+ΔJ

< LΔT

1.0

0.9

0.8

0.7

0.6

102

103

104

teff

[sec]

ΔT=0.26K

ΔT=0.40K

ΔT+ΔJ

ΔT+ΔJ data with ΔT= 0.26 K

~ ΔT data with ΔT= 0.40 K

ΔT+ΔJ data with ΔT= 0.26 K

~ ΔT data with ΔT= 0.40 K

contribution of ΔJ perturbation with ΔT= 0.26 K

~ 014 K

contribution of ΔJ perturbation with ΔT= 0.26 K

~ 014 K


· check of ΔJ perturbation · check of ΔJ perturbation

1. Illumination on carbon side surface 1. Illumination on carbon side surface

6

4

2

010

210

310t [sec]

p=1500sec

p=3000sec

p=3000sectp=4500sec

tw tp= 6000sec

= 6% (ΔT=0.25K)(ΔT=0.49K)

(tw=6000sec)

ttt

+

noillumination

4

Open: I/I0Solid: I/I0 =12%


1. Illumination on carbon side surface 1. Illumination on carbon side surface

6

4

2

010

210

310t [sec]

p=1500sec

p=3000sec

p=3000sectp=4500sec

tw tp= 6000sec

= 6% (ΔT=0.25K)(ΔT=0.49K)

(tw=6000sec)

ttt

+

noillumination

4

Open: I/I0Solid: I/I0 =12%

Independent of strength and duration of perturbationIndependent of strength and duration of perturbation



2. Photon energy hν smaller than energy gap Eg 2. Photon energy hν smaller than energy gap E

g

hν 149 eV

Eg = 2.18 eV

hν 149 eV

Eg = 2.18 eV

>>

5

4

3

2

1

0

102

103

10

[sec]

= 3000sec

t

tw = 3000sec

tp= 3000sec

4

no illumination

I / I0 = 0.246tw + tp



5

4

3

2

1

0

102

103

10

[sec]

= 3000sec

t

tw = 3000sec

tp= 3000sec

4

no illumination

I / I0 = 0.246tw + tp

hν 149 eV

Eg = 2.18 eV

hν 149 eV

Eg = 2.18 eV

>>

Intrinsically identicalIntrinsically identical

There is no contribution from photo illumination with low photon energy.There is no contribution from photo illumination with low photon energy.


2. Photon energy hν smaller than energy gap Eg 2. Photon energy hν smaller than energy gap E

g

B. bond perturbationB. bond perturbation

no illumination tw

= 6000 secno illumination tw

= 6000 sec


chaoticchaotic

accumulativeaccumulative


· tpeak

· tpeak


· tpeak

· tpeak accumulative aging

: tpeak

= tp + t

w

accumulative aging

: tpeak

= tp + t

w


· tpeak

· tpeak

chaoticchaotic

accumulativeaccumulative



slow decrease(chaotic)slow decrease(chaotic)

decrease independent of strength of perturbation decrease independent of strength of perturbation

Two-step changes in bond interaction ?Two-step changes in bond interaction ?



ΔT = 0.40K temperature cycle ΔT = 0.40K temperature cycle

Difference between ΔJ and ΔT perturbations ?Difference between ΔJ and ΔT perturbations ?


4. Summary of aging behavior of spin glass under bond perturbation4. Summary of aging behavior of spin glass under bond perturbation

1. Effective ΔJ perturbation by photo excitation in spin glass semiconductor. 1. Effective ΔJ perturbation by photo excitation in spin glass semiconductor.

2. Observation of rejuvenation (chaotic) effect by ΔJ perturbation.2. Observation of rejuvenation (chaotic) effect by ΔJ perturbation.

3. Plausible features of decrease in overlap length with ΔJ perturbation.3. Plausible features of decrease in overlap length with ΔJ perturbation.

4. Difference between ΔJ and ΔT perturbations in detail.4. Difference between ΔJ and ΔT perturbations in detail.

1. Effective ΔJ perturbation by photo excitation in spin glass semiconductor. 1. Effective ΔJ perturbation by photo excitation in spin glass semiconductor.

2. Observation of rejuvenation (chaotic) effect by ΔJ perturbation.2. Observation of rejuvenation (chaotic) effect by ΔJ perturbation.

3. Plausible features of decrease in overlap length with ΔJ perturbation.3. Plausible features of decrease in overlap length with ΔJ perturbation.

4. Difference between ΔJ and ΔT perturbations in detail.4. Difference between ΔJ and ΔT perturbations in detail.

4. Summary of aging behavior of spin glass under bond perturbation4. Summary of aging behavior of spin glass under bond perturbation

OutlineOutline




Behavior of spin glass nanoparticle in magnetic fieldBehavior of spin glass nanoparticle in magnetic field





1. Why is spin glass nanoparticle necessary1. Why is spin glass nanoparticle necessary

Quantitative evaluation of spatial length scales and critical exponents, e.g.,Quantitative evaluation of spatial length scales and critical exponents, e.g.,



Quantitative evaluation of spatial length scales and critical exponents, e.g.,Quantitative evaluation of spatial length scales and critical exponents, e.g.,

SG domain sizeCritical exponent ΨField crossover lengthCritical exponent δ ···




· SG domain size· SG domain size

NanoparticlesNanoparticles

DD

Domain growth is restricted to the particle size D.Domain growth is restricted to the particle size D.

BulkBulk

L → ∞L → ∞

t → ∞t → ∞

Large droplet cannot reach the equilibrium state in experimental time scale.Large droplet cannot reach the equilibrium state in experimental time scale.

L = DL = D



· SG domain size· SG domain size

NanoparticlesNanoparticles

DD

Domain growth is restricted to the particle size D.Domain growth is restricted to the particle size D.

BulkBulk

L → ∞L → ∞

t → ∞t → ∞

Large droplet cannot reach the equilibrium state in experimental time scale.Large droplet cannot reach the equilibrium state in experimental time scale.

L = DL = D

D ~ L(τ) ~ L0[k

BT ln(τ/τ

0)/Δ(T)]

1/Ψ D ~ L(τ) ~ L

0[k

BT ln(τ/τ

0)/Δ(T)]

1/Ψ

Droplet picture Droplet picture

Evaluation of SG domain size and Ψ Evaluation of SG domain size and Ψ



Qualitative evaluation of spatial length scales and critical exponents, e.g.,Qualitative evaluation of spatial length scales and critical exponents, e.g.,





Lh

Lh

· Field crossover length· Field crossover length

DD

Lh

> DLh

> D

Lh

Lh

DD

Lh

< DLh

< D



Lh

Lh

· Field crossover length· Field crossover length

DD

Lh

> DLh

> D

Lh

Lh

DD

Lh

< DLh

< D

Observation of crossoverObservation of crossover

Evaluation of field crossover length and δEvaluation of field crossover length and δ

D ~ Lh ~ l

Th

-δ D ~ L

h ~ l

Th

-δ

Droplet picture Droplet picture


• Reversed micelle method• Reversed micelle method

Ag(11 at.% Mn) nanoparticleAg(11 at.% Mn) nanoparticle

Ag+

Mn2+

H2O

NaBH4

H2O

Oactane

TEM imageTEM image

Anneal in vacuum with excessive addition of surfactants

Sample 1 : 400 °C for 6 hours



Sample 1

Sample 2

Sample 3

D ~ 44 nm

D ~ 51 nm

D ~ 53 nm


1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

χ (10

-6

)emu

2824201612840 ( )Temperature K

= 5 H Oe = 10 H Oe = 50 H Oe = 100 H Oe = 200 H Oe = 300 H Oe = 400 H Oe = 500 H Oe = 1000 H Oe

1.4

1.2

1.0

0.8

0.6

0.4

0.2

χ (10

-6

/ )eum Oe

2824201612840

( )Temperature K

= 5 H Oe = 10 H Oe = 20 H Oe = 25 H Oe = 30 H Oe = 100 H Oe = 500 H Oe

5.0

4.0

3.0

2.0

1.0

0.0

χ (10

-6 )emu



Sample 1 Sample 2 Sample 3


1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

χ (10

-6

)emu



1.4

1.2

1.0

0.8

0.6

0.4

0.2

χ (10

-6

/ )eum Oe

2824201612840

( )Temperature K

= 5 H Oe = 10 H Oe = 20 H Oe = 25 H Oe = 30 H Oe = 100 H Oe = 500 H Oe

5.0

4.0

3.0

2.0

1.0

0.0

χ (10

-6 )emu




Field dependence of peak temperature Tpeak

.Field dependence of peak temperature Tpeak

.


Relation between L and TpeakRelation between L and Tpeak


60

50

40

30

20

10

0

L (nm)

0.500.400.300.200.100.00

Tpeak /Tg



60

50

40

30

20

10

0

L (nm)

0.500.400.300.200.100.00

Tpeak /Tg

D ~ L(τ) ~ L0[k

BT

peak ln(τ/τ

0)/Δ(T)]

1/Ψ D ~ L(τ) ~ L

0[k

BT

peak ln(τ/τ

0)/Δ(T)]

1/Ψ



60

50

40

30

20

10

0

L (nm)

0.500.400.300.200.100.00

Tpeak /Tg

D ~ L(τ) ~ L0[k

BT

peak ln(τ/τ

0)/Δ(T)]

1/Ψ D ~ L(τ) ~ L

0[k

BT

peak ln(τ/τ

0)/Δ(T)]

1/Ψ

Ψ ~ 2.2 Ψ ~ 2.2

Θ Ψ < d-1 = 2Θ Ψ < d-1 = 2a little largea little large

Relation between H and TpeakRelation between H and Tpeak

1000

750

500

250

0

Field (

Oe )

20151050

Tpeak (K)




1000

750

500

250

0

Field (

Oe )

20151050

Tpeak (K)


linear relationlinear relation



1000

750

500

250

0

Field (

Oe )

20151050

Tpeak (K)


E(L) ~ B (L) - qM

L3)1/2

HE(L) ~ B (L) - qM

L3)1/2

H

H ~ - qM

-1/2L-3/2kBT

peak + q

M

-1/2L-3/2B(L)H ~ - qM

-1/2L-3/2kBT

peak + q

M

-1/2L-3/2B(L)

barrier energybarrier energy Zeeman energyZeeman energy

Appearance of peak at kBT

peak ~ E(L)Appearance of peak at k

BT

peak ~ E(L)

Linear relation between H and Tpeak

Linear relation between H and Tpeak

Lh < DL

h < D



1000

750

500

250

0

Field (

Oe )

20151050

Tpeak (K)


deviation from linear relationdeviation from linear relation



1000

750

500

250

0

Field (

Oe )

20151050

Tpeak (K)

Sample 1 Sample 2 Sample 3Deviation from linear relation between H and T

peakDeviation from linear relation between H and T

peak

Lh > DL

h > D

Estimation of Lh

Estimation of Lh


Possible estimation of δ in Lh

~ h

-δPossible estimation of δ in L

h ~

h

-δ

4. Summary of behavior of spin glass nanoparticle in magnetic field4. Summary of behavior of spin glass nanoparticle in magnetic field

1. SG domain size and the critical exponent can be evaluated.1. SG domain size and the critical exponent can be evaluated.

2. Field crossover length and the critical exponent can be evaluated.2. Field crossover length and the critical exponent can be evaluated.


· Ambiguities in temperature perturbation can be removed using bond perturbation based on the photo illumination on SG semiconductor.


· Effect of bond perturbation appears through the decrease in overlap length.· Effect of bond perturbation appears through the decrease in overlap length.

· SG domain size, field crossover length and the corresponding exponent can be quantitatively evaluated using SG nanoparticle.

· SG domain size, field crossover length and the corresponding exponent can be quantitatively evaluated using SG nanoparticle.




· Effect of bond perturbation appears through the decrease in overlap length.· Effect of bond perturbation appears through the decrease in overlap length.

· SG domain size, field crossover length and the corresponding exponents can be quantitatively evaluated using SG nanoparticle.

· SG domain size, field crossover length and the corresponding exponents can be quantitatively evaluated using SG nanoparticle.

Some experimental approaches to study the aging phenomena in spin glasses Tetsuya Sato Keio...

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Transcript of Some experimental approaches to study the aging phenomena in spin glasses Tetsuya Sato Keio...