experimental approach to macroscopic quantum tunneling of magnetization in single domain...

Experimental Approach to Macroscopic Quantum Tunneling of Magnetization

in Single Domain Nanoparticles

H. Mamiya, I. Nakatani, T. Furubayashi

Nanomaterials Laboratory

National Institute for Materials Science

Tsukuba 305-0047, Japan

International Workshop on "Physics on Nanoscale Magnets"

Outline

1. Introduction

2. Sample

3. Conventional approaches and their results

(Suggestions of QTM)

4. Points to be noted

5. Modified approach and its results

(Predominance of classical relaxations)

6. Summary


Introduction


Macroscopic Quantum Tunneling of magnetization vector

was observed in molecular magnets.

N SSZ= m

SZ = m-1

SZ=-m

SZ =-m+1

N S

Molecular Magnets | S |

Nano-Antiferromagnets | S |

Nano-Ferromagnets | S | > 103

N S

How about larger systems ?

Do antiferromagnetic nanoparticles show QTM ?

Sample


Examined sample was natural horse-spleen ferritin protein, which stores antiferromagnetic ferrihydrite in its cage ( 8 nm) .

Each core has a small magnetization vector ~300B

due to its uncompensated spins.

A conventional approach and its results— Temperature dependence of relaxation rate —


Decay function:

Exponential: No

Logarithmic: Yes

Relaxation rate S, IRM/ln t

is discussed as usual.

S flattens out at lower T.

Relaxations appear to be temperature-independent.

Isothermal remanent magnetization

IRM and its relaxation rate S

0.1 0.5 1 5 100.30

0.31

0.32

0.33

0.34

t (ks)

IRM

(em

u/g)

Happl = 30 kOeT = 5.0 K

dln

t

1 4 7 100

5

10

T (K)

S (

=

)dI

RM

The conventional approach ( Next Step ) — Scaling of relaxation curves at various T —


If thermal process: k ( Happl=0, T ) = 0 exp[-Bk(Happl=0)/kBT]

IRM( t )

m

H T t

jj k

k

0

ap p l

,

, . 0

mt

jj j

0

ex p

m B H T E k T tjj k

k0

ap p l c B, , ln ( / ) .0 0

Logarithmic decay :

Sum of exponential decays of poly-dispersive particles

IRM( t ) 　 =

Exponential function in ln t Step function

IRM( t )

As long as thermal processes, IRM( t ) can be scaled by Ec.

Except for

Only

10-10 10-5 100 105 10100

0.5

1.0

t (s)

f()=e-t/:=1s

2.0 2.5 3.0 3.5R (nm)

Results of the scaling analysis —Relaxations at various temperatures —


IRM( t ) cannot be mapped

onto an unique master curve

at the lower temperatures.

Non-thermal relaxations ?

We observe Pure QTM ?

Isothermal remanent magnetization

as a function of EC/kB = T ln( t/0 )

500.12

0.20

0.28

0.36

T·ln(t·f0) (K)

IRM

(em

u/g)

Happl = 30 kOe

T=2.0K

100 200 300

T=5.0K

Points to be noted — Initial States of IRM( t ) —


Though Happl = 30 kOe is large,

M is not saturated

owing to complex coupling with antiferromagnetic spins.

The initial states of IRM( t ) are not always uniform at different T.

The scaling ???

M-H curves of ferritin

-80 -40 0 40 80

-1.2

-0.6

0

0.6

1.2

M (

emu/

g)

H (kOe)

5 K 60 K180 K

This problem is common to nanoparticles, since they have disorder of surface spins

A conventional approach — A maximum of ( T ) —


Thermal energy kBT »Barrier height B

fluctuates and 1/T.

kBT « B

is blocked and is small.

On their boundary,

a maximum of should appear.

( this temperature is Tmax )

Hence, Tmax B is assumed,0

TemperatureD

ynam

ical

Sus

cept

ibili

ty

TmaxTBB

: small : Curie law

kBT

Results — Field-dependence of the maximum —


the rise in Tmax with H

If Tmax B

Increase of effective B in H.

N S

(a) H = 0

Beff

N S

(b) H > 0

Beff

M( T ) in various H

Thermally assisted resonant QTM

and its suppression by H ?

10 12 14 16 18 200.9

1.0

1.1Tmax 200Oe

T (K)

M/M

(Tm

ax) 600Oe

1000Oe

50 100 150

2

4

6

0

MZFCMFC

T (K)

M (

10-2

emu/

g )

Points to be noted — Final states of zero-field-cooled M ( t ) —


Tmax depends not only on the relative speed

but on unknown temperature-dependence of the final state

Distance Relative Variation during

to final states speed the observations

T

Meq =

T 1

-ex

p(-t

/)

TBB

T

Ob

serv

ab

le　M

ZF

C

Tmax

Modified approach —Initial and final states independent of T, Hmeas—


Note: mjFC ( Hcool,TB) is given by mj at TB on cooling in Hcool.

Each distance of relaxation is independent of T, Hmeas.

For j th particle, equilibrium m: mjeq ( Hmeas, T ), j ( Hmeas, T )

Zero-field-cooled magnetization,

MZFC(Hmeas,T ) is M m H T

t

H Tjj j

eqeq

m easm eas

, ex p

,.

M m H T m H T

t

H Tj jj j

eqeq

m easF C

co o lm eas

, , ex p,

,

m H T

t

H Tjjj

F Cco o l B

m eas

, ex p,

,

Reversed-thermoremanent magnetization RTRM:

Their sum Msum is

Scaling of Msum curves at various T, Hmeas — An overview —


Msum( t ) at each Hmeas can be mapped onto a master curve

at all the temperatures.

Thermally activated mechanism

The master curve shifts downward with Hmeas.

Acceleration by the fieldMsum( t ) vs. EC/kB = T ln( t/0 )

100 200 3000

0.1

0.2

0.3

0.4

50 80T·ln(t·f0) (K)

Msu

m (

emu/

cm3 )

Hmeas0 kOe3 kOe6 kOe

Hcool = 1 kOe

Distribution of barrier heights in Hmeas — An overview —


Msum( Ec ) = mjFC of Bj>Ec

A cumulative distribution

with weights m(B).

Msum/Ec ( = S/T )

n(B):

Distribution of barrier heights.

The barrier height B reduces with Hmeas in Hmeas> 1 kOe.

Distribution of barrier heights in Hmeas = 0 — Details at lower temperatures —


Distribution of barrier heights

Msum/Ec ( = S/T ) n(B)

100 200 300

0.001

0.002

0.003

0.004

0

n (B

)

B/kB (K)

Hcool (kOe) 0.1 30.0

Msum( t ) vs. EC/kB = T ln( t/0 )

The scaling holds above 1.8 K.Thermally activated processes are dominant at a few kelvins.

T = 2.0 K

T = 3.0 K

40 80 120 1600.8

0.9

1.0

T·ln(t/0) (K)

Msu

m (

t, T

, Hm

eas=

0 ) Hcool (kOe)

0.130.0

Only in the larger cooling field, lower barriers are observable.

The origin of non-zero-relaxation rate Why lower barriers appear when Hcool is large?


A1. Since smaller particles with smaller B have smaller , they are magnetized only when Hcool is large enough.

A2. Even when Hcool is large, M is not saturated owing to complex coupling with antiferromagnetic spins.

The spin arrangement at that time may be metastable in Hmeas = 0 after cutting off Hcool. Escape from such local, shallow minima can be observed at the lower temperatures.

Relaxations during thermal cycles — Another approach using uniform initial states —


The relaxation exponentially slows down

during the temporary cooling

while it exponentially accelerates

during the temporary heating.

Relaxations with thermal cyclesand effective time during the cycles

5 10 50 100183

184

185

186

T (K) 0.05-0.05 isothermal

t (ks)t-(t2-t1)+teff

M (

103 em

u/g

)

t2.0

T2.0+T

t1 t2

1.7 2.0 2.310-2

10-1

100

101

t eff/

(t2-

t 1)

Tm+T (K)

E/kB 60 K

An additional proof of predominance of thermal processes

Distribution of barrier heights in Hmeas

— Details in weak fields —


At the low fields Hmeas< 0.3kOe

no detectable change of n( B ) is observed.

n( B ) in low Hmeas

normalized by n( B ) in Hmeas= 0

Relaxations do not slow down when Hmeas is applied,in contrast with the prediction for resonant QTM.

As shown in the overview,

the barrier height B reduces with Hmeas in Hmeas> 1 kOe.

10-4 10-3 10-2 10-1 100 1010

0.5

1.0

1.5

Hmeas ( kOe )

n(B

), [

=

Msu

m/

Ec

]

2 K 5 K11 K

Relaxation time in weak fields — Explanation by classical fluctuations —


The relaxation is accelerated, as predicted for classical activated mechanisms.

Half-life t1/2

0.1 0.2 0.3 0.4 0.5 0.6

0.2

0.4

0.6

0.8

1.0

0Hmeas ( kOe )

t 1/2

( H

= ±

Hm

eas)

Angle 0 /3 2/3

HK = 20 kOe

t 1/2

( H

= 0

)

T = 8.0 K

Summary

1. We show that lack of the uniformity of initial ( or final ) states of relaxations seriously affects the results of the conventional approaches to QTM in nanomagnets.

2. For this reason, we propose a modified approach.

3. Its results clearly indicate that the relaxations observed in natural ferritin are dominated by classical superparamagnetic fluctuations in the Kelvin regime.

4. Existence of QTM below 2 K is still debatable.

Further study using the modified approach is required.


experimental approach to macroscopic quantum tunneling of magnetization in single domain...

Documents

nanoscale magnets irm

nanoscale magnets tmax

irmln t

maximum international

ln t step functionirm

molecular magnets

japaninternational workshop

sampleinternational