Competing tunneling and capacitive channels in granular insulating thin

films: universal response

Competing tunneling and capacitive channels in granular insulating thin

films: universal responseMontserrat García del Muro, Miroslavna Kovylina, Xavier Batlle and

Amílcar Labarta

Departament de Física Fonamental and Institut de Nanociència i Nanotecnologia, Universitat de Barcelona, 08028 Barcelona, Catalonia, Spain

Introduction: magnetic granular solids

Nonmagnetic insulating matrix (ZrO2, Al2O3)

FM metallic particles (Co, Fe, CoFe, FeNi)

thinfilm

J. Phys. D: Appl. Phys. 35, 15 (2002)

Introduction: magnetic granular solids

Fundamental properties of the FM nanoparticles (new phenomena): finite-size, surface and proximity effects, and interparticle interactions.

Model systems for studying electric transport properties in disordered media.

Applications

• High coercivity films for magnetic storage

• High permeability and resistivity films for applications at high frequency

• Tunneling magnetoresistance (TMR) (magnetic sensors)

CoPt:C xV= 0.7

M. Yu et al. APL 75 3992 (1999)

CoPt:C xV= 0.7

M. Yu et al. APL 75 3992 (1999)

Introduction: dc electric transport properties

dielectric

transition

metallic

Regime:

x

Co-ZrO2

Introduction: dc electric transport properties

0 exp 2 / BB k T

Dielectric regime: quantum tunneling among metallic particles

Charging energy:0 2 /C effE e k d

e-

Coulomb Blockade

P.Sheng y B. Abeles, PRL 28, 34 (1972)

0 22 /CB sE m

-+

ln (

R[k

])

Co-ZrO2 (x=0.27)

sd

Sample preparation

Out-of-equilibrium methods (ultrafast cooling)

turbopump

substrateheater

pressuregauge

vacuumchamber

substrate

target

motor

holdertargets

laser beam

lensfocussing

Co

ZrO2

Laser ablation

Composedtarget

Nanotechnology 17, 4106 (2006)

Structural characterization

Low metal content (x<0.2)

APL 91, 052108 (2007)

Structural characterization

Intermediate metal content (x > 0.2 < xp)x

The bimodal distribution collapses in a single broader effective log-normal function.

Further increase of the metal content: the size distribution shifts to larger sizes keeping the width almost constant.

About x=0.35, the size distribution broadens abruptly because of the massive particle coalescence just before percolation.

0.25 0.30 0.35

Structural characterization

5 nm

Beam

2 nm

Z-contrast image HRTEM

Ultra-small glue particles in between the bigger ones are present at any composition below the percolation threshold

Tunneling magnetoresistance (TMR)

Fermi energy

H H = 0

lowresistance

highresistance

DD

DDP

TMR in granular solids

)cos1( 20 PGG

Conductance between two particles:

Average over all orientations:

0

20 )cos1()( dPgGG

2

2

cos mM

M

S

22

22

1

11

1)0(

)()0(TMR

mP

mP

G

HGG

Inoue and Maekawa, PRB 53, R11927 (1996)

TMR in granular solids

PRB 73, 045418 (2006)

x=0.27

TMR in granular metals can be well reproduced by fitting experimental data to the model of Inoue and Maekawa.

TMR in granular solids

“cotunneling”

One electron is transferred between two large particles through a collective process involving several small particles

One electron is transferred between two large particles through a collective process involving several small particles

S. Mitani et al., PRL 81, 2799 (1998)PRB 73, 045418 (2006)

Glue particles

TKmPMRmax /122

The role of glue particles

These granular solids are model systems for studying electric transport properties in disordered media with tunneling conduction among particles.

tunneling channels

Glue particles

Ac response

tunneling conductance among particles

capacitance among particles

C does not depend on T2 /C d s

ac conduction mechanisms

0 exp 2 /t BB k T

Ac response

tunneling conductance among particles

capacitance among particles

C does not depend on T2 /C d s

ac conduction mechanisms

0 exp 2 /t BB k T

Ac conductance: dominant mechanisms

Random competition among tunneling and capacitive channels throughout the system

2

i p

p

C

dC d

s

1

tR T Tunneling conductance

Capacitance

e- e-

sd

const.s

d

Homogeneity of the sample at the macroscopic scale

Ac conductance: logarithmic mixing rule

1

ln lnn

ii

111 1 1 2(1 / ) ( ) errr r r r

i xxx x x xt pR i C i

rx fraction of tunneling channels

(1 )2rx (1 )Re rx

Simple case: the conductance of both capacitive and tunneling channels become comparable.

Simple case: the conductance of both capacitive and tunneling channels become comparable.

x=0.27

Constant phaseregime for the

impedance

41 K

rx1

60 K90 K

0

0.1

0.2

0.3

0.4

log 1

0(σ

/σ0)

Fractional powerlaw

Ac conductance: modulus of the impedance

PRB 79, 094201 (2009)

Ac conductance: real and imaginary parts

0, ( , )r iT T C T , ( , )i rT C T

1 / R i C

r iC C iC 0 i rC i C

)(0 T

Ac capacitance: real and imaginary parts

x=0.27

29 K

29 K

290 K

290 K

pFrC

pFiC

x=0.24

pFiC

pFrC

Ac capacitance: real and imaginary parts

Arrhenius law

TBW/keW 18 meV

By using ντ as scaling variable, all the curves for the real and imaginary (dielectric loss) parts of the capacitance collapse onto two master curves.

This absorption phenomenon imitates the universal response of disordered dielectrics.

PRB 67, 033402 (2003); PRB 79, 094201 (2009)

p=0.5

x=0.27

x=0.27

pFrC

pFiC

Simple model: random R-C network

WINSPICE by M. Smith, University of Berkeley

11 14

' 21 19

19 18p

10 10

10 10 F

10 10 F

t

p

R

C

C

Capacitance among large particles

Tunneling among small particles

Simple model: random R-C network

Simple model: random R-C network

x=0.34

x=0.29

x=0.24

The average tunneling resistance between neighboring particles is in qualitatively agreement with experimental dc resistance of the samples multiplying it by an arbitrary scale factor.

PRB 79, 094201 (2009)

Final remarks

The ac transport properties in granular magnetic thin films originates from the competition between interparticle tunneling and capacitance throughout an intricate three-dimensional random R-C network.

The effective ac behavior mimics the universal response observed in many disordered dielectric materials, but at much lower frequencies.

A random R-C network of resistors and capacitors reproduces very well the overall experimental behavior.