1. Competing tunneling and capacitive channels in granular insulating thin films: universal response
Montserrat García del Muro, Miroslavna Kovylina, Xavier Batlle and
Amílcar Labarta
Departament de Física Fonamental and Institut de Nanociència i Nanotecnologia,
Universitat de Barcelona, Barcelona, Catalonia, Spain

2. Introduction: magnetic granular solids
Nonmagnetic insulating matrix (ZrO2, Al2O3)
thin
film
FM metallic particles (Co, Fe, CoFe, FeNi)
J. Phys. D: Appl. Phys. 35, 15 (2002)

3. 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
CoPt:C xV= 0.7
M. Yu et al. APL (1999)
High coercivity films for magnetic storage
High permeability and resistivity films for applications at high frequency
Tunneling magnetoresistance (TMR) (magnetic sensors)

4. Introduction: dc electric transport properties
Regime:
Co-ZrO2
dielectric
ρ(T) changes in many orders of magnitude
In the dielectric regime, ρ(T) decreases abruptly with the temperature.
The slope of ρ(T) becomes positive in the metallic regime x
transition
metallic

5. - Introduction: dc electric transport properties + e- Charging energy:
Dielectric regime: quantum tunneling among metallic particles e-
Charging energy:
Coulomb
Blockade - + s d
Co-ZrO2 (x=0.27)
ln (R[k])
P.Sheng y B. Abeles, PRL 28, 34 (1972)

6. Sample preparation Out-of-equilibrium methods (ultrafast cooling)
Laser ablation Co
ZrO2
Composed
target
Nanotechnology 17, 4106 (2006)

7. Structural characterization
Low metal content (x<0.2)
Co particles are crystalline and show sharp interfaces with the amorphous matrix.
Particle size distribution is bimodal.
There is a majority of very small particles through which tunneling can take place.
APL 91, (2007)

8. Structural characterization
Intermediate metal content (x > 0.2 < xp) x
0.25
0.30
0.35
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.

9. Structural characterization
Z-contrast image
HRTEM
Ultra-small glue particles in between the bigger ones are present at any composition below the percolation threshold

10. Tunneling magnetoresistance (TMR)H
H = 0
low
resistance
high
resistance
Fermi energy

11. TMR in granular solids q Conductance between two particles:
Average over all orientations:
Inoue and Maekawa, PRB 53, R11927 (1996)

12. TMR in granular solids
x=0.27
TMR in granular metals can be well reproduced by fitting experimental data to the model of Inoue and Maekawa.
PRB 73, (2006)

13. TMR in granular solids “cotunneling” Glue particles
One electron is transferred between two large particles through a collective process involving several small particles
Glue particles
S. Mitani et al., PRL 81, 2799 (1998)
PRB 73, (2006)

14. 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

15. tunneling conductance among particles capacitance among particles
Ac response
ac conduction mechanisms
tunneling conductance among particles
capacitance among particles
does not depend on T

16. tunneling conductance among particles capacitance among particles
Ac response
ac conduction mechanisms
tunneling conductance among particles
capacitance among particles
does not depend on T

17. Ac conductance: dominant mechanisms
Random competition among tunneling and capacitive channels throughout the system e-
Tunneling conductance
Capacitance
Homogeneity of the sample at the macroscopic scale

18. Ac conductance: logarithmic mixing rule
Simple case: the conductance of both capacitive and tunneling channels become comparable.
fraction of tunneling channels
Constant phase
regime for the impedance
Fractional power
law
41 K
60 K
90 K
0.1
0.2
0.3
0.4
log10(σ/σ0)
x=0.27

19. Ac conductance: modulus of the impedance
PRB 79, (2009)

20. Ac conductance: real and imaginary parts

21. Ac capacitance: real and imaginary parts
x=0.24
x=0.27
290 K
29 K
290 K
29 K

22. Ac capacitance: real and imaginary parts
x=0.27
Arrhenius law
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, (2003); PRB 79, (2009)

23. Simple model: random R-C network
Tunneling among small particles
Capacitance among large particles
WINSPICE by M. Smith, University of Berkeley

24. Simple model: random R-C network

25. 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, (2009)

26. 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.