Transition in spin dependent transport from superparamagnetic-superparamagnetic to superparamagnetic-ferromagnetic in sputteredCu100–xCox granular filmsDinesh Kumar, Sujeet Chaudhary, and Dinesh K. Pandya Citation: J. Appl. Phys. 112, 083924 (2012); doi: 10.1063/1.4761965 View online: http://dx.doi.org/10.1063/1.4761965 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v112/i8 Published by the American Institute of Physics. Related ArticlesTemperature-dependent dynamic magnetization of FeCoHf thin films fabricated by oblique deposition J. Appl. Phys. 112, 083925 (2012) Magnetic and magnetotransport properties of Ba2FeMoO6 pulsed laser deposited thin films J. Appl. Phys. 112, 083923 (2012) Magnetically and thermally induced switching processes in hard magnets J. Appl. Phys. 112, 083919 (2012) Spin-wave modes and band structure of rectangular CoFeB antidot lattices J. Appl. Phys. 112, 083921 (2012) Perpendicular magnetic anisotropy in Nd-Co alloy films nanostructured by di-block copolymer templates J. Appl. Phys. 112, 083914 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

Transition in spin dependent transport from superparamagnetic-superparamagnetic to superparamagnetic-ferromagnetic in sputteredCu100–xCox granular films

Dinesh Kumar, Sujeet Chaudhary, and Dinesh K. Pandyaa)

Thin Film Laboratory, Indian Institute of Technology Delhi, New Delhi 110016, India

(Received 5 September 2012; accepted 3 October 2012; published online 25 October 2012)

The transition in the spin-dependent transport from superparamagnetic-superparamagnetic (SPM-

SPM) to superparamagnetic-ferromagnetic (SPM-FM) in room temperature co-sputtered granular

Cu100�xCox (x¼ 15.1–30.9 at. %) thin films is tracked by varying the cobalt concentration. It is

found that at lower cobalt concentrations of x� 20.9, the spin dependent transport is governed by

the scattering which electrons undergo while they move through SPM-SPM network. At higher

cobalt concentration x> 20.9, the transport behavior changes due to predominant electronic

scattering through SPM-FM networks. From the isothermal magnetoresistance behavior in

20–300 K range, transmission electron microscopy analysis, and magnetization behavior, three

different composition regimes are identified. These are (i) x� 15.1, consisting of nearly spherical

monodispersed single uncoalesced non-interacting small SPM particles only; (ii) 15.1< x� 20.9,

having bimodal distribution with small monodispersed SPM and weakly interacting bigger SPM

particles, and (iii) x> 20.9, having monodispersed small SPM particles and FM clusters having

broad distribution with stronger interactions. The work provides an insight to understand the

transition of spin dependent transport from SPM-SPM to SPM-FM and the gradual increase in the

strength of magnetic interaction among the particles vis-�a-vis cobalt concentration. VC 2012American Institute of Physics. [http://dx.doi.org/10.1063/1.4761965]

I. INTRODUCTION

Granular magnetic systems, where nanometer-sized,

superparamagnetic (SPM) particles of a ferromagnetic (FM)

metal are dispersed in a non-magnetic metal matrix, are par-

ticularly attractive owing to their isotropic magnetoresist-

ance (MR) behavior.1–5 The transport properties of granular

systems have been strongly related to the microstructure of

the system, in particular the mean particle diameter, inter-

particle distance, and the volume fraction of FM element.5 In

granular systems, MR is ascribed to spin-dependent scatter-

ing. But the transport phenomena in granular systems are

complicated due to the presence of a distribution of the parti-

cle sizes.6–8 The MR behavior of such films could be quite

different as some particles can be SPM and others FM.

According to Wiser and Hickey model,8,9 when both FM and

SPM particles are simultaneously present, the MRA-B has

three contributions: (i) MRSPM-SPM, (ii) MRFM-FM, and (iii)

MRSPM-FM (¼MRFM-SPM), wherein the term MRA-B corre-

sponds to a spin dependent scattering event for an electron

path, “magnetic region A ! nonmagnetic region ! mag-

netic region B.”10–12 Accordingly, three cases could be con-

sidered for over all MR behavior. Case (i) – if only SPM

particles are present for which MR(H) / [L(x)], where L(x)

is a Langevin function.2 Case (ii) – if the particles undergo

FM ordering, they are aligned at relatively small magnetic

fields and there is no further effect on the resistivity at higher

fields, i.e., no contribution to MR at higher fields from this

term. Case (iii) – if both FM as well as SPM particles are

present, the magnetization of the FM particles is aligned at

small saturation fields, and at higher magnetic fields, the cor-

relation of the two involved magnetizations depends on the

time average of the spatial orientation of the SPM particles

only. This was shown to lead to a linear dependence of the

magnetoresistance on the magnetization of the SPM particles

at high fields, i.e., MR(H) / L(x).10,11

Most of the experimental work on granular systems,

showing SPM-FM spin dependent transport, published so far

has been on thin films with very broad distribution of particle

size with both SPM and FM particles being present.8,9 These

reports have mainly addressed the temperature evolution of

the MR in such granular systems. The effect of increasing

density of monodispersed SPM particles on the magnetotran-

sport properties of granular systems is yet not clear, primar-

ily due to the difficulty in synthesizing such monodispersed

granular alloys. One of the benchmark systems in this con-

text has always been Co in Cu which is well suited due to

the bulk immiscibility of the two components below 400 �C,

preventing homogeneous alloying.13 In the present work, we

present a systematic study showing the effect of increasing

cobalt concentration (“x”) on magnetotransport properties of

granular Cu100�xCox thin films to identify a concentration re-

gime of nearly monodispersed cobalt particles exhibiting iso-

tropic MR response typical of SPM particles and other

regime wherein bimodal particle distribution exists, which

may or may not be dominated by bigger FM particles. Films

a)Author to whom correspondence should be addressed. Electronic

mail: dkpandya@physics.iitd.ac.in. Phone: þ911126591347. Fax:

þ911126581114.

0021-8979/2012/112(8)/083924/8/$30.00 VC 2012 American Institute of Physics112, 083924-1

JOURNAL OF APPLIED PHYSICS 112, 083924 (2012)

are prepared by increasing the sputtering rate of Co, but

keeping the sputtering rate of Cu constant, and hence con-

trolled variation in relative Co-Cu concentration is obtained

in the granular films. While nearly monodispersed Co par-

ticles are observed at lower cobalt concentration as a result

of inhibited growth in terms of suppressed adatom mobility

on substrates kept at room temperature, the random coales-

cence induced by increasing the relative cobalt flux resulted

in the progressive formation of bigger particles having arbi-

trary shape and broad distribution. Consistent with this, a

transition of spin dependent transport from SPM-SPM to

SPM-FM with the increase of Co concentration is observed.

A model based upon monodispersed uncoalesced particles

and coalesced particle clusters is proposed to understand this

transition. The presence of magnetic interactions within the

particles is also investigated in detail.

The paper is organized as follows. The details of film

growth and their different characterizations are presented in

Sec. II. In Sec. III, the MR data of all the films recorded at

300 K are presented, and fitting results are analyzed. This is

followed by transmission electron microscopy (TEM) results

on selected films. Subsequently, the magnetization hysteresis

(M-H) behavior of these films at 300 K is presented and dis-

cussed. The evolution of magnetic interactions within the

particles with increase in cobalt concentration is carefully

analyzed based on the correlation between MR and M-H

data recorded at 300 K, the isothermal MR behavior recorded

at various T in 20–300 K, and isofield temperature depend-

ence of magnetization in one of the selected film.

II. EXPERIMENTAL DETAILS

Granular Cu100�xCox thin films were deposited by dc

magnetron co-sputtering from two confocal sputter magne-

tron guns with Cu and Co targets (purity better than 99.9%).

The deposition rate of Cu was kept constant at 0.14 nm/s and

that of Co was varied from 0.02 to 0.04 nm/s to get different

Co concentration films. The deposition chamber was evac-

uated to a base pressure of 1.5� 10�6 Torr and films were

deposited at a working pressure of 5� 10�3 Torr. Granular

films having six different Co concentrations “x”¼ 15.1,

17.8, 20.9, 25.3, 27.5, and 30.9 were prepared at room tem-

perature, each having a nominal thickness �100 nm. The

composition of the thin films was determined by energy dis-

persive x-ray spectroscopy (EDX). The MR was measured at

room temperature using the four-probe method in a magnetic

field (H) varying up to 0.9 T. The MR measurements were

made in two configurations, with H and I in the plane of

film, (i) I parallel to H (LMR) and (ii) I perpendicular to H

(TMR). MR was calculated using DR/R¼ [R(H) � R(0)]/

R(0), where R(H) and R(0) are the resistances measured in

the presence and absence of H, respectively. TEM studies

were made using JEOL-JEM-2100 F transmission electron

microscope. Magnetization isotherms were measured in

SQUID magnetometer, at room temperature in the field

range 61 T. Magnetization vs. temperature measurements

were performed in 10–300 K range following the zero field

cooling (ZFC) and field cooling (FC) protocols from 300 K

in presence of constant field of 50 Oe.

III. RESULTS AND DISCUSSION

A. Magnetotransport behavior

In Fig. 1, we present %MR as a function of H for three

films x¼ 15.1, x¼ 17.8 and 20.9. It can be seen that the MR

is negative in all the three films. Further, none of the film

exhibits any hysteresis in the observed data. The identical

MR behavior observed for LMR and TMR configurations

confirms that MR is isotropic for these lower concentration

Co films. It can be further seen that the MR curves do not

show any signature of saturation up to the highest investi-

gated magnetic field strength of 0.9 T. This kind of MR

behavior clearly suggests the presence of small SPM par-

ticles in these films. For a collection of SPM particles, MR is

often estimated by the Langevin function L(x),11 given by

MRðHÞ ¼ �AL2ðxÞ; (1)

where A is a constant of proportionality, x¼ (H/x0) and

x0¼ (kBT/l), l being the average magnetic moment of the

SPM particles, H is the applied magnetic field and kB is the

Boltzmann constant. The MR data for sputter deposited films

is generally fitted by considering more than one distribution

in the sizes of the magnetic particles. Hence, considering

more than one distribution in the particle size for such films,

the MR response is given by

MRðHÞ ¼ �A

Xn

i¼1

wiL2 H

xi

� �; (2)

where wi (i¼ 1,n) is the weighing factor for the particles

with average particle diameter di (i¼ 1,n), such thatPni¼1 wi ¼ 1. Initially, we tried to fit our data by taking

n¼ 2–6 used in the previous works done on such sys-

tems,3,7,15 but we could not fit the MR data by considering

“n” in this range. Quite interestingly excellent fitting (Fig.

1(a)) is obtained in case of x¼ 15.1 film using only single

Langevin term (i.e., when n¼ 1). Assuming, the spherical

shape of particles, the average particle size estimated from

FIG. 1. Magnetoresistance curves for films with (a) x¼ 15.1, (b) x¼ 17.8,

and (c) x¼ 20.9 (While the symbols represent the experimental data, the

line represent fit; see text for details). The MR behavior in these samples is

identical for LMR and TMR configuration.

083924-2 Kumar, Chaudhary, and Pandya J. Appl. Phys. 112, 083924 (2012)

the fitting is 2.4 nm (Table I). The lower value of particle

size together with excellent fit of its MR behavior using a

single Langevin function makes us believe that there is a

presence of narrow distribution of particles in this x¼ 15.1

granular film. In contrast to this, the MR data for films

x¼ 17.8 and 20.9 data could not be fitted using Eq. (1).

Instead, as shown in Figs. 1(b) and 1(c), excellent fit was

obtained by using Eq. (2) with n¼ 2 only (two Langevin

functions). The fitting with n¼ 3 or higher revealed unrealis-

tic error (in excess of 100%) in the value of fit parameter xi,

compared to maximum 8% in case of n¼ 2. Therefore, we

can conclude that in x¼ 17.8 and 20.9 films, there exists two

types of particle distributions having different average parti-

cle size. Table I shows the parameters calculated from the fit-

ting of the MR data of these two films with Eq. (2). We can

see that the smaller average particle size described by d1 is

almost same for all the three films with x¼ 15.1, 17.8, and

20.9. It may be noted that, in case of x¼ 17.8 and 20.9 films,

the value of average size of the bigger particles described by

d2 is approximately twice that of d1. This can be understood

in terms of nucleation and growth mechanism taking place

during the film growth in which two or three identically

growing (i.e., same diameter �d1) adjacent nuclei coalesce

to form bigger particles. Understandably, in this scenario,

the value of d2 obtained from the fitting (Table I) is oversim-

plified. The fitting of MR response of the x¼ 17.8 and 20.9

films therefore suggests the presence of single monodis-

persed SPM particles as well as clusters of these single

particles.

From Table I, we note that w2<w1. So, we can say that

compared to monodispersed character of x¼ 15.1 film, the

x¼ 17.8 and 20.9 films exhibit limited abundance of mono-

dispersed particles (� 88% for x¼ 17.8 and �78% in case

of x¼ 20.9), and the observed increase of w2 with increase

in “x” understandably signifies the increase in the number

density of coalesced particles. In our opinion, the change in

the shape of MR curve from convex (x¼ 15.1) to �linear

(x¼ 17.8) and finally to concave at lower H and linear at

higher H (x¼ 20.9) with the increase in cobalt concentration

is, in fact, a manifestation of the progressive evolution of co-

alescence of cobalt nuclei in these films. Therefore, based on

the excellent fit of MR data and its isotropic character

(LMR�TMR), we conclude that in films with x¼ 15.1, 17.8,

and 20.9, both the uncoalesced as well as coalesced particles

are in the SPM regime. In these films, the electrons are mov-

ing from one SPM particle to another SPM particle, so that

the predominant spin dependent transport is of “SPM-SPM”

type.

As the cobalt concentration is increased to x¼ 25.3, the

Fig. 2(a) (Exp data) reveals that the H-dependence of MR

starts to become different from that observed at lower ‘x’

values. It may be stressed here that, similar to lower cobalt

concentration films, this film did not exhibit any discernible

difference in its TMR and LMR response (not shown for

brevity). However, as “x” reaches 27.5, a kink like feature in

the TMR curve gets fully developed at 0.08 T (see Fig. 2(c)).

At this Co concentration of x¼ 25.3, the film basically starts

exhibiting characteristically two different MR contribu-

tions—a rapidly varying low field MR component (up to

0.08 T) and a slowly varying high field MR component with

no sign of saturation up to the maximum available applied

field 0.9 T. In addition, the presence of anisotropic magneto-

resistance (AMR) in films with x¼ 27.5 and 30.9 is distinctly

evidenced in the form of splitting of LMR and TMR curves

(Fig. 2(c)). The LMR in x¼ 27.5 and 30.9 films shows posi-

tive MR up to 0.08 T field and negative beyond that field. It

is well known that in films consisting of SPM particles only,

the LMR and TMR components are indistinguishable since

bulk-like scattering events leading to AMR cannot be due to

small size of SPM particles. It should be noted that the exis-

tence of rapidly varying low field anisotropic component and

non-saturating nearly linear MR behavior at higher field pro-

vides significant evidence of the simultaneous presence of

FM as well as SPM particles in these films.

In order to quantitatively analyze the observed MR

behavior of the higher cobalt concentration films, their MR

data are decomposed by using a procedure described by

Bakonyi et al.10–12 In this procedure, the observed MR(H) is

considered to be consisting of a MRFM term (from FM con-

tribution) and MRSPM term (from SPM contribution). In the

present case, it is observed that for H>HS (HS¼ 0.08 T, the

saturation field of the FM particles present in the film), the

MR(H) curves for x¼ 25.3, 27.5, and 30.9 films could be

well described by Eq. (3) as suggested in Refs. 10–12

MRðHÞ ¼ MRFM þMRSPMLH

x0

� �: (3)

TABLE I. Fitting parameters of Eq. (2) for x¼ 15.1, 17.8, and 20.9.

“x” A x1 x2 w1 w2 d1 (nm) d2 (nm)

15.1 0.92 3815 6 70 … 100 0 2.4 …

17.8 1.94 3655 6 172 658 6 52 0.88 0.12 2.4 4.3

20.9 2.51 3323 6 112 461 6 14 0.78 0.22 2.5 4.9

FIG. 2. (a) Decomposition procedure employed for fitting of MR curve for

film with x¼ 25.3. While the data symbols represent the experimental TMR

data (TMR�LMR), the solid line represent the fit corresponding to the

SPM contribution to MR; (b) decomposed MR curves obtained from fitting

of the data of film with x¼ 25.3, (c) experimental data for films x¼ 27.5 and

30.9, and (d) decomposed MR curves obtained from fitting of the data of

film with x¼ 27.5.

083924-3 Kumar, Chaudhary, and Pandya J. Appl. Phys. 112, 083924 (2012)

For H>HS, the magnetizations of the FM regions lie com-

pletely along the direction of applied field and no more

increase of MRFM is expected. Fig. 2(a) shows the fitting of

the MR(H) data obtained following the so-called decomposi-

tion method.10–12 Here, for H>HS(¼0.8 T), the MR data

could be well fitted by a Langevin function L(H/x0) (solid

line in Fig. 2(a)), representing the SPM contribution MRSPM

to MR(H). By subtracting the fitted MRSPM values from the

experimental data, the FM component MRFM to the MR(H)

was calculated. The decomposed curves for x¼ 25.3 are

shown in Fig. 2(b). The above procedure is also applied to

films x¼ 27.5 and 30.9. H field variation of MRSPM and

MRFM is shown in Fig. 2(d) for x¼ 27.5 (H field variation

for film x¼ 30.9 is not shown as it is similar to x¼ 27.5 film,

except increase in MRFM and decrease in MRSPM compo-

nent). From Fig. 2(b), it can be seen that total MR is domi-

nated by the non-saturating SPM contribution. But a clear

increasing dominance of MRFM over MRSPM can be seen in

Fig. 2(d) as “x” is increased beyond x¼ 25.3. We did not

observe any difference between TMR and LMR for x¼ 25.3

and the –ve MRFM (Table II) observed in this case clearly

indicates the presence of giant-magnetoresistance type of

contribution to MRFM. But for x¼ 27.5 and 30.9, the MRSPM

remains �ve in both cases of TMR and LMR, but the sign of

MRFM depends on measurement configuration, i.e., MRFM

�ve in case of TMR and þve for LMR. This indicates the

dominance of AMR (¼LMR–TMR) component in MRFM.

Thus, the increase in magnitude of AMR with the increase of

“x” possibly indicates the increasing tendency of formation

of clusters of progressively larger size with FM like charac-

ter in these films. The particle size d1 calculated from the

Langevin function still gives the average size of �2 nm for

SPM particles present in these higher Co concentration films.

From Tables I and II, we can see that SPM particle size d1 is

almost equal in all the films, which shows the presence of

uncoalesced monodispersed particles in all the films with dif-

ferent concentrations of Co. Particles with size d2 which cor-

responds to the coalesced single particles behave as SPM till

x� 20.9 and as FM for x> 20.9 due to a cluster-size increase

with increase in “x” to the extent that FM character sets in.

The increasing number of such coalesced particles in turn

results in an enhanced FM contribution to overall MR behav-

ior in films with x> 20.9. The increase in the MRFM/

(MRSPMþMRFM) ratio calculated from the fitting (see Table

II) can be taken as an overall measure of magnetic interac-

tions among the coalesced single particles present in the

film. Wiser-Hickey8,9 reported that in the simultaneous pres-

ence of SPM and FM particles, magnetoresistance varies lin-

early with magnetization of SPM particles at higher fields,

i.e., MR(H) / L(x). This type of linear behavior is indeed

observed in our films for x> 20.9. Hence, the predominant

spin dependent transport in these higher Co concentration

films is SPM-FM. Thus, higher density of coalesced clusters

in films with the higher “x” is responsible for this transition

of spin dependent transport from SPM-SPM to SPM-FM.

From the foregoing analysis of the development of magnetic

interactions within the bigger particles in these higher cobalt

concentration films, we argue that although the MR data of

the intermediate cobalt concentration films (at least in case

of x¼ 20.9 film) fit satisfactorily well using Eq. (2), and the

2nd Langevin term corresponding to bigger coalesced par-

ticles cannot be ascribed to the presence of strictly non-

interacting SPM particles. In order to validate the finding of

MR response of these films, we now present and analyze

their TEM and magnetization behavior.

B. TEM investigations

In Cu-Co system, it is difficult to determine the Co parti-

cle size by TEM because of the high coherency of Co and

Cu lattices and also in part due to the relatively smaller lat-

tice mismatch between them. In fact, very few reports exist

showing TEM of this system. But even then, we tried to get

some picture of the microstructure from the TEM investiga-

tion. Fig. 3 shows the bright field TEM images of

TABLE II. Fitting parameters of equation (3) for x¼ 25.3, 27.5, and 30.9.

x (at. %) MRFM MRSPM x0 MRFM/(MRFMþMRSPM) Avg. size of the SPM particle d1 (nm)

25.3 (TMR and LMR) �0.165 �1.711 4604 6 217 0.09 2.2

27.5 (TMR) �0.350 �1.411 5186 6 192 0.19 2.2

27.5 (LMR) 0.210 �1.408 6625 6 218 0.13 2.0

30.9 (TMR) �0.322 �1.228 5584 6 259 0.21 2.1

30.9 (LMR) 0.298 �0.955 4922 6 163 0.24 2.2

FIG. 3. TEM bright field images (a) x¼ 17.8, (b) x¼ 20.9, (c) x¼ 25.3, and

(d) x¼ 30.9.

083924-4 Kumar, Chaudhary, and Pandya J. Appl. Phys. 112, 083924 (2012)

Cu100�xCox (x¼ 17.8, 20.9, 25.3, and 30.9) thin films. The

dark black spots are identified as Co regions from the EDX

study performed during TEM. The other regions are of Cu.

The presence of two kinds of dark black particles can be

seen in all the micrographs. One kind of particles, which are

almost spherical in shape and isolated from each other, is

considered as “uncoalesced particles” or “single particles.”

This kind of particles possesses size which can be described

by 7.2 6 1.8 nm, and it remains almost same in films of all

the concentrations. This also supports our MR results where

we have calculated the almost same size of the smaller d1

particle in all the films. Other kinds of particles seen are the

ones that are touching each other and we have termed them

as coalesced particles. Though the second kind of particles

are not spherical in shape, but the presence of coalesced and

uncoalesced particles is supporting our MR fitting results

which suggested the presence of two average sizes of par-

ticles in our films. From Fig. 3(a) for x¼ 17.8 film, one can

observe the abundance of uncoalesced particles and very few

coalesced particles. As “x” is increased to 20.9 (Fig. 3(b)),

the number density (numbers per unit area) of the uncoal-

esced particles as well as the number density of coalesced

particles in the film can be qualitatively seen to have

increased, a trend also revealed by MR fitting (the decreasing

w1 and increasing w2 with increase in x, Table I). With fur-

ther increase in Co concentration to x¼ 25.3 and x¼ 30.9,

the particle density for the single particles increases to the

extent that larger clusters of coalesced particles are formed

(Figs. 3(c) and 3(d)) compared to smaller coalesced clusters

observed in case of x¼ 17.8 and 20.9 films. Increasing tend-

ency of coalescence of Co particles with increase of “x” is

expected due to the fact that increase in sputtering rate of Co

(obtained by increasing the power applied to Co target) leads

to the enhancement of Co nucleation rate during growth of

film. This results in the formation of more and more Co

uncoalesced particles with a reduced average inter-particle

distance, which in turn is responsible for the statistical

increase in density of coalesced particles. It is interesting to

note that our growth process yields the formation of predom-

inantly nearly monodispersed particles for x� 15.1.

Although the tendency of formation of the adjacently

nucleated particles is finite, it is small in case of film with

x¼ 17.8. The expected general trend of increase in this coa-

lescence can undoubtedly be seen to progressively increase

with “x” in these four films. This growth (cobalt flux) con-

trolled micro-structural model forms the basis of our under-

standing of the magnetotransport behavior of our films. In

our view, since the growth temperature is �300 K and cobalt

flux changes by a factor of two, the co-deposition process

used by us leads to near monodispersed particles. Thus TEM

results on these films are supporting the two particle model

proposed on the basis of fitting results. It should be noted

that the particle sizes obtained from the TEM and fitting are

quite different. We believe that this difference could arise

due to the over simplified assumption of the spherical and

non-interacting nature of magnetic particles in the fitting.6,14

Overall, the TEM investigations of these four films provide a

qualitative support to the values and trend of the fitting pa-

rameters related to their MR behavior.

C. Magnetization measurements

The magnetization (M-H) measurements were also per-

formed at 300 K on films with x¼ 17.8, 20.9, 25.3, and 30.9.

The M-H loops recorded up to magnetic field of 1 T are

shown in Fig. 4. It is found that the films having x¼ 17.8

and 20.9 could not reach to complete saturation state even at

a maximum applied field of 1 T, clearly confirming the SPM

nature by and large, although the coalesced particles are

present. This agrees with MR results obtained for these films.

There are reports of particle sizes as large as 17 nm to be

behaving like SPM in Cu-Co system.3 No hysteresis can be

seen for x¼ 17.8 at low field values (see inset of Fig. 4), but

a little hysteresis seen for film x¼ 20.9 possibly arises from

the interactions between larger fraction of bigger particles

present in this film compared to x¼ 17.8 film. A careful look

at the M-H plots of the x¼ 25.3 and 30.9 films reveals weak

SPM character as inferred from the lack of complete satura-

tion. But rapid rise of magnetization at low field indicates

the predominance of FM nature of the coalesced particles in

these high “x” films. This is further substantiated by the hys-

teretic behavior in their M-H data observed at low fields

(inset of Fig. 4). It may be recalled that these films (x¼ 27.5

and 30.9) exhibited distinctly non-saturating high field MR

behavior and no signature of hysteresis therein. This

observed difference in MR and M-H behavior in these granu-

lar films is in agreement with the previous reports18,19 and is

understood to arise due to the fact that whereas MR is domi-

nated by electronic transport across the smaller particles and

magnetization is dominated by the presence of larger par-

ticles. The results of MR and M-H behavior taken together

as along with TEM clearly establish the presence of two kind

of distributions present in films with cobalt concentration

x> 20.9.

Percentage of the FM contribution to the total magnet-

ization of the films is calculated from the magnetization

value at which loop closes to the magnetization value at 1 T.

It is found to be 0.22 and 0.36 for x¼ 25.3 and 30.9, respec-

tively, which is quite consistent with the values obtained

FIG. 4. Room-temperature M-H loops recorded for different alloy samples,

x¼ 17.8, 20.9, 25.3, and 30.9. The inset shows extended view near the low

field regime highlighting the presence of small hysteresis corresponding to

films having higher cobalt concentrations.

083924-5 Kumar, Chaudhary, and Pandya J. Appl. Phys. 112, 083924 (2012)

from MR data (Table II), though values are little higher. This

difference can be attributed to the fact that the magnetization

ratio is determined by the volume fractions of the two com-

ponents only, whereas for the MR, the magnitudes of the FM

and SPM contributions also depend strongly on the mutual

spatial spin arrangement in the two regions. Moreover, MR

is mainly governed by the transport of electrons across mag-

netic/non-magnetic interfaces. Thus, the magnetization

measurements also, by and large, support the inferences

drawn from the MR investigations vis-�a-vis the magnetic

microstructure present in these films.

D. Cobalt concentration and magnetic interactions

1. Correlation between MR and M-H data

It is reported that MR data can be fitted by Langevin

function even in the presence of interactions, but the average

particle size so calculated from the fitting is always underes-

timated compared to the actual average value.14 In the pres-

ent case as well, the particle size calculated from MR fitting

is smaller than the particle size calculated from the TEM

data. In order to gain further insight about the presence of

interactions in our films and distribution of particle sizes, we

considered the procedure as described in Refs. 3 and 17

based on point-to-point correlation between normalized

MR(H) and M(H) as the field is varied. We showed in

Figs. 5(a)–5(d), the MRn (MR/MR(0.9 T)) vs. M/MS

(MS¼M(0.9 T)) plots for our films. Figs. 5(a) and 5(b) show

that MRn vs. M/Ms plot is fitted well by a parabola in the

higher field regime for x¼ 17.8 (in M/Ms range of 0.8 to

1.0) and for x¼ 20.9 (in M/Ms range of 0.9 to 1.0). The para-

bolic fitting at higher fields regime is generally taken as evi-

dence of narrow size distribution of the particles present in

films,17 and thus it supports the presence of narrow distribu-

tion of particles in our films. On the other hand, for films

with cobalt concentration x¼ 25.3 and 30.9, the high field

region of the MRn vs. M/MS plot (Figs. 5(c) and 5(d)) is not

fitted by a parabolic curve. Instead the data in this region fol-

lows almost a vertical straight line fit. This feature is known

to originate from the presence of broad distribution of the

particles.17 These results also match with the TEM results

where the broad distribution is observed in the large sized

particles. The flatness at low fields in the MRn vs. M/MS plot

is correlated with the distribution of the particles and pres-

ence of interactions between the particles.16,17 Instead we

see from Fig. 5(a) that x¼ 17.8 film is fitted well by the pa-

rabola at lower fields and the presence of narrow distribution

is seen from TEM data, this shows the presence of weak

interactions in this film. Although data are also fitted by a pa-

rabola for x¼ 20.9 at lower fields, but the parabola is quite

flat than observed in case of x¼ 17.8 and thus points to

stronger interactions in this film. This is in consonance with

the increase in the fraction of larger particles (inferred from

MR response, Table I) and decrease in the inter-particle sep-

aration (cf. TEM micrograph, Figs. 3(a) and 3(b)). On the

other hand, for x¼ 25.3 and 30.9 films, the MRn vs. M/MS

curves are almost flat in the low field regime (see Figs. 5(c)

and 5(d)). This shows the increasing nature of magnetic

interactions at higher “x.” These inferences find natural ex-

planation in terms of increasing tendency of coalescence, at

the cost of reduced inter-particle separation, when cobalt

flux is increased during co-sputtering. The bigger sized, arbi-

trarily shaped cobalt particles observed in TEM in fact result

from statistical random coalescence of the cobalt nuclei

formed in proximity. We also point out that the increase in

MRFM/(MRFMþMRSPM) ratio (Table II) observed in the

MR analysis of higher cobalt concentration films is in agree-

ment with their MRn vs. M/MS analysis.

2. Low temperature MR behavior

We have seen till now films with x> 20.9 are showing

the presence of strong interactions due to the presence of

larger FM particles. In order to further investigate the

strength of magnetic interactions arising from the larger par-

ticles in the low cobalt concentration films (i.e., x� 20.9)

FIG. 5. MRn vs. M/Ms curves for x¼ 17.8, 20.9, 25.3, and 30.9 films (lines

are guides to the eye). Solid (dotted) red line represents the fitting of experi-

mental data at low (high) field regime.

FIG. 6. MR curves for films x¼ 15.1, 17.8, and 20.9 at different tempera-

tures. MR behavior in these samples is identical for LMR and TMR

configuration.

083924-6 Kumar, Chaudhary, and Pandya J. Appl. Phys. 112, 083924 (2012)

showing SPM behavior at room temperature, in Fig. 6 we

present isothermal MR data recorded (in HkI configuration)

at various temperatures in the range of 20–300 K for the

three films (i.e., x� 20.9). The negative MR behavior is

observed at all the temperatures and we find that the LMR

and TMR coincide (data not shown for sake of conciseness)

even at low temperatures. The data of Fig. 6 clearly show

that none of the films exhibit any sign of saturation even

down to lowest temperature of 20 K. But the curvature of the

MR curve is found to change as x changes from 15.1 to 20.9.

At 20 K, the MR behavior of x¼ 15.1 film showed almost

linear dependence on H. Compared to this, the x¼ 17.8 and

x¼ 20.9 films displayed weak tendency of saturation, which

increases further in case of higher “x” films. This increasing

saturation tendency of MR at 20 K is in agreement with our

fitting results (Table I showing an increase in fraction of

larger particles as concentration increases from x¼ 15.1 to

20.9). Figs. 6(a)–6(c) show that maximum MR observed at a

particular temperature increases quickly as temperature is

reduced from 300 to 20 K in case of x¼ 15.1 and 17.8 films,

but quite slowly in case of x¼ 20.9 film.

Another approach for ascertaining the critical concentra-

tion up to which SPM particles remain non-interacting at

room temperature could be to see how the ratio of

MR(20 K,0.9 T)/MR(300 K,0.9 T) [¼MR20] varies with

cobalt concentration “x.” It is reported that as the tempera-

ture is decreased, the MR increases slowly in the presence of

interactions compared to the case when such interactions are

negligible.2 In the present case, this ratio MR20 is found to

be 11.2, 4.6, and 1.7, for the films x¼ 15.1, 17.8, and 20.9,

respectively, indicating the successive strengthening of inter-

actions. This ratio remains below 2 for higher x> 20.9 films,

given the dominance of FM interactions and AMR in those

films. This suggests that though no AMR is exhibited by

x¼ 20.9 film, its bigger particles have non-negligible mag-

netic interactions which dominate the MR response at low

temperature and manifest as increase in saturation tendency.

On the other hand, the significantly larger value of MR20 in

x¼ 15.1 film clearly confirms the presence of almost non-

interacting particles in the film which could not be blocked

even at 20 K. The significant reduction in MR20 for x¼ 17.8

confirms the presence of a finite number of magnetically

interacting particles (�12% as per estimates based on fitting

of its MR (300 K) response and supported qualitatively by

TEM micrograph of Fig. 3(a)) which are blocked at

T> 20 K. Thus, these quantitative data of MR20 clearly con-

firm an increase in interactions-strength, from negligible to

non-negligible values with increase in “x,” among SPM par-

ticles at all temperatures up to 300 K is also supporting our

MR fitting at room temperature. We can now say that at

300 K, the films can be classified on the basis of strength of

magnetic interactions among the particles (in increasing

order of increasing magnetic interactions) as (i) x¼ 15.1;

nearly monodispersed and non-interacting small SPM par-

ticles, (ii) x¼ 17.8 and 20.9; bimodal distribution, with

smaller SPM particles and weakly interacting bigger SPM

particles, and (iii) x¼ 25.3, 27.5, and 30.9; monodispersed

smaller SPM particles and FM-clusters having broad distri-

bution with stronger interactions.

3. Thermomagnetic irreversibility behavior via M(T)[ZFC/FC]

We recorded the M vs. T data on one of the film, namely

x¼ 20.9, in the presence of 50 Oe field in ZFC as well as FC

protocols. This film corresponds to the cobalt concentration at

which presence of maximum interactions among SPM par-

ticles is established from MRn vs. M/MS and low temperature

MR data. Fig. 7 shows the M vs. T plot of this x¼ 20.9

film. There are three main observations to be noted from

the plot: (i) The thermomagnetic irreversibility (TMI), i.e.,

MFC(T) 6¼MZFC(T) exists all the way up to the highest investi-

gated temperature of 300 K. (ii) Instead of usually expected

parabolic shape of MFC(T) below the irreversibility tempera-

ture Tirr of 300 K, there exists a pronounced and sharp upturn

in MFC(T) on cooling below� 75 K. (iii) MZFC(T) mimics this

pronounced upturn below �40 K and exhibits a rise in M

while it is warmed all the way till 300 K. The pronounced

upturn in M (observed in both FC and ZFC) clearly reflects

the presence of significant fraction of SPM particles having

very small particle size, so much small that they could not be

blocked till 10 K. This, together with MR, M-H, and TEM

analyses, provides strong evidence in favor of small average

size of SPM particles. This is further substantiated by the lin-

ear MFC(T) vs. 1/T plot observed in 10–30 K range (see inset

of Fig. 7). Needless to mention, these non-interacting (uncoal-

esced) particles will continue to behave as SPM at higher tem-

peratures. On the other hand, the observation of TMI in this

20.9% cobalt film confirms the finite presence of larger coa-

lesced particles and provides support to the proposed bimodal

distribution in this film. The observation of upturn in FC mag-

netization can therefore strengthen our conjecture of dominant

SPM nature of the smaller particles over the bigger particle in

case of x¼ 20.9 film. This is further supported by the strict

isotropic MR response shown by this film.

IV. CONCLUSIONS

The nature of spin dependent magnetotransport is inves-

tigated in the co-sputtered granular Cu100�xCox thin films

FIG. 7. ZFC and FC magnetization as function of temperature for film

x¼ 20.9 (lines are guides to the eye), and inset shows the MFC vs. 1/T plot

with linear fit in the range of 10–30 K.

083924-7 Kumar, Chaudhary, and Pandya J. Appl. Phys. 112, 083924 (2012)

having constant thickness of 100 nm. It is demonstrated that

although the isolated SPM particles are present within the

entire investigated range of cobalt concentration of 15.1–

30.9 at. % in these films, a transition in the spin dependent

transport from SPM-SPM to SPM-FM type occurs at a

threshold cobalt concentration of �21 at. % in copper ma-

trix. Based on this analysis, it is concluded that below about

15 at. % concentration of cobalt, the Cu100�xCox thin films

possess nearly monodispersed cobalt particles. A model

based on nearly spherical monodispersed uncoalesced par-

ticles and coalesced particles of cobalt having arbitrary

shapes is proposed to quantitatively explain the magnetore-

sistance behavior of these granular films. The TEM images

and magnetization behavior of these films provide qualitative

support to this model. Further insight to the development and

strength of magnetic interactions within these coalescing

cobalt particles is gained by analyzing their low temperature

magnetoresistance behavior and the correlation of their room

temperature magnetoresistance and the magnetization data.

It is found that consideration of interactions is crucial for

better understanding of these systems. Through this work,

we tried to develop a detailed understanding of complex

granular system, which is important not only to satisfy the

scientific curiosity but also in order to fully exploit such sys-

tems in the development of high performance magnetic

materials and spin dependent electronic devices.

ACKNOWLEDGMENTS

D.K. acknowledges MHRD-India for the SRF Fellow-

ship. We thankfully acknowledge Department of Science

and Technology, Govt. of India for Quantum Design (MPMS

XL-7) SQUID facility at Indian Institute of Technology

Delhi.

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