arXiv:cond-mat/9810061v1 [cond-mat.mes-hall] 6 Oct 1998
Magnetoresistance of Granular Ferromagnets - Observation of a Magnetic Proximity
A. Frydman and R.C. Dynes
Department of Physics, University of California, San Diego, La Jolla, CA 92093
We have observed a superparamagnetic to ferromagnetic transition in films of isolated Ni grains
covered by non-magnetic overlayers. The magnetoresistance (MR) of the films was measured as a
function of the overlayer thickness. Initially, the granular Ni films exhibited negative MR curves
peaked at H=0. As different materials were deposited onto the grains hysteresis developed in the
MR. This behavior is ascribed to an increase of the typical domain size due to magnetic coupling
between grains. The strength of the inter-grain coupling is found to correlate with the magnetic
susceptibility of the overlayer material.We discuss possible mechanisms for this coupling and
suggest that the data may reflect the existence of a magnetic proximity effect (analogous to the
well-known effect in superconductivity) in which a ferromagnetic moment is induced in the metallic
PACS numbers: 75.50.Tt, 75.70.Pa, 73.40.Rw, 74.50.+r
The proximity effect is a well known phenomenon in
superconductivity and has drawn a lot of interest both
from the fundamental and the practical points of view.
In a high transmission superconductor-normal metal con-
tact the superconductive wave-function varies smoothly
across the interface causing a suppression of the pair am-
plitude in the superconductor and an enhancement of
superconductivity on the normal side. An analogue in
magnetism, in which the magnetization varies smoothly
across a ferromagnet-non magnetic metal interface, has
been considered theoretically [1–4]. Experimentally, the
observation of a magnetic proximity effect is much more
challenging. In the first place the coherence length of
a typical ferromagnet, such as Ni or Fe, is of the order
of a few atomic spacings (this should be compared with
ξs of thousands of˚ A in a conventional superconductor)
and the means to measure the proximity effect are not as
straightforward as in the superconducting case. Further-
more, one has to be able to distinguish between a “real”
proximity effect and other magnetic phenomena such as
magnetostatic interactions. One experimental approach
in the past has been to study the suppression of magneti-
zation in thin ferromagnets deposited on a normal metal
substrate [5–8]. The first few monolayers were found to
be magnetic “dead layers” exhibiting no ferromagnetic
signal. In a different type of experiment Moodera et-al
 used spin-polarized tunneling measurements to show
that a finite spin polarization of electrons persists in a
Au film coupled to a Fe layer up to a thickness of a few
tens of˚ A. A question arises as to whether the spin polar-
ization detection is indeed indicative of a ferromagnetic
interaction inside the Au .
In this paper we describe an experiment which is de-
signed to probe a potential magnetic analogue to the
Josephson-like proximity coupling between superconduc-
tors across a SNS weak link. We measure the magne-
toresistance (MR) of a granular magnetic film covered by
various non-magnetic overlayers and study the impact of
these layers on the magnetic coupling between the grains.
1820 222426 28303234
R (Ω )
thickness of 18˚ A and 23˚ A evaporated on a room tempera-
ture Si-SiO substrate. Line scans show that the average hight
of the grains is 35˚ A. Right: Sheet resistance versus nominal
thickness of a quench-condensed Ni film.
Left: AFM micrographs of Ni films with nominal
The samples were prepared using the “quench-
condensation” technique, i.e.
cooled substrate under UHV conditions within the mea-
surement apparatus. This method has a number of ad-
vantages for proximity effect experiments. First, the high
vacuum in the system gives rise to barrier-free interfaces
between different evaporated materials. These are es-
sential for proximity effect observation.
the low substrate temperature all but eliminates inter-
metallic diffusion, making the possibility of material al-
loying highly unlikely. Another advantage of this fab-
evaporation on a cryo-
rication method is that it enables the evaporation of se-
quential layers of material in-situ; thus one can study the
properties of a single sample as a function of the amount
of deposited material while keeping the sample at low
temperatures and in a UHV environment.
Our measurements were performed on thin layers of
Ni quench-condensed onto a Si-SiO substrate. The mor-
phology of such samples is illustrated in Figures 1a and
1b. For thin enough films the structure contains isolated
grains with diameters of a few hundreds of˚ A  and
heights of 30-40˚ A. As more material is deposited, grains
begin to coalesce with each other (Figure 1b). The av-
erage grain size thus increases and inter-grain spacing
decreases until, beyond a percolation threshold, the film
becomes continuous. This behavior is also demonstrated
by the dependence of resistance on nominal film thickness
(Figure 1c). For small thicknesses the resistance drops
exponentially with thickness implying that the conduc-
tion mechanism is tunneling or hopping between grains.
For larger thicknesses the film becomes continuous and
the resistance crosses over to an ohmic 1/d dependence.
quench-condensed Ni film for different steps of the evapora-
tion. The field was swept from -1T to 1T and back. The
nominal film thicknesses were 20˚ A(a), 21˚ A(b), 21.8˚ A(c) and
Magnetoresistance curve at T=4.2K of a
Figure 2 shows MR curves of a Ni film for different de-
position steps. The thinnest films exhibit curves which
show a negative MR centered at H=0 (Figure 2a). This
behavior is similar to that observed in other insulating
granular ferromagnets prepared using different fabrica-
tion techniques [12–16] and is a result of spin dependent
tunneling between grains which have randomly oriented
magnetic moments . Applying a field aligns these
moments causing a resistance decrease. These thin films
consist of small grains which are isolated from each other
and are superparamagnetic at T=4K, thus, when the field
is removed, the thermal energy is large enough to ran-
domize the spin orientation and the MR curve does not
exhibit hysteretic behavior.
As more material is deposited and the sheet resistance
is reduced hysteresis develops in the curve, resulting in
two resistance peaks at finite magnetic field. The position
of the peaks shifts towards larger fields as the film thick-
ens (figures 2b, 2c and 2d). Apparently, as the grains coa-
lesce, the effective magnetic domain sizes become larger,
the superparamagnetic blocking temperature rises and
the film exhibits ferromagnetic behavior at T=4K. In-
deed, the temperature dependence of these MR curves is
consistent with well known relations for the superparam-
agnetic transition . Adding material also causes the
amplitude of the MR to decrease. This is a result of the
percolation network for conductivity becoming denser,
thus reducing the number of tunneling events which oc-
cur between grains with different oriented moments.
-1.0-0.50.0 0.5 1.0
Ni (R≈4MΩ) covered by different overlayers. The initial MR
curve for the bare Ni was similar to that of figure 2a. For
the Pd, Ti and Ag the overlayer thickness, d, is 6-7˚ A and the
sheet resistance is 2kΩ. For Ge d=65˚ A and R=10KΩ.
MR curves at 4.2K of 20˚ A thick films of granular
Having observed the above effect of adding magnetic
material to a granular magnetic film, we proceeded to
study the effects of adding non-magnetic materials to su-
perparamagnetic grains. We prepared films of isolated Ni
grains (20˚ A nominal thickness) which showed no hystere-
sis in the MR curve, and we added overlayers of Pd, Ti,
Ag, or Ge in-situ. Figure 3 shows the MR curve of the
samples in which an overlayer of 6˚ A (or 65˚ A in the Ge
case) was added to the 20˚ A Ni film. Despite the fact that
Pd, Ti and Ag overlayers are non ferromagnetic, their
presence gives rise to a hysteresis in the MR. Such a hys-
teresis is indicative of coupling between magnetic grains
which were originally isolated. The coupling strength is
different for the different overlayer materials.
-0.6-0.4-0.2 0.00.2 0.40.6
thick Ni film evaporated at room temperature . The arrow
marks the position of the coercive field, Hc.
MR and M-H curves taken at T=4.2K for a 23˚ A
We quantify the degree of hysteresis in the system by
studying the coercive field, Hc, for which the magnetiza-
tion in the system, M, equals zero. In a granular film this
is the field required to totally randomize the magnetic
orientations, hence it should correlate with the field at
which the resistance peaks in the MR. Figure 4 compares
the MR measurements and measurement of the magne-
tization versus field (M-H) hysteresis loop performed in
a SQUID magnetometer. Though Hc differs slightly in
these two experiments (the differences will be discussed in
length elsewhere ) the behavior as a function of tem-
perature or film thickness is similar. The dependence of
Hc on sheet resistance for the different overlayered ma-
terials, depicted in figure 5, clearly demonstrates that
there is a correlation between the coupling strength of
the medium and its magnetic susceptibility. Pd, which
is a strong paramagnet (χ ≈11·10−6emu/gr·Oe) has an
effect which is nearly as strong as that of adding Ni itself.
Ti, a weaker paramagnet (χ ≈1.5·10−6emu/gr·Oe), has
a significant but smaller coupling coefficient. Diamag-
netic materials, such as Ag or Cu , also couple be-
tween the Ni grains, though the influence of diamagnetic
overlayers is much weaker than that of paramagnets. In
contrast, Ge, which is an insulator, does not induce any
magnetic coupling at all. Notice that we have deposited
a Ge overlayer which is much thicker than that of the
metallic cases. Nevertheless, Ge seems to have no im-
pact on the MR curve shape, in particular, it does not
generate hysteretic behavior.
R (kΩ )
FIG. 5. Coercive field at T=4.2K as a function of sheet
resistance for the different overlayer materials.
We have considered a number of possible scenarios for
magnetic coupling through the normal medium. Classi-
cal magnetostatic coupling (dipole-dipole interaction be-
tween the grains) can be ruled out since the grains are
isolated to begin with, hence, the magnetic interaction
is obviously too weak to cause grain coupling. A strong
candidate for the coupling mechanism is an exchange in-
teraction between the grains mediated by the conduc-
tion electrons in the metal.
many magnetic heterostructures where magnetic layers
are separated by non-magnetic spacers.
tems it is found that the magnetic layers couple ferro-
magnetically or anti-ferromagnetically depending on the
spacer thickness . This behavior has been attributed
to an RKKY-like interaction [21,22] which is oscillatory
in space with a period of 1/2kf. There are a number of
problems in trying to ascribe this mechanism to the re-
Such behavior is seen in
In these sys-
sults in our case. In the first place the RKKY process is Download full-text
very sensitive to the spacing between the magnets. Cal-
culations show  that thickness roughness on the order
of atomic spacing reduces the amplitude of short period
oscillations by more than an order of magnitude. In our
granular film there is no single grain spacing and the
grains themselves are far from being atomically smooth,
hence, the effect of an RKKY interaction is expected to
average out. Furthermore, RKKY coupling is a Coulomb
effect which depends mainly on the Fermi surface de-
tails and not on the magnetic properties of the spacing
layer. There is no apparent reason why Ti should in-
duce stronger coupling than Ag. In fact, Cu, which is
the prototype spacer in multilayer systems, has hardly
any effect in our granular samples. The fact that we
observe a strong correlation of hysteresis with magnetic
susceptibility implies that the relevant mechanism is one
in which a magnetic moment is induced in the intermedi-
ate medium which, in turn, couples the magnetic grains.
We note the similarity to superconductivity, where the
proximity effect is enhanced for a normal material which
is characterized by an internal strong electron-phonon
coupling, such as a superconductor above its TC.
In conclusion we have shown that isolated magnetic
grains can be coupled via an intermediate medium
which is not magnetic, resulting in a superparamagnetic-
ferromagnetic crossover. This effect is stronger for para-
magnetic media but exists also for diamagnets. We ob-
serve a clear relation between the coupling strength and
the magnetic properties of the overlayer medium. This
phenomenon bears a striking resemblance to an analo-
gous experiment performed on granular superconductors
in which an overlayer of Ag proximity couples isolated
superconducting Pb grains . The proximity coupling
is expected to decay exponentially with the distance be-
tween grains. Within the framework of the current ex-
periment we cannot yet provide an accurate evaluation of
the relevant coherence length. Extraction of a coherence
length will be pursued in future work. However, a rough
estimation of the distance between our grains (≈10˚ A)
points towards relatively short coherence lengths, espe-
cially in the diamagnetic layers. Hence, in high quality
multilayers, the proximity effect can be expected to dom-
inate for short scales (depending on the spacer magnetic
properties) and the magnetic layers will couple ferromag-
netically. For thicker spacers an RKKY- like exchange
process, which decays like a power law, may set in and
the sign of the coupling will oscillate with the thickness.
We are grateful for technical help we received from
T. Kirk and for illuminating discussions with D. Arovas,
A.M. Berkowitz, F. Hellman, S. Sankar and H. Suhl. This
research was supported by AFSOR grant no. F49620-92-
 M.J. Zuckermann, Solid State Commun. 12, 745 (1973).
 B.N. Cox, R.A. Tehir-Kheli and R.J. Elliott, Phys. Rev.
B20, 2864 (1979).
 J. Tersoff and L.M. Falicov, Phys. Rev. B26, 6186 (1982).
 R.M. White and D.J. Friedman, J. Magn. Magn. Mater.
49, 117 (1985).
 L. Libermann, J. Clinton, D.M. Edwards and J. Mathon,
Phys. Rev. Lett. 25, 232 (1970);
 G Bergmann, Phys. Rev. Lett. 41, 264 (1978); Phys. To-
day 32(8), 25 (1979).
 E.M. Gyorgy, J.F. Dillon, D.B. Mcwhan, L.W. Rupp and
L.R. Testardi, Phys. Rev. Lett. 45, 5151 (1980).
 J.S. Moodera and R Meservey, Phys. Rev B29, 2943
(1984) and references within.
 J.S. Moodera, M.E. Taylor and R. Meservey, Phys. Rev
B40, 11980 (1989).
 P.M. Tedrow and R. Meservey, Phys. Rep. 238, 173
 The size of the grains depends on the substrate temper-
ature during deposition. The lower this temperature, the
smaller the grain diameter.
 J.I. Gittelman, Y. Goldstein and S. Bozowski, Phys. Rev.
B5, 3609 (1972).
 A. Milner, A. Gerber, B. Groisman, M. Karpovsky and
A. Gladkikh, Phys. Rev. Lett. 76, 475 (1996).
 W. Yang, Z.S. Jiang, W.N. Wang and Y.W. Du, Solid
State Commun. 104, 479 (1997).
 S. Honda, T. Okada, M. Nawate and M. Tokumoto, Phys.
Rev. B56 14566 (1997).
 S. Sankar and A.E. Berkowitz, App. Phys. Lett. 73 535
 J.S. Helman and B. Abeles, Phys. Rev. Lett. 37, 1429
 A. Frydman, T. Kirk and R.C. Dynes, in preparation
 Cu has a similar but slightly weaker effect to that of Ag.
 J. Unguris, R.J. Celotta and D.T. Pierce, Phys. Rev.
Lett. 67, 140 (1991); M.T. Johnson, S.T. Purcell, N.W.E.
McGee, R.Cochoorn, J. aan de Stegge and W. Hoving,
Phys. Rev. Lett. 68, 2688 (1992).
 M. A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954);
T. Kasuya, Prog. Theor. Phys. 16, 45 (1956); K. Yosida
Phys. Rev. 106, 893 (1957).
 P. Bruno and C Chappert, Phys. Rev. Lett. 67, 1602
(1991); Phys. Rev B46, 261 (1992).
 S. Y. Hsu, J. M. Valles Jr., P. W. Adams and R. C.
Dynes, Physica B 194-196, 2337 (1994); L.M. Merchant
et-al, in preparation.