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Nucleation of Magnetization Reversal in Individual
Nanosized Nickel Wires
W. Wernsdorfer, B. Doudin, D. Mailly, Klaus Hasselbach, A. Benoît, J Meier,
J.-Ph Ansermet, B. Barbara
To cite this version:
W. Wernsdorfer, B. Doudin, D. Mailly, Klaus Hasselbach, A. Benoît, et al.. Nucleation of Magneti-
zation Reversal in Individual Nanosized Nickel Wires. Physical Review Letters, American Physical
Society, 1996, 77 (9), pp.1873. �hal-01659966�
VOLUME 77, NUMBER 9 PHYSICAL REVIEW LETTERS 26AUGUST 1996
Nucleation of Magnetization Reversal in Individual Nanosized Nickel Wires
W. Wernsdorfer,
1,2
B. Doudin,
3
D. Mailly,
4
K. Hasselbach,
1
A. Benoit,
1
J. Meier,
3
J.-Ph. Ansermet,
3
and B. Barbara
2
1
Centre de Recherches sur les Très Basses Températures, CNRS, BP166, 38042 Grenoble Cedex 9, France
2
Laboratoire de Magnétisme Louis Néel, CNRS, BP166, 38042 Grenoble Cedex 9, France
3
Institut de Physique Expérimentale, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
4
Laboratoire de Microstructure et Microélectronique, CNRS, 196 Av. H. Ravera, 92220 Bagneux, France
(
Received 3 January 1996)
The switching of the magnetization of single Ni wires with diameters 40–100 nm was measured
at temperatures between 0.13 and 6 K. The angular dependence of the switching field was studied
for several wire diameters. Repetitive measurements allow us to obtain histograms of the switching
field values. For the smallest diameters, the measurements of the probability of reversal revealed a
thermally activated switching following an Arrhenius law with an activation volume much smaller than
the volume of the wire. [S0031-9007(96)01046-0]
PACS numbers: 75.60.–d, 75.10.Hk
The mechanisms of magnetization reversal in small
magnetic particles have been much discussed in the last
decades and prompted intense research activities, moti-
vated in particular by applications in magnetic recording
technology [1]. However, experiments were performed,
in general, on large assemblies of particles, and the dis-
persion of morphologies, compositions, orientations, and
separations of the magnetic entities limited the interpre-
tation of the results. Furthermore, interactions between
particles were difficult to take into account. Single par-
ticle studies were possible only in few cases [2]. Re-
cently, insights into the magnetic properties of individual
and isolated particles were obtained with the help of near
field magnetic force microscopy [3], electron Lorentz mi-
croscopy or holography [4], and micro-SQUID (supercon-
ducting quantum interference device) magnetometry [5].
It is now possible to make a clear link between experi-
ments performed on nanometer-sized single objects (par-
ticles, wires, etc.) and the numerical calculations based on
the Brown micromagnetic equations [6].
We report the first study of isolated nanoscale wires
with diameters smaller than 100 nm, for which single-
domain states could be expected. The cylindrical geome-
try, with its large shape anisotropy, is well suited for
comparison with theory. We obtained unique insight
into the process of magnetization reversal by measur-
ing histograms of the switching field as a function of
the orientation of the wires in the applied field, their
diameter, and the temperature. Furthermore, we mea-
sured the probability of switching as a function of
the applied field and the temperature. Our studies re-
veal that the magnetization reversal proceeds by a dis-
tortion of the magnetization followed by a nucleation
and a propagation process. The observed behavior il-
lustrates the fundamental importance of the study of
single, isolated magnetic particles in comparing models
and experiments.
We developed planar microbridge dc SQUID [7], made
of Nb (thickness 20 nm), which were shown to be able
to detect 10
4
m
B
[8]. The SQUID is made of a thin
(20 nm) Nb layer in order to prevent flux trapping. The
experimental setup allows measurements of hysteresis
loops in magnetic fields of up to 0.5 T and temperatures
below 6 K, with a time resolution of 100 ms.
Ni wires were produced by electrochemically filling
the pores of commercially available nanoporous track-
etched polycarbonate membranes of thicknesses of 6 to
10 mm [9]. The pore size was chosen in the range of
30 to 100 nm [10]. In order to place one wire on the
SQUID detector, we dissolved the membrane in chlo-
roform and put a drop on a chip of some hundreds of
SQUID’s. Magnetization measurements were performed
on SQUID’s with a single isolated wire. Scanning elec-
tron microscopy (SEM) (Fig. 1) was used to determine
the position and morphology of the wire. The surface
roughness was around 5 nm, corresponding to our SEM
resolution.
FIG. 1. Scanning electron micrograph (JEOL 6300) of
a microbridge dc SQUID and a Ni wire of diameter of
65 6 4 nm.
0031-9007y96y77(9)y1873(4)$10.00 © 1996 The American Physical Society 1873
VOLUME 77, NUMBER 9 PHYSICAL REVIEW LETTERS 26AUGUST 1996
The magnetic field was applied in the plane of the
SQUID at an angle u with respect to the wire axis (easy
anisotropy direction), and the flux induced by the wire
was detected by the SQUID. If the sample has one end
in the SQUID loop (Fig. 1), the signal is approximately
proportional to the projection of the magnetization in the
direction of the wire axis. This is the reason for the
negative slope in the curves in Fig. 2. Under a slowly
varying applied field (typically a few mTys), we observed
an abrupt change of the signal, in less than 100 ms, at the
switching field value (Fig. 2).
The measured switching field had the character of a sto-
chastic variable, as expected for sufficiently small wire di-
ameters. We measured histograms of the switching field
of several individual wires with diameters between 40 and
100 nm. The angular dependence of the mean switch-
ing field H
SW
and its standard deviation s of a wire
92 6 4 nm in diameter is shown in Fig. 3. We checked
by transmission electron microscopy techniques that our
Ni wires were polycrystalline (typical crystallite size of
10 nm), allowing us to suppose that the magnetocrys-
talline anisotropy was negligible. As the wires have a
very high aspect ratio (100:1), we can compare our obser-
vations to the predictions of the curling mode of mag-
netization reversal in an infinite cylinder [11]. In this
case, the angular variation of the switching field can be
expressed by
H
SW
M
S
2
as1 1 ad
p
a
2
1 s1 1 2 ad cos
2
u
, (1)
where a 21.08sd
0
ydd
2
. The exchange length d
0
2
p
A yM
s
(A is the exchange constant) defines the tran-
sition from uniform rotation to curling. By fitting mea-
surements on several wires of diameters between 75 and
100 nm, we found d
0
sNid 34 6 4 nm. This result can
be compared favorably to the values commonly cited in
FIG. 2. Typical hysteresis loops of the wire of Fig. 1 (diame-
ter 65 6 4 nm) at several values of the angle between the
applied field and the wire axis.
the literature: d
0
sNid 41 nm [6]. The angular depen-
dence of the switching field of Ni wires with larger diame-
ters (100–450 nm) was measured at room temperature
by Lederman et al. [12]. The angular dependence they
observed was also fitted by Eq. (1), although the de-
duced value of d
0
was not as close to the theoretical
value.
In repeating hysteresis measurements at a given angle,
we obtained the distribution of the switching field values
(Fig. 3). It revealed that the switching field histogram
can split in some few and distinct peaks, each one
corresponding to a different spin configuration with a
different energy barrier of nucleation. The width of the
histograms varied strongly with the angle u, but remained
always smaller than a few percent of H
SW
(Fig. 3).
Measurements performed on wires of diameters smaller
than 75 nm presented an angular variation of the switch-
ing field with a new local maximum appearing at u 0.
It can be thought of as the reminiscence of the maximum
predicted by the Stoner-Wohlfarth model of uniform rota-
tion [13]. When the sample diameter approaches d
0
, the
curling mode is present at small u angles, and the uniform
rotation occurs at larger u values [11]. Our observations
(Fig. 4) agree qualitatively with this picture. An alterna-
tive theoretical explanation is a reversal of the magneti-
zation by uniform rotation, but affected by the presence
of defects of the samples, limiting the height of the maxi-
mum at zero angle [14]. This is also qualitative, as our
measured values are systematically smaller than the pre-
dictions of the two models. The histograms of the switch-
ing fields were narrow (0.1% to 0.4% of H
SW
) with a
single maximum (Fig. 4).
Extensions of analytical [11] to numerical [6,15] cal-
culations of the micromagnetic equations allow a descrip-
tion of the magnetization reversal process beyond small
angle deviations of the magnetization. In cylinders of
finite length, the curling mode is immediately followed
by the formation of a vortex at one end of the cylinder
FIG. 3. Angular variation of the switching field of a wire of
Ni, 92 6 4 nm in diameter, 5 mm in length. Bars: width of
the histograms. Line: prediction of the curling model. Inset:
histogram of the switching field at the angle u 29
±
.
1874
VOLUME 77, NUMBER 9 PHYSICAL REVIEW LETTERS 26AUGUST 1996
FIG. 4. Angular variation of the switching field of a wire of
Ni, 50 6 5 nm in diameter, 3.5 mm in length. The width of the
switching field distribution is smaller than the dot size. Inset:
histogram of the switching field at the angle u 5
±
.
which sweeps across the sample [16]. The concept of the
magnetization reversal triggered by a nucleation process
has also been recently treated analytically [17]. The com-
plex histograms of the wires of larger diameters indicate
that several sites compete for the nucleation, nonetheless
with switching fields approaching the value given by the
curling model. The narrow histograms of the wires of
smaller diameters suggests that a single energy barrier is
dominant.
In order to estimate the volume of activation, we
performed switching time measurements. At a given
temperature, the magnetic field was increased to a set
value H
W
, at which we measured the elapsed time until
the magnetization switches. This process was repeated
about two hundred times, in order to obtain a switching
time histogram. The integral of this histogram gave us the
switching probability. We fitted the results by a stretched
exponential:
Pstd e
2stytd
b
, (2)
where t defines the mean waiting time. The case of
hopping over a single energy barrier corresponds to b
1. Values of b,1correspond to a distribution of energy
barriers. We found a value of b between 0.1 and 0.5
with wires of diameters between 75 and 100 nm. The
wires of smaller diameters had b values close to unity
(Fig. 5).
We verified that the field and temperature depen-
dence of t followed an Arrhenius law tsT, H
W
d
t
0
expfEsH
W
dykT g with EsH
W
d E
0
s1 2 H
W
yH
0
W
da
and with a ø 1.5 [18]. We present our data of tsT , H
W
d
in the form of a scaling plot of the applied field values
H
W
as a function of fT lnstyt
0
dg
2y3
(Fig. 6). We found
that the data of tsT , H
W
d obtained at temperatures higher
than 1 K fell on a line provided t
0
ø 10
28
s (Fig. 6).
Possible explanations for the deviation at temperatures
smaller than 1 K will be discussed elsewhere [19]. The
slope and intercept of the scaling plot (Fig. 6) gave
FIG. 5. Probability of not switching of the magnetization as a
function of the time at four different applied fields, measured
at 0.13 K for a wire of Ni, 45 6 5 nm in diameter at u ø 30
±
.
Lines: formula (2) with b 1 and t as indicated.
E
0
ø 15 000 K and H
0
W
ø 63.5 mT. The energy barrier
E
0
can be approximately converted to a thermally acti-
vated volume by using V ø E
0
ym
0
M
S
H
SW
s20 nmd
3
,
which is more than 200 times smaller than the wire vol-
ume. Therefore, we propose that the magnetization jumps
are triggered by a nucleation process. This hypothesis is
confirmed by the measurements of the switching field as
a function of the external field sweeping rate and of the
temperature [5,18].
In conclusion, our measurements on single wires of di-
ameters smaller than 100 nm give several experimental
pieces of evidence that the magnetization reversal in a
ferromagnetic wire results from a nucleation and propa-
gation process. For wires with diameters larger than 2
times the exchange length d
0
, we observed that the nucle-
ation occurs at several nearly degenerate fields at values
close to the curling instability. For wires of diameters
approaching the exchange length, the Stoner-Wohlfarth
FIG. 6. Scaling plot of the mean switching time tsH
W
, T d for
several waiting fields H
W
and temperatures f0.1 , tsH
W
, T d ,
60 sg. Each arrow is a guide to the eye for data obtained at one
temperature and several waiting fields. The field is applied at
an angle of 30
±
with respect to the wire axes.
1875
VOLUME 77, NUMBER 9 PHYSICAL REVIEW LETTERS 26AUGUST 1996
model becomes relevant. In this case, the switching time
and switching field measurements reveal that only a single
energy barrier is dominant and the reversal process could
be described by an Arrhenius law.
We acknowledge the contributions of B. Pannetier and
T. Crozes (CRTBT-CNRS) to the success of this work,
the hospitality of the Center of Electron Microscopy of the
EPFL (CIME), and the help of B. Senior for the electron
microscopy pictures. This research was partly financed
by the Swiss National Fund, Grant No. 20-42034.94.
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