Mechanisms of the ultrafast magnetization switching in
bistable amorphous microwires
M. Ipatov1, V. Zhukova1, A.K. Zvezdin1,2, A. Zhukov1,3,a)
1
Dept. Phys. Mater., Chem. Fac., Universidad del Pais Vasco UPV/EHU, San
Sebastian, Spain
2
A. M. Prokhorov General Physics Institute of RAS, 119991 Moscow, Russia
3
TAMAG Ibérica S.L., Parque Tecnológico de Miramón, Paseo Mikeletegi 56, 1ª
Planta, 20009 San Sebastián, Spain
Two magnetization reversal regimes were found in magnetically bistable Fe-rich
microwires. The first one, exhibiting almost linear dependence of the DW velocity v
on magnetic field H reaching 1.7 km/s is related with single domain wall (DW)
propagation. The second essentially non-linear regime is observed when H exceeds
some critical magnetic field, HN, determined by the microwires inhomogeneities. At
H> HN, new reverse domains can be nucleated and consequently tandem
remagnetization mechanism can be realized. Ultrafast magnetization switching
through additional nucleation centers created artificially can be applied in spintronic
devices for enhancing their performance.
a)
Author to whom correspondence should be addressed: E-mail: arkadi.joukov@ehu.es
1
I. INTRODUCTION
Recent growing interest on domain wall (DW) propagation in thin magnetic wires with submicrometric and micrometric diameter is related with proposals for prospective logic and memory
devices1,2. In these devices, information can be encoded in the magnetic states of domains in
lithographically patterned nanowires2. DW motion along the wires allows manipulation of the
stored information. The speed at which a DW can travel in a wire has an impact on the viability of
many proposed technological applications in sensing, storage, and logic operation2. When a DW
is driven by a magnetic field, H, parallel to the wire axis, the maximum wall speed is found to be
function of magnetic field and the wire dimensions1, 3-7. This propagation can be driven by
magnetic fields8 reaching velocities up to 1000 m/s or by spin-polarized electric currents in the
nanowires9. In fact it is essentially important not only fast domain wall propagation itself, but also
controlling of domain wall pinning in thin magnetic wires. Several methods of controlling domain
walls in nanowires have been reported. For example, domain walls can be introduced to
nanowires at low fields by injection from a large, magnetically soft region connected to a wire
end7,10, using a lithographically fabricated current carrying wire to provide local field11 or
heating12. Elsewhere, domain walls have been pinned at artificially created defects in thin wires11,
13-15
.
Amorphous glass coated microwires are ideal material for study domain wall dynamics16-19.
As a result of magnetoelastic interaction between the magnetic moments and stresses introduced
during the microwires production, the domain structure of amorphous microwire with positive
magnetostriction consists of single axial domain, which is surrounded by the radial domain
structure17,18. Moreover, small closure domain appears at the end of microwire in order to
decrease the stray fields17. One of the most interesting properties of amorphous microwires is that
related with the observation of spontaneous magnetic bistability in Fe-rich compositions related
with perfectly rectangular hysteresis loop and attributed to the nucleation or depining of the
reversed domains inside the inner single domain and the consequent propagation of head to head
remagnetization front17-19. It is worth mentioning that usually this magnetization switching in
2
magnetically bistable microwires is associated with the domain wall propagation, although the
micromagnetic origin of this remagnetization front is still unclear.
Among the most unusual results observed in these microwires is that the depined DW created
by small nucleation coil propagates along the microwire at magnetic field below the switching
field19. Recently quite high domain wall velocity, v, (up to 18 km/s) and essentially non-linear
v(H) dependence have been reported18-21. It is worth mentioning that reported velocity exceeds
estimated maximum velocity (Walker limit) for DW propagation (about 1000m/s). This is an
additional argument confirming that the so-called DW in magnetically bistable microwires can
have more complex structure than just a plain head-to-head domain wall. At the same time role of
defects on domain wall propagation in glass-coated microwires is still unclear. Recent studies
showed that fluctuations of local nucleation field, Hn, should be attributed to local defects22.
Considering a number of unusual effects found studying DW propagation in amorphous
microwires in this paper we are trying to reveal contribution of local defects on peculiarities of
domain wall propagation and correlation of linearity of v(H) dependence with defects existing in
amorphous microwires. Consequently, we present comparative study of single domain wall
dynamics and local nucleation fields in Fe-rich amorphous glass-coated microwires. It is
important to underline that we introduced modification to the classical Sixtus-Tonks experimental
set-up24. In order to assure constant magnetic field when measuring v(H) dependence we used the
magnetizing coil with reduced inductivity that provided fast settling of the magnetic field. We
also added the third pick-up coil in order to detect the multiple DW (tandem) propagation regime.
II. EXPERIMENTAL DETAILS
The domain wall (DW) propagates along the wire with a velocity:
v=S(H-H0)
(1)
where S is the DW mobility, H is the axial magnetic field and H0 is the critical propagation field.
Quite simple Sixtus-Tonks method24 allows one to obtain the dependence of DW velocity on
magnetic field which is calculated as:
3
v
b
t
(2)
where b is the distance between pick-up coils and t is the time difference between the maximum
in the induced emf.
In classical Sixtus-Tonks experiment, the reverse domain is created by special nucleation
coil. In the case of bistable microwires, reverse closure domains appear at the microwires ends in
order to diminish the otherwise large stray field’s energy17 and therefore, use of nucleation coil is
unnecessary. Also we place one end of the sample outside the magnetization coil (the right end on
the Fig. 1) to control the direction of DW propagation. Such configuration provides the depinning
of the DW only from one end of the wire.
In order to obtain the dependence of the DW velocity on magnetic field v(H), it is
necessary i) create a reverse domain in the certain, well-defined region of the sample, and ii)
apply a stable magnetic field, H, of the required value along the wire axis. A set of coils (Fig. 1)
was especially designed to fulfill these requirements. It consists of a long exciting coil Lexc (with
length B of 140 mm, 10 mm in diameter) and tree pick-up coils p1, p2 and p3 (2 mm long and 1
mm inner diameter) with distances b1-2 and b2-3 between coils of 27 mm. Each pick-up coil is
connected to corresponding input of digital oscilloscope. Resistors have been connected in
parallel to the pick-up coils to suppress the oscillations. A low frequency (5 Hz) square waveform
current, i, feeds the exciting coil.
We used single layered wounding of magnetizing solenoid with reduced number of turns
in order to avoid the situation when the DW can start propagating while H is still growing. The
time of transient process is mainly defined by the inductance of the exciting coil (it also depends
on slew rate of the signal source), which is proportional to the square of the number of turns, N.
Therefore, reducing N we shall reduce the transient time and increase the sweep rate, dH/dt. In
order to achieve high enough magnetic field (H~iN) we used a power amplifier. The distance
between the wire end and the first pick-up coil b0 (approx 40 mm) was set in the way that the
transient process has finished when the DW reaches the pick-up coil. In this way we achieved
steady magnetic field, H, when the DW reaches the first coil p1. The voltage drop Uh on the
4
resistor R0 is proportional to the magnetic field in the exciting coil and is captured by channel 4 of
the oscilloscope. In this way we control stability of magnetic field when measuring DW
propagation. The described above technique guarantees that the DW velocity measurements are
done at stable magnetic field.
In order to study the effect of magnetic field on single DW propagation, we need to control
that this DW depins from the wire end (point 0) and to avoid contribution of nucleation of the new
DWs in the other parts of the microwire. From previous paper 22 we can assume existence of the
other centers of easy nucleation randomly located along the microwire that are related with
macroscopic inhomogeneities (defects of different kind) existing in the microwire. In the case if
applied magnetic field, H, is above some value, few DWs (one from the wire end and others from
the reversed domains nucleated in the central part far from the wire’s ends) can propagate
simultaneously. In this case two pick-up coils set-up, previously employed elsewhere 18-21,
probably does not allow to reveal such situation.
To detect the possible nucleation and subsequent propagation of several DWs, we applied
the three pick-up coils set (Fig.1). It is worth mentioning that Novak at el.23 proposed using the
third pick-up coil to demonstrate that the domain wall is propagating at constant magnetic field
and its velocity is constant. They studied the DW propagation at low fields (below 140 A/m) , i.e.
below the typical fields for reverse domain nucleation at macroscopic defects in amorphous
microwires. Consequently they did not reach the magnetic fields required for reverse domain
nucleation in the central part of the samples. Here we show that the 3rd pick-up coil is required for
detection the multiple DW propagation.
We expect that DW depined from the wire end will sequentially induce emf in the pick-up
coils while propagating along the microwire. The waveforms of a single DW propagating through
the wire are shown in Fig.2a. As one can see, there are two voltage peaks induced in each pick-up
coil. The first one appears simultaneously in all tree coils and is caused by the sharp change of the
magnetic field, dH/dt, induced by the exciting coil when the magnetic field is reversing. The
second peaks are caused by moving DW. When the reverse magnetic field is applied to the
5
previously saturated sample (moment of time t=0), the closure DW start propagating toward the
other end of the microwire. Moving DW induces signals in pick-up coils p1, p2 and p3 on passing
through their sections at the moments of time t1, t2 and t3 respectively. As can be seen from the
Fig.2a, at the moment of time t1, when the measurement begins, the magnetic field has reached its
steady-state value. The DW velocity then can be found from Eq.(2). If we continue increasing the
magnetic field, at some threshold value the peaks order change (see Fig.2b). The peak in the
central pick-up coil appeared before those in the first and third pick-up coils. This situation is only
possible when a new reversed domain is nucleated between the pick-ups coils. Without the central
pick-up coil we could not detect the nucleation of a new domain in the center part of the wire, as
the peak order of the side coils is correct.
Considering constant DW velocity it is apparent that the criterion of single DW
propagation in the whole range of applied magnetic field is the following:
t1 2  t 23 
t13
2
(3)
where t1-2=t2-t1, t2-3=t3-t2 and  t1-3=t3-t1. If, for some reason, new DWs moving inside the
measurement zone appear, then the condition (3) is not satisfied and the correct calculation of
single DW velocity from the time distance between peaks in the voltage peaks induced in pick-up
coils is no more possible.
III. RESULTS AND DISCUSSION
We studied the remagnetization dynamics in magnetically bistable Fe74Si11B13C2 (wire 1)
and Fe75Si12B9C4 (wire 2), with metallic nucleus d and total (with glass-coating) D diameters
12.0/15.8 and 13.6/16.0 m respectively.
Fig.3a shows the measured dependences of DW velocity on applied magnetic field in two
bistable amorphous glass-coated microwires. From the observed v(H) dependences, the
magnetization switching can be divided in two regimes. The first one (shown with closed figures
6
and solid lines), which ends at to 294 and 340 A/m for samples 1 and 2 respectively, has almost
linear dependence v(H) with DW mobility S about 5 m2/As and maximum DW velocity v of 1.7
km/s. In the second regime (shown with open figures and dot lines), the DW velocity, calculated
through the time difference between the maximum in the induced emf in pick-up coil 1 and 3,
reaches values as high as 6 km/s and even more and DW mobility S is more than 50 m2/As. The
mechanism of such ultrafast magnetization switching in second regime of the sample
magnetization reversal is considered below in details. The characteristic of the samples are
summarized in Table 1. The parameters DW mobility S and the critical propagation field H0 (see
Eq.1) are found by linear fit of the experimental data. We also obtained the minimum field HD
(the depinning field of the closure domain) below which the closure DW does not propagate. This
field should be related with intrinsic coercivity.
We analyzed the time order of the peaks induced in the pick-up coils and concluded that in
the first regime, where the Eq. 3 is satisfied and the oscillograms of induced emf in the pick-up
coils have form shown in Fig 2.a, the sample magnetization switching runs trough the single DW
propagation from the wire’s end. In the regime of ultrafast magnetization switching, the voltage
peak order changes like those shown in Fig. 2.b, and consequently, the Eq. 3 is violated.
We assume that such drastic change of the remagnetization process is caused by possible
nucleation and consequent growing of additional reversed domain with lowest local nucleation
field, HN. This new reverse domain can be located at any place inside the sample. In order to
verify this assumption, we measured the distribution of the local nucleation fields Hn along the
sample length, x, as described in ref.22, i.e. using short magnetizing coil placed far from the
samples ends and measuring magnetic field for local magnetization reversal .The distributions of
the Hn(x) for the studied samples are shown in Fig.3b. We observed a number of dip holes in the
curves for samples 1 and 2, attributed previously to the positions of localized defects existing
within the microwire22. It is worth mentioning that the amplitude of the Hn(x) oscillations in
sample 2 is higher. The overall minimum HN observed for both microwires correlate quite well
with the border between single and multiple DW propagation regimes (compare Figs 3a and 3b).
7
Considering aforementioned, we assume that when the applied magnetic field has reached
the HN, the new domain is nucleated and two more DW starts to propagate towards the wire's
ends. As it was noted above, in such situation it is not possible to measure correctly single DW
velocity and we can only consider the effective DW velocity. It is worth distinguishing an
interesting mechanism of magnetization reversal in magnetically bistable microwires. This
mechanism is conditioned by the microwires inhomogeneities. The inhomogeneities can lead to
considerable acceleration of the sample magnetization switching. On the other hand, neglecting of
this factor can result in exaggerated estimation of DW velocity from Sixtus-Tonks experiment.
We believe that at magnetic field above HN, the contribution of defects can be essential. In this
case, under the action of external magnetic field, a new reversed domain can be spontaneously
nucleated in front of the propagating head-to head closure domain as schematically shown in
Fig.4. Appearance of these additional domains at H> HN can accelerate remagnetization switching
resulting in higher effective DW velocity.
The essence of this process is clearly shown in Fig.4. There left front of propagating headto-head domain wall dw2 moves toward the dw1. Finally these two reversed domains clamping
and the right front, dw3, becomes the unique. Obviously, this process, which can be nominated as
tandem remagnetization, results in significant decrease of the magnetization switching time and
acceleration of magnetization switching in magnetically bistable microwires. Proposed
mechanism of ultrafast magnetization switching can explain non-linearity of v(H) dependences
and ultra-fast DW propagation reported in magnetically bistable microwires18-21.
IV. CONCLUSION
The mechanism of the fast magnetization reversal is studied in magnetically bistable
microwires. Below some critical magnetic field, HN, determined by the microwires
inhomogeneities, almost linear v(H) dependence is found. This regime is controlled by the single
domain wall propagation. Quite fast DW propagation (v till 1730 m/s at H about 300 A/m) has
been observed. When the applied magnetic field exceeds HN, new reverse domains can be
8
nucleated and consequently tandem remagnetization mechanism can be realized. The nucleation
of new reversed domains is determined by natural or artificially created defects in the microwires.
This results in significant decrease of the magnetization switching time and acceleration of
magnetization switching in magnetically bistable microwires. Proposed mechanism of tandem
ultrafast magnetization switching through additional nucleation centers created artificially can be
applied in spintronic devices for enhancing their performance.
ACKNOWLEDGMENTS
This work was supported by EU ERA-NET program under project DEVMAGMIWIRTEC
(MANUNET-2007-Basque-3). One of the authors, A.K.Z, wishes to thank Ikerbasque Foundation
for fellowship.
9
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11
Table I: Parameters of studied microwires. S* and H0* are the DW mobility and the critical
propagation field for single DW regime, HD is the depining field, HN is the sample’s global
nucleation field, S** is the effective DW mobility for multiple DW regime.
Sample
d/D
S*, m2/As
H0*, A/m
HD, A/m
HN, A/m
S**, m2/As
1
0.76
5.52
112
82
294
70.5
2
0.68
4.79
-81
211
340
53.7
12
Figures captions
Fig.1. Schematic picture of the experimental set-up
Fig.2. Waveform of the signal captured by the oscilloscope. Pick-up coils p1, p2 and p3 are
connected to the oscilloscope channels 1, 2 and 3. The voltage Uh is captured by the channel 4.
Fig.3. Dependences of domain wall velocity versus applied magnetic field measured in
magnetically bistable amorphous microwires (a) and distribution of local nucleation fields
measured in the same samples (b)
Fig.4. Magnetization switching through tandem mechanism, cd – closure domain, rd-reversed
domain appeared within the microwire.
13
Fig.1
14
Fig. 2
15
Fig.3
16
Fig.4
17