In-plane magnetic field dependence of
electric field-induced magnetization
switching
Cite as: Appl. Phys. Lett. 103, 072408 (2013); https://doi.org/10.1063/1.4818676
Submitted: 08 May 2013 • Accepted: 22 July 2013 • Published Online: 16 August 2013
S. Kanai, Y. Nakatani, M. Yamanouchi, et al.
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© 2013 AIP Publishing LLC.
103, 072408
APPLIED PHYSICS LETTERS 103, 072408 (2013)
In-plane magnetic field dependence of electric field-induced magnetization
switching
S. Kanai,1 Y. Nakatani,2 M. Yamanouchi,1,3 S. Ikeda,1,3 F. Matsukura,4,1,3 and H. Ohno1,3,4,a)
1
Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku
University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
2
University of Electro-communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan
3
Center for Spintronics Integrated Systems, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577,
Japan
4
WPI-Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba-ku,
Sendai 980-8577, Japan
(Received 8 May 2013; accepted 22 July 2013; published online 16 August 2013)
Electric field-induced magnetization switching through magnetization precession is investigated as
a function of in-plane component of external magnetic field for a CoFeB/MgO-based magnetic
tunnel junction with perpendicular easy axis. The switching probability is an oscillatory function of
the duration of voltage pulses and its magnitude and period depend on the magnitude of in-plane
magnetic field. Experimental results are compared with simulated ones by using Landau-LifshitzC 2013
Gilbert-Langevin equation, and possible factors determining the probability are discussed. V
AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4818676]
Magnetic tunnel junction (MTJ) is one of the most
attractive devices for future high performance memory in
very large scale integrated circuit, because of its possible
high density integration, fast switching, and low power operation in addition to non-volatility.1,2 Scalable spin-transfertorque (STT) magnetization switching for MTJs has been utilized to realize high density and low switching power at the
same time, and sub pJ/bit switching was recently achieved
for a 40-nm-size CoFeB/MgO MTJ with perpendicular magnetic anisotropy (PMA).3 Power consumption of magnetization reversal by STT is determined by applied charge
current, voltage, and writing time. For further reduction of
power consumption, it is required to develop a new magnetization reversal scheme without resorting to charge current.4
Electric field-control of magnetism through carrier density modulation, which was first demonstrated for III–V ferromagnetic semiconductors,5–8 has recently been applied to 3d
transition-metal and its alloy ferromagnets. The observations
of sizeable changes in coercivity, magnetic anisotropy, and
the Curie temperature in capacitor structures with Fe, Co, or
their alloy electrode at room temperature by the application of
electric field were reported.9–13 The electric field effects are
now utilized to switch the magnetization direction in a free
layer in MTJs, and electric field-assisted magnetization reversal6,14,15 and electric field-induced precessional magnetization
switching were demonstrated.16–18 Magnetization reversal
solely by electric field consumes only charging/discharging
energy to a capacitor, and thus, reduces switching power by a
few orders comparing with that by STT switching.
The scheme of electric field-induced magnetization reversal focused here relies on the temporal change of the
direction of magnetic easy axis by the application of voltage
pulses Vpulse.4,10,16–18 The change of the easy axis induces
a)
Author to whom correspondence should be addressed. Electronic mail:
ohno@riec.tohoku.ac.jp. Telephone: þ81-22-217-5553. Fax: þ81-22-2175553.
0003-6951/2013/103(7)/072408/4/$30.00
the precessional motion of magnetization about the effective
magnetic field (Heff; sum of anisotropy, stray, and external
fields), and magnetization switching takes place through the
motion when the pulse duration (tpulse) is half integer times
the precession period. In the previous work, we showed that
electric field-induced 180 magnetization reversal of a free
CoFeB layer in a sputtered CoFeB/MgO based MTJ with
perpendicular magnetic easy axis.17 We applied Vpulse to
change temporary the direction of magnetic easy axis from
perpendicular to in-plane. A tilted external magnetic field
(H) was applied to the MTJ to compensate the perpendicular
stray field (HS) from the reference layer and to fix in-plane
magnetization precessional axis of the free layer. The
obtained magnetization reversal probability was an oscillatory function of tpulse, indicating the switching takes place
through magnetization precession about Heff under electric
field. It is expected that the oscillatory period is determined by
the in-plane component of Heff, which is proportional to
Larmor frequency, i.e., larger in-plane component Heff results
in a shorter precessional period, and thus, makes faster magnetization switching possible. In this letter, we investigate the
electric field-induced magnetization switching probabilities as
a function of the magnitude of in-plane magnetic fields.
The stuck structure, Ta(5)/Ru(10)/Ta(5)/Co0.2Fe0.6B0.2(0.9)/
MgO(1.4)/Co0.2Fe0.6B0.2(1.8)/Ta(5)/Ru(5) (numbers in parenthesis are thicknesses in nm), is deposited on a sapphire substrate by rf magnetron sputtering at room temperature. The
film is processed into a 70-nm-diameter MTJ on a coplanar
strip line by using electron beam lithography and Ar ion milling. The device is annealed in vacuum (104 Torr) under a
magnetic field (0.4 T) for 1 h at 300 C. The two CoFeB
layers have perpendicular magnetic easy axis, and PMA field
of a top free CoFeB layer is 50 mT. This is the same device as
that used in Ref. 17, in which basic characteristics of the device are presented.
All measurements are conducted at room temperature.
We measure resistance R versus H curves as a function of
103, 072408-1
C 2013 AIP Publishing LLC
V
072408-2
Kanai et al.
FIG. 1. Astroid curves, which show sets of perpendicular and in-plane components of switching magnetic fields, Hy (in-plane component of external
magnetic field) and Hz (perpendicular component of external magnetic field)
at bias voltage Vdc ¼ 800, 30, and 800 mV. Inset shows the definition of
axes in this study.
the direction hH of H with respect to the normal of the device
surface. Thus, perpendicular (z) and in-plane (y) components
of H (Hz and Hy) correspond to HcoshH and HsinhH, respectively. We fix magnetization direction of the bottom reference CoFeB layer to -z direction. Figure 1 shows astroid
curves, which indicate magnetization switching fields as
functions of Hz and Hy, determined from minor R-H curves
under various bias voltages Vdc. The positive Vdc corresponds to the situation with positively biased bottom layer
with respect to top layer, in which electrons flow from top to
bottom. The astroid curve at Vdc ¼ 30 mV shifts to positive
z direction, due to stray field from the reference bottom
layer. The magnitude of shift takes a constant value of
29 mT independent of hH, which indicates that the direction
of magnetization in the reference layer is not tilted so much
from the normal in tilted H applied in this study. The elongated shape along Hy than Hz axis is may be related to the
presence of the second-order anisotropy energy density K2,19
which is several times smaller than the first-order K1,20 and/
or incoherent magnetization reversal mode. At higher Vdc,
astroid curves become narrower at positive Vdc and wider at
negative Vdc in z direction. This distortion results from the
electric field modulation of K1.19,20 The application of higher
Vdc disturbs also the symmetry of curves along z direction,
which can be explained by the presence of STT.21
Appl. Phys. Lett. 103, 072408 (2013)
The probabilities of electric field-induced magnetization
reversal are measured by a setup similar to the one drawn
schematically in Fig. 2(a) in Ref. 17. We use an arbitral
wave function generator to apply Vpulse of 900 mV with various tpulse to the MTJ. The rise and fall times of Vpulse are set
to 80 ps. Actual pulse voltage applied on MTJ is
(1 þ C)Vpulse 1.8 V with reflectivity coefficient C 1
because of the impedance mismatch between MTJ and the
50 X transmission line. The resulting magnetization configuration after Vpulse application is detected by two-terminal resistance of MTJ with Vdc ¼ 30 mV. The low resistance
state corresponds to parallel (P) magnetization configuration
in the two CoFeB layers and high resistance state to antiparallel (AP) configuration. The magnetization switching
probabilities are determined from measuring 100 times the
magnetization configuration after Vpulse application at each
tpulse, H, and hH.
The contour plots in Fig. 2(a) summarize probability of
magnetization switching from P to AP and then to P by successive two voltage pulses, P10P01, as functions of tpulse and
Hy with various hH. The P10P01 corresponds to the product
of the probabilities of P to AP transition (P10) and AP to P
transition (P10). Clear oscillatory probabilities with tpulse are
observed, and the oscillatory period decreases with the
increase of Hy. The magnitude of Hz ( ¼ Hcos hH ¼ Hycot hH)
at which P10P01 takes maxima is 29 mT independent of hH at
hH > 10 . This value of Hz shows good correspondence with
stray field obtained from the astroid curve at Vdc ¼ 30 mV
(Fig. 1), which is the center of minor hysteresis loop at which
the two distinct energetically stable states (P and AP states)
exist. The oscillatory period is expected to be the period s of
the precessional motion of magnetization. When Vpulse is
switched on, magnetization, which initially points to one of
the two energetically stable directions, starts to precess about
y axis. Then, when Vpulse is switched off, magnetization
direction starts to stabilize again to one of the two directions
through precession around z axis. For tpulse of half-integer
times s, magnetization at which Vpulse is switched off, rotates
by 180 net about y axis, and thus, a high probability of magnetization switching is expected. On the other hand, for tpulse
of integer times s, magnetization rotates by 360 net, and the
switching hardly occurs. Since the period of magnetization
precession under Vpulse is given by the inverse of Larmor frequency in an ideal case, s may be expressed as s ¼ 2p/
cl0Heff, where c and l0 are gyromagnetic constant and permeability in vacuum. This is approximated to s 2p/cl0Hy
because Vpulse induced in-plane magnetic anisotropy field is
FIG. 2. (a) Measured and (b) simulated
probabilities of back-and-forth magnetization switching by two successive
voltage pulses as functions of pulse duration and in-plane component of
external magnetic field.
072408-3
Kanai et al.
Appl. Phys. Lett. 103, 072408 (2013)
2 mT at most.17 Solid (dashed) curves in Fig. 2(a) show
tpulse ¼ ns, where n is half integer (full integer). The lines
trace well the minima and maxima in probabilities, which
confirm that magnetization switching takes place indeed
through precessional motion of magnetization. The oscillatory behavior becomes blurred for n 2 especially at l0Hy
below 10 mT (at hH < 15 ) and above 20 mT (at hH > 33 ).
In order to gain insights into the observed experimental
characteristics, magnetization dynamics in a single-domain
magnet is simulated by using Landau-Lifshitz-GilbertLangevin equation
^
^
~
~
dm
^ ðl H
^ dm
~
~
~
~
¼ cm
;
0 eff þ l0 h T Þ þ am
dt
dt
(1)
^ , a, and h~T are time, magnetization vector normal~
where t, m
ized by saturation magnetization MS, Gilbert damping constant, and thermal fluctuation field, respectively. The effective
~eff is given by the sum of anisotropy
magnetic field vector H
^ and external field vector H
~
z)
field HK vector (HK mz~
~
~eff ¼ HK ðVMTJ Þmz~
z^ þ H;
H
(2)
~ and unit vector directing
z^ are z component of m
where mz and ~
perpendicular to the plane, respectively. The h~T is assumed to
have a three dimensionally isotropic Gaussian amplitude, and
its thermal average in time Dt is expressed as22
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2kB Ta
hjh~T j2 i ¼
:
(3)
l0 clDt
Here, kB is the Boltzmann constant, temperature T is 300 K,
and l ¼ MSV* is net coherent magnetic moments in the free
layer with volume V* in which magnetization dynamics is
coherent. The dynamics of magnetization is simulated in the
following sequence by using Eqs. (1)–(3); (i) magnetization
direction is initialized to take one of the two energy minima
at l0HK ¼ 50 mT and Hy, (ii) l0HK is set to 2 mT during
tpulse, and (iii) l0HK is returned back to 50 mT. Because in
experiments, we apply Hz to compensate stray field from the
~ in simreference layer, we do not consider z component of H
ulations. We determine P10P01 by repeating 100 simulations
for the same parameter set of tpulse and Hy. From a number of
simulations with different values of V* and a, we find that
experimental results can be reproduced well for the situation
with V* ¼ V/9 and a ¼ 0.2 as shown in Fig. 2(b), where V is
volume of the free layer.
The obtained small V* and large a (which is ten times
greater than that of as-deposited CoFeB/MgO film determined by ferromagnetic resonance measurement) indicate
that the coherence of precessional motion is disturbed. For
the present nanoscale MTJ, non-uniform distribution of stray
field from the reference layer on the free layer as well as inplane demagnetizing field, which are not considered in the
present simulation, may deteriorate the coherence.20,23
Magnetization reversal with nucleation may also affect the
magnitudes of apparent V* and a obtained by simulation
done of a single domain.24 At hH < 20 , the increase of tpulse
for magnetization switching due to the reduction of the
Larmor frequency becomes prominent. Along with it, the
reversal probability decreases owing to the thermal agitation
induced decoherence. The switching probability at half precession cycle increases with the increase of Hy and then
starts to decrease at larger Hy above 20 mT. This is due to
the reduction of angle between the two energy minima,
which reduces the magnitude of the initial precessional angle
(e.g., <120 at l0Hy ¼ 25 mT). Because precessional angle
decreases towards 0 with time due to damping, smaller initial precessional angle and larger Larmor frequency in larger
Hy lead to faster magnetization decay to y direction during
tpulse. For such a case, the effect of thermal agitation may
become more remarkable again and thus results in the
decrease of the probabilities.
In order to clarify the origin of the decoherence, we perform micromagnetic simulation by taking into account a
stray field distribution from the reference layer and demagnetization field in addition to thermal agitation. We consider
70 nm/-circular and 1.4 nm-thick free layer (subtracting
0.4 nm-thick magnetically dead layer).3,25 The free layer is
divided into 1024 magnetic cells with a ¼ 0.02 and MS ¼ 1.4
T. We use exchange stiffness constant of 13 pJ/m estimated
for the present device from magnetization reversal probability measurement with pulse magnetic field,26 which is comparable to the value obtained from magnetic domain
structure.27 We simulate the magnetization direction of the
free layer as a function of time from the time at which magnitude of HK is changed. The simulation at T ¼ 0 shows that
the magnetization precessional frequency decreases slightly
with the increase of time due to the increase of demagnetization field opposed to Hy. We find that thermal agitation does
not change much the magnetization relaxation time, but it
gives rise to random phase shifts of precessional motion.
This irregular phase shift is enhanced in the presence of distribution of stray field from the reference layer. A stochastic
nature of thermal agitation results in different magnetization
trajectory at every event and thus averaged switching probabilities decrease with tpulse. Figure 3 shows magnetization
switching probabilities obtained by 300 micromagnetic simulations. The simulated probabilities capture the experimental features well, indicating that the increase of apparent a
results from the thermal agitation enhanced by the distribution of stray field.
For better controllability of magnetization switching,
one needs more distinct contrast in the switching
FIG. 3. Switching probabilities obtained from micromagnetic simulation.
072408-4
Kanai et al.
probabilities for a wide range of tpulse as well as Hy. The
increase in not only coherence but also PMA and its modulation ratio by electric field should improve the contrast in
probabilities. High PMA at zero bias enables us to apply a
large Hy without reducing the precessional angle; a high
PMA modulation by electric field is also required to switch
the direction of Heff. The micromagnetic simulation shows
that a high PMA modulation can improve coherence of magnetization precession (not shown). The realization of material systems meeting the requirements is a future challenge.
The energy consumption to reverse magnetization in the
present devices is estimated to be 56 fJ/bit at hH ¼ 38 and
tpulse ¼ 0.83 ns, which is consumed almost entirely by Joule
heating and not by charging and discharging the device capacitance. By adopting an appropriate MgO barrier thickness, one can reduce considerably the tunnel current through
the barrier at high Vdc,28 which should result in drastic reduction in power consumption.
In conclusion, we investigate the magnitude of in-plane
magnetic field dependence of electric field-induced magnetization switching probabilities in a CoFeB/MgO-based magnetic tunnel junction. The switching probabilities show
oscillation with duration of voltage pulse, whose oscillatory
period decreases with the increase of the in-plane component
of external magnetic field because of the increase of Larmor
frequency. The comparison of simulated probabilities by
Landau-Lifshitz-Gilbert-Langevin equation with a single magnetic domain to experimental ones indicates the presence of
the sources of decoherence. Micromagnetic simulation shows
that decoherence is induced by thermal agitation enhanced by
distribution of the effective field.
The authors thank H. Sato, I. Morita, T. Hirata, and H.
Iwanuma for their technical supports and discussion. This
work was supported in part by JSPS through FIRST program,
a Grant-in-Aid for JSPS Fellows, and a Grant-in-Aid for
Scientific Research (No. 23360002) from JSPS, and
Research and Development for Next-Generation Information
Technology of MEXT.
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