156
6 Magnetic Domain Wall Motion
It should be noted that measurement of domain wall velocity using GMR method
has an advantage over dynamical measurements because of its simplicity (Ono et al.
1999). As discussed in Sect. 6.2.1, GMR detection method gives us information about
domain wall position [Eq. (6.1)]. Hence, domain wall velocity, v = dx/dt, can also be
determined by the time-domain measurements. Rearranging the terms in Eq. (6.1),
we obtain
x =
L
R ↑↓ − R
R ↑↓ − R ↑↑
(6.2)
v =
dx
dt
= −
L
R ↑↓ − R ↑↑
d R
dt
.
(6.3)
Equation (6.3) clearly shows that GMR method can provide us information on
the time variation of the domain wall position, i.e., domain wall velocity. This technique offers an advantage over conventional experimental methods (Sixtus and Tonks
1931), where domain wall velocity measurements, employing Kerr microscopy, can
provide only the average velocity of a domain wall.
Let us give a simplified experimental description of DW velocity measurement.
In order to carry out DW velocity measurements, trilayer structures of Ni 81 Fe 19
(40 nm)/Cu(20 nm)/Ni 81 Fe 19 (5 nm) have been considered. The width of the wire
is 0.5 mm and four current–voltage terminals have been attached to the sample
with voltage probe being placed at a separation distance of 2 mm. The magnetic
field has been applied along the wire axis. The voltage across two voltage probes
has been monitored by a differential pre-amplifier and a digital oscilloscope. The
current flowing through the electromagnet has also been monitored by the digital
oscilloscope. In this way, we obtain both the resistance of the trilayer structure and
applied magnetic field during the magnetization reversal simultaneously (Fig. 6.11).
It exhibits the change in resistance as a function of an externally applied magnetic
field of the trilayer structure at 77 K temperature. At the beginning of the measurement, a magnetic field of 500 Oe has been applied in order to align the magnetization
of the device structure in one direction, i.e., along the direction of the applied field.
After that, the measurement of resistance has been carried out at 10-ms intervals
by sweeping the applied magnetic field towards the counter direction at a sweeping
rate of 20 Oe/s. Experimental results, exhibiting the largest value of resistance in
the magnetic field range between 80 and 120 Oe, suggest antiparallel alignment of
magnetization in that magnetic field range. The appreciable change in resistance at
80 and 120 Oe is attributed to the magnetization reversals of the 5-nm-thick NiFe
and 40-nm-thick NiFe layers, respectively. The absence of any measured point in
our experimental results, as shown in Fig. 6.11, during the magnetization reversal
of the 40-nm-thick NiFe indicates that the magnetization reversal is accomplished
within 10 ms. However, magnetization reversal of the 5-nm-thick NiFe takes place
gradually with increasing the applied magnetic field. This, in turn, indicates that the
magnetization reversal of this 5 nm thin NiFe layer takes place by the successive
pinning and depinning of a magnetic DW. Let us focus on the magnetization reversal
6 Magnetic Domain Wall Motion
It should be noted that measurement of domain wall velocity using GMR method
has an advantage over dynamical measurements because of its simplicity (Ono et al.
1999). As discussed in Sect. 6.2.1, GMR detection method gives us information about
domain wall position [Eq. (6.1)]. Hence, domain wall velocity, v = dx/dt, can also be
determined by the time-domain measurements. Rearranging the terms in Eq. (6.1),
we obtain
x =
L
R ↑↓ − R
R ↑↓ − R ↑↑
(6.2)
v =
dx
dt
= −
L
R ↑↓ − R ↑↑
d R
dt
.
(6.3)
Equation (6.3) clearly shows that GMR method can provide us information on
the time variation of the domain wall position, i.e., domain wall velocity. This technique offers an advantage over conventional experimental methods (Sixtus and Tonks
1931), where domain wall velocity measurements, employing Kerr microscopy, can
provide only the average velocity of a domain wall.
Let us give a simplified experimental description of DW velocity measurement.
In order to carry out DW velocity measurements, trilayer structures of Ni 81 Fe 19
(40 nm)/Cu(20 nm)/Ni 81 Fe 19 (5 nm) have been considered. The width of the wire
is 0.5 mm and four current–voltage terminals have been attached to the sample
with voltage probe being placed at a separation distance of 2 mm. The magnetic
field has been applied along the wire axis. The voltage across two voltage probes
has been monitored by a differential pre-amplifier and a digital oscilloscope. The
current flowing through the electromagnet has also been monitored by the digital
oscilloscope. In this way, we obtain both the resistance of the trilayer structure and
applied magnetic field during the magnetization reversal simultaneously (Fig. 6.11).
It exhibits the change in resistance as a function of an externally applied magnetic
field of the trilayer structure at 77 K temperature. At the beginning of the measurement, a magnetic field of 500 Oe has been applied in order to align the magnetization
of the device structure in one direction, i.e., along the direction of the applied field.
After that, the measurement of resistance has been carried out at 10-ms intervals
by sweeping the applied magnetic field towards the counter direction at a sweeping
rate of 20 Oe/s. Experimental results, exhibiting the largest value of resistance in
the magnetic field range between 80 and 120 Oe, suggest antiparallel alignment of
magnetization in that magnetic field range. The appreciable change in resistance at
80 and 120 Oe is attributed to the magnetization reversals of the 5-nm-thick NiFe
and 40-nm-thick NiFe layers, respectively. The absence of any measured point in
our experimental results, as shown in Fig. 6.11, during the magnetization reversal
of the 40-nm-thick NiFe indicates that the magnetization reversal is accomplished
within 10 ms. However, magnetization reversal of the 5-nm-thick NiFe takes place
gradually with increasing the applied magnetic field. This, in turn, indicates that the
magnetization reversal of this 5 nm thin NiFe layer takes place by the successive
pinning and depinning of a magnetic DW. Let us focus on the magnetization reversal