Information Technology Reference
In-Depth Information
compensate the damping of spin waves, one needs to include an amplification
mechanism (gain). One of the possible gain mechanisms may be parametric spin-
wave amplification, which has been experimentally demonstrated [17].
7.9. THE PRINCIPLE OF OPERATION
In order to illustrate the principle of operation, we consider the propagation of a
spin wave excited by an ACPS transmission line. The spin dynamics can be
described using the Landau-Lifshitz's equation as follows:
h
i
d
m
dt
¼
~
g
1
þ a
2
~
m
H
eff
þ a
m
H
eff
~
;
ð
7
:
1
Þ
m
¼
M
=
where
M
s
is the unit magnetization vector, M
s
is the saturation magne-
tization,
g
is the gyro-magnetic ratio, and
a
is the phenomenological Gilbert
damping coefficient. The first term of Equation 7.1 describes the precession of
magnetization about the effective field and the second term describes its dissipa-
tion. H
eff
is the effective field that consists of the superposition of the external field
and contributions from anisotropy, and exchange fields.
2A
M
s
r
2K
M
s
ð~
H
eff
¼r
e
þ
H
pulse
;
2
F þ
2
m
þ
~
m
~
e
Þ~
ð
7
:
2
Þ
2
F ¼
4
p
M
s
r~
where
r
m, A is the exchange constant, K is the uniaxial anisotropy
e is the unit vector along with the uniaxial direction, H
pulse
is the
pulse field produced by the source-drain current. The first terms in Equation 7.2
are defined by the material properties of the ferromagnetic sample, while the last
term, the excitation pulse field, can be artificially controlled. Theoretically, by
adjusting the form of the external field pulse, it is possible to excite a spin wave of
any desired frequency and amplitude. To be realistic, we use experimental data
and an analytical model developed in [2], where spin wave excitation in NiFe film
by applying current pulses has been investigated in detail. It was found that a short
current pulse (
constant, and
~
100 ps) through a conducting strip placed close to the NiFe film
(0.54
m
m oxide thickness) excites a spin-wave packet, which is a linear super-
position of spin waves. An analytical solution to Equation 7.1 was found, and it
describes the propagation of the wave packet through the ferromagnetic film. The
results of the numerical simulations demonstrated a good agreement with
experimental data [2].
In Figure 7.14, we have show two ACPS lines, one as input and one output. If
we add another ACPS line, it can be used as a second input port. Each of the input
devices (ASPC lines) excites a spin-wave packet consisting of a Gaussian
distribution of wave vectors that is 2/
d
in width and centered about k0. The
wave packet propagates along with the y direction and can be described with one
o
Search WWH ::
Custom Search