Page 106 - Maxwell House

86 Chapter 2

when two magnetic fields are applied simultaneously. The first is the bias and uniform
exerted some external source like permanent magnet or electromagnet. The second is RF
0
0
alternative () = () + () oriented perpendicular and belongs to harmonic EM
0 0
wave propagating in ferrite. Therefore, the total H-field is
() = + () = + () + () (2.90)
0

0
0
0

0
0
Σ
To be sure that ferrite devices we are going to consider below in Chapter 6 are linear, assume
the relative weak RF component, i.e. |()| ≪ . Assume for a while that ferrite is fully
0
magnetized, i.e. > (see Section 2.6.3 in this chapter). Doing such, we automatically
0

excluded from our study the domain wall oscillation described in the previous sections and
related to low frequency resonances in the range of several megahertz. We come back to this
issue later. Following the neoclassical interpretation, we can consider each electron spin as a
charged ball spinning like gyroscope around its own axis (see Figure 2.7.1a ) while having the
17
ℎ
2
spin magnetic moment | | = = 9.27x10 −24 [A⋅ m ]. Here the Plank’s constant h is
4
2
−34 [m ⋅ kg / s].
6.6226 ⋅ 10

Figure 2.7.1 Spin magnetic moment precession illustration: a) Free precession, b)
Extinguishing free precession, c) Forced precession

2.7.2 Free Precession in Fully Magnetized Ferrite
Let us first look at the magnetizing process assuming that () = 0. In general, due to the
predominantly chaotic spin orientation from domain to domain (see Figure 2.6.2a) the bias
at some moment of time is not aligned with . Then the strong force tries to turn
0
0
0
each domain spin moment in parallel to the bias or z-axis thereby transferring part of its energy
to spin moment movement. From the course of mechanics [10], we know that the combination
of gravitation and external bias force creates the torque force = − x =
0

x . This torque vector generates the rotating force similar to the push force closing
0 0 0
or opening the revolving door, as shown in Figure 2.1.1 and discussed in details above. If so,
the tip of the vector starts tracing circles around the bias magnetic vector as Figure
0
0
2.7.1a demonstrates. In the absence of damping forces, such free rotation or precession will
continue indefinitely. The mechanical gyro model analysis shows that the precession frequency
called ferromagnetic resonance frequency is proportional to the external torque (rotating) force
≈ = (2.91)
0
0
0
0
17 elements of drawing are not in actual scale