NMR Techniques at Liquid Helium Temperatures - Low ...

2.2 Basics of NMR 8
decreases, the amount of atoms in the low energy state increases, and vice versa.
With NMR, very small population differences can be detected, making it a very
sensitive tool for spectroscopy.
Continuous wave NMR (cw-NMR) is the simplest NMR method, and also the
one we use in our measurements. It can be performed in two ways. In the first
method, the RF field is continuously oscillating at a constant frequency ω and
probing the energy levels of the sample while the static magnetic field is varied.
In the second method, the frequency of the RF field is varied while H is kept
constant. In both cases, the resulting signal is the same absorption signal, but in
the first case it is measured as a function of H, and in the second case as a function
of ω. The transformation between these two variables in 3 He-B measurements is
presented in Sec. 2.3.4.
2.2.2 Relaxation processes
The material response to an applied magnetic field H is determined by the pressure
and temperature dependent static magnetic susceptibility χ0(p,T ). The relationship
between the equilibrium magnetization of the material, M0, and the strength
of the applied external field, H, is defined as
M0 = χ0H. (2.10)
We can also write Mz = γ¯hn
2 , where n = N+ − N − [28] and +z is the direction of
the static magnetic field H. In thermal equilibrium M0 = Mz and M0 points in
the +z direction since N + > N − , and there is no stable transverse magnetization
(< Mx >=< My >= 0).
The net magnetization changes when the transverse oscillating RF field induces
transitions in the spin system. If enough energy is put into the system, i.e.,
the amplitude of the RF field is high enough, it is possible to saturate the spin
system and make Mz = 0. After the transverse excitation field is turned down, Mz
relaxes to its equilibrium value according to the equation [29]
Mz = M0(1 − e −t/T1 ), (2.11)
where T1 is the time constant called the longitudinal or spin-lattice relaxation time.
The oscillating transverse magnetic field Hrf also creates the transverse magnetization
Mxy which rotates around the z axis at the Larmor frequency ωL. The
transverse net magnetization starts to dephase because each of the spins experiences
a slightly different magnetic field and rotates at its own frequency. This is
both due to the combination of molecular interactions and to local variations in
H. Dephasing causes Mxy to return towards its equilibrium value, Mxy = 0. The