Transverse Magnetisation (QM)
INCORRECT. This incorrect answer mixes the classical and QM descriptions of MRI. For example: How does equalisation of the number of spins in the two Zeeman energy levels produce transverse magnetisation? Surely it only destroys longitudinal magnetisation (since there is no overall net magnetisation vector in the direction of the external magnetic field). A transverse magnetisation is not produced.
In fact, spins do not occupy specific energy levels in the QM description of MRI. See Zeeman eigenstates. In the QM description of MRI, we must be very careful when thinking about the state of individual spins, especially when diagrams are used depicting individual spins to communicate only the overall state of an ensemble of spins.
Net polarisation perpendicular to the field (the degree of polarisation is greatly exaggerated).
CORRECT. If there is no net polarisation with or against the external magnetic field, then there is no net magnetisation vector Mz. However, a net polarisation can occur perpendicular to the field (for spins in superposition states). Quantum coherences may form between the two Zeeman energy eigenstates, which may be depicted as partial alignment of spins perpendicular to the external magnetic field direction. A net magnetisation is formed in the transverse plane. This is magnetisation in the x-axis (Mx) and/or the y-axis (My).
The "arrow" representation of quantum coherences in the energy diagram does not indicate transition between states, only that coherences exist between spins in superpositions of the Zeeman eigenstates, which results in net spin polarisation perpendicular to the field. These coherences may be imagined as partial alignment of spins in the transverse plane. Though a picture such as this is not strictly correct, it may help to give a sense of quantum coherences without involved mathematical explanation (see Further Reading).
A 90° (π/2 radians) RF excitation pulse accomplishes two tasks. It equalises the observable population difference between the two Zeeman eigenstates, and it converts the population difference into coherences.
Further reading on this topic:
Books: Spin Dynamics p280