Why Spin angular momentum effect (quantization) is observed only under varying magnetic field? Is there some reason behind the appearance of spin effects only under the application of variable magnetic field.
I know that we need variable magnetic field to act force on charge particle with some angular momentum, but I am comparing spin angular momentum with orbital angular momentum, i.e. we can detect orbital angular momentum without application of magnetic field, so why not spin angular momentum?
Do we consider this as just inherent property of spin, or do we have suitable reasons to justify it?
 A: Quantization in a narrow sense refers to discreteness of energy levels. In the context of atomic levels such discreteness is usually observed via optical experiments -e.g., via absorption, which has resonance at the frequency corresponding to the level spacing: $\hbar\omega = E_2 - E_1$. Studying optical absorption spectrum necessarily implies the use electromagnetic radiation, i.e. of time-dependent electromagnetic field.
Orbital momentum designates the states of a charge particle (electron) in the electrostatic field of the nucleus. As such these states are coupled to the electromagnetic field via charge, i.e. they are coupled to the electric field. In order to observe absorption on needs both constant and time-dependent fields: the former one to cause level splitting (via the Stark effect) and the latter to case absorption.
Spin is a kind of magnetic moment, i.e. it is coupled to the magnetic field, and consequently a constant magnetic field is needed to split spin levels, and a time-dependent field is necessary to cause absorption.
Finally, an experimental setup my use additional time-dependent fields to facilitate more precise measurements -e.g., by causing the Rabi oscillations.
A: Spin effects do not only occur in a variable magnetic field.  It is certainly true that a Stern-Gerlach type experiment is a clear demonstration of the existence of spin-1/2 objects, but the existence of spin could have (eventually) been deduced without this result.
Important examples of where spin comes up explicitly are the Pauli exclusion principle, the computation of average values in fermionic systems, and various spin-orbit interactions affecting the energy levels at the atomic or nuclear level.
