Magnetic field as a relativistic effect
Unfortunately, the Veritasium videos contain some truth but follow a misleading teaching tradition, going back to Purcell's book on Electromagnetism, which presents the magnetic field as a relativistic effect.
There are different reasons this claim is false.
- Special Relativity shows that there is a unique tensor quantity, the electromagnetic field, whose components are both the $E$ and the $B$ fields. Moreover, $E^2-B^2$ and ${\bf E}\cdot {\bf B}$ are relativistic invariants, easily obtained from the tensor field. Therefore, if ${\bf E}\cdot {\bf B}=0$, and $E^2-B^2$ is positive, it is possible to find an inertial reference frame where the $B$ field is zero, while if it is negative, this is never possible (but it is possible to find a reference frame where the electric field is zero).
- As Jefimenko showed more than 25 years ago, if one can think of the magnetic field as a relativistic effect, it would also be possible to think of the electric field as a relativistic effect. The two possibilities are not consistent with each other. Again, this fact points to the full electromagnetic field as a unique quantity made by two independent components, the electric and the magnetic fields.
- Maxwell equations in a single reference system show that both the electric and magnetic fields are necessary to describe a scenario where both charge density and current are present.
Purcell's approach shows that the relativistic consistency of the description of the physical effects requires properly taking into account the relativistic transformations of the sources (electric density and currents) and the fields (electric and magnetic).
To summarize, let's forget about the magnetic field as a relativistic effect. In a given reference frame, electric and magnetic fields are required to describe the effects of charges and currents. In the particular case of stationary sources, one can separate the electric field due to the charge density and the magnetic field due to the current density.
Magnetic moment due to the spin
This is not something really different from the usual magnetic fields due to currents. It has been shown that the quantum description of particles with spin implies a probability current density due to the spin (see Mita, K. (2000) Virtual probability current associated with the spin. American Journal of Physics, 68(3), 259-264). If the particle is charged, this probability current density is a current density that acts as a source of a (spin) magnetic field. Starting from the spin magnetic moment, quantum mechanics explains the ferromagnetic or antiferromagnetic couplings as a phenomenon connected to the electrostatic advantage of a parallel or antiparallel spin ground state.
Starting from this essential step, one can understand the ferromagnetism of macroscopic samples in terms of aligned domains.
In summarizing, there are no competing explanations for magnetism. The basis is electromagnetism as encoded in Maxwell's equations. Electric currents are always the basis of static magnetic fields. Spin is a key ingredient for two reasons: i) it implies the presence of microscopic magnetic moments, and ii) it requires the antisymmetry of the wavefunctions at the basis of the possibility of ferromagnetic couplings. Notice that the magnetic moment due to the spin can also be interpreted in terms of a current density connected to the multicomponent nature of the wavefunctions.
Best Answer
The protons are not isolated but they are inside a material with a non-zero temperature. The thermal motion will provide the energy for the protons to be excited in a state with higher energy, corresponding to the alignment opposite to the field. This is a dynamic process, after some the times they go back to the ground state but other protons are excited all the time. For a specific temperature, there is an average fraction of protons aligned in the opposite direction. The same mechanism explains why the magnetization of a piece of iron in a magnetic field depends on temperature or how the magnetization of a paramagnetic material depends on temperature. See for example this typical curve of magnetization versus temperature: http://www.irm.umn.edu/hg2m/hg2m_b/Image9.gif