Notice for the moment that the canting of the orbit planes is characterized by the inclination of each L vector. Notice too that each L has a color-coded vertical component, which is variable in length (the lengths, from top-to-bottom, are in the ratios 2 : 1 : 0 : -1 :-2 ... which you may recognize as the m_l quantum numbers for L = 2) .

Also shown in the figure (just to the left of the circular electron orbits) are the five energy levels available to a "d" type electron. Each level has a color that matches that of a corresponding m_l [reading from top-to-bottom, orange, cyan, red, yellow, white).
. In the absence of an external magnetic field (the case for the figure above), these orbitals have a common energy value, due to lack of a second magnetic field with which to align or oppose their own magnetic fields.
In the figure, this means the energy of the d electron is independent of its orbital inclination to any direction; all five orbits share a common energy, and you see five 5 horizontal lines merged at the "zero" of magnetic energy.
..When the vertical magnetic field is turned on, each orbital path has a different degree of inclination to the vertical external field and the "merged" levels will separate into distinct levels of different energy, all because of the appearence of an external magnetic force.
... [If two or more "d" electrons are present, the magnetic fields of the separate electrons do interact - in the absence of an external, instrumental magnet, and require a more compex analysis than is given here. This phenomenon is known as "spin-orbit coupling" in atoms and molecules. ]

According to quantum mechanics these 5 orbit paths available to a d electron remain in fixed relative orientation - a feature incorporated here - but in a strictly classical world they could have access to a continum of relative orientations (remember, the electrons are charged and so don't like to be too close!).

The orbits are shown here with the common vertical alignment they will take on when a vertically aligned magnetic field is introduced in the animation. Notice that this vertical field direction is that of the color-coded component of L. Noted above, the lengths of these are given in quantum mechanics as integral multiples of h/2π, the integers being the m_l values of 2, 1, 0, -1, -2. {It is the ratios of m_l to L that determine the relative angles of orbit inclination to the field (vertical). }
When a non-zero field is present (not the case shown here, as emphasized by the non-separation of the five magnetic energy levels), the electron magnetic dipole, µ, is drawn as a beige-color line which opposes the L line (because the electron has a negative charge, its rotation path makes it act like an atomic coil of wire carrying electrical current - which is to say that its orbit motion generates a magnetic field about the orbit axis, as would a magnetic dipole lying along that axis; more info on this is here ).

..To the far left are the "start/stop"(Play) and Magnetic field "On/Off" buttons to control the animation.
Note that with Magnetic Field "on", you observe every motion possible:
      the electron orbit motions,
      the appearance of the orbit magnetic dipole, µ,
      the precession of µ about the vertical magnetic field, and
      the separation of the energy levels.
Note that with Magnetic Field "off", you can observe the electron orbit motions alone.
Tip: If you set all motions in play and then toggle the Magnetic Field 'OFF", you will freeze the precession motion as it is at that instant, leaving a non-side-on view of the electron circulating.

Clean the slate by:

• turning off all orbits and
  
• turn off, then on, the "Play" button.

Have fun!