Why is Yttrium required?
I had a hunch these things ran on fairy dust but HUH?
"Physics. It works, bitches."

That was an incomplete description, but yttrium is indeed involved -- the module is a YTO (YIG Tuned Oscillator). The active ingredient is a YIG (yttrium iron garnet) sphere. YIG is a ferrite (i.e., a compound of some metal oxide with Fe2O3, or to put it another way, iron(III) ferrate), specifically one taking the garnet crystal structure. (Whereas most ferrites are in the spinel group*.)
*Chemistry aside:
The mineral spinel has the formula MgO.Al2O3, but the Al can be substituted with Fe giving a ferrite, and the Mg with a variety of metals (Fe, Mn, Zn, Ni, etc.), making this a huge family of continuous mixtures of similar atoms. Soft ferrites are (Mn,Zn) and (Ni,Zn) ferrite. The mineral magnetite is actually iron ferrite, FeO.Fe2O3!
In terms of electrical properties, YIG has lower saturation flux density (because there's less active magnetic iron, and more diluting or opposing atoms), lower relative permeability, higher resistivity, lower losses, and notable paramagnetism.
It's the last property we're interested in. When subject to a static magnetic field, unpaired electrons (the part responsible for bulk magnetism in the first place) precess at a frequency proportional to that field. (The physics is similar to the precession of a spinning top, where the precession rate depends on the force trying to tip it over, i.e., gravity in that case, ambient magnetic field in this case.) The precession in turn manifests as electromagnetic energy (photons; this is a quantum process too, after all), which is to say, light waves. Or at typical field strengths, radio waves more specifically.
So the really interesting property is this: when an inductive loop is coupled to a YIG crystal, and the crystal is placed in a magnetic field, there is a blip in the frequency response of that loop, which varies with magnetic field intensity. The blip looks much like the impedance response of a quartz crystal, having a series and a parallel resonance, and you can tune in either one. Or, as far as I know, it's usually done with two perpendicular inductive loops, so that they are only coupled through the YIG crystal's resonance (getting a bandpass characteristic), and serve as the input and output terminals of a microwave-frequency resonator. Add an amplifier and buffer, and you've got a YTO module!
The tunable range doesn't go all the way to zero, of course; that would be kind of horrible to design (those inductive loops won't work very well at DC!). Usually it's, like, say, 3-6GHz or such. Which is perfectly fine because as mentioned before, LO1 will be somewhere at high frequency
A few other practical considerations include magnetic design (the module housing is usually steel, cut in a "pot core" sort of shape to give good shielding to external fields, and better field intensity (and uniformity) around the crystal itself), thermal design (the electromagnets are normally wired differentially, so as to maintain the same total heat dissipation while varying the total field), and so on.
So, because the YTO is tuned by magnetic field, it can be tuned electronically. Fantastic, huh?

Tim