YIG (yttrium iron garnet) resonators are one of the most elegant tricks in microwave engineering: a tiny polished sphere of magnetic ceramic, suspended between bond wires inside a DC magnetic field, becomes a tunable bandpass filter or oscillator element from roughly 0.5 GHz to 50 GHz. Sweep the magnetic field, sweep the resonant frequency. They're how spectrum analyzers and signal generators achieved multi-decade tuning long before wideband synthesizers existed.

The OP raises a question that anyone who has admired a YIG-tuned oscillator (and the linked qsl.net page is genuine nerd porn — exposed bond wires, machined pole pieces, gold-plated everything) eventually asks: why a sphere? A cylinder would be vastly easier to fabricate and would let you wrap coupling loops more tightly around it. So why does every YIG ever made look like a tiny ball bearing?

The answer, teased out in the comments, comes down to demagnetization factors. When you place a ferromagnetic body in an external field, the body's own magnetization creates an internal field that opposes the applied one, and the strength of that opposition depends on the body's shape. For a sphere, the demagnetization factor is isotropic — exactly 1/3 along every axis — so the internal field is uniform and the resonance frequency depends only on the applied field, not on which way the sphere is oriented relative to it.

For a cylinder, the demagnetization factor is different along the axis than across it. That means:

• The resonant frequency would shift depending on the cylinder's orientation in the field.
• The internal field is non-uniform, which broadens the linewidth (kills Q).
• Multiple magnetostatic modes get excited instead of the clean uniform-precession (Kittel) mode you want.

A sphere gives you a single, narrow, orientation-independent resonance — which is precisely what you need for a tunable filter with predictable behavior. The price is that you have to polish tiny YIG spheres to optical tolerances (surface roughness directly degrades Q by scattering spin waves at the surface), which is a whole craft unto itself.

It's a beautiful example of how a piece of "obvious" engineering geometry isn't aesthetic at all — it's the only shape where the math works out cleanly enough to build a useful device.