Diode speed is essentially irrelevant: diodes are normally rated in terms of reverse recovery, but there's no hard off-switching in this application. With such high inductance in the coil, recovery can be as long as possible* and it really doesn't matter: the coil takes whole to tens of milliseconds to discharge.
*Maximum carrier lifetime in lightly-doped silicon is something like 10µs. High voltage PIN junction rectifiers approach this; 1N4007 (a diffused junction, I believe?) is typically around 3µs.
What is important, is sufficient conductivity, in short enough time to avoid overvoltage of the driving transistor. Note this includes two things:
1. Loop inductance
simulate this circuit – Schematic created using CircuitLab
Consider the scenario where the power supply has some lead length, a few meters for example; this adds up to a few microhenry of source inductance. When M1 turns off, the current flowing in L1 commutates to D1, which constrains its energy, but notice L1 is in series with L2 and L3, both of which M1 sees. L4 (a small amount, stray inductance in the loop between C1, M1 and D1) also acts in series, as seen by M1. If we don't have a nearby capacitor or other clamp, M1's peak voltage can overshoot quite a bit.
As shown, we get only a very small blip:
If we reduce C1 to 200pF and set R2 = 10Ω, we get:
Suddenly the peak voltage is over double the supply! While this can be handled by adequate switch ratings in some cases, in others, there might simply be so much energy available that the transistor is destroyed. Providing adequate local bypass, and co-locating the diode and transistor with it, is the best way to ensure ratings are respected.
This may seem a bit extra, or excessive, or even complicated, but it addresses a negative pattern I have seen from time to time: the diode doesn't associate with the coil, it associates with the switch. The coil is not the cause, per se, of the flyback -- while it's the dominant source of flyback energy in the system, the causative agent is the switch, and the transient starts at the switch. Therefore, we best handle the transient by handling it at the source, the switch.
Any other clamping method will suffice, of course. A TVS diode or MOV might be used, or a "protected" MOSFET or load switch IC. These tend to dissipate power in a component, so it's effective when the energy is relatively low, and the switching rate is infrequent.
This also introduces, in a way, the second effect:
2. Diode forward recovery
This is a rarely-documented aspect of PN junction diodes, but is the relevant "speed" parameter for this scenario.
As mentioned, reverse recovery per se is essentially irrelevant, but it's not the only speed parameter that diodes have. In fact there is the complementary case: whereas reverse recovery is the diode remaining "on" longer than required, forward recovery is the diode remaining "off" longer than required.
It's not an often-specified parameter, because it's usually pretty inconsequential: VF might be higher by a couple of volts, for a couple (or tens of) nanoseconds; and who cares about that?
An excellent illustration is this application note by the late Jim Williams (no relation, heh):
AN122-1, Diode Turn-On Time Induced Failures in Switching
Regulators | Jim Williams, Linear Technology
The effect is a sort of turn-on inductance, hence the rate-dependent voltage overshoot. That is, D1 has some effective inductance, which adds in series with L4, contributing to total loop inductance. (The energy of the apparent inductance is also dissipated by the junction, so is another loss mechanism in the diode.)
The effect can be quite significant in extreme circumstances -- I've personally had up to 60V forward applied to a diode in one test, of which maybe 20V I could attribute to lead inductance of the part itself. But that was a snubber in a switching application, with corresponding extreme peak current (~100A in 20ns, I think it was?).
For selection, prefer diodes with forward-recovery ratings, and mind the dI/dt and peak voltage specifications.
For diodes that don't include these ratings -- eh, maybe just don't mind it; it is rare that it's a problem, outside of fast / powerful switching applications. We can mitigate it through other means: provide extra overhead on the transistor voltage rating, consider using transient voltage protection, and consider slowing turn-off to reduce dI/dt and thus peak voltage across the loop inductance (diode forward recovery, and L4, and potentially L2-L3 too).
For a MOSFET switch like M1, simply increasing the gate series resistance effects slowing of turn-on and off. This also reduces EMI, helpful if the coil will be connected on long leads itself. Typical values for relay-coil sized MOSFETs (say 100s mA, 30V ratings) might be 1-10k ohms.
