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I'm doing experiments as a hobby and was trying to find a material with good (very good) magnetic permeability at least at 100 MHz (higher frequencies are even better). Ideally the material would have low conductivity and if it has a high dielectric permittivity (at 100 MHz) then better.

Was looking at ferrite as a possible material but there are so many types of ferrites (M400HH for example) that I got lost. There is also this question (High permeability core material at high frequency) but the frequency goes to ~500 kHz.

Are there other, more suitable, materials? If not, can you provide a ferrite model (and somewhere to shop)?

Please keep in mind this is for a hobby, so I don't have 1+ k$ to spend.

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    \$\begingroup\$ The frequency you are considering is right at the domain rates for simple spontaneous photon absorption and subsequent re-emission. Finding a material able to rapidly rotate its magnetic moments so as to keep up... I would say it is improbable. But I'm open to being wrong. \$\endgroup\$
    – periblepsis
    Commented Apr 15 at 7:20

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Well, MnZn ferrite is out: too much conductivity, it's eddy-current dominated up there. Maybe not in granular or powder form, but a compacted powder will have poor permeability anyway.

NiZn may be a contender, though most samples show roll-off by 100MHz.

(MnZn and NiZn ferrites are just that, the respective ferrate(III) compounds: (Mn/Ni,Zn)Fe2O4, maybe with small amounts of doping for particular purposes, or impurities like SiO2 to decrease conductivity or aid sintering. As for ratio, and impurities or dopants, you'd have to analyze some commercial materials to see exactly what it is they're doing. These crystallize in the spinel cubic family.)

The next candidate is probably YIG (yttrium iron garnet, in the garnet crystal family as the name suggests), which isn't usually described in terms of permeability as its more distinctive aspect is bias-dependent ferrimagnetic resonance, but I believe it also finds use in components such as microwave circulators, thanks to its permeability, high Verdet constant, and low loss.

There are probably other less common or more exotic magnetic materials, but these are the most common materials in industry, probably for good reason.

I don't know offhand the detailed physical properties of these materials; you quickly get into the nuances of ferro- and ferri-magnetism, paramagnetic electron spin resonance, and especially for crystals (YIG is usually used in single-crystal form), anisotropy. For more information, I would suggest asking on the Physics stack.

It seems unlikely a hobbyist needs to know physical parameters, anyway; but it also seems unlikely a hobbyist needs the headline claim, either -- there are almost certainly other solutions to whatever the underlying problem is, which obviate the need for raw permeability. You haven't offered any background along those lines, though, so I'm afraid I cannot be of further assistance here.

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    \$\begingroup\$ Permalloy and some of its composites could be a contender if the low conductivity wasn't a strict requirement. \$\endgroup\$
    – Rohat Kılıç
    Commented Apr 15 at 8:18
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    \$\begingroup\$ Thanks, Tim. +1. Before I commented, I checked my view by reading this from Feynman. I doubled back through again and although I can imagine tiny atomic current density (or a portion assigned to \$j_{_\text{mag}}\$) having short times (high frequency), the atomic level just doesn't accumulate. Much cancels out there. It's more at larger aggregate levels with exterior surfaces, where these do not cancel entirely, that ferromagnetism occurs. So I'm still struggling to see that time constant getting where it needs to be. But, eh, I'm an idiot. \$\endgroup\$
    – periblepsis
    Commented Apr 15 at 9:43
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    \$\begingroup\$ @periblepsis Like I said, I'm no expert on the physics of magnetism myself; I know there's relaxation rates-and-domain movement-and-paramagnetic spins-oh-my in there, but I don't know what macroscopic field or in-circuit effects they amount to. \$\endgroup\$
    – Tim Williams
    Commented Apr 15 at 17:05
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    \$\begingroup\$ @RohatKılıç I do see references looking at permalloy films sort-of in this range, but some digging will be required to see what actual mu'(f), mu''(f) is, or if it's meaningful at all since we're almost certainly talking microelectronics applications here. \$\endgroup\$
    – Tim Williams
    Commented Apr 15 at 17:06
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    \$\begingroup\$ @TimWilliams actually I find Feynman's descriptions excellent and easy to picture. The upshot is that the tiny induced current loops, fast as they might be, largely cancel with their neighbors. Left atom up pointing on right side canceling right atom down pointing on left side. It's only where a domain surface is found that these cancellations aren't made. But these are far apart and require time. I think. Seems like difficult solid state physics and materials science to get there. No time to spend on problem. Not simple. Not experienced here. Tricky, especially to be quantitative in time. \$\endgroup\$
    – periblepsis
    Commented Apr 15 at 17:30
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There is in general a tradeoff between frequency of operation and permeability--the higher the frequency at which a material becomes lossy, the lower its permeability. The main thing driving this is, as I understand it, lowering the electrical conductivity of the material by using a lower-permeability nickel-zinc formulation instead of the more common manganese-zinc and by mixing the ferrimagnetic but slightly conductive ferrite with non-magnetic but insulating filler; electrically conductive cores lose energy in eddy currents as well as in hysteresis, so lowering conductivity lets them work to higher frequencies.

When working with high-frequency magnetics, if air-core coils can't be used, you're limited to only a handful of materials: Fair-Rite material 67 (up to about 70 to 80 MHz) or 68 (up to about 200 to 250 MHz), Ferroxcube material 4D2 (up to about 150 MHz) or 4E1 (up to about 200 to 300 MHz), or TDK/Epcos material K1 (up to about 100 MHz). Most of these are hard to find; the Ferroxcube ones I've never seen from distributors, while K1 is only available in relatively small cores. Fair-Rite 68 is only available in toroids, and 67 only in toroids, rods, and beads. Any of these could be custom-ordered in other shapes, naturally, but that gets expensive.

The problem, though, is that all of these have very low permeabilities; K1 has the highest μᵣ at 80, while 4D2 has one of 60, 67 just 40, 68 even lower at 16, and 4E1 at the lowest with 15. While an improvement over air, this is nowhere near high enough for common magnetic assumptions (such as "all the flux is confined to the core" and "the inductance is independent of where the wire is within the toroid") to be valid; making transformers out of these is not trivial. They can, however, make reasonably good inductors, and even common-mode chokes if wound with coax. They can also be effectively used for Guanella baluns. Be aware that they will leak flux due to the low permeability, so they may interfere with other nearby components.

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    \$\begingroup\$ Hmm, looking it up, I guess TDK K10 would be analogous to Fair-Rite #43, and K1 to #61 (μi = 125) or #67. Indeed, they aren't commonly seen, at least at the component distributor level. Of Ferroxcube, 4C65, 4F1, 4D2 and 4E1 would be analogous. \$\endgroup\$
    – Tim Williams
    Commented Apr 17 at 20:04
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    \$\begingroup\$ Ferroxcube 4C65 and 4F1 aren't really high enough frequency to be noted among the others here, I don't think. I can't find any reference to 4D2. 4E1 is, though; I'll add a mention of that to my answer, I plan to rework it soon (it kind of needs some mention of μ' and μ'' and how to interpret datasheet graphs, I think). I'll mention K1 too; I never found any reference to it when looking for my own project, but it does look to be just barely suitable for 100 MHz operation. \$\endgroup\$
    – Hearth
    Commented Apr 18 at 19:50
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    \$\begingroup\$ Note that mu plots depend on geometry; you get a peak or bump where standing waves pass through the material and reinforce (Z peak?) or cancel out (R peak?). It's hard to say what exactly is representative of true bulk material properties; if nothing else, the plot is correct for the test piece measured (usually 10 or 18mm toroid, something like that). Also, compare plots of ferrite bead impedance for example. \$\endgroup\$
    – Tim Williams
    Commented Apr 18 at 22:55

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