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Web sites that provide tables of permeability
https://en.wikipedia.org/wiki/Permeability_(electromagnetism)#Values_for_some_common_materials (This is a pretty long list!)
http://www.kayelaby.npl.co.uk/general_physics/2_6/2_6_6.html
(That link seems to have disappeared, maybe someone could chase it down for us...)
Update July 2020: This came from Joakim:
I was reading https://www.microwaves101.com/encyclopedias/high-permeability-materials and saw that you want to find a reliable source on difference permeability for different materials. The relative permeabilities can be calculated if you know the magnetic susceptibility, the density and the molar mass (or atomic weight) of the material. These values are listed for a lot of materials on Wikipedia. You calculate it like so: µr = 1 + 4 * pi * Xm * d * mm, where µr is the relative permeability, Xm is the magnetic susceptibility in emu units (the unit used in Wikipedia), d is the density in g/cm³ and mm is the molar mass in g/mol.
Special case: high permeability metals
Relative permeability refers to a material's ability to attract and conduct magnetic lines of flux. The more conductive a material is to magnetic fields, the higher its permeability. Most materials have μR near 1, including copper, and gold. The exceptions are nickel, iron, etc. Permeability of most metals is 1.0. However, metals such as nickel are a special case, and can have permeability as high as 100 or more. Permeability is a magnetic property of a material, and is often expressed as μ0 x μR, where μ0 is a physical constant equal to exactly 4*pi*10-7 Henries/meter and μR is the relative permeability. μR is equal to one for free space, and a whole lot of other materials including gold and copper. The metals that are notable exceptions are nickel, cobalt, manganese, chromium and iron, which are called ferro-magnetic materials. While we're on the subject, if anyone knows where we can obtain reliable info to construct a table of permeabilities of different materials, please send it in and win a Microwaves101 pocketknife! Speaking of which, the following was provided by Stephen D. Winchell, a physicist working at United States Naval Academy:
"I was looking for some further information on permalloy because another ferromagnetics researcher has used it in some eddy current field experiments and I stumbled upon your page. I am currently working as a physicist, on eddy current research in bulk ferromagnetic materials. The question about a table of permeabilities is actually, depending on how in depth you want to answer it, a very fascinating question. Now, diamagnetic and paramagnetic materials are quite boring in terms of permeability (like 10-5 - 10-3) but ferromagnetic materials are totally different. It depends on many, many factors like annealing and crystalline structure, but typically, for all ferromagnetic materials we measure permeabilities between 1 and 10000 or more, depending on their magnetic state (which is a function of its history and applied field). when you look at a ferromagnetic hysteresis curve you can see (whether its in B(H) or M(H)) that the rate at which the material responds to external fields is in fact totally nonlinear (I believe the best description of it currently is a piecewise exponential "cooperative" element and an extrapolated virgin curve "anisotropic" element.) Ferromagnetism is very complex because of grain and domain cooperation and exchange interaction between atoms... so the answer is that there are functions which, with some accuracy, describe permeability as a function of applied field, but there are no tables that give an answer. In the steel I work with I have measured permeabilities from about 10 to about 10000 as I move through a hysteretic cycle."
Thanks for the help, from another Steve! Looks like we won't try to hold a breath on providing such a table...
The problem with nickel plating
As Wally pointed out in the this timeless story, if you have nickel plating as your first metallization in the microstrip conductor, it is unlikely that over-plating it with thick gold will fix your RF loss problems. Nickel is one of the worst conductor metals you can use, for reasons described below.
Looking up the bulk resistivity of nickel you'll see that it isn't that much worse than copper or gold, perhaps three time the resistance. However, looking back at the skin depth equation, note that μ0 x μR is buried in the denominator. This is what causes trouble. Check this out: nickel has a bulk resistivity of 8.7 versus gold at 2.44, so you'd expect it to have maybe three times as much loss if you plate up to the rule of thumb of five skin depths. WRONG! The maximum conductivity of a nickel thin film is about 3% of what you'd get with gold. This is because the skin depths are much thinner due to the relative permeability term, which is often reported at 100 for nickel. There are good reasons that manufacturers want to use nickel plating, it has excellent adhesion to ceramic surfaces, and it is a good barrier metal in some solder schemes. However, putting a layer of nickel down first in any plating scheme is about the worst thing you can do to a substrate from an RF loss point of view.
Update November 2015: this warning came from Reto:
If you include strongly ferro-magnetic materials any results past a few GHz or so will not be realistic. Permeability is a strong function of frequency once you go past a few GHz. The magnetic domains can’t follow the fast-changing magnetic field anymore and relative permeability drops down towards unity. Nickel, for example, with an initial relative permeability of 100 -600, will drop to somewhere between 1 and 2 at 10 GHz. Permeability and frequency are both in the denominator of the skin-depth formula. In the frequency range where the relative permeability drops from several hundred to about 1, the frequency only increases ten-fold. So, the skin depth is actually increasing in that frequency range. Hence the sheet resistance (assuming that layer is much thicker than one skin depth) is actually dropping in that range of frequency.
EMI enclosures
When is a high-permeability material a good thing for microwaves? When when trying to shield from electromagnetic interference (EMI), especially at low frequencies where the skin depth is greater, a high permeability metal will kill off the fields before they penetrate your module. High magnetic permeability gives an ability to absorb magnetic energy. Mumetal® (say moo-metal or mew-metal, it is pronounced both ways), and Permalloy® are trade names of materials that are designed for high permeability. They are alloys of iron and nickel. Permeability is as much a property of the material's grain structure as it is a bulk property. Thus the secret recipes for high-permeability metals include proprietary annealing.