I am not aware of any other single material in musical instrument manufacture with such a cult following, and such a lot of confusion. I'm going to try and help gather some good data here for folks to reference.
What is AlNiCo (and why do you spell it so weirdly?)
AlNiCo is an acronym for Aluminum, Nickel & Cobalt, using their chemical symbols. All magnetic alloys contain Iron, so it doesn't typically get listed. AlNiCo can also include other metals such as Copper or Titanium. AlNiCo was the first permanent magnetic material that allowed for high flux density solutions without needing large coils or high voltage. It also had more than twice the coercivity of other known magnetic steels, which in English means it is generally harder to de-magnetize. When we generally talk about magnetic materials, there are soft magnetic materials like Silicon Steel that we use in transformers precisely because they are magnetically "soft" - they are easy to change polarity on and they don't stay magnetized, and then there are "hard" materials, like AlNiCo, that become magnetized and want to stay magnetized. The ease with which they change polarity is what creates their hystersis transfer curve.
AlNiCo V makeup
8% Aluminum
14% Nickel
24% Cobalt
3% Copper
With the balance being Iron. (51%)
History
AlNiCo was discovered in the early 1930's by Japanese inventor Tokushichi Mishima. He was granted a patent in 1936. If you're wondering why we didn't see it in retail products until the 1950's, you can thank World War II. Critical materials like Aluminum, Iron & Nickel were needed for the war effort. Fortunately for all of us, by the 1950s it was available to make things like pole magnets in Fender bass & guitar pickups and speaker magnets. Oh, and Jensen speakers (ad: Wikipedia)
Alloys
There are multiple AlNiCo alloys; the guitar pickup world seems to focus more on specific alloys and how they affect pickup tonality. Which if you stop and think about it, is strange - why would magnetic flux impact fidelity and/or frequency response in a coil? Similarly, some speaker gurus I know have experienced similar effects in speakers - the old speakers with whatever alloy they used at the time can sound different than recent alloys.
When you make an alloy, you will typically have percentages of the key ingredients and then some allowable % of other materials, perhaps scrap from some other process. Purity costs money and if the other stuff doesn't lower your quality or affect your performance, then why spend more?
The AlNiCo alloys got numbers assigned but they do not indicate strength, they are somewhat arbitrary. They run 1-15 roughly (not sure if there are more). AlNiCo II, III & V seem to be the most popular in musical gear. V is the strongest, roughly 70% stronger than II. II is advertised as a weaker, warmer sounding magnet where V is stronger and brighter for guitar pickups. Interestingly, this is roughly how speaker magnets run - stronger magnets give better motor control and tend to have stronger lows and highs. Do stronger pickup magnets do a better job capturing string vibrations? Or is it something else entirely. Ceramic and rare earth magnets are as strong or stronger and don't sound as good. (so far). So it's not just about strength.
Strength
AlNiCo is the strongest permanent magnetic material except for rare earth magnets (Neodymium and Samarium Cobalt) AlNiCo V has a Gauss of 12,500. It has the highest operating temperature of all permanent magnetic materials; roughly 1,000F. Its coercivity while higher than some other permanent magnet steels is not as strong as newer materials like Ferrite and rare earth magnets. Depending on which articles you read, that either makes it strong or weak! It's all relative I suppose.
I have read articles that either claim it is stronger or weaker than Ferrite magnets. I have not found specifics in those articles to quote, and since Ferrite comes in a bunch of flavors and AlNiCo comes in 15 alloys we probably need to nail down what we're comparing here.
Shape
Why are ferrite magnets pancake-shaped and AlNiCo magnets are cylindrical? This relates to the relatively low coercive force. "Because of the low coercive force, they are subject to demagnetization and must be used in a closed magnetic circuit or with a high length/diameter ratio." (The history of permanent magnets, Croat & Ormerod)
What is special about AlNiCo in speakers
Why do we pay large sums of money and carry around extra weight to have this magnetic material in our speakers? In short, how it acts in the presence of other strong magnetic fields. Your voice coil is an air-core magnetic coil. We send in a very strong signal current to the voice coil. 50W into 4 Ohms is 3.54A. 8 ohms is 2.5A and 16 Ohms is 1.77A. This effectively squashes the local magnetic field momentarily (it is moving, and the signal is changing) and compresses the signal. The magnet bounces right back though.
There are extreme cases of high power solid state HiFi amps driving AlNiCo magnet woofers which can take enough power to actually impact the AlNiCo structure. But this is really a recent development; AlNiCo magnets in vintage tube guitar amps and guitars are not at risk. Ferrite magnets don't exhibit this behavior. (source cited below)
Pricing
A Celestion G12 speaker is listed at 9.3 lbs; if we take say 3/4lb for the basket and paper/fabric bits, that leaves us with around 8.5lbs of magnet. At 2018 prices (per Wikipedia) that is $170 worth of magnet at what I assume is retail. Even if these numbers are 20% off, the story doesn't change. The Cobalt and Nickel are very expensive. Ferrite magnet speakers are far less expensive to manufacture.
Care and feeding
As mentioned above, AlNiCo has good coercivity - it wants to remain magnetic. You can de-mag it for repair and re-mag it (pro re-cone shops will have the machine for this) but otherwise there is usually nothing it needs from you. They are very rugged and have the highest operating temp of any permanent magnetic material; 1,000F. They are still magnetic when red-hot. If you store them poorly, next to other big magnets or run very large magnetic fields around them you can impact their magnetic properties. But mounted in a guitar amp, or in your guitar in pickups there is no real risk of damage.
References:
Coercivity: https://en.wikipedia.org/wiki/Coercivity
Coercive force: https://www.sciencedirect.com/topics/engineering/coercive-force
Magnetic Susceptibility: https://en.wikipedia.org/wiki/Magnetic_susceptibility
AlNiCo's behavior in speakers: https://www.premierguitar.com/pro-advice/speaker-geeks/alnico-vs-ceramic-speakers
Electromagnetic Coils: https://en.wikipedia.org/wiki/Electromagnetic_coil
Pros and cons of AlNiCo: https://www.jobmastermagnets.com/the-ups-and-downs-of-alnico-magnets
Hi Fi degaussing from large currents: https://greatplainsaudio.com/alnico-magnets-degaussing-losing-magnetic-field/
John J. Croat, John Ormerod, in Modern Permanent Magnets, 2022
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