# Maintaining constant magnetic field strength with temperature

We use SmCo magnets to create a field strength of around 300mT. We choose this material, rather than NdFeB because the former has a much smaller change in field with temperature. For SmCo it is (apparently) around 0.03%/degC or roughly 1 part in 3000 per degree.

Since the magnet is integral to a device that resolves to 1 part in 10^7 you can see how critical it is.

We can overcome this problem a couple of ways.

(a) Maintain a constant temperature as far as possible during measurements

(b) Do a post measurement compensation to the data

I am looking at a possible third way, which is to monitor magnetic field strength and use an auxiliary coil to adjust the field in real time to maintain the constant field. This means measuring the field to a resolution at least 10x better than the drift.

The problem then becomes: Are there any cheap ways of doing this? Hall sensors, for example, also drift with temperature. Linearity is not too much of a problem because we are holding a null position.

Any suggestions?

• I don't know anything about your sensor but, when "detecting" something, doesn't it rely on the magnetic field changing and, might any attempt to compensate for it naturally changing with temperature, be counter-productive to the device's sensitivity. I'm playing devil's advocate of course. Commented Jul 13, 2022 at 10:49
• @Andyaka Ideally we want a fixed field to remove one of the variables, but it's a whole load of interlocking problems Commented Jul 13, 2022 at 10:55

This boils down to a 1e-7 precision measurement of magnetic field without gain drift. The 1e-7 is "easy"; gain drift is hard.

• Hall sensors easily resolve 7 orders of magnitude, but are probably too temperature sensitive, but maybe it is easier to temperature-control the Hall sensor than the magnet itself.

• Faraday effect depends pretty sensitively on the electronic structure of the material, which usually is rather temperature sensitive too. But maybe there are some special materials with negligible tempco.

• There are other pretty stable effects such as Zeeman splitting of optical atomic transitions or deflection of electron beams (only works in vacuum), but I can't comment if those can be easily used to achieve the 1e-7 precision.

• To get around the drift problem without any temperature control, I see this option. Build a pickup coil, which is attached to a rotating arm, so it is spinning through the magnet stray field. The induced voltage amplitude will depend linearly on the field. You need a 1e-7 AC voltmeter to measure this obviously. This method is sensitive to changes in the environmental field. The earth magnetic field drifts slightly, as does the field of tables/tools/phones etc. So you would need to shield it all if you are after 1e-7 precision. Of course the mechanical positioning also needs to be very constant (thermal expansion..)

Probably looking at a fluxgate sensor. COTS devices can have +/-100pT/°C tempco and reasonable noise over a 1Hz bandwidth (which should suffice for thermal compensation).

But this sounds a bit like a physics experiment, intended or otherwise. Lots of 'interesting' details to be sure.

• I second fluxgate as the to-go option. Two are needed, at different distances from the magnet. The external fields will largely cancel that way, although the gain needed for this may be slightly different than 1.000 Commented Jul 13, 2022 at 18:32
• These 100pT/K over ~10K are already 1nT. So one would need a fluxgate with this rating and a full range of at least 10 mT. Do such large range flux gates exist? I am not so familiar with them. Also, although not relevant to this question, could you please comment on the linearity of flux gates ? Commented Jul 13, 2022 at 18:41