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Sometimes the hysteresis curves for magnetic materials that I see in articles have this noticeable discontinuity at the saturation points, the curve doesn't exactly close into a loop.

For the example pictured below it seems like the measurement starts at positive saturation, then decreases until negative saturation, then increases again until it reaches positive saturation again. The curve looks to be perfectly continuous at negative saturation, but at positive saturation it's clearly not, the saturation magnetization at the end is consistently greater than it was at the start.

However, other real measured curves look pretty much how they theoretically should, no jumps on either end. So, is this just a measurement error or is there an underlying phenomenon here?

hysteresis loop diagram

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    $\begingroup$ This can happen depending on the material and the specifics of the measurement. If the material is slightly demagnetized (e.g. if no external H-field has been applied for a while) prior to the measurement, it can start at a slightly lower B-field than that attained at the end of the cycle. $\endgroup$
    – Puk
    Commented Dec 25, 2023 at 20:19

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These measurements are done with variable current in a coil, that creates a variable magnetic field. Current can be a sawtooth or a sine, for example.

This means these curves have a starting point (1) then the current sweeps to the other polarity (2), then changes direction (3) and sweeps back to the starting value. The curves are directional: I've drawn arrows to represent this.

enter image description here

A lot more time passes between measurements points 1,4 than between points 2,3. Therefore:

  • Low frequency noise, drift, and other phenomena that cause errors that accumulate with time will be visible between the start and end of the plot (1,4), but not on the other side.

  • The measurement system may itself have some hysteresis, it should be tested (in this case by doing a measurement without magnetic material, just the air core coil).

  • Transient phenomena slower than the measurement signal period may not have settled yet. Normally you would sample several periods of the test signal to check for this, and only grab the measurement when each period becomes identical enough to the previous one, but this is not always possible to do.

  • If the properties of the sample being measured change in a time-dependent manner during the measurement, this will also affect the start/end side of the plot, but not the other side.

This happens in pretty much all measurements where we take one period out of a periodic phenomena (here, a periodic sine or sawtooth current) and plot just this period, in a manner that makes differences between the start and end of the period obvious.

For example, if you measure the properties of a semiconductor device, like a transistor, it will be heated by the measurement current. So, referring to the above curve, it ends up hotter at point 4 than it was at point 1, thus its temperature-dependent characteristics are different. So the ends of the plot don't meet. You'd have to let it run for many more periods, to reach thermal equilibrium. But if it would burn out before reaching thermal equilibrium, then... you can't.

The fact all the curves have the same spacing between beginning and end of the plot, and this spacing does not seem proportional to the thing being measured, makes me lean towards measurement artifact.

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