When I calculate first derivative of M versus H curve measured for an ensemble of FM nanoparticles (below they blocking temperature) I obtain a very clear maximum, very close to the so called coercive field, that is when the magnetization changes sign, of course at negative fields.
Q1. Is the maximum of the derivative the good measure of the coercive field, meaning to what extent it is a coincidence?
Q2. The FWHM of this dM/dH peak depends on temperature in which I measured M(H). To what extent the shape of the dM/dH is a measure of the switching field distribution in the ensemble.
After you look on your results from Preisach model of magnetic hysteresis perspective, you will see that dM/dH is nothing else but projection of 2D Presach distribution of hysterons onto H field axis. If the observed peak is sharp then your sample consists predominantly of hysterons with up- and down-switching fields practically equal to + or - coercive field.
Q2: dM/dH is already called in literature a switching field distribution. However, this name makes sense only when the field sweep is very slow. Otherwise it is called field dependent dynamical susceptibility (even if evaluated at H not equal to zero).
Additional comment: nanoparticles are usually small enough to be in single domain state. When H is parallel to the easy axis of such magnetic particle then its hysteresis loop is rectangular (see established Stoner-Wohlfarth model of hysteresis). Consequently, if your nanoparticles are well oriented (and cannot move), and the field orientation is appropriate, then maximum of dM/dH is located exactly at coercive field. Nevertheless the width of this peak may be affected by distribution of particles' diameters ...
After you look on your results from Preisach model of magnetic hysteresis perspective, you will see that dM/dH is nothing else but projection of 2D Presach distribution of hysterons onto H field axis. If the observed peak is sharp then your sample consists predominantly of hysterons with up- and down-switching fields practically equal to + or - coercive field.
Q2: dM/dH is already called in literature a switching field distribution. However, this name makes sense only when the field sweep is very slow. Otherwise it is called field dependent dynamical susceptibility (even if evaluated at H not equal to zero).
Additional comment: nanoparticles are usually small enough to be in single domain state. When H is parallel to the easy axis of such magnetic particle then its hysteresis loop is rectangular (see established Stoner-Wohlfarth model of hysteresis). Consequently, if your nanoparticles are well oriented (and cannot move), and the field orientation is appropriate, then maximum of dM/dH is located exactly at coercive field. Nevertheless the width of this peak may be affected by distribution of particles' diameters ...
This is precisely the differential magnetic susceptibilty: dM/dH. It depends on the frequency of the magnetic field and on temperature.
Of course, it is related to the coercivity: just think in the energy landscape where the anisotropy is the barrier that prevents the magnetization switching of each nanoparticle.
The full width at half maximum (FWHM) is related to the monodisperse character of your ensemble of nanoparticles (shape, purity of phases, etc). For instance, if you are planning to use the nanoparticles in Magnetic Particle Imaging (MPI), the FWHM is an indication of the potential spatial resolution in MPI experiments: the narrower the better.
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Dear Marek and Jose-Miguel thank you for such elaborate replies. I understand that indeed independently if I use the Preisach model or not the relative height and FWHM of dm/dH does carry a microscopic insight into the nanoparticles dispersion.
In my case, indeed these are FM nanocrystals embedded in semiconductor matrix, so they are mechanically stabilized, but small enough to be considered as single domains (macrospins) subjective to thermal agitation. More importantly to me, having some samples with different NCs (even different compounds) I understand I can make comparative, semi-qualitative studies by investigating the shape of the dm/dH
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