S17_ZeroMagnetizationState
Magnetization Curve Dependence on the Zero Magnetization State
Aaron Hamann and Ryan Vogt
Introduction
When a magnetic field is applied to a ferromagnetic material, the material gains a magnetization, which can persist even after the applied field is removed. The remaining magnetization is known as the remanence. When a field is applied to a ferromagnetic sample that is initially demagnetized (its net magnetization is zero), the remaining magnetization is called more specifically the remagnetization remanence. Researchers often measure this property for different samples, or use models such as the Wohlfarth Model to predict its behavior. However, researchers do not always specify how their samples were originally brought to the demagnetized state, and the method used to do so can have a large impact on the properties of a sample, including its remagnetization remanence.
For our experiment, we used the Wohlfarth Model to make predictions about how the remagnetization remanences of multiple samples would depend on the methods used to demagnetize them. We measured these remanences after applying magnetic fields of various strengths, and also measured the demagnetization remanences of the same samples. Demagnetization is measured instead after applying and removing a demagnetizing magnetic field from a sample that was initially saturated (its net magnetization was at the maximum possible value). By measuring these values, we were able to compare our results to the behaviors predicted using the Wohlfarth Model.
Theory
Wohlfarth Model:
The Wohlfarth Model of ferromagnetism considers a system of noninteracting particles with varying orientations. These particles can only be magnetized along their long axes, and each particle requires a magnetic field of some magnitude to switch its magnetization from one direction to the other.
A system of ferromagnetic particles with has a switching field distribution (SFD) which describes the number of particles that flip their direction for an applied field of a given magnitude. The SFDs to the left show three states for which the net magnetization is zero. Particles which require the weakest fields to flip are on the left and those which require the strongest are on the right. The arrows indicate the direction of the particles’ magnetizations.
While bulk ferromagnetic materials do not consist of independent magnetic particles, we used this as a basic model for understanding our system and analyzed deviations from this model’s predictions.
when I_R (H) is measured after placing the particles’ magnetizations in random directions. When a ferromagnetic sample is demagnetized by forming randomly-distributed state, the deviations from this model are attributed in literature to inter-particle interactions. We generate Henkel plots for our samples to determine the validity of this conclusion and to observe the different remanent behavior for other demagnetization preparation methods.
Experimental Methods
Experimental Setup:
The remanence of our samples was measured using a Vibrating Sample Magnetometer (VSM) setup as shown above. In this setup, the vibrating magnetized sample induces an EMF across the induction coils on either side of it. The differential voltage between each set of coils is sent to a lock in amplifier which receives a reference signal from the function generator which drives the oscillator vibrating the sample. The magnetization is varied by supplying a current to an electromagnet, the direction of which is controlled by a relay.
The Wohlfarth Model makes a simple-to-test prediction that doesn’t require a sample’s switching field distribution to be known. It predicts that the demagnetization remanence, ID(H), and the remagnetization remanence, IR(H), for a given applied field strength H will be related by:
Demagnetization Methods:
•DC Demagnetization: A sample is saturated in one direction and then a magnetic field is applied in the opposite direction until the remanent magnetization is zero. This corresponds to the top or bottom switching field distribution above.
•AC Demagnetization: A sample is saturated in one direction by applying a magnetic field. The direction of field is alternated while the magnitude is slowly decreased. This leaves the SFD essentially randomly distributed, like the middle SFD above.
Ferromagnetic Samples Used:
•VHS tape- Particulate material expected with least interactions to match Wohlfarth most closely
•Nickel Wire- Bulk material expected to have weak ferromagnetic interactions
•Alnico 5- Bulk material expected to have stronger magnetic interactions and deviate most from Wohlfarth model predictions
Results and Conclusion
Plotting I_R (H) against I_D (H) for each of the samples and preparation methods resulted in the plots below. In each graph, the remanences are shown in units of the saturation remanence of the sample. The dotted lines show the relationships we expected between the remagnetization and demagnetization remanences, while the data points show the remanences we measured. Each graph corresponds to data from one sample, and each color corresponds to one demagnetization method, as shown.
Legend
Red: AC demagnetized
Blue: Forwards DC demagnetized
Black: Backwards DC demagnetized
Dotted lines: Predictions
Individual points: Experimental data
VHS Nickel Alnico
We found that the VHS tape and Nickel wire samples behaved essentially as predicted using the Wohlfarth Model. The VHS tape does contain ferromagnetic particles, so the agreement for that sample was unsurprising. However, the Nickel wire is a solid ferromagnet that does align as well with the Wohlfarth Model's assumptions, so the agreement of that data with the predictions was more surprising. The Alnico, however, deviated significantly from predictions and the results for Nickel. This deviation did not appear like the effect of ferromagnetic internal interactions, either, but it was found that others had predicted the behavior we saw by using more sophisticated models that modeled magnetization as domain wall motion.
In any case, all three of these sets of data showed clearly that remagnetization remanence depended strongly on preparation method. While any deviations from the linear relationship described in the equation above are sometimes used as evidence about the type and strength of magnetic interactions within a sample, our data shows that such deviations can systematically occur from other effects. The strong preparation dependence we have shown also indicates that researchers should explain the method by which they demagnetize their samples in order for their data to be understood in context and compared to only analogous data from others.
References
One of the papers explaining the Wohlfarth Model and its predictions:
E. P. Wohlfarth, Journal of Applied Physics 29, 595 (1958).
A paper that discusses the preparation-dependence of remagnetization remanence and provides data for this in magnetic recording media:
P. Bissell, R. Chantrell, G. Tomka, J. Knowles, and M. Sharrock, IEEE Trans. Magn. 25, 3650 (1989).