The individual steps of FORC measurements are as follows:

• The material is saturated in a magnetic field (H_sat)
• The field is reduced to a reversal point H_a
• The field is then returned to saturation in steps of H_b
• The magnetic moment is measured

A coordinate transformation produces the FORC diagram. Two new parameters are defined with Hc and Hu: \(H_{ c }=\frac{H_{ b }-H_{ a }}{2}\)  and \(H_{ u }=\frac{H_{ b }+H_{ a }}{2}\)

H_c contains information about the coercive fields and H_u about the interaction fields. The FORC diagram is the mixed second derivative ("curvature" of the curve). 

Fig. 1 shows schematically how the FORC diagram is created from the individual measurement curves. A FORC diagram not only provides information about the distribution of interaction and switching fields, but also serves as a kind of "fingerprint" that provides insights into the domain state and the nature of magnetic interactions in a material. In a FORC diagram, completely closed contours typically represent single-domain behavior. Open contours that spread in the direction of the Hu axis indicate multi-domain behavior. A combination of open and closed contours indicates pseudo-single-domain behavior.

The peak in the FORC distribution is usually at a switching field H_c that correlates with the coercive field strength from a hysteresis measurement. Multiple peaks in the FORC diagram indicate that multiple magnetic phases are present in the material.

Measurement example: Refrigerator magnet

• Sample: presumably iron oxide
• Measurement: >27,000 data points in 186 FORC curves
• Measurement time: 1h 7 min
• System: 8604 with HF pole caps without temperature insert

Result: The FORC diagram (Fig. 2) shows detailed information about local interactions and coercivity distributions that would not be visible with a classic hysteresis loop.

Conclusion

FORC measurements are a powerful tool for in-depth analysis of magnetic properties, especially in nanostructured materials. They provide information about irreversible processes and magnetic couplings that are relevant for modern applications such as spintronics, data storage, medical technology, and basic research.
If you have any questions about FORC or the VSM systems of the 8600 series, please do not hesitate to contact us.

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