Residual Magnetization Curve Measurement and Analysis: Principles, Methods, and Applications

Residual magnetization curve measurement and analysis is a core technique for characterizing the magnetic performance of permanent magnet and soft magnetic materials, quantifying critical parameters such as remanence (Br), coercivity (Hcb, Hcj), and maximum energy product ((BH)max). By mapping how a magnetized material retains and loses its magnetization, engineers can verify material grades, validate design margins, and control quality in motors, sensors, and magnetic assemblies. This article explains the underlying principles, standard test methods, applicable standards, and typical applications of remanence curve determination.

Technical Overview

The residual magnetization curve describes how a ferromagnetic material retains magnetization after an external magnetizing field is removed, and how that retained magnetization evolves as demagnetizing fields are applied. In engineering practice, the most widely used form is the demagnetization curve, which is the second-quadrant portion of the hysteresis loop measured after the sample has been saturated to technical saturation.

Two related curves are typically recorded during a measurement: the normal curve B(H), which relates magnetic flux density to the applied field, and the intrinsic curve J(H), which represents the polarization of the material itself and is derived from B by subtracting the contribution of the applied field in vacuum. From these curves, the characteristic parameters that define the quality and grade of a permanent magnet are extracted, including remanence Br, normal coercivity Hcb, intrinsic coercivity Hcj, and maximum energy product (BH)max.

Residual magnetization curve analysis is essential because these parameters directly determine how much torque a motor can produce, how stable a magnet will be under operating conditions, and whether a delivered batch of material conforms to the specified grade. Reliable measurement requires controlled saturation, closed magnetic circuit conditions, calibrated sensing electronics, and traceable reference standards.

Testing Samples

Sintered Rare-Earth Magnets

Sintered neodymium-iron-boron (NdFeB) and samarium-cobalt (SmCo) magnets are the most frequently tested materials. Specimens are typically machined or supplied as cylinders or rectangular blocks with parallel end faces so that they can be clamped in a closed magnetic circuit between the poles of an electromagnet.

Hard Ferrite and Alnico Magnets

Barium and strontium ferrite magnets, as well as cast or sintered alnico magnets, are characterized using the same curve-tracing principles, although their lower coercivity and different saturation behavior require adjusted magnetizing field strengths.

Bonded Magnets and Magnetic Powders

Injection-molded, compression-bonded, and 3D-printed magnetic components can be evaluated to verify that binder content and processing have not degraded the intrinsic magnetic properties of the powder. For loose powders, specialized sample holders and vibrating sample magnetometer techniques are commonly used.

Soft Magnetic Materials and Components

Soft magnetic materials such as pure iron, silicon steel, and soft magnetic composites are characterized for residual induction and coercivity using permeameter-based methods. Finished components, including magnetized rotor assemblies, can also be assessed for residual field levels after demagnetization or magnetization processes.

Testing Items

Typical parameters determined from residual magnetization curve measurements include:

• Remanent flux density Br, the residual induction at zero applied field after saturation
• Normal coercivity Hcb, the reverse field at which flux density in the material reaches zero
• Intrinsic coercivity Hcj, the reverse field at which the intrinsic polarization vanishes
• Maximum energy product (BH)max, the peak of the B–H product on the demagnetization curve
• Complete normal and intrinsic demagnetization curves over the second quadrant and beyond
• Knee field and squareness ratio Hk/Hcj, indicating the onset of irreversible demagnetization
• Recoil permeability and recoil line behavior for dynamic operating conditions
• Initial magnetization curve and saturation behavior of as-delivered or thermally demagnetized samples
• Temperature coefficients of Br and Hcj, and magnetization stability after thermal cycling or aging

Testing Methods

Closed-Circuit Hysteresisgraph (B–H Tracer)

The reference method for permanent magnet materials, described in IEC 60404-5, ASTM A977/A977M, and GB/T 3217, uses an electromagnet with shaped pole pieces to form a closed magnetic circuit around the specimen. Search coils or a calibrated Hall probe measure flux density while the applied field is swept. The sample is first magnetized to saturation in one direction, and the demagnetization curve is then traced as the field is reversed. Height-to-diameter ratio corrections are applied according to the standard to account for self-demagnetization effects.

Vibrating Sample Magnetometer (VSM)

VSM measurement is suited to small specimens, cut sections, coatings, powders, and research samples. The sample vibrates within pickup coils while the applied field is swept, producing a signal proportional to its magnetic moment. VSM offers high sensitivity but requires careful correction for the open-circuit demagnetizing factor of the sample geometry.

Pulsed Field Magnetometry

Pulsed field magnetometers subject the sample to capacitor-discharge field pulses of tens of tesla, enabling complete hysteresis loop capture in milliseconds. This approach is valuable for high-coercivity grades and for high-throughput production screening, with techniques addressed in IEC TR 61807.

Permeameter Methods for Soft Magnetic Materials

Direct-current properties of soft magnetic materials, including residual induction and coercivity, are measured with permeameters and ballistic or fluxmetric methods in accordance with IEC 60404-4 and ASTM A341/A341M. Ring specimens or bar specimens with yoke closure are used depending on material form.

Measurement Quality Assurance

Accredited third-party laboratories perform these tests with calibrated field and flux measurement chains, reference magnets traceable to national metrology institutes, controlled ambient temperature, and documented procedures for sample saturation, dimensional measurement, and demagnetizing factor correction. Measurement uncertainty statements are provided together with the reported curves and parameters.

Applications

Residual magnetization curve measurement supports a wide range of industrial and research activities:

• Grade verification and batch quality control in permanent magnet production, ensuring conformity with IEC 60404-8 series material specifications
• Incoming inspection of purchased magnets for electric traction motors, servo motors, and generators in the automotive and aerospace sectors
• Design validation of magnetic circuits, including operating point placement relative to the knee of the demagnetization curve
• Thermal stability studies and demagnetization risk assessment under elevated temperature, reverse fields, and mechanical stress
• Failure analysis of demagnetized or degraded magnet assemblies returned from service
• Research and development of new magnet compositions, grain boundary engineering effects, and additive-manufactured magnetic materials
• Calibration support and interlaboratory comparison programs using certified reference materials
• Sensor, actuator, loudspeaker, magnetic coupling, and medical device industries requiring documented magnetic performance

FAQ

What is the difference between remanence and residual magnetism?

Remanence Br is a defined material property measured under closed-circuit, saturated conditions as specified by standards. Residual magnetism refers to the actual magnetization remaining in a component in its real, open-circuit geometry, which is always lower than Br due to self-demagnetization and depends on the shape and circuit of the part.

Why must the sample be saturated before measuring the curve?

Remanence and coercivity are only meaningful when the material has reached technical saturation, where all magnetic domains are aligned. Insufficient magnetizing fields produce a minor hysteresis loop and understate Br, Hcj, and (BH)max, leading to false rejection of conforming material.

What sample shapes and sizes can be tested?

Cylinders and rectangular blocks with parallel, ground end faces are preferred for hysteresisgraph testing, commonly with diameters of about 10 mm and heights chosen to meet standard aspect ratio requirements. Oddly shaped parts can often be tested after sectioning, or evaluated open-circuit by VSM with appropriate geometric corrections.

How accurate are remanence curve measurements?

With calibrated equipment and proper demagnetizing factor correction, typical expanded uncertainties on Br and Hcj are in the range of 1 to 3 percent, depending on material class, sample geometry, and temperature control. Reported results should always be accompanied by the measurement conditions and an uncertainty statement.

Which standards govern residual magnetization curve testing?

The primary standards are IEC 60404-5 and ASTM A977/A977M for permanent magnet hysteresisgraph testing, GB/T 3217 for the corresponding Chinese national method, IEC 60404-4 and ASTM A341/A341M for soft magnetic materials, and the IEC 60404-8 series for material grade specifications.

Can finished magnet assemblies be tested?

Complete assemblies can be characterized for residual flux or open-circuit surface field and compared against simulation, while precise curve parameters are normally obtained on representative specimen magnets from the same production lot. Temperature-dependent curve measurements on assemblies are also possible using environmental chambers integrated with the measurement system.