How to Characterize Magnetic Materials With Lock-in Amplifiers

July 15, 2021 by Jelena Trbovic

In this webinar we covered two basic magnetic characterization techniques, the vibrating sample magnetometry (VSM) and AC susceptibility where lock-in amplifiers are essential part of the measurement and the detection chain. We teamed up with Yury Bugoslavsky, who is managing VSM products at Cryogenic Ltd, as the MFLI Lock-in Amplifier plays a major role in boosting the performance of this system. In this blog post we provide a broad summary of what we discussed during the webinar and cover some of the answers to the questions we received.

There are a number of cutting-edge magnetization measurement and sensing applications where Zurich Instruments' lock-in amplifiers with various frequency ranges and functionality of PID, PLL control and multi-frequency capabilities play a major role: high-frequency AC susceptibility, NEMS sensing, nano-mechanical AC susceptometry, and time-resolved magneto-optics, just to name a few. We thought that in this webinar we should cover basic magnetization characterization techniques using the VSM and AC susceptibility and establish a solid foundation for future work.

Lock-in amplifiers are an essential part of the measurement technique: on the one hand, modulation provided by the lock-in amplifier is a way of measuring in the best possible noise environment and also provides the playground to utilize the physical phenomena associated with the measurement, i.e., use the Faraday low of induction which induces the voltage measured in the pickup coils. This the base of the measurement principle of the VSM, as shown in Figure 1. VSMs are extremely good for measuring magnetization of bulk materials, thin films and materials where the magnetization is on the order and higher than μ emu. The measurements can be done in the temperature range from few to more than 1000 Kelvin.


Figure 1: MFLI differential measurements of the voltage induced in the VSM pick-up coils generated by a periodically oscillating sample magnetized in a homogeneous magnetic field. The vibration frequency of the VSM is provided by the lock-in amplifier and the signal is demodulated at the same frequency.

With Cryogenic VSM magnetometers you can measure the temperature dependence of magnetization as well as the magnetization behavior at a fixed temperature where for ferromagnetic materials a hysteresis loop reveals information on magnetization saturation, coercive field and anisotropy. The sample is placed in the center of pick-up coil configuration.


Figure 2: The plot on the left shows temperature sweep of Fe and Ni samples with abrupt temperature changes revealing their Curie temperatures. The room temperature hysteresis curve is a typical example of ferromagnetic material characterization.

In addition, the VSM system is particularly powerful at characterizing superconducting materials in a contactless mode that allows measuring high critical currents without the need to attach the leads.


Figure 3: Type I and II superconductors characterized using Cryogenic VSM.

Complementary to VSM magnetometer, AC susceptometer measures AC susceptibility or the ability of the sample to respond to an external magnetic field. As the susceptibility is a derivative of magnetization curve at a certain filed (in the linear regime), measuring susceptibility we can better distinguish between different material types and have sharper transition curves. The method is used for studying magnetic phase transitions, superconducting phase transition, magnetic losses, and spin-glasses. Figure 4 depicts measurement geometry with a time varying external field and sample positioned in the center of one of the pickup coils.


Figure 4: The susceptometer features two pick-up coils symmetrically positioned with respect to the primary coil. One coil contains the sample, where


Figure 5: Susceptibility measurements of Titanium disk, courtesy of Cryogenic Ltd. Both amplitude and phase contain physical information about the magnetic field response and the losses.

In the above graphs, Titanium's onset of superconductivity shows through a sudden change from close to zero to negative values as it becomes diamagnetic. The losses shown in the peak of the phase are due to the change of the field penetration depth and most prominent close to Tc. The field dependence is shown in Figure 5 (right panel). The complementary information measured by amplitude and phase can only be accessed using lock-in amplifiers.

In particular, the benefits of the MFLI is that you can achieve better measurements faster by:

  • Improving speed and sensitivity.
  • Replacing several pieces of equipment.
  • Having higher resolution, accuracy and SNR.
  • Relying on long-term stability.

For more information or individual questions, please get in touch with Jelena ( and Yury ( The video recording of the webinar can be found here.