Magnetic Permeability

We have developed a new method to image variations of magnetic permeability on the surface of metal samples.

1. A microwave signal is sent to the sample locally, through a microwave microscope, which allows us to measure the local reflected signal. Due to the coupling between the microscope resonator and the sample, the boundary condition of the resonator changes, and therefore changes the resonant frequency and Q factor of the resonator.

2. By using a close-ended loop probe, the electric field at the end of the probe is minimized. On the other hand, the magnetic field is dramatically enhanced. Therefore, this probe is sensitive to the magnetic perturbation due to the local variation of magnetic properties of the sample.

1. The coupling between the loop probe and the sample can be modeled as an equivalent circuit as shown in the figure.

2. L0 is the effective inductance of the loop probe coupling to the effective inductance of sample, Lx, through the mutual inductance M. Assuming the sample is a perfect conductor, then Lx = L0 is the image inductance of L0. Zx represents the sample impedance appearing to the resonator through this coupling, and M is a geometrically determined quantity, including a geometrical factor, k.

3. The μ-dependence of the measured Δf and Q are due to the μ-dependent sample impedance, Zx, as shown above.

1. To test the unique ability of this near-field microwave microscope, measurements on 2 metallic samples, with approximately the same resistivity, but very different permeabilities, are shown. The samples are measured with two probes, one electric and the other magnetic.

2. Presented are line scans across these 2 samples. The sample on the left is ferromagnetic, with m>>1, and the sample on the right is paramagnetic, with m~1. Permeabilities of both samples were determined independently by a SQUID susceptometer.

3. Magnetic loop probe. Based on the fact that the variation in the imaginary part of the load impedance shows up in the shift of resonant frequency, and the real part in the variation of Q factor, the frequency shift variation along the line scan in the upper plot represents the geometrical topography, which overwhelms the variation due to different permeabilities. On the other hand, the Q data shows contrast from variation of the permeability.

4. Electric probe. As a comparison, we use the open-ended probe, which enhances electric field but minimizes magnetic field at the end, to repeat the line scan measurement across the samples. As we expect, this type of probe is not sensitive to the variation of magnetic properties of the samples.

5. We conclude that only the Q factor of a resonator with a closed-ended probe is sensitive to the variation of sample permeability, as expected from the model.

1. To test the model and its dependence on complex permeability, we use a colossal magneto-resistive (CMR) material, a La0.8Sr0.2MnO3 (LSMO) single crystal, whose averaged complex permeability as functions of externally applied magnetic field was measured by our colleague, and converted to complex impedance of the sample (red and blue curves).

2. The shift of resonant frequency and variation of Q factor are measured on the sample as a function of the applied magnetic field (thick black dots). Compare these experimental results with the model predictions (thin black lines) using the converted complex impedance and some experimentally reasonable fitting parameters, they basically agree with each other.

3. Since the model predictions are based on the averaged permeability data, not the local value, some minor differences between the experimental results and model predictions are expected.

1. Both the frequency shift and Q vs. applied field curves have a part which is linear in the applied field, as shown above (around the green dots). The minimum of Q(H), also the steepest of Df(H), are determined to be the Ferromagnetic Resonance (FMR). Since both curves shift together when FMR field (field applied corresponding to the FMR) varies, we can use the linear part of Df(H) and Q(H) to convert the variations of Df and Q to the shift of FMR field over the sample.

2. Shown above are the images of the variations of frequency shift and Q factor over the sample, respectively. Each image is taken at different fixed external magnetic fields, corresponding to the linear part of the Df(H) and Q(H) curves (green dots). Converting the Df and Q variations to the variation of FMR field over the sample, the overall variations are consistent and found to be ~230 Oe.

For further details, see:

Sheng-Chiang Lee, C. P. Vlahacos, B. J. Feenstra, Andrew Schwartz, D. E. Steinhauer, F. C. Wellstood, and Steven M. Anlage, "Magnetic Permeability Imaging of Metals with a Scanning Near-Field Microwave Microscope," Appl. Phys. Lett. 77,

We wish to acknowledge the NSF Division of Materials Research for supporting this research under NSF MRSEC DMR 0080008. We also acknowledge support from the Maryland Center for Superconductivity Research, and the Maryland MIPS program.

The LSMO crystals used in this work were grown by Y. Mukovskii and colleagues at the Moscow State Steel and Alloys Institute.

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