Electromagnetic origin of the microwave absorption response of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ thin films

Low-field microwave absorption techniques are ultrasensitive, nondestructive methods for probing electric and magnetic properties of solids. Nonresonant low-field microwave absorption techniques such as magnetic field modulated microwave spectroscopy (MFMMS) can easily detect electromagnetic phase transitions in minute and inhomogeneous samples. While this technique can easily and almost selectively identify superconducting transitions, magnetic phase transitions produce more varied responses. Here, we present a technique to investigate the electric and magnetic properties of a sample with complex electromagnetic responses. This technique involves taking a series of magnetic hysteresis loops and magnetoresistance measurements. These can be compared to MFMMS data to identify features having electric or magnetic origin. This approach is applied to magnetite $\left({\mathrm{Fe}}_3{\mathrm{O}}_4\right)$, which possesses an electric, magnetic, and structural phase transition across its Verwey transition. By measuring high-quality ${\mathrm{Fe}}_3{\mathrm{O}}_4$ thin films in MFMMS and complementary techniques, the previously inscrutable MFMMS signal is analyzed. Furthermore, a model of the MFMMS signal can be calculated from the magnetic and electric data, which reproduces most of the features of the experimentally obtained MFMMS signal. This technique broadens the capabilities of MFMMS beyond the detection of superconductors.

Figure 1

Characterization of 50-nm ${\mathrm{Fe}}_3{\mathrm{O}}_4$ thin films on MgO. (a) The structural integrity of the film characterized from the (0 0 1) Bragg peak from x-ray diffraction in the monoclinic phase. (b) Magnetic and resistance measurements to pinpoint the electronic Verwey transition temperature. (c) The integrated intensity of the ($00\frac{1}{2}$) superlattice peak measured at the Fe $L$-edge and O $K$-edge resonant energies, normalized to their value at 20 K. This shows the monoclinic to cubic structural transition occurring at the Verwey transition, just below 120 K.

Figure 2

MFMMS temperature sweeps of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ films at a range of DC fields and 15 Oe AC field, applied in parallel to the microwave magnetic field. Temperature was swept from low temperature to high during measurements.

Figure 3

Magnetic and resistive behavior of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ thin films as a function of temperature. Magnetic moment (a), its derivative with magnetic field (b), magnetoresistance (c), and the magnetic field derivative of the resistance (d) are presented at a range of applied DC fields (200–1600 Oe). Data is taken from isothermal magnetic hysteresis loops and magnetoresistance measurements (Supplemental Material Fig. S1) [27]. For each subfigure, the legend indicates the ordering of data at low temperature (e.g., at low temperature, data taken with 1600 Oe magnetic field has the highest magnetic moment).

Figure 4

MFMMS measurements of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ thin films (blue; noisier data) and data calculated from magnetic and resistive data (orange; smoother data). Measurements are presented with a range of DC magnetic fields (a)–(f). To facilitate this comparison, calculated data is vertically scaled and offset. Note that the difference in the transition temperatures observed in experimental and calculated data is a result of the MFMMS flow cryostat (see above).