Dielectric measurements via a phase-resolved spintronic technique

The phase-resolved ferromagnetic resonance spectra has been electrically measured via a spintronic Michelson interferometer, where the nonlinear coupling between the microwave electric field and magnetic field results in time-independent fields and currents. Besides the microwave power the strength of the electrical signal strongly depends on the relative phase of microwave fields at the ferromagnetic material. Therefore, using a ferromagnetic sensor enables a quantification of microwave transmission in both the phase and amplitude, and demonstrates precision and feasibility in the determination of complex dielectric constants in both ideal dielectric materials and strongly absorbing materials.

Figure 1

$(x,y,z)$ and $(x^{\prime },y,z^{\prime })$ coordinate system in which a ferromagnetic strip is along $z^{\prime }$, the external applied $\mathbf{H}$ is along $z$, and $\mathbf{M}$ precesses around $\mathbf{H}$ elliptically.

Figure 2

(a) The setup of a spintronic Michelson interferometer. A first generation spin dynamo including two Py strips and a ground-signal-ground (GSG) coplanar waveguide (CPW) is used as a sensor. (b) Typical FMR PV spectra measured at 8 GHz under different conditions: path A on (A), path B on (B) and both paths on (A $+$ B). From the line-shape of FMR one can deduce ${\mu }_0{H}_r=68.7$ mT and ${\mu }_0\Delta H=2.3$ mT. (c) Turning the phase shifter a sinusoidal oscillation of the PV signal at 60 mT only appears for the case of both paths on (A $+$ B).

Figure 3

Phase $\Phi$ resolved FMR spectra. Open symbols are experimental data and solid lines are calculated with $V_1=$ 11.8 $\mu V$, ${\mu }_0{H}_r=69.2$ mT, and ${\mu }_0\Delta H=2.3$ mT.

Figure 4

(a) Sinusoidally oscillating PV spectra with $V(\Phi )$ controlled by a phase shifter at FMR (${\mu }_{0}H=70$ mT) and two other fields far from FMR. The symbols are experimental data and solid lines are the fitting results according to Eq. (2). (b) The deduced ${\Phi }_0+\Theta$ as a function of the external applied $H$ for the case with (open squares) and without (open squares) a Teflon block, respectively. The curves are calibrated by taking into account the difference in traveling time between two paths without any under test objects, i.e., vertically offset by ${\Phi }_0$(Air). The solid lines are the calculated $\Theta$ and an offset of ${37}^{°}$ is found for the case with a Teflon block.

Figure 5

(a) $V(\Phi )$ (open symbols) measured for PMMA blocks with different thickness for $d=1$ cm (open squares), 2 cm (open triangles), 3 cm (open inverse triangles), and 4 cm (open diamonds) at 8 GHz. Solid symbols are the data for air ($d=0$). Solid lines are the fitting results according to Eq. (2). For clarity the background $V_0$ is removed for all curves and arrows are used to indicate the phase shift. (b) $\Delta \Phi$ as a function of thickness and its linear fitting (solid lines).

Figure 6

(a) $V(\Phi )$ (open symbols) measured for water-isopropyl alcohol mixtures with several water concentrations, $x$. The liquid mixtures are filled into a 0.6-cm thickness container. Solid lines are fitting results according to Eq. (2). For clarity arrows are used to indicate the shift of phase. (b) $\Delta \Phi /d$ as a function of water content for two containers with a thickness of 0.16 (squares) and 0.60 cm (circles), respectively.

Figure 7

(a) The phase change with respect to air as a function of water content. Open symbols (solid symbols) represent water-isopropyl alcohol (water-methanol) mixtures. (b) The deduced amplitude $V_S$ of sinusoidal oscillation for water-isopropyl alcohol mixtures (open symbols) and water-methanol mixtures (solid symbols) as a function of water content. The dotted line is $V_S$ measured for air. The inset shows the background signal $V_0$ for the same mixtures and the dotted line is $V_0$ measured for air.

Figure 8

(a) The real part and (b) imaginary part of the relative dielectric constant $\varepsilon$ for water-isopropyl alcohol mixtures (open symbols) and water-methanol mixtures (solid symbols). The deduced data in this work (solid circles) are compared with the previous data for water-methanol mixtures (solid squares).[3]