Phase-resolved ferromagnetic resonance using a heterodyne detection method

This paper describes a phase-resolved ferromagnetic resonance (FMR) measurement using a heterodyne method. Spin precession is driven by microwave fields and detected by 1550 nm laser light that is modulated at a frequency slightly shifted with respected to the FMR driving frequency. The evolving phase difference between the spin precession and the modulated light produces a slowly oscillating Kerr rotation signal with a phase equal to the precession phase plus a phase due to the path length difference between the excitation microwave signal and the optical signal. We estimate the accuracy of the precession phase measurement to be 0.1 rad. This heterodyne FMR detection method eliminates the need for field modulation and allows a stronger detection signal at higher intermediate frequency where the $1/f$ noise floor is reduced.

Figure 1

(a) Schematic of the heterodyne ferromagnetic resonance detection method. The SG feeds RF current to the IQ mixer and the EOM. The AWG provides 100 kHz in-phase and quadrature signals to the I and Q inputs of the IQ mixer to produce a frequency-shifted excitation microwave to the CPW. In the reflected light, the spin precession and the linearly polarized and modulated light produce a slowly oscillating Kerr rotation signal component with a phase conveniently equal to the spin precession plus a phase caused by the path length difference between the microwave and the optical signal. This signal is then demodulated by the lock-in amplifier for analysis. (b) Illustration of field-modulation and heterodyne methods showing the advantage in signal strength afforded by the heterodyne method.

Figure 2

The FMR spectra of (a) heterodyne and (b) homodyne FMR detection method (dots). The lines in the figures are the fits for the ferromagnetic resonance line shapes. Microwave power and optical power are the same for both sets. The signals are plotted on the same scale for comparison. The heterodyne detection method produces a stronger signal even at higher frequencies. The spectra are $20\mu \mathrm{V}$ offset vertically for clarity.

Figure 3

(a) The resonance field and the half-line width (inset) variation of heterodyne, homodyne, and microwave transmission FMR detection method as a function of the resonance frequency The dashed lines represent the fits for the saturation magnetization and damping constant of the heterodyne detection data. The fitting results of saturation magnetization $\left(M_s\right)$, damping constant $\left(\alpha \right)$, and half-width $\left(\delta H_0\right)$ are shown in (b)–(d), respectively. Error bars are one-sigma uncertainties of the fit values.

Figure 4

The phase ${\varphi }_{\mathrm{PL}}$ is evaluated by introducing an optical delay. (a) The FMR spectra [lock-in output $X\left(H\right)$, black dots] with fits (green line), as the optical delay is changed from 0 mm to 80 mm. (b) The estimated ${\varphi }_{\mathrm{PL}}$ varies linearly with increasing optical delay. The linear fit shows a slope of $\left(-0.094\pm 0.003\right)\mathrm{rad}\mathrm{m}{\mathrm{m}}^{-1}$, corresponding to the optical wave length at the driving frequency, 4.5 GHz. The small error bars represent the standard deviation from the line shape fits. (c) The residuals of the fits.

Figure 5

(a) The FMR spectra [lock-in $X\left(H\right)$, black dots], as the resonance frequency changes from 4.001 GHz to 4.030 GHz. The symmetric and antisymmetric Lorentzian fits (red lines) provides the ${\varphi }_{\mathrm{PL}}$ variation as a function of the resonance frequency. (b) The details of linear ${\varphi }_{\mathrm{PL}}$ variation over the frequency range from 4.981 GHz to 5.199 GHz. (c) The periodic phase modification produces a linear fit, corresponding to an effective path length difference of $8.485\mathrm{m}\pm 0.006\mathrm{m}$. The residuals of the fit indicate systematic errors.

Figure 6

(a) Reflection image for the left (L) and right (R) samples on the CPW chip. (b), (c) The FMR intensity images taken under constant resonance frequency and magnetic field. (b) Similar lock-in intensities for L and R samples are observed at 3.1 GHz with 18 mT applied field. (c) On the other hand, L and R samples show different FMR intensity at 3.4 GHz with 23 mT applied.

Figure 7

The FMR spectra of left (L) and right (R) samples as a function of the magnetic field, when the resonance frequency changed from 3.1 GHz to 3.6 GHz. The FMR spectra of the left and right samples show different phase due to the microwave propagation along the coplanar waveguide. The blue and red arrows indicate the magnetic field for the FMR images shown in Figs. 6 and 6, respectively.