Observation of an inverse Doppler shift from left-handed dipolar spin waves

We report the experimental observation of an inverse Doppler shift from the motion of an ordinary solid object. The experiment used left-handed, or backward, spin waves in a magnetic thin film. As a pick-up antenna was moved toward the spin wave source, the measured frequency decreased. In contrast, an increase would be expected in everyday experience as the observer approaches the source. The backward spin wave wavelength in the experiment was $1.83\mathrm{mm}$ at $3\mathrm{GHz}$, resulting in a Doppler shift of $546\mathrm{Hz}\sec ∕\mathrm{m}$, or about 50 times larger than would be observed on an ordinary electromagnetic wave at the same frequency. The measured shifts and dispersion relation agree well with the established theory.

Figure 1

(Color) Experimental configuration for the Doppler shift measurements. Spin waves are excited in the magnetic thin film and sensed by a moving microstrip antenna on a rotating pickup. (a) Diagram of test geometry with bias magnet in the orientation for left-handed (backward) waves. (b) Diagram with bias magnet in the orientation for right-handed (forward) waves. (c) Photograph of test setup. The Doppler-shifted rf output from the rotor passes through a rotary coaxial joint to the upper left (magnet shown in the orientation for left-handed waves).

Figure 2

Measurement system configuration. Excitation was provided by the network analyzer for delay line transmission response measurements, while the rf signal generator was used for the Doppler measurements. Only one source was operating at a time.

Figure 3

Frequency spectra and time envelopes of measured signals. (a) Signal spectrum with no rotation showing a clean single frequency excitation. (b) Signal pulse envelopes from left-handed (backward) waves with a rotation rate of $208.2\mathrm{rpm}$. Signal pulses are created twice during each pickup rotation as the antennas pass near the film. (c) Signal spectrum centered at $3.01\mathrm{GHz}$ from left-handed waves with a rotation rate of $208.2\mathrm{rpm}$. A downshifted peak showing the inverted Doppler shift is apparent. (d) Signal spectrum centered at $3.61\mathrm{GHz}$ from right-handed (forward) waves with a rotation rate of $208.6\mathrm{rpm}$. In this case, an up-shifted peak is observed as expected from everyday experience.

Figure 4

Doppler shifts obtained as the rotation rate is varied. The tangential linear velocity is given across the top axis. The left-handed waves generate a negative shift, while the right-handed waves generate a positive shift.

Figure 5

(Color online) Spin wave dispersion relations. The curve labeled “Phase” was obtained by unwrapping the phase measured from the auxiliary signal output, the points labeled “Doppler” were obtained from the slopes in Fig. 4, and the theory is the conventional theory for spin waves in a thin film above a ground plane (Ref. 24).