Time Refraction of Spin Waves

We present an experimental study of time refraction of spin waves (SWs) propagating in microscopic waveguides under the influence of time-varying magnetic fields. Using space- and time-resolved Brillouin light scattering microscopy, we demonstrate that the broken translational symmetry along the time coordinate results in a loss of energy conservation for SWs and thus allows for a broadband and controllable shift of the SW frequency. With an integrated design of SW waveguide and microscopic current line for the generation of strong, nanosecond-long, magnetic field pulses, a conversion efficiency up to 39% of the carrier SW frequency is achieved, significantly larger compared to photonic systems. Given the strength of the magnetic field pulses and its strong impact on the SW dispersion relation, the effect of time refraction can be quantified on a length scale comparable to the SW wavelength. Furthermore, we utilize time refraction to excite SW bursts with pulse durations in the nanosecond range and a frequency shift depending on the pulse polarity.

Figure 1

Scanning electron microscopy (SEM) image of the investigated structure. A ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ waveguide (width $w=2\mu \mathrm{m}$, thickness $t=30\mathrm{nm}$) is fabricated on top of a $\mathrm{Cr}(10\mathrm{nm})/\mathrm{Au}(25\mathrm{nm})$ conduction line ($w=3.2\mu \mathrm{m}$), insulated by 50 nm ${\mathrm{SiO}}_2$. SWs are excited by a coplanar waveguide (CPW) and propagate along the $+x$ direction, with $x=0\mu \mathrm{m}$ defined by the right edge of the CPW. An external magnetic field ${\mathit{H}}_{\mathrm{ext}}$ is applied along the $+y$ direction. Fabrication steps on the right highlight the insulation layers, which are not visible in the SEM image.

Figure 2

(a) BLS intensity measured for SWs excited at $f_{\mathrm{rf}}=3.65\mathrm{GHz}$ as a function of the externally applied field. The arrows A–C depict different sequences of the time-varying magnetic fields. (b) Effective field $B_{\mathrm{eff}}$ and effective localization width $w_{\mathrm{eff}}$ determined from micromagnetic simulations for different external magnetic fields. (c) Dispersion relations calculated considering the resulting $B_{\mathrm{eff}}$ and $w_{\mathrm{eff}}$ as in (b). The dotted vertical line indicates the wave vector $k_{\max }$, which is excited most efficiently by the CPW. The horizontal dashed line indicates the excitation frequency $f_{\mathrm{rf}}$, fixed in all measurements at 3.65 GHz. (d) BLS measurement of the thermal SW intensity as a function of frequency and time with the BLS intensity color coded. (e) Frequency spectra integrated in time windows when the dc pulse is on and off, respectively.

Figure 3

TR-BLS signal measured at $x=4\mu \mathrm{m}$ for (a) ${\mathit{H}}_{\mathrm{Oe}}\uparrow \uparrow {\mathit{H}}_{\mathrm{ext}}$ with ${\mu }_0{H}_{\mathrm{Oe}}=12.2\mathrm{mT}$ and (b) ${\mathit{H}}_{\mathrm{Oe}}\uparrow \downarrow {\mathit{H}}_{\mathrm{ext}}$ with ${\mu }_0{H}_{\mathrm{Oe}}=6.8\mathrm{mT}$. The excitation was fixed at $f_{\mathrm{rf}}=3.65\mathrm{GHz}$ (horizontal dashed lines). (c) SW intensities integrated over all times and measured at different distances $x$ to the edge of the CPW. Plots for different $x$ are drawn with different intensity offsets to separate the plots vertically and thus increase readability. (d) Frequencies measured for the shifted SW peak as function of $x$ (black squares) compared to frequencies calculated from the dispersion relation for the wave vector $k_{\max }=1.04\mathrm{rad}/\mu \mathrm{m}$ as function of the total magnetic field (red circles). The light blue area highlights the field range covered by the dc pulse.

Figure 4

(a) Time-resolved BLS signal measured at $x=3\mu \mathrm{m}$ for ${\mathit{H}}_{\mathrm{Oe}}\uparrow \downarrow {\mathit{H}}_{\mathrm{ext}}$ with ${\mu }_0{H}_{\mathrm{ext}}=34.5$ and ${\mu }_0{H}_{\mathrm{Oe}}=19.0\mathrm{mT}$. The excitation frequency was fixed to $f_{\mathrm{rf}}=3.65\mathrm{GHz}$ (horizontal dashed line). (b) BLS spectra integrated over time for different $x$ with the same field configuration as in (a). (c),(d) Frequencies and detection times of the SW bursts measured at different $x$ for (c) the rising edge of the dc pulse and (d) the falling edge. The 3 ns rise and fall time are highlighted in light blue.