Controlled Switching of Intrinsic Localized Modes in a One-Dimensional Antiferromagnet

Nearly-steady-state locked intrinsic localized modes (ILMs) in the quasi-1D antiferromagnet $({\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}_3{)}_2{\mathrm{CuCl}}_4$ are detected via four-wave mixing emission or the uniform mode absorption. Exploiting the long-time stability of these locked ILMs, repeatable nonlinear switching is observed by varying the sample temperature, and localized modes with various amplitudes are created by modulation of the microwave driver power. This steady-state ILM locking technique could be used to produce energy localization in other atomic lattices.

Figure 1

AFMR absorption vs time in the presence of a low frequency driver. $f_2=1.330\mathrm{GHz}$. Darker density represents stronger absorption. (a) $\mathrm{\text{Driver power}}=1.1\mathrm{W}$ and (b) $\mathrm{\text{Driver power}}=1.4\mathrm{W}$. At about 9 ms a transition occurs to a broadened resonance. (c) Enhanced view of the broadening transition at 9 ms in (b). The four-wave mixing $(\mathrm{\text{emission}}{)}^{1/2}$ is superimposed. The nonlinear emission step occurs in tandem with the broadening of the AFMR.

Figure 2

Step hysteresis in $(\mathrm{\text{emission}}{)}^{1/2}$ vs temperature. (The abscissa also identifies the linear temperature dependence of the AFMR frequency in the presence of the $f_2$ driver.) (a) $f_2=1.350\mathrm{GHz}$ with three powers: 50 mW, 47.4 mW, and 45.7 mW. Dotted lines: increasing temperatures; solid lines: decreasing temperatures. The hysteresis due to capture and loss of a single ILM is evident. (b) Comparison of the 50 mW data with a model. Thick line: hysteresis characteristic of the amplitude response for a driven nonlinear oscillator.

Figure 3

$(\mathrm{\text{Emission}}{)}^{1/2}$ vs time during $f_2$ power modulation. Solid lines plot the ILM emission as $f_2$ is modulated at 100 Hz and scanned from 112 to 200 mW in 4.7% increments from bottom to top. The 25% sine wave amplitude modulation begins at $t=0\mathrm{ms}$. The dashed curve illustrates the time pattern of $f_2$. The emission has a phase shift of $\sim -\pi /5$ relative to the driver.

Figure 4

$(\mathrm{\text{Emission}}{)}^{1/2}$ at constant times as a function of $f_2$ power. The traces extracted from Fig. 3 are separated by 1.25 ms. Dotted data lines: 10–15 ms (ILM creation); solid data lines: 15–20 ms (ILM loss). The $f_2$ power on the abscissa is calculated separately for each slice, and includes a phase shift of $-\pi /5$ to that of the applied field. The dashed lines are guides to the eye that follow the proportionality given in Eq. (1).