PT-Symmetric Magnon Lasing and Anti-Lasing

Abstract

A mechanism for electrically tunable PT-symmetric magnonic lasing and anti-lasing is proposed along with a device consisting of a current-biased region in a magnetically ordered planar waveguide. Within the bias area, several heavy-metal wires carrying dc charge current are periodically attached to the waveguide and exert so spatially periodic spin-orbit torques, producing current-controllable modulated magnon gain and loss. It is demonstrated that this decorated waveguide can emit a strong, single frequency magnon mode at the Bragg point (lasing) and also absorb at the same frequency phase-matched incoming coherent magnons (anti-lasing). The underlying physics is captured by an analytical model and validated with full material and device-specific numerical simulations. The magnonic laser absorber response is tunable via the current density in the wires, the extent of the biased region, and the intrinsic damping, enabling the control of lasing frequency and emission power. The structure is shown to amplify thermal magnons, offering a route to low-noise on-chip microwave sources. The concept is compatible with planar waveguides, ring geometries, and antiferromagnets. The results establish an experimentally realistic platform where a single element functions simultaneously as both magnon laser and absorber, opening opportunities for reconfigurable non-Hermitian magnonics and integrated magnon signal processing.

Figures (4)

• Figure 1: (a) Schematic of a $\mathcal{PT}$-symmetry-based magnonic laser absorber. A number of electrically separated heavy metal stripes carrying opposite charge current densities $J _{\rm c}(x)$ (flowing in $y$ direction) are attached to a magnonic planar waveguide, generating alternating gain and loss of magnetic oscillations. (b) Spatial profiles of the sine and step functions of current density $J _{\rm c}(x)$ adopted in the model. The period length $\Lambda = 100$ nm, and the total SOT region length is $L = 5000$ nm. For (c-d) $\alpha = 0$ and (e-f) $\alpha = 0.005$, transfer matrix elements ($M _{\rm11}$, $M _{\rm22}$) and output ratio $U$ (logarithmic scale) dependence on the electric current amplitude $c _{\rm A}$ at the Bragg point $\Re[k _{\rm x}] = k _{\rm p}$. The inset of (e) shows the $\alpha$ dependent positions of $M _{\rm11} \approx 0$ (anti-lasing condition) and $M _{\rm22} \approx 0$ (lasing condition). The inset of (f) is the frequency $f$ dependent $U$ under the lasing and anti-lasing conditions. The lasing case responds to the single input excitation [$S(0) \ne 0$, $R(L) = 0$], and anti-lasing case means magnon excitation under two coherent inputs with $R(L)/S(0) = M _{\rm21}$. Results follow from Eq. (\ref{['transfer']}).
• Figure 2: Top panel is the schematic for magnon lasing with single input $S(0) \ne 0$. The magnon outputs are detected as time-dependent $M _{\rm z}(t)$ at left side $x = -2000$ nm [blue curve, related to $R(0)$] and right side $x = 7000$ nm [red curve, related to $S(L)$]. The red curves are in the same range with blue curves, which are intentionally offset for clarity. Under different $c _{\rm A}$, magnon outputs are excited by a microwave field $\hbox{\boldmath$\mathrm{h}$} = h _{\rm0} \sin(2 \pi f t) \hbox{\boldmath$\mathrm{z}$}$ lasting 10 ns (a,c) and continuously (b,e, f, g), where frequency $f = 4.701$ GHz and amplitude $h _{\rm0} = 1000$ A/m is localized at left side $x = -4000$ nm. Frequency spectra are obtained from the laser induced long lasting oscillation. These results are obtained from micromagnetic simulations with Eq. (\ref{['LLG']}), where the laser region realized by step-type function is limited in $0 \le x \le 5000$ nm with period $\Lambda = 100$ nm.
• Figure 3: Top panel is the schematic for magnon anti-lasing with two coherent inputs $R(L) = S(0) A e^{i \phi _{\rm0}}$. In the micromagnetic simulation with step-type electric current region in $0 \le x \le 5000$ nm, we apply two microwave fields $\hbox{\boldmath$\mathrm{h}$} _{\rm1} = h _{\rm0} \sin(2 \pi f t) \hbox{\boldmath$\mathrm{z}$}$ (at $x = -4000$ nm) and $\hbox{\boldmath$\mathrm{h}$} _{\rm2} = A h _{\rm0} \sin(2 \pi f t + \phi _{\rm0}) \hbox{\boldmath$\mathrm{z}$}$ (at $x = 9000$ nm) to realize the inputs. Here, $A = 1$ and $\phi _{\rm0} = -1.26$ are used to approach the absorber condition, $f = 4.701$ GHz and $h _{\rm0} = 1000$ A/m. (a) The spatial profiles of $M _{\rm z}$ oscillation amplitude under different $c _{\rm A}$. (b-c) At the critical value $c _{\rm A} = 1902$ A/m, the time dependent $M _{\rm z}(t)$ profiles exited by (b) 10 ns pulsed and (c) continuous microwave fields, where the red curves with $|M _{\rm z}| < 50$ A/m are intentionally offset for clarity.
• Figure 4: (a) Schematic for the magnetic ring structure (gray region) with periodically varying SOT induced gain (blue regions) and loss (red regions). The ring is coupled to a planar waveguide. Magnons are injected at the left side of waveguide, amplified in the ring laser, and detected at the right side in the waveguide. For (b) $c _{\rm A} = 0$ and (c) $c _{\rm A} = 1475$ A/m, time dependent $M _{\rm z}$ at $x = 400$ nm in the waveguide. Magnons are injected at $x = - 600$ nm by applying $h _{\rm0} \sin(2 \pi f t) \hbox{\boldmath$\mathrm{z}$}$ lasting 10 ns with $h _{\rm0} = 1000$A/m and $f = 4.73$ GHz. (d) At $c _{\rm A} = 1558$ A/m, time dependent $M _{\rm z}$ at $x = 400$ nm under finite temperature $T = 1$ K, with the above frequency spectrum. Results are obtained from micromagnetic simulations.