Narrow-band tunable terahertz detector in antiferromagnets via staggered-field and antidamping torques

We study dynamics of antiferromagnets induced by simultaneous application of dc spin current and ac charge current, motivated by the requirement of all-electrically controlled devices in the terahertz (THz) gap (0.1–30 THz). We show that ac electric current, via Néel spin-orbit torques, can lock the phase of a steady rotating Néel vector whose precession is controlled by a dc spin current. In the phase-locking regime the frequency of the incoming ac signal coincides with the frequency of auto-oscillations, which for typical antiferromagnets falls into the THz range. The frequency of auto-oscillations is proportional to the precession-induced tilting of the magnetic sublattices related to the so-called dynamical magnetization. We show how the incoming ac signal can be detected and formulate the conditions of phase locking. We also show that the rotating Néel vector can generate ac electrical current via inverse Néel spin-orbit torque. Hence, antiferromagnets driven by dc spin current can be used as tunable detectors and emitters of narrow-band signals operating in the THz range.

Figure 1

Scheme of a bilayer system of an antiferromagnet (AF) and a heavy metal (Pt) for detection of THz signal. The dc spin-polarized current with spin polarization $\mathbf{s}$ induces rotation of the staggered magnetization ${\mathbf{M}}_1\uparrow \downarrow {\mathbf{M}}_2$ within the film plane. The incoming signal is created by an ac charge current with the current density ${\mathbf{j}}_{\mathrm{ac}}$ within an AF layer.

Figure 2

Average frequency of spin-current-induced rotation of the Néel vector $\mathbf{n}$ as a function of dc current density calculated for ${\mathrm{Mn}}_2\mathrm{Au}$ from Eq. (1). ${\theta }_{\mathrm{s}}$ is the angle between the spin current and hard axis. The horizontal line shows the AFR frequency ${\omega }_{\mathrm{AFR}}/2\pi$. The field-current conversion $H_{\mathrm{dc}}/j_{\mathrm{dc}}=10$ mT/(MA/${\mathrm{cm}}^2$) corresponds to spin pumping via the spin Hall effect with the Hall angle ${\theta }_{\mathrm{H}}=0.1$ [19] into the sample with thickness $d_{\mathrm{AF}}=1$ nm.

Figure 3

Illustration of the phase-locking effect: The purple solid lines show (a) the amplitude ${\psi }_{\mathrm{amp}}$ of the lowest harmonic at frequency $(\mathrm{\Omega }-{\omega }_{\mathrm{ac}})$ and (b) the auto-oscillation frequency $\mathrm{\Omega }$ as a function of dc current $H_{\mathrm{dc}}$, calculated from Eq. (1) for ${\mathrm{Mn}}_2\mathrm{Au}$ at ${\omega }_{\mathrm{ac}}/\left(2\pi \right)=1.512$ THz and $j_{\mathrm{ac}}^{\left(0\right)}=70$ MA/${\mathrm{cm}}^2$. Dashed blue lines show the approximate solution for (a) ${\psi }_{\mathrm{amp}}$ according to (5) and for (b) the auto-oscillation frequency ${\mathrm{\Omega }}_{\mathrm{dc}}$ in the absence of an ac signal.

Figure 4

Frequency of auto-oscillations $\mathrm{\Omega }$ as a function of dc current calculated for ${\mathrm{Mn}}_2\mathrm{Au}$ from Eq. (1) for different amplitudes of ac signal. The frequency of the ac signal ${\omega }_{\mathrm{ac}}/\left(2\pi \right)=1.512$ THz. Vertical dashed lines outline the phase-locking interval $\mathrm{\Delta }{H}_{\mathrm{dc}}$ for $j_{\mathrm{ac}}^{\left(0\right)}=50$ MA/${\mathrm{cm}}^2$. Inset: Phase-locking region in a parameter $j_{\mathrm{ac}}^{\left(0\right)}\text{−}{H}_{\mathrm{dc}}$ space: markers show numeric simulation, and dashed lines show theoretical prediction.

Figure 5

Effect of (a) polarization and (b) nonmonochromacity on phase locking. The frequency of auto-oscillations $\mathrm{\Omega }$ as a function of dc current is calculated from Eq. (1) for ${\mathrm{Mn}}_2\mathrm{Au}$ with ${\omega }_{\mathrm{ac}}/\left(2\pi \right)=1.512$ THz and $j_{\mathrm{ac}}^{\left(0\right)}=50$ MA/${\mathrm{cm}}^2$. The inset shows the influence of the relative phase of the ac signal for the quality factor ${10}^3$. The position of the horizontal segment depends on the phase of the ac signal (e.g., for zero and $\pi /2$) and can differ from ${\omega }_{\mathrm{ac}}$; in some cases (e.g., for $3\pi /2$ and $\pi$) phase locking occurs at two sideband frequencies.

Figure 6

Average frequency of spin-current-induced rotation of the Néel vector $\mathbf{n}$ as a function of dc current density calculated for (a) CuMnAs and (b) ${\mathrm{Mn}}_2\mathrm{Au}$ from Eq. (1) of the main text for two values of the angle ${\theta }_{\mathrm{s}}$ between the spin current and hard axis: ${\theta }_{\mathrm{s}}=0^{\circ }$ (blue line) and ${\theta }_{\mathrm{s}}={20}^{\circ }$ (magenta line). The horizontal line shows the AFR frequency ${\omega }_{\mathrm{AFR}}/2\pi$. The vertical scale is the same.

Figure 7

Frequency of auto-oscillations $\mathrm{\Omega }$ as a function of dc current calculated for CuMnAs from Eq. (2) of the main text for (a) different amplitudes of the monochromatic ac signal and (b) different quality factors at $j_{\mathrm{ac}}^{\left(0\right)}=7$ MA/${\mathrm{cm}}^2$. The frequency of the ac signal ${\omega }_{\mathrm{ac}}/\left(2\pi \right)=0.9104$ THz. Vertical dashed lines outline the phase-locking interval $\mathrm{\Delta }{H}_{\mathrm{dc}}$ for $j_{\mathrm{ac}}^{\left(0\right)}=11$ MA/${\mathrm{cm}}^2$.