Control of the Oscillatory Interlayer Exchange Interaction with Terahertz Radiation

The oscillatory interlayer exchange interaction between two magnetic layers separated by a metallic spacer is one of the few coherent quantum phenomena that persists at room temperature. Here, we show that this interaction can be controlled dynamically by illuminating the sample (e.g., a spin valve) with radiation in the 10–100 THz range. We predict that the exchange interaction can be changed from ferromagnetic to antiferromagnetic (and vice versa) by tuning the amplitude and/or the frequency of the radiation. Our chief theoretical result is an expression that relates the dynamical exchange interaction to the static one that has already been extensively measured.

Figure 1

Upper panel: schematic of a spin valve irradiated with terahertz voltage $V(t)$. The magnetizations of the two ferromagnetic layers $F_a$ and $F_b$ lie along the two unit vectors ${\overrightarrow{m}}_a$ and ${\overrightarrow{m}}_b$ that form an angle $\theta$. The characteristic time scale of the system is the time of flight $\tau$ through the normal spacer $N$ whose thickness is $l_N=v_F\tau$ ($v_F=\mathrm{Fermi}$ velocity). Lower panel: the scattering model for the magnetic layers is defined in terms of the transmission (${\widehat{d}}_a$, ${\widehat{d}}_b$) and reflection (${\widehat{r}}_a$, ${\widehat{r}}_b$) complex matrices.

Figure 2

Interlayer exchange energy $J(\theta =\pi /2)$ as a function of the frequency $\omega$ and amplitude $V_0$ of the terahertz radiation. The dc exchange interaction is described by Eq. (15) and corresponds to the Co-Ru-Co system of Ref. [28] with a Ru thickness of 2.4 nm. The color code goes from $-0.05\mathrm{mJ}/{\mathrm{m}}^2$ (antiferromagnetic coupling, dark blue) to $+0.05\mathrm{mJ}/{\mathrm{m}}^2$ (ferromagnetic coupling, red).

Figure 3

Example of numerical calculation of the exchange energy $J(\theta =\pi /2)$ as a function of the spacer thickness $d$ (in angstroms) and frequency (in terahertz) for a voltage amplitude $V_0=100\mathrm{mV}$. The parameters used for the calculation were $|d_{aM}{|}^2=0.41$, $|d_{am}{|}^2=0.22$, $|d_{bM}{|}^2=0.83$, $|d_{bm}{|}^2=0.59$, ${\lambda }_F=11\AA$, and $v_F=10^6\mathrm{m}/\mathrm{s}$. The color code indicates antiferromagnetic coupling (red) and ferromagnetic coupling (blue) with a maximum intensity of the order of $1\mathrm{mJ}/{\mathrm{m}}^2$.