Competition between Electronic and Magnonic Spin Currents in Metallic Antiferromagnets

We investigate the spin-orbit torque in a $\mathrm{Ta}/\mathrm{Ir}\text{−}\mathrm{Mn}/\mathrm{Cu}/\mathrm{Ni}\text{−}\mathrm{Fe}$ multilayer heterostructure and relate it to spin current transmission through the $\mathrm{Ir}\text{−}\mathrm{Mn}$ layer. We identify several spin current transport regimes as a function of the temperature and the thickness of the $\mathrm{Ir}\text{−}\mathrm{Mn}$ layer. To interpret this experiment, we develope a drift-diffusion model accounting for both electron and magnon transport in the heterostructures. This model allows us to discriminate between the contributions of electrons and magnons to the total spin current in $\mathrm{Ir}\text{−}\mathrm{Mn}$. We find that the electron-magnon spin convertance is one order of magnitude larger than the interfacial electronic spin conductance, while the magnon diffusion length is about ten times longer than the electronic spin relaxation length. This study demonstrates that magnonic spin transport dominates over electronic spin transport even in disorder metallic antiferromagnets.

Figure 1

(a) Illustration of the deposited film stack. (b) Schematic of second harmonic measurements. Cyan array denotes the in-plane rotated magnetic field. (c) Magnetic moment measured with the in-plane magnetic field at 300 K. (d) Planar Hall voltage measured using a locked-in amplifier at 20 K with in-plane constant magnetic field 100 Oe. (e) Anomalous Hall resistance measured at 300 K. (f) A typical second harmonic voltage measured at 300 K with in-plane magnetic field 2 kOe. The red line shows the fit of data. The blue and yellow lines show $\sin \phi$ and $\sin \phi \cos 2\phi$ terms, respectively. Data is captured in $\mathrm{Ir}\text{−}\mathrm{Mn}$ 3.0 samples.

Figure 2

(a),(b) Extracted fieldlike (a) and dampinglike (b) terms measured at different temperatures and magnetic fields. (c),(d) Linear relationship between the fieldlike (c) and dampinglike (d) terms and the reciprocal of the effective field.

Figure 3

(a) Spin conductivity measured at different temperatures for $\mathrm{Ir}\text{−}\mathrm{Mn}$ 1.0 sample. (b) Exchange bias and coercivity measured at different temperatures for the $\mathrm{Ir}\text{−}\mathrm{Mn}$ (1.0)/$\mathrm{Ni}\text{−}\mathrm{Fe}$ (3.0)/$\mathrm{Ru}$ (5) (thickness in nanometers) sample. The inset shows a typical exchange-biased hysteresis loop.

Figure 4

(a) Spin conductivity as a function of temperature for samples with different $\mathrm{Ir}\text{−}\mathrm{Mn}$ thicknesses. (b) Spin conductivity as a function of $\mathrm{Ir}\text{−}\mathrm{Mn}$ thickness at various temperatures.

Figure 5

Schematics of the model magnetic multilayer. The heterostructure is composed of four layers: a heavy metal (HM - gray) providing SHE with efficiency ${\theta }_{\mathrm{HM}}$, an antiferromagnetic layer (AFM, coral) providing SHE with efficiency ${\theta }_{\mathrm{AF}}$ and with an order parameter along z (out-of-plane orange arrows) enabling magnon propagation (brown and green wavy arrows), a light metal space (S, light blue), and finally a ferromagnet (FM, red) with magnetization along the y axis (red arrow).

Figure 6

Spin torque as a function of the antiferromagnetic thickness for ${\lambda }_{\alpha }=6\mathrm{nm}$ and (a) ${\sigma }_{\alpha }={10}^6{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-1}$, (b) ${\sigma }_{\alpha }={10}^7{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-1}$, and (c) ${\sigma }_{\alpha }={10}^8{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-1}$. The curves are calculated for various spin convertances $G_{\alpha }^0$. The units are given in ${\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$.

Figure 7

Anatomy of the torque as a function of the AFM thickness for ${\lambda }_{\alpha }=6\mathrm{nm},{\sigma }_{\alpha }={10}^7{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-1}$, (a) $G_{\alpha }^0={10}^{14}{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$, (b) $G_{\alpha }^0={10}^{16}{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$, and (c) $G_{\alpha }^0={10}^{17}{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$, and ${\sigma }_{\alpha }={10}^8{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-1}$, (d) $G_{\alpha }^0={10}^{14}{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$, (e) $G_{\alpha }^0={10}^{16}{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$, and (f) $G_{\alpha }^0={10}^{17}{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$. The black curve represents the total spin current (which equals the spin torque) at the AFM/S interface, the solid (dashed) blue lines represent the magnon (electronic) spin currents due to the SHE of the AFM layer, while the solid (dashed) red lines represent the magnonic (electronic) spin currents due to the SHE of the HM layer.

Figure 8

Schematic of the electron-magnon conversion at (a) HM/AFM and (b) AFM/S interfaces. The curved arrow represents the SHE that generates an electronic spin current and the straight blue (red) arrow represents the electronic (magnonic) spin current contributions. The shaded blue (red) puddles represent electronic (magnonic) spin accumulation at the interface and the wavy black arrow represents the electron-magnon interaction.

Figure 9

Spin torque as a function of the antiferromagnetic thickness for different magnon diffusion lengths. Here, ${\sigma }_{\alpha }={10}^7{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-1}$ and $G_{\alpha }^0={10}^{16}{\mathrm{\Omega }}^{-1}{\mathrm{m}}^{-2}$.

Figure 10

Numerical fit of the experimental data of (a) Fig. 4 of the present work and (b) Fig. 3 from Ref. [9]. The fitting parameters are given in Table 1.