Intrinsic Spin Decay Length in Antiferromagnetic Insulator

TL;DR

This paper measures the intrinsic spin decay length in antiferromagnetic insulators, revealing it is significantly longer than previously thought, and highlights the impact of magnetic phase transitions on spin transport.

Contribution

It demonstrates the intrinsic spin decay length in NiO and shows how it varies across the paramagnetic to antiferromagnetic transition, eliminating two-magnon scattering effects.

Findings

Spin decay length exceeds 100 nm in the antiferromagnetic state.

Spin decay length varies by two orders of magnitude across the magnetic transition.

Two-magnon scattering strongly suppresses spin current at interfaces.

Abstract

We report intrinsic spin decay length of an antiferromagnetic insulator. We found that at an antiferromagnetic/ferromagnetic interface, a spin current generated by spin pumping is strongly suppressed by two-magnon scattering. By eliminating the two-magnon contribution, we discovered that the characteristic length of spin decay in NiO changes by two-orders of magnitude through the paramagnetic to antiferromagnetic transition. The spin decay length in the antiferromagnetic state is longer than 100 nm, which is an order of magnitude longer than previously believed. These results provide a crucial piece of information for the fundamental understanding of the physics of spin transport.

Equations

$$j_{\mathrm{s}}({\theta }_M)=\frac{g{h}^2\hslash {\gamma }^2\omega }{4\pi {\alpha }^{2}A({\theta }_M)\left[(4\pi M_{\mathrm{s}}{)}^2{\gamma }^2{\sin }^4{\theta }_M+4{\omega }^2\right]},$$

Full text

Spintronics relies on the transport of spins in condensed matter Žutić et al. (2004); Maekawa (2006); Maekawa et al. (2012). Spin transport has been investigated in a variety of materials, including metals, semiconductors, and insulators. In metals and semiconductors, spins are transported by the diffusion of conduction electrons Maekawa et al. (2012). In contrast, in magnetically-ordered materials, spins can be transported even in the absence of conduction electrons; spins are carried by the elementary excitations of magnetic moments, magnons Kajiwara et al. (2010). The magnonic spin current in insulators is of particular recent interest because this sets a new direction for experimental and theoretical studies of the physics of spin transport Cornelissen et al. (2015); Wesenberg et al. (2017).

Antiferromagnetic insulators is a new class of materials for spin transport Jungwirth et al. (2016); Jungfleisch et al. (2018); Baltz et al. (2018). This class of materials potentially entails a number of advantages as compared to ferromagnets: antiferromagnets are robust against external magnetic fields, produce no stray fields, and display ultrafast dynamics. Since the first observation of the transmission of spins through an antiferromagnetic insulator NiO Wang et al. (2014a); Hahn et al. (2014); Wang et al. (2015), intense experimental and theoretical efforts have been invested in unraveling the physics of the spin transport in antiferromagnetic insulators Wang et al. (2014a); Hahn et al. (2014); Wang et al. (2015); Moriyama et al. (2015); Takei et al. (2015); Seki et al. (2015); Lin et al. (2016); Takei et al. (2014); Rezende et al. (2016); Bender et al. (2017); Qaiumzadeh et al. (2017); Lebrun et al. (2018); Yuan et al. (2018). In antiferromagnetic insulators, the spin-decay length is known to be typically limited to only a few nanometers Baltz et al. (2018), although theories predict long-distance spin transport in antiferromagnets Khymyn et al. (2016). This is in stark contrast to the situation for ferromagnetic insulators, where long-distance spin propagation has been observed Kajiwara et al. (2010); Cornelissen et al. (2015).

In this Letter, we reveal the intrinsic character of magnonic spin transport in an antiferromagnetic insulator. We found that, in the conventional spin-injector/antiferromagnetic-insulator/spin-detector structure, the spin-transmission signal is strongly suppressed by two-magnon scattering. By eliminating the two-magnon contribution in the spin-transmission signal, we show that the spin decay length of a prototypical antiferromagnetic insulator NiO changes by two-orders of magnitude through the paramagnetic to antiferromagnetic transition. This result shows that the intrinsic spin decay length of the antiferromagnetic NiO is an order of magnitude longer than the previously believed, providing an important information for the fundamental understanding of antiferromagnetic spintronics.

To quantify the intrinsic spin decay length of NiO, we prepared Ni81Fe19(8)/NiO($d_{\mathrm{NiO}}$)/Pt(5) trilayers on thermally oxidized Si substrates by RF magnetron sputtering at room temperature [see Fig. 1(a)]. The numbers in brackets represent the thickness of each layer in nm unit, where $d_{\mathrm{NiO}}=0$ to 10.5 nm. The Ni81Fe19 layer, capped by 4-nm-thick SiO2, is a $1\times 1.5$ mm2 rectangular shape. For the Ni81Fe19/NiO/Pt trilayers, we measured the spin pumping by varying a magnetic field ${\bf H}$ applied at an angle of $\theta_{H}$ from the film normal at room temperature [see Fig. 1(a)]. The spin pumping from the Ni81Fe19 layer injects a spin current into the NiO layer Tserkovnyak et al. (2002). The spin current reaching the Pt layer is converted into an electric voltage $V_{\text{ISHE}}$ through the inverse spin Hall effect (ISHE) in the Pt layer Saitoh et al. (2006), and thus the spin-current decay in the NiO layer can be characterized by measuring the $d_{\mathrm{NiO}}$ dependence of $V_{\text{ISHE}}$. In Fig. 1(b), we show the $H$ dependence of the microwave absorption intensity $I(H)$ and voltage $V(H)$ signals for the Ni81Fe19/NiO/Pt trilayers with $d_{\mathrm{NiO}}=0$ and 4.1 nm at $\theta_{{H}}=90^{\circ}$. For the measurement, the Ni81Fe19/NiO/Pt trilayer was placed at the center of a TE011 cavity with the frequency of $f=9.43$ GHz and power of $P=200$ mW, and we measured dc electric voltage $V$ between electrodes attached to the edges of the film [see Fig. 1(a)]. Figure 1(b) shows that the ISHE voltage $V_{\text{ISHE}}$ is generated around the FMR field $H=H_{\mathrm{res}}$. This result also shows that $V_{\text{ISHE}}\equiv V(H_{\mathrm{res}})$ is strongly suppressed by inserting the NiO layer, as expected for the spin-current decay in the antiferromagnet.

Our finding is that magnetic-field angle $\theta_{H}$ dependence of $V_{\text{ISHE}}$ strongly depends on the NiO thickness $d_{\mathrm{NiO}}$. In Fig. 2(a), we show the $\theta_{H}$ dependence of $V_{\text{ISHE}}$ for the Ni81Fe19/NiO/Pt trilayers with various $d_{\mathrm{NiO}}$. This result shows that the $\theta_{H}$ dependence of $V_{\text{ISHE}}$ for the trilayers with different $d_{\mathrm{NiO}}$ is the same only around $\theta_{H}=0$. Here, the variation of $V_{\mathrm{ISHE}}$ for the film with $d_{\mathrm{NiO}}=0$ nm is consistent with the standard model of the spin pumping and ISHE Ando et al. (2011). In this model, when the magnetic damping constant $\alpha$ is independent of $\theta_{H}$, the spin current generated by the spin pumping is expressed as Ando et al. (2011)

[TABLE]

where $g_{\text{eff}}^{\uparrow\downarrow}$ is the effective spin-mixing conductance, $h$ is the microwave magnetic field, $\gamma$ is the gyromagnetic ratio, $M_{\mathrm{s}}$ is the saturation magnetization, and $\omega=2\pi f$. $\theta_{M}$ is the out-of-plane angle of the magnetization-precession axis [see Fig. 1(a)]. $A(\theta_{M})={2\omega}\left[{4\pi M_{\mathrm{s}}\gamma\sin^{2}\theta_{M}+\sqrt{(4\pi M_{\mathrm{s}}\gamma)^{2}\sin^{4}\theta_{M}+4\omega^{2}}}\right]^{-1}$ is the precession ellipticity factor. When the magnetization-precession axis is oblique to the film plane, the ISHE voltage $V_{\mathrm{ISHE}}$ is proportional to ${j_{\mathrm{s}}}(\theta_{M})\sin\theta_{M}$ because of ${\bf j}_{\mathrm{s}}^{\mathrm{Pt}}\parallel{\bf j}_{\mathrm{c}}^{\mathrm{Pt}}\times{\bm{\sigma}}$ Ando et al. (2011), where $j_{\mathrm{s}}^{\mathrm{Pt}}$ is the spin current density injected into the Pt layer and $j_{\mathrm{c}}^{\mathrm{Pt}}$ is the charge current density generated by the ISHE. $\bm{\sigma}$ is the spin-polarization direction of the spin current, which is parallel to the magnetization-precession axis. As shown in Fig. 2(a), this model well reproduces the experimental data only for $d_{\mathrm{NiO}}=0$ nm [see the solid curve]. For the calculation, we determined $\theta_{M}$ and $M_{\mathrm{s}}$ from measured $\theta_{H}$ dependence of $H_{\mathrm{res}}$, shown in Figs. 2(b), by solving $\omega={\gamma}\sqrt{H_{X}H_{Y}}$, where $\omega=2\pi f$, $H_{X}=H_{\mathrm{res}}\cos(\theta_{H}-\theta_{M})-M_{\mathrm{eff}}\cos^{2}\theta_{M}$, and $H_{Y}=H_{\mathrm{res}}\cos(\theta_{H}-\theta_{M})-M_{\mathrm{eff}}\cos(2\theta_{M})$ Mizukami et al. (2002); Lindner et al. (2009); Landeros et al. (2008); Arias and Mills (1999, 2000) [see the inset to Figs. 2(b) and 2(c)]. $M_{\mathrm{eff}}\simeq M_{\mathrm{s}}$ is the effective demagnetization field.

To clarify the origin of the anomaly in the $\theta_{H}$ dependence of $V_{\mathrm{ISHE}}$ for the Ni81Fe19/NiO/Pt trilayers with $d_{\mathrm{NiO}}\neq 0$ nm, we plot $\theta_{M}$ dependence of $V_{\mathrm{ISHE}}$ in Fig. 2(c). Since $j_{\mathrm{c}}^{\mathrm{Pt}}(\theta_{M})$ does not change drastically with $\theta_{M}$, $V_{\text{ISHE}}$ is approximately proportional to $\sin\theta_{M}$. In fact, the $\theta_{M}$ dependence of $V_{\text{ISHE}}$ is consistent with this scenario for the Ni81Fe19/Pt bilayer ($d_{\mathrm{NiO}}=0$ nm). However, for the Ni81Fe19/NiO/Pt trilayers, the measured $V_{\mathrm{ISHE}}$ values are proportional to $\sin\theta_{M}$ only at $|\theta_{M}|<45^{\circ}$ as shown in Fig. 2(c); $V_{\mathrm{ISHE}}$ deviates from $\sin\theta_{M}$ at $|\theta_{M}|>45^{\circ}$ with increasing the thickness of the NiO layer.

The drastic change in $V_{\mathrm{ISHE}}$ at $|\theta_{M}|>45^{\circ}$ indicates that the nontrivial variation of $V_{\mathrm{ISHE}}$ is caused by two-magnon scattering in the Ni81Fe19/NiO/Pt trilayers. The two-magnon scattering can be induced only when $|\theta_{M}|>45^{\circ}$ because the degenerated states with $k=0$ mode disappear at $|\theta_{M}|<45^{\circ}$ Kurebayashi et al. (2013); Arias and Mills (1999, 2000). Here, as shown in Fig. 1(b), the peak-to-peak FMR linewidth $\Delta H$ is clearly enhanced by inserting the NiO layer, despite the negligible change in the effective demagnetization field $M_{\mathrm{eff}}$ [see the inset to Fig. 2(b)]. To quantitatively study the damping enhancement induced by the NiO insertion, we plot $\theta_{H}$ dependence of $\Delta H$ in Fig. 3(a). Figure 3(a) shows $\Delta H(\theta_{H}=\theta_{M}=0^{\circ})\simeq\Delta H(\theta_{H}=\theta_{M}=90^{\circ})$ for $d_{\mathrm{NiO}}=0$ nm, while $\Delta H(\theta_{H}=\theta_{M}=0^{\circ})<\Delta H(\theta_{H}=\theta_{M}=90^{\circ})$ for $d_{\mathrm{NiO}}=4.1$ nm. This result indicates that $\Delta H(\theta_{H}=90^{\circ})$ for the Ni81Fe19/NiO/Pt trilayer is influenced by the two-magnon scattering.

The two-magnon scattering is known to be activated by the random fluctuation of uniaxial anisotropy, surface/interface roughness, and defects Azevedo et al. (2000); Arias and Mills (1999, 2000); Landeros et al. (2008); Lindner et al. (2009). We note that in the Ni81Fe19/NiO/Pt trilayers, the NiO layer is polycrystalline, as evidenced by the X-ray diffractometry sup . This suggests that the two-magnon scattering can be induced by the random fluctuation of uniaxial anisotropy due to randomly oriented exchange bias fields Sakimura et al. (2018). In fact, the measured $\theta_{H}$ dependence of $\Delta H$ is well reproduced by a calculation which takes into account the additional damping due to the two-magnon scattering as shown in Fig. 3(a) Sakimura et al. (2018); Lindner et al. (2009) [for details, see sup ]. In the Ni81Fe19/NiO/Pt trilayers, the random fluctuation of uniaxial anisotropy due to the randomly oriented exchange bias increases with $d_{\mathrm{NiO}}$ Sakimura et al. (2018); although the surface roughness of the NiO layer is almost unchanged with $d_{\mathrm{NiO}}$ sup , the amplitude of the two-magnon scattering $C_{\mathrm{TMS}}$ increases with $d_{\mathrm{NiO}}$, which is reminiscent of the increased suppression of $V_{\mathrm{ISHE}}$ with $d_{\mathrm{NiO}}$ shown in Fig. 2(c). Here, we characterize the suppression of $V_{\mathrm{ISHE}}$ induced by the NiO insertion as the difference between the measured $V_{\mathrm{ISHE}}$ and $V_{\mathrm{ISHE}}$ calculated using the conventional spin-pumping model, $\Delta\bar{V}_{\mathrm{ISHE}}\equiv V_{\mathrm{ISHE}}^{\mathrm{calc}}(\theta_{H}=90^{\circ})/V_{\mathrm{ISHE}}^{\mathrm{calc}}(\theta_{H}=10^{\circ})-V_{\mathrm{ISHE}}^{\mathrm{exp}}(\theta_{H}=90^{\circ})/V_{\mathrm{ISHE}}^{\mathrm{exp}}(\theta_{H}=10^{\circ})$, where $V_{\mathrm{ISHE}}^{\mathrm{calc}}(\theta_{H})$ and $V_{\mathrm{ISHE}}^{\mathrm{exp}}(\theta_{H})$ are the calculated and measured ISHE voltage at $\theta_{H}$, respectively [see Fig. 2(a)]. To clarify the relation between $C_{\mathrm{TMS}}$ and the voltage suppression, we plot $\Delta\bar{V}_{\mathrm{ISHE}}$ with respect to $C_{\mathrm{TMS}}$, extracted by the calculation shown in Fig. 3(a). As shown in Fig. 3(b), $\Delta\bar{V}_{\mathrm{ISHE}}$ increases with $C_{\mathrm{TMS}}$, supporting that the suppressed $V_{\mathrm{ISHE}}$ signals at $|\theta_{M}|>45^{\circ}$ is caused by the two-magnon scattering.

From the calculation of the $\theta_{H}$ dependence of $\Delta H$, we also extracted the damping constant $\alpha=\mu_{0}[\Delta H-(\Delta H_{\mathrm{inhomo}}+\Delta H_{\mathrm{TMS}})]({\sqrt{3}}/{2})({\gamma\Xi}/{\omega})$, where $\Delta H_{\mathrm{inhomo}}$ and $\Delta H_{\mathrm{TMS}}$ are the linewidth due to inhomogeneity and two-magnon scattering, respectively. $\Xi$ is the dragging function sup . Figure 3(c) shows that $\alpha$ decreases at $d_{\text{NiO}}=2.0$ nm, while $\alpha$ increases above $d_{\text{NiO}}=4.1$ nm, consistent with previous reports Wang et al. (2014a, 2015); $\alpha$ decreases due to the decoupling of the Ni81Fe19 and Pt layers by the insulating and non-Néel-ordered NiO layer because the Néel temperature of 2-nm-thick NiO is below the room temperature Gruyters (2002); Baruth and Adenwalla (2008); Wang et al. (2014b). Above $d_{\text{NiO}}=4.1$ nm, $\alpha$ increases because of the enhanced antiferromagnetic correlation due to the thickness growth Wang et al. (2014a); Lang et al. (2007).

Commonly, the spin decay length $\lambda_{\mathrm{NiO}}$ of NiO is obtained from the thickness $d_{\mathrm{NiO}}$ dependence of $V_{\mathrm{ISHE}}$ at $\theta_{H}=\theta_{M}=90^{\circ}$ Wang et al. (2014a, 2015); Hahn et al. (2014). Following this procedure, we plot the $d_{\mathrm{NiO}}$ dependence of $V_{\mathrm{ISHE}}$ at $\theta_{M}=90^{\circ}$ in Fig. 3(d). This result shows that the spin decay length is increased from $\lambda_{\mathrm{NiO}}=1.8$ nm for $d_{\mathrm{NiO}}<3$ nm to $\lambda_{\mathrm{NiO}}=8.8$ nm for $d_{\mathrm{NiO}}>3$ nm. The increase of $\lambda_{\mathrm{NiO}}$ can be attributed to the paramagnetic to antiferromagnetic transition; for $d_{\mathrm{NiO}}<3$ nm, the Néel temperature is lower than the room temperature, while the NiO layer with $d_{\text{NiO}}>3$ nm is antiferromagnetic at room temperature  Wang et al. (2014a); Baruth and Adenwalla (2008); Gruyters (2002). $\lambda_{\mathrm{NiO}}=8.8$ nm in the antiferromagnetic state is consistent with previous reports Wang et al. (2014a, 2015). However, we note that, as is clear from Fig. 2(a), the $V_{\mathrm{ISHE}}$ signals at $\theta_{H}=90^{\circ}$ are strongly suppressed by the two-magnon scattering. This results in under estimation of the spin decay length in the antiferromagnetic state because the voltage suppression increases with $d_{\mathrm{NiO}}$.

The intrinsic spin decay length, where the two-magnon contribution is excluded, can be determined only from the $d_{\mathrm{NiO}}$ dependence of $V_{\mathrm{ISHE}}$ at $|\theta_{M}|<45^{\circ}$, where the voltage suppression due to the two-magnon scattering is absent. As shown in Fig. 3(d), the $d_{\mathrm{NiO}}$ dependence of $V_{\mathrm{ISHE}}$ at $\theta_{M}=40^{\circ}$ is clearly different from that at $\theta_{M}=90^{\circ}$. From the data at $\theta_{M}=40^{\circ}$, for the antiferromagnetic NiO, we obtain $\lambda_{\mathrm{NiO}}=109$ nm, which is almost ten times longer than previously reported values Wang et al. (2014a, 2015). We also note that the characteristic length of spin decay in NiO changes by two-orders of magnitude through the paramagnetic to antiferromagnetic transition, illustrating the crucial role of the antiferromagnetic order for efficient spin transport in antiferromagnetic insulators.

In summary, we investigated magnonic spin transport in an antiferromagnetic insulator NiO. We found that in the in-plane magnetic field geometry, the spin transport signal is strongly suppressed by the two-magnon scattering. By changing the magnetic-field angle, the two-magnon scattering contribution can be eliminated, which enables to determine the intrinsic spin decay length of the antiferromagnetic insulator. Although the spin transport signal for the Ni81Fe19/NiO/Pt trilayer with much thicker $d_{\mathrm{NiO}}$ is difficult to measure because the surface roughness of the NiO layer increases with $d_{\mathrm{NiO}}$, our result shows that the intrinsic spin decay length of the prototypical antiferromagnetic insulator NiO is longer than 100 nm, which is an order of magnitude longer than previously believed. The result shows that the spin decay length changes by two-orders of magnitude through the paramagnetic to antiferromagnetic transition. Our results therefore demonstrate the crucial role of the antiferromagnetic order for efficient spin transport in antiferromagnetic insulators, as well as the two-magnon scattering in quantifying the spin transport in antiferromagnets.