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Intrinsic Spin Decay Length in Antiferromagnetic Insulator

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.

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.
Spintronics relies on the transport of spins in condensed matter [1][2][3]. 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 [3]. 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 [4]. 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 [5,6].
Antiferromagnetic insulators is a new class of materials for spin transport [7][8][9]. 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 [10][11][12], intense experimental and theoretical efforts have been invested in unraveling the physics of the spin transport in antiferromagnetic insulators [10][11][12][13][14][15][16][17][18][19][20][21][22]. In antiferromagnetic insulators, the spindecay length is known to be typically limited to only a few nanometers [9], although theories predict longdistance spin transport in antiferromagnets [23]. This is in stark contrast to the situation for ferromagnetic insulators, where long-distance spin propagation has been observed [4,5].
In this Letter, we reveal the intrinsic character of magnonic spin transport in an antiferromagnetic insulator. We found that, in the conventional spininjector/antiferromagnetic-insulator/spin-detector structure, the spin-transmission signal is strongly suppressed by two-magnon scattering. By eliminating the twomagnon 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, provid- ing an important information for the fundamental understanding of antiferromagnetic spintronics.
To quantify the intrinsic spin decay length of NiO, we prepared Ni 81 Fe 19 (8)/NiO(d 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 NiO = 0 to 10.5 nm. The Ni 81 Fe 19 layer, capped by 4-nm-thick SiO 2 , is a 1 × 1.5 mm 2 rectangular shape. For the Ni 81 Fe 19 /NiO/Pt trilayers, we measured the spin pumping by varying a magnetic field H applied at an angle of θ H from the film normal at room temperature [see Fig. 1(a)]. The spin pumping from the Ni 81 Fe 19 layer injects a spin current into the NiO layer [24]. The spin current reaching the Pt layer is converted into an electric voltage V ISHE through the inverse spin Hall effect (ISHE) in the Pt layer [25], and thus the spin-current decay in the NiO layer can be characterized by measuring the d NiO dependence of V ISHE . In Fig. 1 Figure 1(b) shows that the ISHE voltage V ISHE is generated around the FMR field H = H res . This result also shows that V ISHE ≡ V (H 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 θ H dependence of V ISHE strongly depends on the NiO thickness d NiO . In Fig. 2(a), we show the θ H dependence of V ISHE for the Ni 81 Fe 19 /NiO/Pt trilayers with various d NiO . This result shows that the θ H dependence of V ISHE for the trilayers with different d NiO is the same only around θ H = 0. Here, the variation of V ISHE for the film with d NiO = 0 nm is consistent with the standard model of the spin pumping and ISHE [26]. In this model, when the magnetic damping constant α is independent of θ H , the spin current generated by the spin pumping is expressed as [26] where g ↑↓ eff is the effective spin-mixing conductance, h is the microwave magnetic field, γ is the gyromagnetic ratio, M s is the saturation magnetization, and ω = 2πf . θ M is the out-of-plane angle of the magnetization-precession axis [see Fig. 1 is the precession ellipticity factor.
When the magnetization-precession axis is oblique to the film plane, the ISHE voltage V ISHE is proportional to j s (θ M ) sin θ M because of j Pt s j Pt c × σ [26], where j Pt s is the spin current density injected into the Pt layer and j Pt c is the charge current density generated by the ISHE. σ is the spin-polarization direction of the spin current, which is parallel to the magnetization-precession axis. As shown in Fig. 2 [27][28][29][30][31]  The drastic change in V ISHE at |θ M | > 45 • indicates that the nontrivial variation of V ISHE is caused by two-magnon scattering in the Ni 81 Fe 19 /NiO/Pt trilayers. The two-magnon scattering can be induced only when |θ M | > 45 • because the degenerated states with k = 0 mode disappear at |θ M | < 45 • [30,31,33]. Here, as shown in Fig. 1(b), the peak-to-peak FMR linewidth ∆H is clearly enhanced by inserting the NiO layer, despite the negligible change in the effective demagnetization field M eff [see the inset to Fig. 2(b)]. To quantitatively study the damping enhancement induced by the NiO insertion, we plot θ H dependence of ∆H in Fig. 3(a). Figure 3 The two-magnon scattering is known to be activated by the random fluctuation of uniaxial anisotropy, surface/interface roughness, and defects [28][29][30][31]34]. We note that in the Ni 81 Fe 19 /NiO/Pt trilayers, the NiO layer is polycrystalline, as evidenced by the X-ray diffractometry [32]. This suggests that the two-magnon scattering can be induced by the random fluctuation of uniaxial anisotropy due to randomly oriented exchange bias fields [35]. In fact, the measured θ H dependence of ∆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) [28,35] [for details, see [32]]. In the Ni 81 Fe 19 /NiO/Pt trilayers, the random fluctuation of uniaxial anisotropy due to the randomly oriented exchange bias increases with d NiO [35]; although the surface roughness of the NiO layer is almost unchanged with d NiO [32], the amplitude of the two-magnon scattering C TMS increases with d NiO , which is reminiscent of the increased suppression of V ISHE with d NiO shown in Fig. 2(c). Here, we characterize the suppression of V ISHE induced by the NiO insertion as the difference between the measured V ISHE and V ISHE calculated using the conventional spin-pumping model, are the calculated and measured ISHE voltage at θ H , respectively [see Fig. 2(a)]. To clarify the relation between C TMS and the voltage suppression, we plot ∆V ISHE with respect to C TMS , extracted by the calculation shown in Fig. 3(a). As shown in Fig. 3(b), ∆V ISHE increases with C TMS , supporting that the suppressed V ISHE signals at |θ M | > 45 • is caused by the two-magnon scattering.
Commonly, the spin decay length λ NiO of NiO is obtained from the thickness d NiO dependence of V ISHE at θ H = θ M = 90 • [10][11][12]. Following this procedure, we plot the d NiO dependence of V ISHE at θ M = 90 • in Fig. 3(d). This result shows that the spin decay length is increased from λ NiO = 1.8 nm for d NiO < 3 nm to λ NiO = 8.8 nm for d NiO > 3 nm. The increase of λ NiO can be attributed to the paramagnetic to antiferromagnetic transition; for d NiO < 3 nm, the Néel temperature is lower than the room temperature, while the NiO layer with d NiO > 3 nm is antiferromagnetic at room temperature [10,36,37]. λ NiO = 8.8 nm in the antiferromagnetic state is consistent with previous reports [10,12]. However, we note that, as is clear from Fig. 2(a), the V ISHE signals at θ H = 90 • are strongly suppressed by the twomagnon scattering. This results in under estimation of the spin decay length in the antiferromagnetic state because the voltage suppression increases with d NiO .
The intrinsic spin decay length, where the two-magnon contribution is excluded, can be determined only from the d NiO dependence of V ISHE at |θ M | < 45 • , where the voltage suppression due to the two-magnon scattering is absent. As shown in Fig. 3(d), the d NiO dependence of V ISHE at θ M = 40 • is clearly different from that at θ M = 90 • . From the data at θ M = 40 • , for the antiferromagnetic NiO, we obtain λ NiO = 109 nm, which is almost ten times longer than previously reported values [10,12]. 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 twomagnon 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 Ni 81 Fe 19 /NiO/Pt trilayer with much thicker d NiO is difficult to measure because the surface roughness of the NiO layer increases with d 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.