Observation of magnon-mediated current drag in Pt/yttrium iron garnet/Pt(Ta) trilayers

Pure spin current, a flow of spin angular momentum without flow of any accompanying net charge, is generated in two common ways. One makes use of the spin Hall effect in normal metals (NM) with strong spin–orbit coupling, such as Pt or Ta. The other utilizes the collective motion of magnetic moments or spin waves with the quasi-particle excitations called magnons. A popular material for the latter is yttrium iron garnet, a magnetic insulator (MI). Here we demonstrate in NM/MI/NM trilayers that these two types of spin currents are interconvertible across the interfaces, predicated as the magnon-mediated current drag phenomenon. The transmitted signal scales linearly with the driving current without a threshold and follows the power-law Tn with n ranging from 1.5 to 2.5. Our results indicate that the NM/MI/NM trilayer structure can serve as a scalable pure spin current valve device which is an essential ingredient in spintronics.

Zhang et al. 23,24 predicted a phenomenon with a different origin in sandwich structures, analogous to the conventional spin-valve device for spin-polarized charge currents 25,26 . Rather than exciting a coherent precession of magnetization, at one interface, electrons in the NM create/annihilate magnons in the MI. The individual magnon creation/annihilation does not need to overcome any threshold; therefore, the interconversion takes place at any current. Due to the long magnon decay length in MI 27 , this effect couples two remote electrical currents, which is called the magnon-mediated current drag. Moreover, the on and off states are controlled by the relative orientation between the polarization of the spin current and MI magnetization. In small lateral devices similar to that of Kajiwara, Cornelissen et al. 28 reported both oand 2o nonlocal current responses in the a.c. measurements (o is the frequency of a.c. current). The o-response indicates a linear nonlocal current relation, which apparently does not share the same origin as that of the effect reported by Kajiwara. Nonlocal magnetoresistance was also reported in similar device geometry 29 . However, it is unclear whether the reported effect indeed arises from the microscopic mechanism predicted by Zhang et al. An objective of this work is to experimentally establish the current drag effect in the sandwich geometry proposed by Zhang et al.
In this work, we first successfully fabricate Pt/YIG/Pt(Ta) trilayer structures using pulsed laser deposition in combination with sputtering and post-growth annealing. Below 220 K, the trilayers are sufficiently insulating and we observe nonlocal responses when an in-plane magnetic field is swept or rotated. We find that the polarity of the nonlocal signal is opposite to each other between Pt/YIG/Pt and Pt/YIG/Ta, indicating the spin current origin of the effect. By investigating the effect at low temperatures, we show that the power-law dependence of the nonlocal signal is consistent with the prediction for the magnon-mediated current drag effect.

Results
Nonlocal device structure. Our NM/MI/NM trilayer device structure is schematically shown in Fig. 1a,b. The MI is a thin YIG film sandwiched by either two identical NM films or dissimilar NM films. Via the spin Hall effect, a charge current (J injected ) generates a pure spin current flowing in the z-direction with the spin polarization (r) parallel to the y-direction. The conduction electrons in the bottom NM interact with the localized moments of the MI via the s-d exchange interaction at the interface, resulting in the creation or annihilation of magnons in the MI accompanied by spin-flips of conduction electrons in the bottom NM layer. Due to the nature of the s-d exchange interaction 24,30 , that is, H sd ¼ À J sd P r Á M, where J sd is exchange coupling strength, when the magnetization of the MI (M) is collinear with r, magnons are created or annihilated depending on whether M is parallel or anti-parallel to r. As such, the interaction creates a non-equilibrium magnon population and spin accumulation in the MI which drives magnon diffusion. The excess/deficient magnons are then converted to a spin current in the top NM layer by the reverse process, which is converted to a charge current (J induced ) again in the top NM layer via the inverse spin Hall effect. When r>M, there is no non-equilibrium magnon population or spin accumulation and the spin current is absorbed by the MI. Consequently, there is no induced spin or charge current in the top NM layer (Fig. 1b). Remarkably, one can switch on and off the magnon creation/annihilation process by controlling the relative orientation between M and r. Conceptually, this structure functions as a valve for pure spin current.
Field-dependent nonlocal response in trilayer devices. Since both Pt and Ta have strong spin-orbit coupling with opposite signs in their spin Hall angle 15,31,32 , we have fabricated three Pt (5 nm)/YIG (80 nm)/Pt (5 nm) devices and two Pt (5 nm)/YIG (80 nm)/Ta (5 nm) reference samples, which were deposited  Supplementary Fig. 2), and exceeds 20 GO at and below 220 K. Therefore, all the nonlocal measurements were performed below 220 K to avoid any parasitic signal from the small leakage current. In V nl , we remove a non-zero background signal that exists even at I b ¼ 0. Figure 2c,d plot the field dependence of V nl at 220 K. When H is swept along I b , that is, y ¼ 90° (Fig. 2c), V nl is a constant at I b ¼ 0 (red). However, at I b ¼ þ 1.5 mA, V nl shows a clear hysteresis with two positive peaks tracking the coercive fields of the YIG film, indicating that V nl is closely related to the magnetization state of YIG. As the I b is reversed, V nl also reverses the sign. In principle, a sign reversal can occur if there is a finite leakage current flowing in the top layer. Through the magnetoresistance, this current can produce a hysteretic voltage signal. Estimating from the leakage current, we find that the relative change in V nl due to this effect is at least three orders of magnitude smaller than the observed nonlocal voltage signal (see Supplementary Note 4 and Supplementary Figs 4 and 5). Therefore, we exclude the leakage current as the source of the nonlocal signal. Note that V nl ( ± 1.5 mA) is the same as V nl (0 mA) at the saturation state (H4200 Oe) when r>M, suggesting that magnon creation/annihilation is totally suppressed. For the field sweeps with y ¼ 0° (Fig. 2d), r is collinear with M at high fields, interface magnon creation/ annihilation results in a full current drag signal. Clearly, V nl ( þ 1.5 mA) is different from V nl (0 mA) at the saturation fields and reverses the sign when I b reverses. It is interesting to note that V nl ( ± 1.5 mA) differ from V nl (0 mA) at the coercive fields. One would expect them to be the same since the average magnetization should point to the x-direction at the coercive fields, which would correspond to the saturation states for y ¼ 90°i n Fig. 2c. This discrepancy can be explained by the multi-domain state of YIG in which the actual M is distributed over a range of angles around y ¼ 90°, and the collinear component of M turns on the magnon channel and yields a nonzero V nl . To investigate the phenomenon in the single-domain state, we perform the following experiments.
Angle-dependent nonlocal response of single-domain YIG. Figure 3a presents V nl in GGG/Pt/YIG/Pt as a function of y between M and r at 220 K, as illustrated in Fig. 2b. The 80 nm (110)-oriented YIG grown on Pt has a well-defined uniaxial anisotropy with an anisotropy field o200 Oe. The applied magnetic field (1,000 Oe) is sufficiently strong not only to set YIG into a single-domain state, but also to rotate M with it. For all positive I b (solid symbols), V nl exhibits maxima at y ¼ 0°and 180°(M collinear with r), but minima at y ¼ 90°and 270°( M>r). V nl changes the sign as I b is reversed (empty symbols). At y ¼ 90°and 270°, the nonlocal signal for ±I b coincides with V nl (0 mA), further validating that the spin current is in the off state when M>r. Similar angular dependent measurements are also taken on a GGG/Pt/YIG/Ta device and the results are depicted in Fig. 3d. For the same measurement geometry and the same polarity of I b , we find that V nl of GGG/Pt/YIG/Ta has the opposite sign to that of GGG/Pt/YIG/Pt, which is just expected from the opposite signs in their spin Hall angle. The V nl sign difference here is another piece of critical evidence for the magnon-mediated mechanism, as opposed to other extrinsic ones such as leakage.
An interesting feature to note here is that V nl at y ¼ 0°and 180°shows a slight but reproducible difference that is independent of the current polarity but increases with the increasing magnitude of I b . We attribute this phenomenon to the SSE contribution since the joule heating in the bottom Pt layer unavoidably generates a small vertical temperature gradient, which in turn launches an upward spin current in YIG entering the top Pt (or Ta) layer. As M reverses, so does the spin polarization, which consequently produces two different SSE signal levels between y ¼ 0°and 180°. Combining these two effects, we can fit the angular dependence data using: where V 0 is an offset voltage insensitive to the magnetization orientation, V SSE is the SSE voltage amplitude and V Drag represents the amplitude of the current drag signal. The solid red curves in Fig. 3a,d fit the experimental data remarkably well, and the extracted fitting results are plotted in Fig. 3b,e for GGG/Pt/YIG/Pt and GGG/Pt/YIG/Ta devices, respectively. Two conclusions can be evidently drawn from these results. First, the magnitude of the current drag signal (red circles) scales linearly ARTICLE with the driving current, that is, V Drag pI b . This is in stark contrast with the highly nonlinear behaviour 16 . Second, the weak current dependence of the SSE contribution follows V SSE $ I 2 b (as shown in Fig. 3c,f), which is characteristic of thermoelectric effects. Compared with usual bilayers, trilayer structures may have an enhanced SSE contribution due to the presence of the second heavy metal layer that draws an extra heat-driven spin current. Carefully designed experiments are needed to separate this effect.
Temperature dependence of nonlocal responses. According to Zhang, et al. 24 , the temperature dependence of the injection , where T c is the Curie temperature of the MI; for the detection interface, the spin convertance G me is proportional to T T F , where T F is the Fermi temperature of the NM layer. In the most simplified picture which is strictly applicable only for very thick films, the current drag signal should be proportional to the product of the two spin current convertances, that is, V Drag pG em Á G me pT 5/2 The representative angular dependence measurements below 220 K are shown in Fig. 4a,c for GGG/Pt/YIG/Pt and GGG/Pt/YIG/Ta devices, respectively. For both the samples, I b is set at þ 2 mA and H is held at 1,000 Oe. The magnitude of the current drag signal decreases progressively with decreasing temperature for both the devices. By fitting V nl using equation (1), we extract the magnitude of V Drag and V SSE shown in Fig. 4b,d. Apart from the expected sign difference, the magnitude of V Drag in both the devices monotonically decreases with decreasing temperature. In fact, both data sets can be well fitted by a power-law V Drag ¼V 0 Drag T n (red solid curves in Fig. 4b,d), where V 0 Drag is a pre-factor. The extracted exponent n is 2.21 for GGG/Pt/YIG/Pt and 1.88 for GGG/Pt/YIG/Ta, falling in the range between 1.5 and 2.5. It should be pointed out that the full picture described in ref. 24 actually contains other quantities that have weak temperature dependence. The deviation of the exponent from 2.5 is fully expected if these factors are considered. On the other hand, the V SSE is found to be relatively insensitive to temperature, suggesting a completely different mechanism.
In conclusion, we experimentally establish the magnonmediated current drag effect in NM/MI/NM trilayer structures by investigating the field, angle, current and temperature dependences of the nonlocal signal. The spin information carried by conduction electrons and magnons in different materials can be interconverted at the interfaces. Such structures can serve as     pure spin current valve devices since rotating the in-plane magnetization of the MI by 90°provides a digital on-off switch of the spin current. Furthermore, such structures also provide analogue functionality since rotating the in-plane magnetization of the MI provides analogue sinusoidal modulation of the spin current. Due to the extremely low damping in the MI, transmission of the pure spin currents can occur over relatively long distances providing the functionality of a pure spin interconnect.

Methods
Fabrication. A Hall bar was first defined in the photo-resist layer on a (110)oriented single crystalline GGG substrate using photolithography with the channel width of 20 mm and the length of 300 mm between two voltage electrodes. Then the bottom Pt layer was deposited on the open Hall bar area by d.c. magnetron sputtering. During sputtering, argon pressure was 5 mTorr, substrate temperature was kept at 300 K, and the d.c. sputtering power was 37.5 W. The deposition rate of Pt was 0.77 Å s À 1 and the Pt layer thickness was 5 nm. After liftoff, an 80-nm-thick YIG film was deposited at 450°C with O 2 pressure of 1.5 mTorr by pulsed laser deposition to cover the surface of the entire sample. The as-grown YIG film became crystallized and magnetized after rapid thermal annealing between 800 and 850°C for 200 s. We had explored a range of growth temperatures, different annealing conditions, different pulsed laser deposition rates and YIG film thicknesses and had experienced many difficulties such as YIG film cracking, peeling off for thicker YIG films, conducting, non-magnetic and so on before we identified the working window. The magnetic properties of YIG were investigated by vibrating sample magnetometer (see Supplementary Note 1 and Supplementary Fig. 1). The surface morphology of YIG was monitored by atomic force microscopy. Clear atomic terraces were observed and the root-mean-square roughness on terraces was B0.14 nm, indicating a very flat YIG surface. The top Pt and Ta patterns were defined using standard e-beam lithography, followed by magnetron sputtering deposition and lift-off procedures. Before Pt (or Ta) deposition, 60 s argon ion milling was used to remove any polymer residues from the YIG surface. The deposition conditions for top Pt and Ta were the same as those for bottom Pt. The top Pt and Ta strips are 2 mm in width, and 70 and 60 mm in length, respectively. To generate a vertical temperature gradient in separate longitudinal Spin Seebeck effect measurements, which we conducted after the nonlocal measurements were finished, we deposited 300-nm-thick Al 2 O 3 on top and then Cr (5 nm)/Au (50 nm), which serves as a heater for SSE measurements.
Transport measurement. For all transport measurements, the current was fed to the devices using a Keithley 2,400 d.c. current source, and the voltage was measured by a Keithley 2182A nano-voltmeter. The field dependence measurements were carried out using a closed-cycle system, while the angular dependent measurements were performed by a physical property measurement system equipped with a rotatory sample holder. For the nonlocal measurements, the excitation current in the bottom Pt is usually no more than 2 mA; for the local magnetoresistance measurements, the current applied in top Pt and Ta was 1 mA, while the current used in bottom Pt is 10 mA. For the SSE measurements, the heating current applied in the top Au layer is 30 mA. In all the measurements, extra precaution was taken to ensure the correct polarity of both current and voltage.