Spin pump and probe in lanthanum strontium manganite/platinum bilayers

Ferromagnetic resonance driven spin pumping (FMR-SP) is a novel method to transfer spin current from the ferromagnetic (FM) layer into the adjacent normal metal (NM) layer in an FM/NM bilayer system. Consequently, the spin current could be probed in NM layer via inverse spin Hall effect (ISHE). In spite of numerous ISHE studies on FM/Pt bilayers, La0.7Sr0.3MnO3(LSMO)/Pt system has been less explored and its relevant information about interface property (characterized by spin mixing conductance) and spin-charge conversion efficiency (characterized by spin Hall angle) is a matter of importance for the possible applications of spintronic devices. In this work, the technique of FMR-SP has been applied on two series of LSMO/Pt bilayers with the thickness of each layer being varied. The thickness dependences of ISHE voltage allow to extract the values of spin mixing conductance and spin Hall angle of LSMO/Pt bilayers, which are (1.8 ± 0.4) × 1019 m−2 and (1.2 ± 0.1) % respectively. In comparison with other FM/Pt systems, LSMO/Pt has comparable spin current density and spin mixing conductance, regardless its distinct electronic structure from other ferromagnetic metals.

icant difference in the value of ↑↓ g r between Py/Pt and Fe 3 O 4 /Pt may be related to the ferrimagnetic nature of Fe 3 O 4 , which requires more experimental evidences to confirm.
Enlighted by our pioneer work on La 0.7 Sr 0.3 MnO 3 (LSMO)/Pt bilayers 25,26 , it is realized that a systematic SP-FMR study should include all essential physical parameters for the investigated materials as well as a comprehensive analysis on FMR data, such that the origin of disagreement among reports could be self-prevailed. In this work we utilize the technique of cavity SP-FMR to investigate the intrinsic spin current properties on two series of LSMO/Pt bilayers with varying the thickness of LSMO and Pt. The interest of this study is two folds. First, from the material aspect of view the hole-doped perovskite LSMO is a material less studied in the subject of ISHE [25][26][27][28][29] but with unique characteristics such as high spin polarization, half-metallic band structure 30 and room temperature colossal magnetoresistance 31 . It is a potential candidate for spin pump because of its low damping constant. Second, from physics point of view, the controlling parameters of spin Hall angle in different FM/NM bilayers have not been well understood yet, thus more investigation is essential for the future applications.

Basic characterizations. SrTiO 3 (STO) single crystal is chosen for the substrate of all LSMO and LSMO/
Pt films. Figure 1 shows the x-ray diffraction patterns for STO/LSMO(20 nm). The blue curve is for STO/LSMO and black one for STO/LSMO(20 nm)/Pt (30 nm). Within the scan range, three sharp peaks corresponding to the (001), (002) and (003) reflections of STO are observed for both samples. The main peaks of LSMO appear next to them and are marked as LSMO(001), LSMO(002) and LSMO(003), indicating that the LSMO layer grows along the STO(001) direction. The two curves are almost identical except that the black curve has an additional peak at 2θ ~ 40°, corresponding to Pt(111). The inset of Fig. 1 displays the AFM (atomic force microscopy) image taken on the surface of STO/LSMO(20 nm). The topological information indicates that the LSMO film is rather smooth with a root-mean-square (rms) roughness around 0.4 nm within the scanning area of 5 × 5 μm 2 .
The FMR spectrum and voltage are recorded simultaneously on the same bilayer samples. Figure 2a shows the derivative FMR spectrum as a function of dc magnetic field (H) for a typical LSMO(20 nm)/Pt(6 nm) bilayer. The corresponding voltage (V) vs. H is plotted in Fig. 2b. The rise of V at resonant field is a direct response of spin pumping. The asymmetric Lorentzian-like curve of the V-spectrum is decomposed into two parts 13 , i.e. the   symmetric FMR-induced ISHE voltage (V ISHE ) and the asymmetric term V AHE from the anomalous Hall effect (AHE), as described by where ΔH and H R are the linewidth and the resonant field respectively. The phase of V AHE originated from the interaction between the microwave electric oscillation and the magnetization of the FM layer has an intrinsic π/2-difference with V ISHE at resonant condition, which is the main cause for the asymmetric part of the voltage spectrum.
The value of V ISHE is shown in Fig. 3a with the variation of excitation microwave power from 20 mW to 100 mW for the entire series of LSMO/Pt(t Pt ) bilayers. A simplified equation is adopted, where j s o is the spin current density, h m the microwave magnetic field and M eff the effective magnetization. Accordingly, j s o should increase linearly with the square of h m , which yields a leaner dependence of V ISHE vs. microwave power. However, for samples with thicker Pt, V ISHE saturates at high power due to the heating effect from high microwave power 27 . To demonstrate this, Fig. 3b plots the temperature dependent field-cooled (FC) and zero-field-cooled (ZFC) magnetization for LSMO(20 nm)/Pt(6 nm), showing the magnetization at 300 K is very sensitive to temperature change. Hence, the microwave heating would substantially decrease the magnetization as well as ISHE voltage. In this work, we focus on the linear microwave power regime (<60 mW) where the theory applies.  Damping constant and effective spin mixing conductance of LSMO/Pt. In the FMR formulation, the total free energy E of a thin magnetic system is considered to be second-order and can be described by the following equation 32 : The coordinate system of the above expression is demonstrated in the inset of Fig. 4 with H, M s , and K ⊥ representing the external magnetic field, the saturation magnetization vector, and the perpendicular uniaxial anisotropy constant, respectively. E includes the contribution of Zeeman energy, demagnetization energy and perpendicular anisotropy energy. The resonance field H R is determined by the following resonance condition [33][34][35][36] The equilibrium state of magnetization is obtained by setting In our FMR measurements, the microwave power is set at 40 mW while the out-of-plane field angle with respect to the film plane θ H is varied from zero to 90 degrees. The angular dependent H R is plotted in Fig. 4a-d for the four bilayers of different LSMO thicknesses (t LSMO ). The red curves in Fig. 4 are the fitting results using Eqs 4 and 5. From the fitting results, the gyromagnetic ratio γ is obtained. The damping constant α is deduced using α = γ∆H/ω, where ∆H is the FMR linewidth and ω is the microwave frequency. Figure 5a shows that α value of bilayer is inversely proportional to t LSMO . The saturation magnetization M s and the effective g-factor (γ = gμ B /ћ) of four LSMO films are plotted in Fig. 5b as function of t LSMO . Both M s and g-factor are independent of t LSMO , with their mean values being 350(3) emu/cm 3 and 1.94(2) respectively. The g-factor is slightly smaller than 2 in consistent with previous report 37 , which may originate from the spin-orbital coupling and the partial quench of orbital moment at interface as the case in Ni-Fe film 38 . Based on spin pumping model 39,40 , the total magnetic relaxation of a bilayer can be described by Gilbert damping s FM r 0 where α is the Gilbert damping constant, α 0 is the intrinsic damping constant ћ is the reduced Plank constant, t FM is the thickness of the FM layer. α 0 in the right side of Eq. 6 comes from the intrinsic FM relaxation and is expected to be equal to the value measured in a single FM layer, whereas the second term is due to the interfacial relaxation. Based on the linear fit in the data of α vs. 1/t LSMO as shown in Fig. 5, ↑↓ g r = (2.2 ± 0.4) × 10 19 m −2 . If one considers the effect of magnetic dead layer at the STO/LSMO interface 41,42 , which is estimated to be 1.7 ± 0.2 nm by fitting the t LSMO dependence of the sheet saturation magnetization M Sh as shown in the inset of Fig. 5a Spin hall angle and spin diffusion length of Pt. Two other important parameters, θ ISHE and λ Pt , are extracted from the Pt-thickness dependent V ISHE in LSMO(20 nm)/Pt(t Pt ). θ ISHE is defined by c ISHE s where j c , j s and σ are the charge current density, the spin current density and the spin polarization vector of the spin current, respectively. j c can be experimentally determined from the charge current (I c ) with an equivalent circuit model 15 : where R FM (ρ FM ), R N (ρ N ), t N and l are the resistance(resistivity) of the FM layer, the resistance(resistivity) of the NM layer, the NM thickness and the bilayer length, respectively. Accordingly, the value of j c depends on the resistivity of LSMO and Pt. The resistivity of LSMO(20 nm) is 1.3 ± 5% mΩcm which is very close to the bulk value of 1.1 ± 5% mΩcm. Whereas for Pt films, 36.6 ± 5% μΩ-cm is the average value which is three times of the bulk value (10.8 μΩcm) 43 . The high resistivity is likely related to the polycrystalline nature of Pt films. It is worthy to note that the ρ Pt is roughly a constant value of 32.5 ± 5% μΩ-cm but start increasing in the film thinner than 11 nm. ρ Pt is 37.8 ± 5% μΩcm for Pt(8 nm), 43.9 ± 5% μΩcm for Pt(6 nm) and 44.6 ± 5% μΩcm for Pt(4 nm), implying a high surface roughness for ultra-thin films.
On the other hand, the value of j s depends on modeling. According to spin pumping model the spin current density at interface j s o (z = 0) could be explicively calculated using FMR technique. It is determined by the dynamics of magnetization and ↑↓ g r with an expression: The data of t Pt dependent j s o are plotted in Fig. 6 for the series of LSMO/Pt(t Pt ) bilayers, indicating that j s o is insensitive to the Pt thickness, in consistent with the assumption of spin accumulation model 39 . The estimated spin current density of LSMO/Pt is 0.75 ± 0.05 nJ/m 2 at 40 mW, comparable to that of Py/Pt (~3.0 nJ/m 2 at 200 mW) 14 , indicating that LSMO is a potential candidate for high efficiency spin pumping.
However, the spin current density could decay along the perpendicular z direction of interface and can be written as 14 SCientifiC RepORtS | 7: 6612 | DOI:10.1038/s41598-017-06861-1 Eq. 10 represents a simple model that the accumulated spins at the interface diffuse into NM layer and it includes a part of spin current diffusing back into the FM layer. In order to extract the spin diffusion length of Pt (λ Pt ), the obtained <J c > (by dividing V ISHE with the total resistance and the width of sample) is fitted using Eq. 10 under the condition of zero-off setting at y axis. The results of fitting are shown in Fig. 7 with the solid line being the fitting result. The fitting is reasonably good except for the thickness thinner than 11 nm. The deviation between data and fitting for thin Pt layer may be due to the interface roughness between Pt and LSMO.

Discussion
One important issue relating to the validation of ISHE voltage is whether the spin rectification effect (SRE) originating from the anisotropic magnetoresistance (AMR that contains both symmetric and asymmetric components) contribute to the obtained ISHE voltage or not. In our voltage measurements, the contribution of SRE effect could be neglected since the applied magnetic field direction is fixed in-plane, along the short side of the bilayer. Although AMR can be effectively reduced by the experimental setup, the elliptical trajectory of the precession magnetization during the resonance process still leads to AMR contribution, which can be quantitatively characterized as the anisotropic magnetoresistance (R A ) 17 . We have obtained R A = −(0.2 ± 0.1) % for 20-nm LSMO, which is in consistent with the finding for epitaxial La 0.7 Ca 0.3 MnO 3 film on STO 44 but one order of  The plot of 〈j c 〉t Pt as a function of Pt thickness. The red curve is the result of a fit with Eq. 10, with an assumption that the spin diffusion length remains constant despite the enhanced resistivity of Pt with a thickness smaller than 11 nm. The fitting yields a spin diffusion length of Pt to be 5.9 ± 0.5 nm.
magnitude smaller than that of Py (R A~2 %) and with an opposite sign 32 . Thus, the AMR effect is neglected in our analysis on ISHE of LSMO. Table 1 24,[45][46][47][48][49][50][51] lists the values of polarization, resistivity and mixing conductance for various materials including LSMO. It shows that the value of g ↑↓ for LSMO/Pt system agrees with those of most FM/Pt bilayer except that for FM = Fe 3 O 4 , indicating the high values of polarization and resistivity (low conductivity) of LSMO does not affect the value of g ↑↓ significantly. The values of λ, θ ISHE and g ↑↓ from different groups are listed in Table 2, showing a significant deviation from various groups which may come from different measurement methods or/and interface properties. As we have clearly demonstrated that the values of λ Pt and θ ISHE are correlated since they are from the same fitting curve, it is more reasonable to examine these two values simultaneously. In a SP-FMR study on Co/Pt and Co/Cu/Pt 51 , a universal relation of λ Pt and θ ISHE for Pt was found as λ Pt × θ ISHE = 0.19 nm. However, a much smaller of λ Pt × θ ISHE (0.07 ± 0.01 nm) is obtained from this work based on the values given in Table 2 with λ Pt = 5.9 ± 0.5 nm. Due to the fact that the interface of LSMO/Pt could be less transparent than other metal/metal interfaces, it is likely that the interfacial spin-memory lost could be the reason 51 .
As stated in the above section III, the value of spin current density of LSMO/Pt (0.75 ± 0.05 nJ/m 2 ) at 40 mW) is comparable to that of Py/Pt (~3.0 nJ/m 2 at 200 mW) 14 which make LSMO a potential material for spin generation. However, this comparison is based on the normalization of j s 0 to microwave power. To be more precise, the effective spin current should be normalized to microwave magnetic field h m instead of power since the conversion coefficient of h m 2 to P depend on the type of cavity. In our TE 102 microwave cavity (Bruker EMX-ER4102ST), the equation is P = 1.4 × h m 2 which converts the power of 40 mW to the h m value of 0.28 Gauss. For typical TE 110 as being used in ref. 16, P = 1.5 × h m 2 and thus the h m value corresponding to 200 mW is around 0.67 Gauss. However, many ISHE studies did not provide the h m value such that a precise comparison is not possible.
In conclusion, the spin pump-and-probe experiments are carried out on two series of LSMO/Pt bilayers with the thickness of LSMO and Pt varied. The experimental results are systematical analyzed by the spin pumping model with the consideration of total magnetization relaxation. Three findings from this work are summarized: 1) the comparable mixing conductance of LSMO/Pt with Py/Pt implies that the spin-charge conversion by FMR-SP method is independent of conductivity of FM layer; 2) the fitting result of charge current density vs. Pt thickness in LSMO/Pt yields a spin Hall angle of (1.2 ± 0.1) % which is comparable to that in Py/Pt; and 3) the considerable large spin current density generated in LSMO/Pt reveals that the half-metallic LSMO has potential to serve as a spin pumping source.

Materials and Methods
One series of single layered LSMO (t LSMO = 12, 16, 20 and 26 nm) and two series of bilayers structured as LSMO(20 nm)/Pt(t Pt = 4, 6, 8, 11, 17, 21 and 30 nm) and LSMO(t LSMO = 12, 16, 20 and 26 nm)/Pt(11 nm) were prepared with a pulsed laser deposition system with a KrF (λ = 248 nm) excimer laser of 160 mJ, at a repetition rate of 1 Hz. The bottom LSMO layer was grown on SrTiO 3 [STO(001)] substrate, which has an in-plane lattice constant of 3.900 Å. The lattice mismatch between STO and LSMO (3.876 Å) is 0.6%, allowing the epitaxial growth of LSMO film at proper deposition conditions. During deposition, the substrate was held at 800 °C in an oxygen environment of 100 mtorr, and subsequently annealed at 400 °C under 760 torr oxygen pressure for 1 hour. The Pt layer was deposited ex situ onto STO/LSMO in a commercial sputtering coater (Quorum Technologies Q150TS) having a base pressure of low 10 −5 torr. The deposition was kept at room temperature with an Ar working pressure of 3.8 × 10 −3 torr with a deposition rate of 0.22 nm/s, and the lattice constant of Pt layer is 3.924 Å, which is 1.2% larger than LSMO. The crystalline structure of bilayers was confirmed with x-ray diffraction (XRD) on a Bruker-D8 diffractometer using Cu K α radiation; whereas the surface morphology was characterized using a Park XEI-100 atomic force microscope (AFM). The saturation magnetization was measured by vibrating sample magnetometer (VSM), and the four-probe method is applied to measure the anisotropic magnetoresistance (AMR) using a Keithley 2182 A nano-voltmeter and a Keithley 2400 source meter.
The bilayer samples were cut into the rectangular shapes of 1.0 × 2.0 mm 2 to fit in the microwave cavity. To perform ISHE voltage measurements, platinum wires were attached on the Pt-layer surface at the both ends of long side using conducting silver paste. The sample was loaded and positioned at the center of a TE 102 microwave cavity where the strength of the microwave electric field is a minimum and the magnetic field a maximum. The microwave was provided by an X-band Bruker EMX (f = 9.8 GHz) system. The DC magnetic field was applied in-plane from 1300 to 2500 Oe, along the short side of sample. ISHE voltage was measured at different microwave power using a Keithley 2182 A nano-voltmeter with respect to sweeping field. All FMR and ISHE measurements were conducted at room temperature.