Role of crystalline and damping anisotropy to the angular dependences of spin rectification effect in single crystal CoFe film

The angular dependence of the microwave-driven spin rectification (SR) effect in single crystalline Co0.5Fe0.5 alloy film is systematically investigated. Due to the strong current-orientation dependent anisotropic magnetoresistance (AMR), the SR effects in CoFe film strongly deviate from the ordinary sin 2φM cos φM relation with φM defined as the magnetization angle away from the current. A giant Gilbert damping anisotropy in the CoFe film with a maximum–minimum ratio of 520% is observed, which can impose a strong anisotropy onto magnetic susceptibility. The observed unusual angular dependence can be well explained by the theory including current-orientation dependent AMR and anisotropic magnetic susceptibility. Our work also suggests that the strong current-orientation dependent AMR in single crystalline CoFe film could exist up to the gigahertz frequency range.

In the devices consisting of ferromagnetic metal/heavy metal bilayer, the SR signals can also arise from the spin-pumping-driven and/or Oersted-field-driven magnetization dynamics [1,[17][18][19][20][21][22], and it was assumed that the contributions from the spin pumping effect and the Oersted field effect can be separated by the angular dependent measurements of the microwave-induced dc voltage. A comprehensive understanding on the angular dependence of SR is essential to study the spin pumping effect and quantify the spin Hall angle [23][24][25]. The angular dependence of SR is determined by AMR and the microwave field. AMR is usually assumed as ΔR ∝ cos2ϕ M with ϕ M as the angle between the magnetization and current. However, such cos2ϕ M dependence of AMR may not be appropriate for crystalline films due to the additional influence from the crystalline symmetry [26]. In single crystalline samples, AMR can exhibit additional four-fold symmetry [27][28][29], asymmetric behavior [30,31], and strong dependence on the current orientation [29,[31][32][33][34]. Such unusual AMR symmetries can be used to engineer the SR signals for new features in detecting magnetization dynamics.
In this paper, we have investigated the angular dependence of the SR effect in the single crystalline Co 0.5 Fe 0.5 (001) alloy film. The CoFe alloy is an important material for industry due to its large magnetization [35] and very low damping with large crystalline anisotropy [34,36,37]. We find that the angular dependence of the SR voltage in CoFe film strongly differs from those reported in the polycrystalline films, and can be well explained by the SR theory under consideration of the unusual angular dependent magnetoresistance (ADMR) in the CoFe film. The strong anisotropy ratio of the damping constant up to 520% is determined, which can induce the strong anisotropy of the resonant susceptibility driven by the microwave field.

Experiment
Single-crystal CoFe films were grown on MgO(001) substrates at room temperature by molecular beam epitaxy in an ultrahigh vacuum chamber with a base pressure of 2 × 10 −10 Torr [28,29,31]. The MgO(001) single-crystal substrate was first annealed at 650 • C for half an hour. Then a 10-nm-thick MgO seed layer was grown on the substrate at 500 • C. The high-quality surface was confirmed by in-situ reflective high energy electron diffraction. The CoFe alloy films were deposited via co-evaporation using Fe and Co sources at room temperature. The composition ratio was determined by the growth rate measured by a calibrated quartz thickness monitor.
We first prepared a 20 nm CoFe film for the current-orientation dependent ADMR measurement, which is covered by a 6 nm MgO layer for protection. The CoFe film was patterned into many standard Hall bars with different crystalline orientations by standard photolithography and Ar + ion milling, as shown in figure 1(a). All the Hall bars have the identical width of 100 μm and length of 300 μm.
The SR measurements were conducted on a Pt(3 nm)/MgO(6 nm)/CoFe (10 nm) trilayer at room temperature, as shown in figure 2(a). To conduct the dynamic measurements in the devices with different crystalline directions, the sample was fabricated into a dozen of 100 μm × 10 μm bars. All the bars orient along a series of crystalline orientations with the increment of 15 • . For electrical measurements, Au(150 nm)/Cr(30 nm) contacts were prepared by magnetron sputtering. As shown in figure 2(a), the microwave current I ac flowing through the top Pt layer can generate the in-plane Oersted field h y in the CoFe layer, thus exiting the magnetization dynamics in CoFe film. A dc voltage V dc can be detected due to the rectification of I ac with the magnetoresistance variation caused by the magnetization precession [1,2]. The 6 nm MgO insulating layer should be thick enough to suppress the spin pumping effect between CoFe and Pt [38,39]. Thus, the magnetization dynamics should be dominantly induced by the microwave field h y .

Results and discussion
We first performed the ADMR measurement on the single crystalline CoFe film with different current orientations at room temperature. Figure 1(a) shows the typical device geometry, which contains many Hall bars with the current along different crystalline directions (θ). The ADMR measurement was conducted by rotating the in-plane field direction (ϕ H ) with respect to the bar. The applied rotating field is 2500 Oe, which is much larger than the magnetic anisotropy field, i.e. less than 300 Oe for the samples. , which indicates the strong current-orientation dependence. The ADMR curves in figure 1 significantly deviate from the traditional AMR in the polycrystalline system, but can be well explained by the phenomenological model [26,27,[29][30][31][32][33].   , which can be well fitted by a modified Kittel formula [40,41] ω γ , so our study provides a further experimental evidence of the giant anisotropic damping by the SR technique in single crystalline CoFe film. The measured anisotropy ratio of the damping constant is 520%, which echoes with our previously reported large value of 440% in reference [34]. Note that the electronic detection of anisotropic damping was performed on the Pt/CoFe bilayer in reference [34], and the experimental results on the Pt/MgO/CoFe trilayer may better reflect the intrinsic damping property of the CoFe layer. Next, we studied the angular dependence of SR voltage in the devices with different current orientations. Although the SR voltage with the field along ϕ M = 45 • direction from a Pt/CoFe bilayer has been reported in reference [34], the role of crystalline and damping anisotropy to the angular dependences of SR effect was still missing. For the in-plane excitation field h y , the ϕ M -dependence of SR voltage can be expressed as [1,42,43] Here, I ac is the microwave current, A xx is the amplitude of antisymmetric term in magnetic susceptibility, which depends on the magnetic anisotropy and magnetic damping of the sample, cosϕ M describes the projection of transverse magnetization motion onto the current direction as to modulate the magnetoresistance, and dR/dϕ M is the partial derivative of ADMR. By considering the magnetic anisotropies, the R (ϕ M ) relation can be calculated from the experimental R (ϕ H ) curve [31,33], thus the dR/dϕ M curve can be experimentally determined. In the polycrystal systems, the ADMR is expressed as R (ϕ M ) = R 0 +ΔR cos2ϕ M , so the angular dependence of V a follows the sin2ϕ M cosϕ M function. However, figure 1 shows that the ADMR curves in single crystalline systems could obviously deviate from the cos2ϕ M function, thus the SR signal could have the angular dependence different from the simple sin2ϕ M cosϕ M relation. shows that the AMR is a combination of the two-fold and four-fold terms, so dR/dϕ M has a sign reversal for ϕ H between 0 • and 90 • , resulting in the sign reversal of the SR signal at ϕ H ∼ 50 • in figure 3(b). Figure 3(d) summarizes the angular dependence of V a from this device, which obviously deviates from the sin2ϕ M cosϕ M relation. Note that V a in figure 3(d) is one order smaller than that in figure 3(c). Figure 3(e) shows the angular dependence of SR voltage for the device with θ = 15 • , which does not contain the conventional symmetric behavior at ϕ H = 180 • due to the non-symmetric behavior of ADMR shown in figure 1(d). So, our results demonstrate that the SR effect in the single crystalline system can have very different angular dependence than that in the polycrystalline system.
In order to quantitatively compare the angular dependence of SR signal with AMR, we measured the ADMR in each device shown in figure 2(a). The measured ADMR with different current orientation is very similar to the data in figure 1, but the AMR ratio is slightly smaller due to the contact resistance from the two-terminal measurements and the shunting effect from the thin Pt layer. The AMR ratio in figure 4(a) strongly depends on the current orientation, with a 12 times difference for the current along the 110 and 100 directions.
With the measured ADMR curve for each device, we can numerically calculate the angular dependence of V a using equation (2). Usually, it is difficult to experimentally determine I ac and h y , which can be normalized by calculating the effective SR resistance R SR = 2V a M s /(I ac h y ) = A xx cosϕ M dR/dϕ M . It should be noted that both A xx and dR/dϕ M could strongly depend on ϕ M . A xx can be determined by [40,44,45] Here, H and H are defined in equation (1). Anisotropic A xx could be induced by magnetic anisotropy and the anisotropy of α. As shown in figure 2, α with the magnetization along 100 and 110 shows more than 500% difference. In this study, the detailed relation between α and the magnetization angle φ M relative to the [110] crystal direction was not determined. However, the α(φ M ) relation of CoFe film has been measured in reference [34], which is replotted as the circles in figure 4(c). So, in order to understand how the anisotropic α influences A xx , we used the α(φ M ) relation represented by the black line in figure 4(c), which also contains a four-fold symmetry from the CoFe(001) plane. Figure 4(d) shows the calculated A xx as a function of φ M , which contains a strong anisotropy ratio of ∼5. The minimum locates at 45 • and 135 • due to the maxim α for the magnetization along the 100 directions. We also calculated the A xx (φ M ) relation with a constant α, and found that A xx only varies ∼0.11%. So, the strong anisotropy of A xx (φ M ) in figure 4(d) is mainly attributed to the giant anisotropic α in the CoFe film.
From the experimental ADMR curves, we can determine the angular dependence of dR/dϕ M , then the ϕ M -dependent R SR can be further calculated. Figures 3(c)-(e) show that the calculated R SR well reproduces the angular dependence of V a , which proves that the SR effect can be correctly described by equation (2). Therefore, in the single crystalline system, it may not be proper to only use the sin2ϕ M cosϕ M relation to separate the contribution from the ordinary SR effect and the spin pumping effect. On the other hand, we notice that both V a and R SR in figures 3(c)-(e) are zero at ϕ M = 90 • and 270 • , so the spin pumping signal can still be separated from the SR effect if aligning the magnetization perpendicular to the microwave current direction [1,24,25].
We also quantify the maxim values from the measured V a (ϕ M ) curves and the calculated R SR (ϕ M ) curves, and both V max a and R max SR in figure 4(b) strongly depend on the device orientation with an in-plane four-fold symmetry, in good agreement with the orientation-dependent AMR ratio in figure 4(a). The amplitude of the measured SR signal could have 13 times difference for the devices along the 110 and 100 directions, so our dynamic measurements confirm the giant current-orientation effect of the AMR up to the gigahertz frequency range.

Conclusions
In conclusion, we have demonstrated very large current-orientation dependent SR signal anisotropy, up to 13 times, due to a combination of crystalline AMR anisotropy up to 12 times and giant Gilbert damping anisotropy up to 520% in single crystalline CoFe film, with both anisotropies absent in ordinary polycrystalline magnetic films. The SR theory can well explain the unusual angular dependence of SR signals by considering both the unconventional ADMR and the anisotropic susceptibility in single crystalline CoFe film. Our measurements show that introducing crystalline symmetry into the magnetic system can significantly modify the microwave detection efficiency at different orientations using SR signals, which provides a new approach to engineer the microwave characteristics in microwave spintronics.