Spin pumping in magnetic trilayer structures with an MgO barrier

We present a study of the interaction mechanisms in magnetic trilayer structures with an MgO barrier grown by molecular beam epitaxy. The interlayer exchange coupling, Aex, is determined using SQUID magnetometry and ferromagnetic resonance (FMR), displaying an unexpected oscillatory behaviour as the thickness, tMgO, is increased from 1 to 4 nm. Transmission electron microscopy confirms the continuity and quality of the tunnelling barrier, eliminating the prospect of exchange arising from direct contact between the two ferromagnetic layers. The Gilbert damping is found to be almost independent of the MgO thickness, suggesting the suppression of spin pumping. The element-specific technique of x-ray detected FMR reveals a small dynamic exchange interaction, acting in concert with the static interaction to induce coupled precession across the multilayer stack. These results highlight the potential of spin pumping and spin transfer torque for device applications in magnetic tunnel junctions relying on commonly used MgO barriers.


Ferromagnetic Resonance
In the classical limit the spin dynamics of a ferromagnet are governed by the damped Landau-Lifshitz-Gilbert (LLG) equation of motion, describing the precession of the magnetisation about an effective field arising from internal and external fields: with γ the gyromagnetic ratio, m is the unit magnetisation vector of the material, α the dimensionless Gilbert damping parameter, and H eff the effective magnetic field. Through H eff the various energy terms, such as the exchange energy, the demagnetisation energy, the in-plane cubic and uniaxial anisotropies, the static exchange, and the Zeeman energy enter the equation. The static interlayer exchange coupling is a general term for any interaction that acts to (anti-)align the magnetisations of the two layers in a magnetic trilayer structure such as a spin valve or an MTJ. Examples of such interactions include Ruderman-Kittel-Kasuya-Yosida (RKKY), superexchange, Néel or orange peel coupling, and direct exchange through a discontinuous spacer layer. The presence of a static interaction modifies the LLG equation with an additional term 17 : where β is the interlayer exchange, and i, j index magnetic layers. The interlayer exchange is defined as 18,19 : with A ex the interlayer exchange constant, t the thickness of the magnetic layer, φ M the equilibrium orientation of the magnetization, and i, j indices label the magnetic layers. The sign of A ex indicates whether the interaction favours parallel (positive) or antiparallel (negative) alignment.
In FMR experiments, additional interaction mechanisms must be considered. As the magnetisation of a ferromagnetic layer precesses on resonance it acts as a spin battery, generating a pure spin current transverse to the axis about which it precesses. When the FM layer is thicker than the ferromagnetic coherence length, a pure spin current can be driven into an adjacent NM layer. A spin current can persist across the spacer layer, and in a trilayer structure either return to the first FM/NM interface, or else flow through to a second NM/FM interface. If it is not reflected here, it crosses the interface and is absorbed by the FM, inducing precession through the STT 4 .
The increased flow of spin momentum out of the FM layer acts as an additional channel for energy loss, leading to an increase in damping. This damping is linear with resonant frequency, and can thus be described in the same terms as Gilbert damping. The absorbed spin current leads to a comparable anti-damping term in the off-resonance layer.
With the addition of these two coupling mechanisms, the LLG for a trilayer system becomes: where superscripts denote magnetic layers, and H i eff is the effective field acting on layer i. The intrinsic Gilbert damping is α i 0 , while α mn i are spin source (m = n) and spin sink (m ≠ n) terms. The XFMR results can be modelled using this a linearised solution of this equation.
The presence of these coupling mechanisms alters the magnetodynamics of the on-and off-resonance layer. The static coupling shifts the resonant field of both layers, as it functions as an additional field term in the Kittel equation. Spin pumping, on the other hand, broadens the resonances by providing an additional energy loss mechanism. However, the most important change is the precession induced in the off-resonance layer, wherein the exchange interactions transfer energy between the two layers. This leads to changes in both the phase and amplitude of precession, with the phase being the more sensitive probe.

Results
Structural properties of the magnetic trilayer structures. The structural properties of the grown magnetic heterostructures were studied using transmission electron microscopy (TEM).   Fig. 2a) the two layers are strongly bound, and there is a single switching step, with a coercive field of 2 mT. As the thickness of the barrier increases, the layers decouple and behave independently. For t MgO = 2 and 3 nm (Fig. 2b,c), the coupling between the two layers appears to cause winding, leading to a smeared out transition as opposed to sharp steps. Nevertheless, two distinct steps in the hysteresis loop can be identified.
As the TEM measurements show that the MgO barrier appears to be continuous, the observed coupling cannot be due to direct, large-area contact between the two ferromagnetic layers, but it is more likely to be resulting from tunnelling across the barrier. However, there is some evidence of surface roughness of the MgO, which could lead to a Néel orange-peel coupling.
Lab-based FMR measurements. VNA-FMR measurements were performed to determine values for the interlayer exchange coupling and magnetocrystalline anisotropy parameters for all samples. Figure 1a shows a Scientific RepoRts | 6:35582 | DOI: 10.1038/srep35582 representative field-frequency map for the sample with t MgO = 1 nm. Fits to resonance fields were performed as a function of RF frequency and magnetization alignment using the Kittel equation 20 , including the interlayer exchange field 17,18 , using Eq. (3).
The extracted interlayer coupling is shown in Fig. 3b, while values for all the fitting parameters are given in Table 1. The complete suppression of the interaction at t MgO = 2 nm is surprising, as it suggests an oscillatory coupling strength, a phenomenon more often associated with coupling across NM conductive layers (see, e.g., ref. 21). This finding is in contrast to previous work on MgO, e.g., ref. 18. Note that in spin-dependent tunnelling such an oscillatory thickness-dependence has been observed for MgO barriers in Fe/MgO/Fe tunnelling structures 22 .
The total Gilbert damping was extracted from the frequency dependence of the linewidth, Δ H, using 23 While a drop in damping with increasing interlayer thickness is usually indicative of spin pumping, the trend here does not match the exponential decay observed in previous studies 7,11,24 . Measurements on comparable bare CoFe layers yielded a Gilbert damping of ~3 × 10 −3 . This suggests that at least some of the spins pumped by the precessing magnetization of the CoFe are absorbed. The lower damping in the case of the thinnest MgO layer could be in part due to the strong static exchange coupling observed.
Synchrotron-based FMR measurements. XFMR measurements were performed to study off-resonance precession induced by static exchange coupling and the STT exerted by pumped spins. Figure 4 shows the amplitude and phase of precession at 4 GHz for each layer in the sample with t MgO = 1 nm, with the magnetic field applied along the easy axis of the CoFe. The resonance in the Ni layer is easily identified, with a peak in amplitude at 28 mT. Off-resonance precession is induced in the CoFe layer; the resulting dynamic XMCD signal is approximately ten times smaller than that of the Ni. There is also a small phase feature in the Co, which is predominantly unipolar in character. Taken together with the bipolar shape of the Co amplitude variation, this indicates that the static interaction is primarily responsible for induced precession in the CoFe.
Solid lines in Fig. 4 are fits to the data using a macrospin solution of the coupled LLG equation, as outlined in, e.g., refs 9 and 24. The values of static exchange coupling and magnetocrystalline anisotropy determined in Table 1 were used to calculate the amplitude and phase of precession for each layer. In order to reproduce the slightly distorted features in the Co, a dynamic interaction had to be introduced, accounting for 50% of the total Gilbert damping in the Ni layer, and assuming perfect transmission of spins. This modifies the shape of the Co features, mixing the characteristics of the two interactions. With this included the model reproduces the experimental data, although it underestimates the linewidth of the Ni mode due to the presence of inhomogeneous broadening arising from non-Gilbert damping in the samples. The measurement of a component of dynamic interaction shows that a suitably thin MgO barrier will permit a spin current to flow, while for thicker barriers the pumped spin current is entirely scattered within the MgO.

Discussion
We have presented a study of the coupled magnetodynamics of magnetic heterostructures, demonstrating that both static and dynamic coupling can exist across a suitably thin MgO barrier. SQUID-VSM and VNA-FMR showed the presence of a static interaction acting to align the two layers, with an apparent oscillatory coupling  strength -a surprising result that will stimulate further investigation of such structures. Moreover, it was observed that the pure spin current generated by ferromagnetic resonance is absorbed by the MgO, increasing Gilbert damping in the ferromagnetic layers. Layer-resolved XFMR measurements showed that the resulting dynamic interaction can persist across a 1-nm-thick barrier and induce off-resonance precession through spin transfer torque. These results demonstrate how the coupling between magnetic layers can be manipulated through the choice of barrier material and thickness, and illustrate the differing regimes of static and dynamic coupling   that can be thus attained. The two interactions can cooperatively transfer energy between layers during ferromagnetic resonance. The pure spin current can persist for a short distance across an insulating barrier, and exert a spin-transfer torque on a neighbouring layer, an important finding for the diverse and active field of STT-MRAM.

Methods
Thin film growth. The magnetic multilayer samples were prepared by MBE on epi-ready MgO(001) substrates. Reflection high-energy electron diffraction (RHEED) measurements were performed throughout the growth to monitor crystal quality (cf. Fig. 1a). The full structure is MgO/Co 50 Fe 50 (15)/MgO(t MgO )/Ni(8)/Ag(4) (nominal thicknesses in nm), with t MgO = 1, 2, 3, and 4 nm (equivalent to ~4. 7, 9.5, 14.2, and 19.0 monolayers). The substrates were annealed at 700 °C to improve surface quality, then cooled to 500 °C for the deposition of stoichiometric Co 50 Fe 50 . The samples were further cooled to room temperature for deposition of MgO onto the epitaxial Co 50 Fe 50 (hereafter referred to as CoFe, for brevity). The MgO barriers were annealed at 300 °C for 20 minutes leading to a sharpening of the RHEED streaks, as shown in Fig. 1a, indicative of good crystalline quality, before being again cooled to room temperature for the deposition of Ni and finally the Ag capping layer.
Electron microscopy. Structural properties of the grown magnetic heterostructures were studied using a JEOL 2200FS double aberration-corrected (scanning) transmission electron microscope (S)TEM. Cross-sectional TEM specimen were prepared using conventional methods that include mechanical thinning and polishing followed by Ar ion milling in order to achieve electron transparency 25 . Magnetometry. Magnetometry was carried out using a SQUID vibrating sample magnetometer (VSM).
FMR measurements were performed using a VNA and octupole electromagnet. Real and imaginary components of the microwave transmission parameter, S 12 , were measured as a function of magnetic field (strength and angle), and RF frequency. Plotting the resonant field as a function of frequency and bias field angle yields anisotropy and exchange coupling parameters using the Kittel equation 20 including static exchange coupling 17,24 . See the Supplementary Information for a discussion of the Kittel equation.
X-ray detected Ferromagnetic resonance. Indirect measurements of spin transfer using VNA-FMR are unable to provide a conclusive determination of the presence of spin pumping within the heterostructures. XFMR measurements address this limitation, studying the coupled magnetodynamics with a layer-resolved probe, which reveals more information about the nature of the coupling mechanisms. Further, XFMR can determine whether a pumped pure spin current is absorbed by the MgO barrier, or whether some component crosses it, to be absorbed by the spin sink layer. The XFMR measurements were performed on beamline I10 at the Diamond Light Source (UK) and beamline 4.0.2 at the Advanced Light Source (USA). The magnetic samples are excited by microwave radiation, phase-locked to the synchrotron master oscillator, resulting in a steady precession about the effective field close to the FMR condition. The oscillating magnetization component along the incident x-ray beam direction is probed using x-ray magnetic circular dichroism (XMCD). Element, and consequently layer specificity, is obtained by tuning the x-ray energy to the Ni and Co L 3 edges. For full details of the XFMR methodology, we refer to ref. 26.