Effect of nanostructure layout on spin pumping phenomena in antiferromagnet/ nonmagnetic metal/ ferromagnet multilayered stacks

In this work we focus on magnetic relaxation in Mn$_{80}$Ir$_{20}$(12 nm)/ Cu(6 nm)/ Py($d_\mathrm{F}$) antiferromagnet/Cu/ferromagnet (AFM/Cu/FM) multilayers with different thickness of the ferromagnetic permalloy layer. An effective FM-AFM interaction mediated via the conduction electrons in the nonmagnetic Cu spacer -- the spin-pumping effect -- is detected as an increase in the linewidth of the ferromagnetic resonance (FMR) spectra and a shift of the resonant magnetic field. We further find experimentally that the spin-pumping-induced contribution to the linewidth is inversely proportional to the thickness of the Py layer. We show that this thickness dependence likely originates from the dissipative dynamics of the free and localized spins in the AFM layer. The results obtained could be used for tailoring the dissipative properties of spintronic devices incorporating antiferromagnetic layers.

Antiferromagnets (AFMs) are attractive materials for spintronic applications. They operate at high frequencies and thus have the potential to functionally fill the "terahertz gap" in electronics. Due to their lack of a macroscopic magnetic moment, AFMs produce no stray fields and therefore potentially can provide higher scalability for magnetic memory devices.
High typical values of the spin-flop fields prevent AFMs from spontaneous thermally-induced switching and increase the data retention times. In addition, recent experimental 1 and theoretical investigations 2 have shown that AFMs are sensitive to spin-polarized currents and can be used as active elements in spintronic devices.
Direct observation of spintronic effects in AFMs is challenging due precisely to the same reasons that make AFMs competitive with their ferromagnetic counterparts: the magnetoresistance in AFM-based devices is low due to the absence of net magnetization in AFM, and the dynamics require very high excitation frequencies, beyond the capabilities of microwave circuits. An alternative technique to detect the spin dynamics of AFM films was recently implemented by a number of groups. [3][4][5][6][7] This technique is based on the spin pumping effect, which is reciprocal to the spin-transfer torque effect. 8,9 A metallic ferromagnetic layer (FM) is excited at its resonance frequency (FMR) and pumps spin current into a neighbouring nonmagnetic layer interfaced with an antiferromagnetic film (AFM) at the other surface. The linewidth of the FMR spectrum increases due to the presence of the AFM layer and thereby provides information about the interaction of the nonequilibrium conduction-electron spins and the localized AFM moments.
The interpretation of such experiments is not quite straightforward, however, as different processes contribute to the effective damping in a multilayered sample: spin-dependent scattering at the interfaces 10 and in the bulk, energy exchange between the free and localised spins, spin-diffusion, etc. An efficient theoretical approach to this problem, based on nonequilibrium thermodynamics, was proposed in Ref. 11 for ferromagnetic (FM)/nonmagnetic (NM) bilayers, and was further generalized for FM/NM/FM systems. 12 Spin-pumping from an AFM layer was recently predicted in Refs. 13 and 14.
In this paper we focus on the dissipative response, expressed via the FMR linewidth, of MnIr/Cu/Py multilayers with different thickness of the Py layer. We generalize the Onsager formalism for the case of the discrete system AFM/NM/FM and calculate the effective Gilbert damping of the FM layer, taking into account the spin-pumping and spinaccumulation effects in both the FM and AFM layers. While the previous experiments 3,4 have studied the damping dependence vs thickness of the AFM layer, we focus on the properties of the FM layer and especially the FM/NM interface. Our experiments reveal an inverse dependence of the additional, AFM-induced damping on the thickness of the FM layer, in agreement with our theoretical predictions. Our results should be useful for tailoring dissipation in spintronic devices. The top Al layer is a protective capping layer. The bottom layers facilitate the formation of the optimal crystalline and magnetic structure of Mn 80 Ir 20 (12). We also fabricated a set of reference samples with identical structure but without Py(3)/Mn 80 Ir 20 (12) layers.
The multilayers were deposited at room temperature (295 K) on thermally oxidized silicon substrates using magnetron sputtering in an AJA Orion 8-target system. 15 The base pressure in the deposition chamber was 5 ×10 8 Torr and the Ar pressure used during deposition was 3 mTorr. The exchange pinning between Py(3) and Mn 80 Ir 20 (12) layers was set in during the deposition of the multilayers using an in-plane magnetic field of 1 kOe.
We use an X-band ELEXSYS E500 spectrometer equipped with an automatic goniometer to measure the out-of-plane and in-plane angular dependencies of the FMR spectra. The operating frequency is 9.85 GHz, the temperature is 295 K. The spectra show no signal from the Py(3) buffer layer, while the signal from Py(d F ) is clearly visible. We record the magnetic-field derivative of the microwave absorption and fit each spectrum by a Lorentzian function to obtain the resonance field H r and the linewidth ∆ in the in-plane and the out-of plane geometries [ Fig. 1(b)]. Typical FMR spectra measured for the in-plane orientation are shown in the inset to Fig. 2

(a).
When FMR is excited, a moving magnetization in the FM pumps a spin current into the NM and AFM layers. 16 The spin current is proportional to the effective field H F , which determines the magnetic dynamics in the FM layer. The spin current can induce exchange of angular momentum between the different subsystems of the conduction and localized electrons in the NM and AFM layers. Moreover, it can stimulate additional spin pumping from the AFM layer induced by the dynamic magnetization M AF , which follows the motion of the localized AFM moments. 13,17,18 In addition, free conduction-electron spins in our metallic AFM can interact with the dynamic magnetization M AF and also accumulate, similar to that in the NM layer. While the spin polarization in FM is so strong that spin accumulation in it can be neglected, in the metallic AFM spin accumulation and spin polarization by the localized moments are comparable. Therefore, the transport of spins through the AFM/NM/FM system and the corresponding dissipative phenomena within the trilayer depend upon the balance between the free and localized spins within all three layers of the structure.
Treating the AFM/NM/FM as a discrete system, one can distinguish between five subsystems, shown schematically in Fig. 1 In the framework of linear nonequilibrium thermodynamics, spin densities s F , s N , s AF , and magnetizations m F , m AF can be treated as thermodynamic variables a j , j = 1 . . . 5.
The conjugated thermodynamic forces are calculated as the derivatives of free energy: 19 X j = ∂F/∂a j (we assume that the temperature is constant). The thermodynamic forces for the free spins coincide with the spin accumulation potentials µ Thermodynamic currents J j ≡ȧ j are related to the thermodynamic forces via the Onsager coefficientsL: where e is electron charge.
Using the Onsager reciprocity principle and the symmetry considerations, one can reduce relations (1) to the following form: where γ is the gyromagnetic ratio and is the Plank constant. We neglect spin accumulations in the NM layer, since the spin-diffusion length in the NM layer is relatively long. We also set µ  Fig. 1(a). Diagonal coefficients L jj for the localized spins are related with the internal damping in the FM (damping parameter α F ) and AFM (damping parameter α AF ) layers. Diagonal coefficients L jj for the free spins are proportional to the corresponding conductances, G F 0 and G AF 0 . The nondiagonal coefficients responsible for the cross-coupling effects between the AFM and FM layers, are of two types. First, the spin-mixing conductances G F S and G AF S originate from the dephasing of the free electrons at the FM/NM and NM/AFM interfaces, 8   To describe the magnetic dynamics of a AFM/NM/FM trilayer one must start from the balance equations for the localized moments in the FM and AFM layers, and take into account the spin flows through the interfaces and the dissipative terms given by Eq. (2). In particular, the equation for the FM moments can be written aṡ

The interpretation of the coefficients in Eq. (2) is schematically shown in
The first term in Eq.
The second term in the r.h.s. of Eq. (4) points to an increase of the effective damping due to the presence of the FM/NM interface, which leads to a corresponding increase in the FMR linewidth ∆. In addition, the last term in Eq. (4) predicts a field-like contribution to the FM dynamics, which results exclusively from the spin pumping by the AFM layer, as the direct exchange between the FM and AFM is fully suppressed by the Cu spacer. This field, ∝ H AF × m F , can contribute to the value of the resonant field H r , and the contribution can be estimated as follows. The typical AFMR frequencies are much larger than the FMR frequency of the FM layer, so the dynamics of the AFM is driven solely by the FM, and  Gilbert damping obtained from ∆ sp . In agreement with the theory, Eq. (4), α sp M F grows linearly with d −1 F . We believe that the observed thickness dependence of the damping parameter points to the important role of free spins in the magnetic dynamics of the AFM/Cu/FM trilayer. We also conclude that the observed H r (d F ) dependence indicates that the localized AFM moments affect the dynamics of the FM layer through the dynamic exchange via conduction electrons in the system. However, this contribution from the localized moments can be partially masked by the exchanges bias due to the second Py layer and thus requires further analysis.
In summary, we observe spin-pumping effect in AFM/NM/FM multilayers as an increase in the linewidth of the FMR and shift of the resonant magnetic field. Basing on Onsager formalism, we calculate additional damping and field-like torque on FM moments due to the presence of AFM layer. The inverse dependence of damping and resonant field vs the thickness of FM layer supports the hypothesis of AFM influence on FM dynamics.
The contribution from the spin-pumping effect to the FMR linewidth is separated and shown be affected by the changes in the thickness of the ferromagnetic layer. The physical mechanisms of the observed ∆ sp vs. d F behaviour are analyzed and show a rich interplay of the conduction-vs-lattice spins in the five effective sub-systems of the structure. These results provide a deeper understanding of the spintronic effects in nanostructures containing antiferromagnets and can prove useful for designing future spintronic devices.