Spin pumping into a partially compensated antiferromagnetic/paramagnetic insulator

Spin pumping from a metallic ferromagnet (FM) into an insulating antiferromagnet has been studied across the magnetic phase transition by means of temperature-dependent, broad-band ferromagnetic resonance (FMR) experiments. A set of spin pumping heterostructures consisting of Permalloy (Ni80Fe20) as FM and Zn 1−x Co x O with x=0.3,0.5 and 0.6 (Co:ZnO) as partially compensated antiferromagnetic insulator has been used for which previous experiments have already pointed out the possibility of the existence of spin-pumping. The present experiments allow to reliably separate the various contributions of the temperature-dependent Gilbert damping parameter to the FMR line-width. A careful analysis of the obtained data demonstrates a significant increase of the temperature-dependence of the Gilbert damping parameter α(T) around the magnetic phase transition of Co:ZnO which extends up to room temperature, confirming spin pumping into the fluctuating spin sink of an antiferromagnetic/paramagnetic insulator.


Introduction
The fields of spintronics and magnonics, which both involve the quantum-mechanical spin degree of freedom were recently joined to open new perspectives in magnon-spintronics [1]. This area of research is driven by the realization of magnetization dynamics, which are achieved, amongst others, via spin pumping [2,3]. Spin pumping is one possibility to generate non-equilibrium spin-currents by the flow of angular momentum which is generated by a precessing magnetization, e.g. by driving a ferromagnet (FM) like Permalloy (Py) into ferromagnetic resonance (FMR) which leads to a consecutive injection of a spin-current into an adjacent non-ferromagnetic material (NM). Usually, spin pumping is electrically detected via the inverse spin Hall effect (ISHE) inside the NM layer which requires conducting high-Z materials such as Pt [4,5]. However for few other materials like semiconducting Ge [6], ZnO [7], or FeRh [8] spin pumping could be detected via the ISHE as well. An alternative method to detect spin pumping is an enhanced FMR linewidth [9]. Here, the spin pumping-related enhancement of the Gilbert-like damping constant α depends on the efficiency of the spin-current absorption of the NM, which is described by the spin-mixing conductance, i.e. also here the NM is considered to be conducting. However, the advantages of using nonconducting materials have been pointed out not only for the FM [10], but also the NM [11]. Insulating NMs have the advantage that the increased magnetic damping is less influenced by other mechanisms like eddy-current damping [11] or the spin Seebeck effect [12]; however, the underlying mechanism of the transfer of angular momentum into an insulator is not fully understood yet. Linear response theory predicts an enhancement of spin pumping near magnetic phase transitions [13] which could recently also be verified experimentally [14], where it was demonstrated that spin-pumping into a fluctuating spin sink leads to an increase in α. These findings have recently been corroborated by element-selective studies of coherent transfer of angular momentum to evanescent spin waves in antiferromagnetic NiO [15]. It should be noted, that fluctuating spins, also called paramagnons, also exist well above the ordering temperature of, e.g. Ni [16] or Pd [17]. Measuring spin pumping in a FM/insulating NM structure across the magnetic order temperature of a NM is thus of fundamental interest for a better understanding of the relevant mechanisms beyond the common picture of a spin-mixing conductance and/or spin-polarized charge carrier transport.
The system of choice for the present study is a heterostructure consisting of Py in contact with Zn 1−x Co x O (Co:ZnO) with x = 0.3, 0.5 and 0.6 (30%, 50% and 60% Co:ZnO), a system where the presence of spin pumping at room temperature has been evidenced before via an increased Gilbert damping parameter derived from broad-band FMR [18]. In addition, the pumped ac spin-polarization of the Co:ZnO could be directly imaged using time-resolved scanning transmission x-ray microscopy in combination with FMR excitation [19]. These experiments were done using the x-ray magnetic circular dichroism and thus the non-compensated fraction of the Co magnetic moments inside the partially compensatred antiferromagnet Co:ZnO. The averaged pumped spin-polarization in Co:ZnO was found to have a different phase compared to Py and the dynamic magnetic contrast was spatially rather inhomogeneous, which stems from the random distribution of the Co cations inside the ZnO host crystal. In general, Co:ZnO above the coalescence limit of x = 0.2 is a partially compensated antiferromagnet with a low ordering temperature which weakly depends on the Co content. For the chosen x the Néel temperature T N ranges from 10 K to 25 K [20]. The net effective magnetic moment of the non-compensated Co moments is of the order of 0.10-0.15 µ B /Co atom and hardly depends on the actual Co concentration above x = 0.3 [20]; nonetheless, it was of sufficient magnitude to image the pumped ac spin-polarization in [19]. All Co:ZnO films are highly resistive and thus they represent a model-system for a paramagnetic insulator with a magnetic phase transition at low temperatures where the influence of increased spin fluctuations around the ordering temperature can be studied. However, to reliably separate the effect of spin pumping seen via an increase of the homogeneous, Gilbert-like broadening from other, inhomogeneous effects, temperature dependent broad-band FMR measurements are required. Such types of measurements are only sparsely found in the literature and the few examples include temperature and frequency-dependent FMR measurements on Py thin films [21], where bulk and interface contributions have been separated by thickness dependent measurements and a temperature-dependent interface contribution has been reported. Since spin-pumping scales inversely with the volume of the FM [9], it behaves like an interface-like effect, and also the results in [21] suggest to use rather thin Py layers to increase the spin-pumping contribution to the overall damping; however, also a sufficient amount of ferromagnetic material has to be used to achieve sufficient FMR signal strengths up to the highest frequency and lowest temperatures.
Here we report on detailed, temperature dependent, broad-band FMR measurements on a set of spin pumping Py/Co:ZnO heterostructures where indications of spin-pumping have been reported earlier [18]. The present experiments allow to reliably separate the various contributions to the FMR linewidth so that the homogeneous, Gilbert damping parameter α, which is linear in frequency, can be separated from the frequency-independent inhomogeneous contribution, and eventual two-magnon processes, which are non-linear in frequency [22,23], become visible. Various control-experiments and control samples with an Al buffer layer demonstrate that beyond other effects stemming from static exchange-bias-like coupling and two-magnon processes, also a true increase of α(T) around T N of the Co:ZnO is detectable thus demonstrating the presence of spin pumping from Py into an antiferromagnetic/paramagnetic insulator which implies a transfer of angular momentum in the absence of a charge current across the interface.

Experimental details
Spin-pumping heterostructures were fabricated on c-plane sapphire [Al 2 O 3 (0001)] in an ultrahigh vacuum (UHV) chamber with a base pressure of 2 · 10 −9 mbar. They consist of a nominally 100 nm thick epitaxial Co:ZnO layer with different Co content. This is followed by a 10 nm Py ferromagnetic layer which is capped with 5 nm Al to prevent the Py from oxidation. Eventually, a 1 nm and 2 nm thick Al buffer is inserted between the Co:ZnO and the Py. While Py and Co:ZnO are grown by (reactive) magnetron sputtering, the Al spacer and capping layers are grown by PLD; the working pressure during deposition is 4 · 10 −3 mbar. These heterostructures exhibit a clean interface with an interfacial roughness of 1-2 atomic layers as verified by transmission electron microscopy [18]. Al and Py are fabricated at room temperature using ten standard cubic centimeters per minute (sccm) Ar as process gas. For the different Co:ZnO layers, samples with three different Co concentrations of 30%, 50%, and 60% are grown under preparation conditions which have been optimized to assure optimum crystalline quality according to [20]. For 30% and 50% Co:ZnO metallic sputter targets with the nominal composition of Co and Zn are used together with an Ar:O 2 ratio of 10:1 sccm, while for 60% Co:ZnO a ceramic composite target of ZnO and Co 3 O 4 in a 3:2 ratio without any oxygen in the sputter gas is used. The optimized growth temperatures are 450 • C, 294 • C, and 525 • C, respectively. Therefore, the subsequent growth of Py/Al or Al/Py/Al requires a cool-down period after the Co:ZnO growth, where the sample is kept at base pressure of the UHV system.
The structural properties of the spin-pumping heterostructures have been studied using x-ray diffraction revealing good crystalline quality of the Co:ZnO while Py is amorphous. The static magnetic properties were measured with conventional superconducting quantum interference device (SQUID) magnetometry and the results have already been published in [18]. In brief, the heterostructures exhibit a combined vertical and horizontal exchange-bias shift of the M(H) curves. The vertical shift stems from a field-imprinted magnetization of the partially compensated moments of the Co:ZnO, see [24] for details. The horizontal shift is the classical exchange-bias effect of the ferromagnetic Py in contact with the (partially compensated) antiferromagnetic Co:ZnO; the horizontal shift of the hysteresis loop is 0 mT, 6 mT and 12 mT, the coercive field is 3 mT, 7 mT and 20 mT for the 30%, 50% and 60% Co:ZnO sample, respectively. Both quantities fall back to the one for Py upon the insertion of a 1 nm thick Al buffer [18]. Note, that in this work the identical samples as in [18] were studied; comparative samples have been newly fabricated to rule out degradation over time; in fact in turns out that the 5 nm Al cap layer is sufficient to prevent oxidation of the Py over several years without significant changes in the magnetic properties.
Broad-band FMR measurements have been carried out using the Cryo-FMR40 setup from NanOsc with a microwave frequency f MW in the range of 2-40 GHz. The sample is placed on a coplanar waveguide and the transmitted power is detected by a diode. A pair of Helmholtz-coils supplies an ac external magnetic field for lock-in detection. The static external magnetic field H ext up to 9 T as well as the temperature control in the range from 4 to 295 K is provided by a Quantum Design PPMS system which is controlled via the NanOsc software allowing a fully automized recording of FMR spectra over a wide range of temperatures and microwave frequencies. The individual FMR spectra are fitted with a Lorentzian which allows to extract the relevant magnetic parameters. The samples can only be measured in a fixed geometry applying H ext either in-plane (IP) or out-of-plane (OOP) using two different waveguide assemblies.

Experimental results
Figure 1(a) shows selected FMR spectra recorded at f MW = 40 GHz of the Py/30% Co:ZnO sample together with the Lorentzian fit of the data. It should be noted that the signal-to-noise ratio (SNR) is lowest for the highest f MW ; nevertheless, the SNR is still around 10 for 10 nm Py even down to 10 K. While the temperature-dependence of the resonance field H res is rather weak, a clear increase of the FMR linewidth ∆H can be seen. Note, that ∆H refers to the full width at half maximum which can be back-calculated to the peak-to-peak linewidth ∆H pp using ∆H = √ 3/2 · ∆H pp . Figure 1(b) compiles the so-called Kittel-plots, i.e. f MW as a function of µ 0 H ext , of the Py/30% Co:ZnO sample at selected temperatures. These data can be fitted with the following equation: Here γ is the gyromagnetic ratio, H ext is the static magnetic field, H k is an effective IP anisotropy and M eff is the effective magnetization, which contains the shape anisotropy as well as an effective OOP anisotropy of uniaxial character. Note, that equation (1) is only valid, when the IP easy axis of the sample is oriented parallel to H ext . In the ideal case of Py where no crystalline anisotropy should be present, H k should equal zero and M eff should be equal to the shape anisotropy and thus the spontaneous magnetization M s . The inset of figure 1(b) shows the temperature dependence of the g-factor as derived from the fit via γ = g · µ 0 /h. It should be noted, that throughout this work γ is not taken from the literature but derived from a fit of the data. The obtained value of 2.095 at 295 K is somewhat lower than the commonly accepted value for bulk Py of 2.11 which can be extracted with high precision from broad-band FMR measurements [25]. However, it has been noted, that a slight uncertainty of the actual H ext behaves as an additional effective anisotropy H k [26]. For the purpose of this work, where relative changes of the magnetic parameters as a function of temperature are the main objective, a precise determination of M eff , H k and the g-factor is deemed not to be essential. Therefore, all three parameters are fitted together as implemented in the software and the increase of the g-factor at low temperatures to 2.112 compared to 295 K is considered to be small but significant only on a relative scale, while its absolute value may be slightly different. This will become clearer further below. Figure 1(c) shows the frequency dependence of the FMR linewidth ∆H for different temperatures. These data can be fitted using the following equation: Here ∆H 0 is the inhomogeneous line broadening which is frequency independent and α is the Gilbert damping parameter which results in a linear frequency dependence. It can be seen in figure 1(c) that both ∆H 0 and α are increasing with decreasing temperature. In addition, while from 295 K to 150 K the data nicely follow a linear behavior, at lower temperature an additional curvature becomes visible at lower f MW which can be seen by the deviation from the linear fit curve, in particular at 20 K and 10 K. This will be discussed further below. For now it is sufficient to continue with the results of the linear fit which is summarized in figure 1(d) for all measured temperatures; the resulting uncertainties from the linear regression of the data, which are exemplarily shown in figure 1(c), are indicated as error bars which do not significantly exceed the point size except for the temperatures for which the data significantly deviate from the linear behavior. It can be seen that the inhomogeneous broadening ∆H 0 (squares) is roughly constant (between 0.05 mT and 0.1 mT) from 295 K down to 50 K where it starts to increase. In contrast, the Gilbert damping parameter α is found to be around 0.007 at higher temperatures while it reaches its maximum of 0.010 around 25 K before it drops again. In a previous publication we had shown, that already at room temperature α was slightly increased in comparison to a single Py film [18] which was assigned to an additional spin pumping from the Py into the insulating 30% Co:ZnO film. This was further corroborated by temperature-dependent conventional X-band FMR measurements at 9.5 GHz which revealed a temperature-dependent increase of the FMR linewidth with a maximum around 10 K [18], i.e. the known T N of 30% Co:ZnO [20]. However, strictly speaking, this was only a necessary but not a sufficient evidence for spin pumping into Co:ZnO. Such a maximum of spin pumping efficiency around a magnetic phase transition was discussed before theoretically [13] as well as experimentally [14] based on the FMR linewidth as well while for the coexistence phase in FeRh this was also based on frequency-dependent ISHE measurements [8]. In the present case of the Py/Co:ZnO heterostructure the data in figure 1(d) evidence, that for the given system both damping contributions increase at low temperatures so that the inhomogeneous broadening has to be considered separately from the homogenous, Gilbert-like broadening which should be representative of spin pumping into the fluctuating spins of the paramagnetic phase of the Co:ZnO. These fluctuations exhibit a maximum around the T N leading to a peak in the α(T) behavior. It should be noted that in Co:ZnO there is no well defined T N in a strict sense, since the coalescence-induced magnetic order depends on the existence of large Co-O-Co-O-. . . configurations extending over large regions of the entire sample; thus, each configuration will have its own T N leading to a smearing out of the phase transition temperature. Therefore we refer to T N as the maximum in the zero-field cooled M(T) curves and its width represents the given size distribution of the magnetic configurations as already discussed in [20].
Finally, the inset of figure 1(d) shows the temperature-dependence of the effective IP anisotropy H k (down triangles) and µ 0 M eff (up triangles) which are derived from the Kittel fit according to equation (1) of the data in figure 1(b). M eff nicely follows the expected M(T) behavior of a FM down to the T N of Co:ZnO where it starts to drop sharply. Around the same temperature H k is increasing following roughly the same functional behavior as the g-factor in figure 1(b). Obviously these three parameters derived from the Kittel fit are closely interrelated. It has been demonstrated before by integral SQUID magnetometry, that in addition to indications of spin pumping, this heterostructure also exhibits a static, exchange-bias like coupling resulting in an increase of the coercive field of the Py and an additional horizontal shift of the M(H) loop [18]. Together with the broad-band FMR data in figure 1 one can draw the following additional conclusions which go beyond the preliminary evidence in [18]: As expected, the presence of an IP exchange bias is accompanied by an increase of the effective IP anisotropy H k . The drop in M eff of the Py can be explained by either an antiparallel alignment of a small fraction of the Py moments close to the interface or by an additional effective out-of-plane anisotropy induced by the Co:ZnO. Note, that Co:ZnO exhibits an open hysteresis loop both in in-plane (IP) as well as OOP orientation [20]. The increase in the g-factor can be associated with the previous finding that the field imprinted magnetization in Co:ZnO, which leads to the vertical exchange bias-like shift of the hysteresis loop [24], is mainly due to an increase of the orbital magnetic moment of the Co as evidenced by x-ray magnetic circular dichroism [27]. It is thus reasonable to assume that this field imprinted orbital magnetic moment in the Co:ZnO in direct contact with the Py also increases the orbital moment of Py itself, leading to a small increase in the g-factor of Py as seen in the inset of figure 1(b). However, all these effects are associated with the static magnetic coupling of Py and the 30% Co:ZnO and not with the transfer of angular momentum associated with spin pumping. This can only be seen in the increase of α as seen in figure 1(d).
In a next step, the identical set of measurements has been conducted for the Py/50% Co:ZnO spin pumping heterostructure and a selection of the data is summarized in figure 2. Figure 2(a) shows the frequency dependence of the FMR linewidth at various temperatures and again it is visible that both, inhomogeneous as well as Gilbert-like damping are increasing with decreasing temperature as shown in figure 2(b). Similar to the 30% Co:ZnO heterostructure there is again a visible non-linearity in the ∆H(f MW )-behavior. Such a non-linear behavior is known to stem from two-magnon-processes [22]. To eliminate such a contribution from the data to first order approximation, different fitting regimes are chosen: On the one hand the full frequency range from 2 to 40 GHz is fitted, which leads to noticeable deviations between data and fit, cf figure 1(c). On the other hand, only the high-frequency part from 25 to 40 GHz is selected for fitting, because eventual two-magnon scattering processes typically exhibit a non-linear frequency dependence at lower frequencies which becomes constant at higher f MW [22] or even decreases [23]. Therefore, a fit in the high f MW -regime, where the data behave linear in f MW should remove most of the contributions of potential two magnon processes on a reasonable basis. The difference between the temperature dependence of the obtained inhomogeneous linewidth (squares) and Gilbert damping parameter α (circles) for the full frequency fit (open symbols) and the high-frequency fit (full symbols) is depicted in figure 2(b). An apparent monotonic increase of α with decreasing temperature turns into a clear maximum in the α(T) curve around 25 K. At the same time ∆H 0 at low temperatures is significantly increased at low temperatures. At high temperatures both fitting intervals do not lead to significantly different results and only a slight offset is visible for both parameters. The origin of the visible curvature/kink in the ∆H(T) curves goes beyond the scope of this work and will be discussed elsewhere. For the purpose of safely extracting the increase of the Gilbert damping due to spin pumping, the ∆H(T) data for all samples were fitted either in the full frequency range or only in the 25-40 GHz range. This confirms, that all visible trends in ∆H 0 (T) and α(T) were qualitatively identical (not shown) with small discrepancies in the quantitative values as exemplarily shown in figure 2(b).
An alternative way to eliminate effects of two-magnon processes as well as spin pumping is measuring the samples in OOP geometry where both contributions are known to be suppressed [8,9,22]. Note, that the case of FeRh discussed in [8] is a special case, since here the coexisting ferro-and antiferromagnetic regions within the FeRh film give rise to a lateral spin-pumping effect within the layer, while the spin-pumping perpendicular to the layer, i.e. in the geometry of the Py/Co:ZnO heterostructures, is absent. The inset of figure 2(b) shows a direct comparison between the fitted α in IP as well as OOP geometry. Since the IP data were only fitted in the high-frequency regime, the contributions of two-magnon processes should be suppressed while in OOP geometry also the contributions stemming from spin pumping are absent. The difference between the data should be the pure, Gilbert-like contribution originating from the transfer of angular momentum. More data in the OOP configuration will be discussed further below for the Py/60% Co:ZnO heterostructure.   figure 2(d). The overall behavior is rather similar to the 30%Co:ZnO sample with a clear increase of H k and the g-factor at low temperatures which goes hand-in-hand with a reduction of M eff ; the main difference is that the temperature range, over which the increase is visible, is somewhat wider and extends to higher temperatures which is consistent with an increased T N of 15 K of 50% Co:ZnO compared to 10 K for 30% Co:ZnO [18,20]. For this sample, where the α(T) exhibits a clear maximum around 25 K, it was exemplarily tested that this increase is not caused by the static coupling. This coupling causes the exchange-bias-like horizontal shift in static SQUID magnetometry which can be influenced by different field-cooling conditions [18]. Figure 2(d) displays the frequency dependent FMR linewidth at 15 K, i.e. around the T N of 50% Co:ZnO, for different field-cooling conditions of the sample. Any significant differences in the ∆H(f MW ) behavior is visible no matter if the sample is cooled down from 295 K to 15 K in either ±5 T (FC) or in nominally zero field (ZFC). Obviously, there is no significant influence of the cooling conditions and thus the static coupling on the obtained homogeneous as well as inhomogeneous damping. It should be noted that also the obtained parameters from the Kittel fit do not change significantly upon FC or ZFC (not shown). This is however not surprising, since even at 2 GHz the resonance field H res of 8.5 mT at 15 K is already above the observed coercive field of 7.5 mT as well as the exchange bias shift of 5 mT for this sample [18]. Figure 3 compiles a selection of the broad-band FMR results taken on the Py/60% Co:/ZnO heterostructure; for this sample a comparison between IP and OOP measurements is exemplarily shown. In figure 3 the frequency dependence of ∆H at various temperatures is shown for the IP (a) and the OOP (b) geometry. The absence of a visible kink in the frequency dependence of the FMR linewidth in OOP geometry in (b) experimentally confirms the absence of two-magnon-processes which are clearly visible in the IP geometry in (a). As discussed above, this implies that also contributions from spin-pumping will be absent in the OOP geometry. However, other than in the data of the Py/50% Co:ZnO in figure 2, an unexpected behavior is found for the data in OOP geometry of the Py/60% Co:ZnO shown in figure 3(b). A closer look at the different temperatures reveals that the FMR linewidth ∆H(f MW ) at 200 K (circles) is significantly larger than for all temperatures below and above. This surprising result is also visible in the Kittel plots in figure 3(c). While in the IP geometry the temperature dependence shows no remarkable anomalies, the OOP data in the inset, which are naturally restricted to higher fields and frequencies and show a purely linear behavior, the 200 K data are significantly shifted to higher resonance fields which goes hand in hand with an increased M eff . Since no obvious anomaly in the M(T) curves is found using conventional SQUID magnetometry (not shown), this increase is more likely to be assigned to an increase of an effective out-of-plane anisotropy. This behavior may be caused by another magnetic transition in the 60% Co:ZnO, which is due to an out-of-plane component of the magnetization. Such a transition has not yet been discussed and experimental evidence is sparse. Since the OOP geometry in this broad band FMR setup is experimentally somewhat challenging due to the lack of an external control of the angle of the sample, there is also the chance that such a behavior may stem from a slight misalignment of the sample with respect to the perfect OOP configuration which may even be temperature dependent due to thermal expansion of the assembly. In any case this behavior of the OOP data around 200 K has to be subject to further investigations which however go beyond the scope of the present work.
Turning back to the evidence for spin-pumping in the Py/60% Co:ZnO heterostructure, figure 3(d) compiles ∆H 0 (T) (squares) and α(T) (circles) for the IP (full symbols) and OOP (open symbols) data from (a) and (b) respectively; for the IP data only the fit from 25 to 40 GHz is shown which should eliminate the contributions from two-magnon-processes. It is obvious that in the OOP geometry the inhomogeneous broadening ∆H 0 is lower at low temperatures compared to the IP geometry, which coincides with the fact that the vertical exchange bias in Co:ZnO is by a factor of 2 more pronounced in IP with respect to the OOP configuration [24]. However, in the OOP configuration an unusual increase around 200 K is also visible in ∆H 0 and in α. The IP α(T) itself follows the same trend as for the 30% and 50% Co:ZnO samples. It increases with decreasing temperature forming a maximum around 25-30 K below which it drops sharply. Similar to the results for the 50% Co:ZnO sample in figure 2(b) also in the 60% Co:ZnO sample the maximum is less pronounced when the full frequency range is fitted (not shown). Below the temperature of this maximum α of 0.010 is comparably low as at 295 K which can be associated with the 60% Co:ZnO being well below its T N . In contrast, the α in OOP geometry remains well-below the α in IP geometry for the entire temperature regime-with the exception of the anomaly around 200 K. Therefore, the increase in α for IP compared to OOP can be safely assigned to a contribution from spin pumping with the caveat that the fitting of only the high-frequency regime of the ∆H(f MW ) may not fully remove the contribution from two-magnon-processes.
For a final separation of the various contributions to the FMR linewidth the broad-band FMR results of all Py/Co:ZnO heterostructures shall be compared to identical measurements on a Py film as well as two Py/60% Co:ZnO heterostructures where a 1 nm and a 2 nm Al buffer layer has been grown in-between the Co:ZnO and the Py. For the latter it has already been shown, that 1 nm Al is sufficient to suppress the static coupling as measured by SQUID while at room-temperature α is still enhanced compared to Py [18]. In contrast, for a 2 nm Al buffer also the α at room temperature is found to be reduced to values similar to those of the Py film [18]. It should be noted that the absolute numbers of [18] and the present work cannot be directly compared, since in [18] f MW was restricted to 3-10 GHz and also γ was fixed to the literature value of 2.11 which according to equation (2) also influences the obtained value of α. The α(T) for all samples which were already investigated in [18] at room temperature are now derived from temperature-dependent broad band FMR and the results are summarized in figure 4(a). This plot represents the central outcome of this work and several observations can be made. Already 10 nm Py alone exhibits a slight temperature dependent α which is however barely visible on the scale of figure 4(a) and will be discussed elsewhere. In direct comparison the Py/30% Co:ZnO heterostructure shows only a slight increase of α(T) at low temperatures which can be associated with spin pumping. In contrast, the 50% and the 60% heterostructures show a significant increase of α(T) already at 295 K which is further increased at low temperatures with a maximum around the Néel-temperature of the respective Co:ZnO film.
On a quantitative basis, α for the 60% Co:ZnO heterostructure at 25 K, i.e. around the transition temperature, is decreased from 0.020 for fitting the full frequency range (not shown) to 0.017 in figure 4(a), i.e. by 0.003 which represents most of the two magnon contribution to the FMR linewidth. The intrinsic Gilbert damping of Py without spin pumping is given by the plain Py film or the heterostructure with the 2 nm Al buffer, which is 0.008. Any inhomogeneous, frequency-independent contribution is already separated by the broad-band FMR and its behavior can be found in the ∆H 0 (T) in figure 4(b). Therefore, the spin-pumping contribution in the Py/60% Co:ZnO heterostructure at 25 K is 0.017-0.008, i.e. 0.009. Such a simple subtraction can be done for all temperatures for each Py/Co:ZnO heterostructure using the data in figure 4(a), where, due to the fitting in the high frequency regime the two-magnon contribution is (mostly) removed and the Py film can be taken as 'zero'-line, so that the difference is the contribution which can be associated with spin-pumping, i.e. the transfer of angular momentum from Py into the Co:ZnO.
Turning back to the shape of the α(T) in figure 4(a), it can be already seen in the conventional X-band FMR study this maximum is rather broad in temperature, cf figure 7(c) from [18]. However, the increase of the FMR linewidth from 50% to 60% Co:ZnO cannot be assigned to spin pumping, since α(T) does not increase further, but is a result of an increased inhomogeneous broadening ∆H 0 which is nicely visible in figure 4(b) where the ∆H 0 (T) of Py/60% Co:ZnO lies up to a factor of 2 higher than for Py/50% Co:ZnO whereas α(T) in figure 4(a) is rather similar for both samples. In fact, the effective magnetic moment per Co atom for 50% and 60% Co:ZnO has been reported to be rather similar, cf figure 7 in [20] and thus, also the size of the (fluctuating) moments should be comparable. It is also nicely visible that the Py/1 nm Al/60% Co:ZnO heterostructure (left triangles) has almost the identical α(T) behavior as the Py/60% Co:ZnO (diamonds) and thus a comparable spin-pumping through the Al buffer. In contrast, the 2 nm buffer (right triangles) leads to a full suppression of the increase on α(T) at low temperatures whereas some finite increase of α is still visible at elevated temperatures which is however clearly reduced compared to the 1 nm Al buffer. It should be noted, that due to the nature of the coalescence-induced, partially compensated antiferromagnetic order not only a sharp phase transition is absent but also the microscopic nature of the spin-dynamics inside the Co:ZnO is difficult to be described. Nonetheless, some kind of evanescent behavior of the generated spin dynamics inside the Co:ZnO, as reported for NiO in [15] can be expected.
In contrast to the α(T) behavior, the influence of the Al buffer on all other parameters is strikingly different. The low-temperature increase of ∆H 0 , which increases with increasing Co content, is almost fully suppressed already by 1 nm Al and indistinguishable from plain Py for 2 nm Al buffer, see figure 4(b). Likewise, the low temperature increase of H k in figure 4(c), which follows the trend of ∆H 0 , also vanishes completely with an Al buffer; the same is true for the low-temperature reduction of M eff shown in the inset of figure 4(c). Moreover, M eff of the Py grown on an Al buffer is systematically higher than for the Py film directly grown on sapphire; this apparent effect of the different interfaces adjacent to Py will be discussed elsewhere. Finally, also the increase of the g-factor visible for Py/60% Co:ZnO, and less pronounced also for 50% and 30% Co:ZnO is fully suppressed by the Al buffer of either thickness. Therefore, all temperature-dependent changes of ∆H 0 , H k , M eff and the g-factor can be correlated with the direct static coupling of the Py with the adjacent Co:ZnO and is thus indicative of exchange bias-like behavior. In turn, the characteristic temperature dependence is an indirect measure of the magnetic properties of the Co:ZnO by means of the broad-band FMR behavior of the adjacent Py.

Discussion and conclusion
We have shown by means of temperature-dependent, broad-band FMR measurements that the increase in the α(T) in Py/Co:ZnO heterostructures due to spin-pumping can reliably be separated from other effects like inhomogeneous broadening, two-magnon processes and changes in anisotropy and the g-factor due to the coexisting static, exchange bias coupling. These findings are corroborated by experiments using an Al buffer layer separating Py from the Co:ZnO thereby ruling out effects of direct coupling and/or intermixing. Therefore, the origin of the increase in α(T) over the entire temperature range is a transfer of angular momentum from Py into the antiferromagnetic insulator Co:ZnO which increases around the phase transition. Since Co:ZnO is non-conducting the increase of α over a wide temperature range well-above T N of the Co:ZnO points towards the possibility of spin pumping into paramagnetic fluctuations of the Co:ZnO which apparently can dissipate angular momentum from the Py leading to a Gilbert-like contribution to damping. It has to be stressed that this transfer of angular momentum has to happen in the absence of any charge current flowing across the interface between the FM and the antiferromagnetic/paramagnetic insulator. Therefore, the common description of spin pumping in terms of a spin-mixing-conductance [9] cannot be applied to the present system and alternative mechanisms have to be discussed. Likewise, contributions to the FMR linewidth of Py originating from any kind of spin Seebeck effect are assumed to be minimal. Although the spin Seebeck effect has been reported for an insulating FM [12], a spin current generated by the spin Seebeck effect from a metallic FM into an insulating NM has not been reported. Therefore, only the reverse effect may be at work, namely a spin current from the magnons in the insulating Co:ZnO into the metallic Py which may counteract the flow of angular momentum from the Py to the Co:ZnO and may actually account for the drop of α below T N . However, this scenario is considered to be unlikely, since it requires significant thermal gradients across the interface as well as along the sample which are considered to be minimal due to the active and homogeneous cooling inside the cryostat; it was also checked that neither the microwave nor the modulation coils affect the temperature at the sample.
A word of caution concerns the role of the Al buffer layer to physically separate the FM and the Co:ZnO. It is known that Al possesses a very long spin coherence length of several 100 nm [28] which was derived from (non-local) spin injection experiments. So one would expect that there should not be any significant difference between a 1 nm and a 2 nm Al buffer layer since the pumped spin polarization from the Py should not be significantly altered or reduced inside the Al. On the other hand, in most experiments the spin coherence length of Al is determined under conditions where charge currents are flowing in parallel (spin injection experiments). This is different from the present case, where no charge current should flow inside the Al because of the adjacent insulator Co:ZnO which may influence the injection of a spin polarized charge current into the Al. Therefore, the long spin coherence length may not play any significant role in the transfer of angular momentum, since the role of the Al/Co:ZnO interface is unclear as well as the effect of spin accumulation inside the Al itself. To further investigate these possible effects a detailed study of Py with different Al buffer thicknesses on an insulating diamagnetic substrate in comparison to the same thickness series on Co:ZnO would be necessary which however goes beyond the scope of the present work.
Another potential issue may be that 1 nm Al is not sufficiently thick to suppress the static coupling between Py and Co:ZnO. However, this scenario appears to be unlikely because (i) it was already demonstrated by integral SQUID magnetometry that the exchange-bias-like static coupling in this heterostructure is already fully suppressed by 1 nm Al [18] and (ii) the TEM cross-sections in [18] demonstrate that the roughness at the interface is at most 1-2 atomic layers so that 1 nm Al should safely suppress the formation of pin-holes and thus direct coupling. Finally, we want to remark that also the origin of the non-linearity of the ∆H(f MW )-behavior cannot be fully clarified which in turn also influences the disentanglement of the actual contributions to the observed α(T). However, if one would assume that, even after the subtraction of the two-magnon contribution via fitting only the high-frequency regime, the remaining increase is still due to some kind of two-magnon effects, the observed temperature dependence of α(T) with a maximum around T N of the Co:ZnO does not correlate with any known temperature dependence of two-magnon processes and thus the transfer of angular momentum appears to be more appropriate to account for the experimental observations.
In summary, as the experimental results stand we can provide evidence that in Py/Co:ZnO heterostructures we have signatures of increased Gilbert-like damping due to the transfer of angular momentum which is maximum around T N of the Co:ZnO. It is similar to the conventional spin-pumping experiments; however, in the absence of a charge current. The transfer of angular momentum occurs into the paramagnetic fluctuations of the insulating Co:ZnO which corroborates previous works where spin pumping near magnetic phase transitions was theoretically predicted [13] which could recently also be verified experimentally for IrMn [14] or NiO [15] as a spin sink. We therefore can add further experimental evidence beyond [18,19] for the possibility of transfer of angular momentum from a FM into an insulating paramagnet which is maximum close to the para-to-antiferromagnetic phase transition.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.