Correlation of magnetic and magnetoresistive properties of nanoporous Co/Pd thin multilayers fabricated on anodized TiO2 templates

In this study, we consider a technological approach to obtain a high perpendicular magnetic anisotropy of the Co/Pd multilayers deposited on nanoporous TiO2 templates of different types of surface morphology. It is found that the use of templates with homogeneous and smoothed surface relief, formed on silicon wafers, ensures conservation of perpendicular anisotropy of the deposited films inherent in the continuous multilayers. Also, their magnetic hardening with doubling of the coercive field is observed. However, inhomogeneous magnetic ordering is revealed in the porous films due to the occurrence of magnetically soft regions near the pore edges and/or inside the pores. Modeling of the field dependences of magnetization and electrical resistance indicates that coherent rotation is the dominant mechanism of magnetization reversal in the porous system instead of the domain-wall motion typical of the continuous multilayers, while their magnetoresistance is determined by electron-magnon scattering, similarly to the continuous counterpart. The preservation of spin waves in the porous films indicates a high uniformity of the magnetic ordering in the fabricated porous systems due to a sufficiently regular pores array introduced into the films, despite the existence of soft-magnetic regions. The results are promising for the design and fabrication of future spintronic devices.

In this study, we consider a technological approach to obtain a high perpendicular magnetic anisotropy of the co/pd multilayers deposited on nanoporous tio 2 templates of different types of surface morphology. It is found that the use of templates with homogeneous and smoothed surface relief, formed on silicon wafers, ensures conservation of perpendicular anisotropy of the deposited films inherent in the continuous multilayers. Also, their magnetic hardening with doubling of the coercive field is observed. However, inhomogeneous magnetic ordering is revealed in the porous films due to the occurrence of magnetically soft regions near the pore edges and/or inside the pores. Modeling of the field dependences of magnetization and electrical resistance indicates that coherent rotation is the dominant mechanism of magnetization reversal in the porous system instead of the domain-wall motion typical of the continuous multilayers, while their magnetoresistance is determined by electron-magnon scattering, similarly to the continuous counterpart. The preservation of spin waves in the porous films indicates a high uniformity of the magnetic ordering in the fabricated porous systems due to a sufficiently regular pores array introduced into the films, despite the existence of soft-magnetic regions. The results are promising for the design and fabrication of future spintronic devices.
The progress in information technologies and smart magnetic sensing requires magnetic data storage with ultrahigh information density and media with high magnetic field sensitivity, possessing nanoscale spatial resolution. The arrays of nanodots and related nanostructures with the basic property of perpendicular magnetic anisotropy (PMA) have shown great potential to satisfy these issues [1][2][3][4][5] . The above-mentioned challenges require advanced but inexpensive technologies for producing high-quality, large-area arrays of nanostructures with stable and well-reproducible magnetic properties. The main methods commonly used in fabricating nanostructures are high resolution lithographic technologies, such as electron-beam and X-ray lithography 2,6-8 . However, these techniques have essential shortcomings associated with the extremely high costs, low throughput and small exposure area. Besides the technical issues, the main physical limitations hindering the progress in these technologies are set by Scientific RepoRtS | (2020) 10:10838 | https://doi.org/10.1038/s41598-020-67677-0 www.nature.com/scientificreports/ thermal instability of magnetically-decoupled superparamagnetic (SP) nanostructures 2,3 since the size of isolated single-domain magnetic islands containing each bit of information is required to be persistently reduced. One approach to delaying the onset of the SP limit is to improve the magnetic anisotropy of nanostructures exploited in bit patterned media (BPM) 8 . The other approach is based on the principally different materials, percolated perpendicular media (PPM) 4,5 , containing a continual perpendicularly-anisotropic film with a dense distribution of defects (nanoholes/antidots) which serve as domain-wall pinning sites 9,10 . Intensive research in recent decades has shown that the PPM concept works well with magnetically coupled 3d/5d multilayers (MLs), such as Co/Pd and Co/Pt, which are deposited on self-organized nanoporous templates (Al 2 O 3 , TiO 2 ) 1,5,11-13 . In the PPM approach, the implemented nanopatterning of a continuous magnetic film is accompanied by conservation of its high PMA, while preserved exchange coupling provides the magnetic stability 9 of nanostructures. Magnetic anisotropy of such nanoporous films demonstrates high sensitivity to the morphological features of templates used as a substrate 5,11,14 . It was shown that a well-developed morphology of nanoporous films with numerous inhomogeneities results in a pronounced deterioration of PMA due to the local misalignments of easy magnetization axes at the edges of nanopores 15 . At the same time, despite an abundant amount of data on the continuous Co/Pd and Co/Pt MLs 16-18 accumulated since 1988 19 , only a few studies were devoted to finding out the correlation between the surface morphology of the corresponding nanostructured films and the strength of their magnetic anisotropy 5,[11][12][13][14]20,21 . Therefore, the present research is focused on elucidating the influence of the morphology of the Co/Pd multilayered films, related to the used TiO 2 templates, on their magnetic parameters (coercive field H C , remanent magnetization M r , etc.) which, in turn, determine their potential functionality. The main aspect of the study is a detailed analysis and interpretation of magnetization reversal mechanisms characterizing porous Co/Pd films with strong PMA. The processes of magnetization reversal in the films were modeled within the frame of the Stoner-Wohlfarth model 15,21,22 and analyzed in relation to the morphology of the films, as well as their phase composition.
Having regard to the high potential of anisotropic magnetic media for spintronics applications, the spindependent electronic transport in the studied MLs is analyzed in detail for determining the magnetoresistance (MR) mechanisms and elucidating the influence of the magnetic ordering and magnetization reversal in the porous Co/Pd films with the specific morphology on their MR signal. A model interpretation of the field dependences of MR was carried out for both continuous and porous multilayered systems with the assumption of electron-magnon scattering as the dominant MR mechanism 23 .

Results and discussion
Scanning electron microscopy. A schematic representation of the composition of the studied Co/Pd multilayered films illustrating the sequence of their layers is shown in Fig. 1a. Typical images of scanning electron microscopy (SEM) demonstrating surface morphology of the nanoporous TiO 2 templates used for Co/Pd films deposition, which are fabricated over Ti foil (Ti/TiO 2 ) and Si wafer (Si/TiO 2 ), are presented in Fig. 1b, c, respectively. The images are taken at an angle of 45° with respect to the surface of the templates for better surface relief illustration.
As can be derived from SEM images, the pore diameter mainly varies between 40 and 60 nm (some even up to 100 nm) for the Ti/TiO 2 template (Fig. 1b), whereas it amounts to 20-40 nm only for the Si/TiO 2 template (Fig. 1c). The distance between the pore centers in the Ti/TiO 2 and Si/TiO 2 templates is about 150 and 130 nm, respectively. The difference in the pore diameters between the two types of templates can be associated with the significantly different thermal conductivity of Si (150 W/mK) and Ti (14-22 W/mK) materials providing better heat dissipation in the case of Si substrate and, consequently, lower temperature during anodization process of Ti film. Therefore, this leads to a lower rate of chemical etching of TiO 2 nanotubes walls within the Si/TiO 2 template 24 . It is worth noting that these two types of templates reveal a significantly different surface relief. The Ti/TiO 2 template demonstrates rather flat inter-pore regions and a wavy surface of the whole template, possibly because of its soft and flexible background formed by Ti foil (Fig. 1b). In contrast, the Si/TiO 2 template has a www.nature.com/scientificreports/ rather homogeneous surface relief, but it contains some undesirable surface peculiarities which are visible as "hills" over the whole template surface, increasing significantly its surface roughness (Fig. 1c). SEM images of the Co/Pd MLs fabricated on the Ti/TiO 2 and Si/TiO 2 templates are presented in Fig. 1d, e. They evidence the porous structure of both films, with the average pore diameter of about 35-40 nm for the MLs on the Ti/TiO 2 template and 30-35 nm for the film on the Si/TiO 2 template. The decrease in the pore size for the films, as compared to the initial templates, indicates that the pores are partially occluded by the deposited film 25 . Generally, the morphology of Co/Pd MLs reproduces well the template morphology (Fig. 1b, c). However, the deposited film smoothens partly the template surface inhomogeneities like small triangular pores between TiO 2 nanotubes (Fig. 1b).
X-ray diffraction. Experimental X-ray diffraction (XRD) patterns both for the continuous (reference sample) and porous Co/Pd MLs are presented in Fig. 2. They are accompanied by the results of their refinement and partial phase contributions evaluated from the fits. The parameters describing crystalline structure of the   (111) peak of a face-centered (fcc) structure of Pd with a = 3.884 Å 26 and originates mainly from the buffer and capping Pd layers. Two additional peaks at 2θ ~ 40.72° and 41.49° are associated with two phases of fcc CoPd alloy with slightly different lattice parameters a = 3.835 Å and 3.766 Å appearing as a result of commonly observed mixing at the interface between Co and Pd layers. The presence of two modifications of CoPd alloy in the film indicates that Co concentration 26 in MLs varies with depth. Based on the a value, the stoichiometry of the CoPd alloys corresponding to the 2θ = 40.72° and 41.49° peaks (Table 1) is estimated to be Co 26 Pd 74 and Co 45 Pd 55 , respectively 15,26 .
XRD analysis of the porous Co/Pd MLs on the Si/TiO 2 template (Fig. 2b) reveals that the structural parameters of the Pd and CoPd phases reproduce well those for the continuous film ( Table 1). The only new aspect, a relatively narrow peak from TiO structure (Fm3m, a = 4.297 Å) 27 appears in the XRD patterns of the porous films originating from the template, with its main TiO 2 phase being amorphous. Additionally, the only peak characterizing CoPd alloy is detected in the porous films, which demonstrates a comparable intensity with the peak of pure Pd (Fig. 2b). These facts indicate a substantial Co and Pd mixing in the porous MLs. In addition, a more uniform mixing in the porous Co/Pd MLs can be stated, as compared to the corresponding flat system. The value of a parameter obtained for the CoPd alloy in the porous Co/Pd MLs (Table 1) allows us to estimate its stoichiometry as Co 30 Pd 70 . The obtained atomic ratio is close to the composition of the CoPd 2 phase 15,28 , which, in turn, corresponds to the ratio of the thicknesses of the deposited Co and Pd layers. This fact indicates a complete mixing of Co and Pd layers inside the Co/Pd MLs that is in agreement with the high tendency to Co and Pd atom mixing 15,16,29 .
The XRD pattern of the porous Co/Pd MLs on the Ti/TiO 2 template is presented in Fig. 2c. Two intense peaks at 2θ ~ 38.4° and 40.2° correspond to the Ti phase of the substrate. The refinement of the XRD pattern allowed revealing the Pd and CoPd phases after the Ti peaks identification. In this way, the extracted lattice parameters (Table 1) are in a good agreement with the corresponding parameters of bulk fcc Pd (a = 3.890 Å 12 ) and fcc CoPd 2 (a = 3.830 Å 8,13 ) phases, although the latter is not supposed to be well-ordered in our films, because the deposition was performed at room temperature. As can be seen in Fig. 2, the diffraction peaks of the CoPd alloy are broadened, especially in the case of the porous MLs, which confirms its poor crystallinity.
Room-temperature magnetometry. Figure   www.nature.com/scientificreports/ multilayered films with strong PMA (H A ~ 15-30 kOe) 15,18,30,31 . High H A value of the studied Co/Pd MLs is supposed to determine mainly the peculiarities of their magnetic and magnetoresistive properties described below.
The RT magnetization curves of the porous Co/Pd MLs reveal a gradual decrease in their M r /M S parameter (see Fig. 3a) when going from Si/TiO 2 to Ti/TiO 2 template. Actually, using the porous Si/TiO 2 template for the film deposition leads to a slight decrease in its M r /M S value down to 0.85. Next, using the porous Ti/TiO 2 template on a flexible Ti foil leads to a further significant decrease in the M r /M S ratio (down to 0.65) of the deposited Co/ Pd MLs that indicates a dramatic decrease in their PMA effect. The latter shows that microscale imperfections and a wavy surface, which are typical of the templates on foils, deteriorate PMA of the deposited films more substantially than local nano-sized inhomogeneities of the Si/TiO 2 templates forming their developed relief (Fig. 1c).
It is worth noting that a huge increase in H C up to 2.4 kOe is detected for the porous Co/Pd films as compared to their continuous counterpart. Remarkably, unusual double-step magnetization curves are observed for the porous films, which are characterized by two distinct steps, with the steps being more pronounced for the film on the Ti/TiO 2 template (Fig. 3). The latter indicates inhomogeneity of magnetic ordering in the films, i.e. the coexistence of the regions with significantly different magnetic hardness and, possibly, obeying different mechanisms of magnetization reversal.
An analysis of the possible mechanisms of magnetization reversal in the Co/Pd MLs demonstrating complex M(H)/M S dependence was carried out. For this purpose, the magnetization curve of the porous Co/Pd MLs on Ti/TiO 2 template is decomposed into two components describing each step separately 32,33 , as it is shown in where M hard (H) is the normalized magnetization curve describing the part of the film with uniaxial magnetic anisotropy, i.e. obeying the Stoner-Wohlfarth mechanism of magnetization reversal 13,15 , and M soft (H) is the component describing the soft-magnetic (or SP) part of the film where magnetization is governed by the Langevin function 33 . The estimated relative contribution of the soft-magnetic material, (1 − n), in the total magnetization makes up 35%.
The soft-magnetic (or SP) component in the magnetization of the porous films possibly originates from the structures which are formed at the pore edges and/or inside the pores. In the first case, small toroid-like nanostructures formed around the pores or spherical inhomogeneities at the film surface (Fig. 1d, e) contain misaligned magnetic moments. These moments are forced by high PMA of the film to be oriented perpendicularly to the curved surface 34 , i.e. divergently, thus forming isotropic magnetic properties of the corresponding film regions 32,34 . The second possibility assumes penetration of Co/Pd material inside the pores during deposition 5,20 . The large pore diameter (up to 100 nm for some pores) in the case of Ti/TiO 2 templates and rather short length of TiO 2 nanotubes (Fig. 1b) Fig. 4. The continuous Co/Pd MLs demonstrate a significant increase in H C with decreasing temperature achieving 2 kOe at 2 K that is almost two times higher than its value at RT. Additionally, a small increase in the saturation magnetization can be noticed with decreasing temperature down to 50 K. Such changes in H C and M S parameters with lowering temperature are associated mainly with the decrement of the thermally activated magnon population, as well as an additional contribution from the magnetic polarization of Pd at low temperature [35][36][37] . Indeed, Pd magnetic polarization due to the adjacent Co layers goes deeply into Pd layers at low temperature which gives an additional magnetic moment (~ 0.3 µB as calculated per Pd atom 38 ) and promotes better interlayer coupling 35,36 , thus enhancing PMA of the MLs at low T 35 . The strictly uniform orientation of magnetic moments in the film due to their reduced thermal fluctuations 36 and an enhanced PMA 35,39 at low temperature, as well as their strong ferromagnetic coupling 35,36 , hinders the process of magnetization reversal, increasing therefore the H C parameter. Further temperature lowering leads surprisingly to M S decrease down to a value close to the one observed at RT. In addition, small upward step appears on the M(H) curves at T < 50 K when H changes sign, i.e. in the vicinity of zero field. The origin of this phenomenon may be in a specific arrangement of a part of magnetic moments inside the MLs at low temperature, possibly related to Dzyaloshinskii-Moriya interaction or antiparallel ordering of Co and Pd magnetic moments, but it needs further studies. However, to our knowledge, such steps were not previously reported for similar systems in literature sources.
The temperature dependence of M S for the continuous MLs studied is shown in the inset to Fig. 4a. It follows well the empirical expression 35  www.nature.com/scientificreports/ correspondence with the experimental data, with a strong deviation at T = 300 K (red line in the insets to Fig. 4).
As the Bloch's law is derived for bulk ferromagnets, it is not fully applicable to nano-scale materials due to finite size effect 40 , since interfaces prevent free propagation of spin waves with a wavelength larger than the layer thickness. Therefore, the detected deviation of the approximation with the Bloch's law from the experimental data at RT can possibly be associated with the excitation of magnons with the energies higher than those implied by the Bloch's law (just with the quadratic dispersion law), as well as with magnons interaction at high temperatures. It should be mentioned that the parameter b obtained from the approximation using the empirical expression also shows its value of 0.025, much lower than the one obtained for similar systems (b = 0.34) 35,36 , indicating a weak temperature dependence of M S . The M(H) curves of the porous Co/Pd MLs (Fig. 4b) demonstrate the tendencies for their H C and M S parameters with lowering temperature similar to their continuous counterpart, namely, a 60% increase in H C achieving 3.5 kOe at 2 K, as well as a 10% growth of M S at 50 K compared to the corresponding RT values. The constant B estimated from the approximation of the M S (T) dependences according to the Bloch's law is revealed to be significantly higher for the porous MLs (1.7 × 10 -5 K −3/2 ) than for the continuous counterpart (0.8 × 10 -5 K −3/2 ). The increased Bloch constant, which is formulated as B ~ A −3/2 (A is a ferromagnetic exchange stiffness constant) 41 indicates a weakened ferromagnetic interaction between spins in the porous MLs due to the edge effects or changes in spin waves propagation caused by the complex morphology of the porous system.
It should be mentioned that in addition to an increase in M S , a gradual increase in M r /M S ratio takes place with decreasing temperature for the porous MLs, which smears out the double-step shape of magnetization loops of the porous films observed at RT (Fig. 3a). Such an increase in M r /M S ratio indicates (1) freezing of temperature induced fluctuations of magnetic moments in the soft-magnetic phase, assuming that it is formed by SP nanodots, or (2) strengthening the exchange coupling in ferromagnetic film at low temperature 39 , i.e. between hard and soft-magnetic phases, if the soft-magnetic phase is supposed to be formed on rough areas of the templates having high surface curvature.
Magnetoresistance. The field dependences of magnetoresistance MR(H) = 100% × (R(H) − R(0))/R(0) of the studied Co/Pd MLs derived from the measured field dependences of their electrical resistance R are shown in Fig. 5 for the continuous and porous (on Si/TiO 2 template) films at different temperatures (T = 2-300 K). The almost linear, unsaturated MR(H) dependence up to high fields (9 T) is the most evident characteristic of both continuous and porous Co/Pd MLs. Despite the metallic properties of each layer in the films, the MLs demonstrate a negative MR that indicates spin-dependent electron transport, with the effect of negative MR being enhanced with increasing temperature. In ferromagnetic metals with strongly coupled spins, their collective excitations (magnons) impede the electric current, initiating the electrons scattering on these excitations, i.e. on magnons 23,42 . Since the external field H tends to align misoriented magnetic moments, as well as to decrease the magnitude of their precession, it decreases the number of scattering events, thus reducing the electrical resistance. It is worth noting that such an almost linear reduction of the resistance in high fields (Fig. 5) corresponds to the saturated magnetization of the MLs (Fig. 4). This reveals a minor role of the static effects related to the magnetic moments misalignment in the described negative MR effect, giving preference to the dynamic effect of magnons. The observed decrease in the slope angle of the MR(H) curves to the field axis with lowering temperature associated with a decrease in the negative MR effect originates from a partial change in the MR mechanism. The contribution of magnon magnetoresistance (MMR) decreases with decreasing temperature, namely because magnons are less populated at low T 23,42 . On the other hand, the contribution of the positive MR via Lorenz mechanism increases with decreasing temperature due to an increase in the mean free path of electrons. The latter contribution reduces the total MR effect and diminishes the linearity of MR(H) curves at low temperatures. www.nature.com/scientificreports/ It should be mentioned that the revealed MMR mechanism, which is associated with a damping of the spin waves in high fields (HF) 42 , is not typical of thin multilayered films similar to the studied Co/Pd MLs, since interfaces prevent the free propagation of spin waves. In doing so, such films with a small thickness of ferromagnetic layers (less than 1 nm) commonly demonstrate the saturated MR(H) dependences in high fields (HF-MR) corresponding to their saturated magnetization 30,43,44 . The existence of spin waves in the studied films is consistent with the mixing of their Co and Pd layers revealed by XRD, which results in the formation of ferromagnetic alloy 29,33 with a thickness of the corresponding layer comparable to that in the systems where magnons are typically detected (no less than 7-10 nm for different 3d metals 23,42,45 ).
One more peculiarity of the MR(H) curves observed at low temperatures (T = 2-10 K) is a faster decrease in the MR value with increasing field than predicted by the MMR model 23,42 . As a result, the MR(H) curve obtained at 2 K lies below the corresponding curve measured at 100 K (Fig. 5). This can be explained solely by the appearance of an additional contribution to the spin-dependent scattering of electrons at low T, enhancing negative MR. The latter correlates with the detected upward steps on the corresponding M(H) curves in the same temperature range (Fig. 4). Both observations are possibly associated with the opposite orientation of a part of magnetic moments in the MLs with respect to the external field. However, the mechanism of such an arrangement is still not fully understood.  www.nature.com/scientificreports/ The low-field part of the MR(H) curves (LF-MR) has more complicated shape than a simply linear HF-MR. An evident correlation with the corresponding M(H) curves is characteristic of the LF-MR of both continuous and porous Co/Pd MLs. Figure 6 illustrates such a correlation for these two films at T = 2 K and 200 K. As it can be seen from the figure, a nearly linear increase in MR with decreasing field (follow the red solid arrows in Fig. 6c) is replaced by its abrupt decrease in the negative field coinciding with the coercive field of the corresponding M(H) curve. In terms of spin excitations, a decrease in a magnetic field, which suppresses spin waves, leads to an increase in the amplitude of spin precession, thus raising the electrical resistance of the film (corresponds to a linear MR increase between points 1 and 2 in Fig. 6c, or, in other words, relates to a decrease in the absolute value of MR). Then, negative external field, i.e. the field applied in the direction opposite to the orientation of magnetic moments (point 2 in Fig. 6c, e) tends to destabilize them 23 , increasing further the amplitude of their precession until their reversal. The latter corresponds to the maximal resistance of the film. Next, switching the magnetization at H = − H C to the opposite direction provides parallel orientation of the magnetic moments to the external field (point 3 in Fig. 6c, e) that decreases rapidly the magnon population 23 , thus leading to a steeply diminishing resistance. Noteworthy, the amplitude of MR drop is proportional to the H C value 23 (Fig. 6). A further increase in a negative field provides an additional gradual decrease in the resistance due to spin waves damping in the HF region.
The approximation of the LF-MR curves of the Co/Pd MLs can be made using their M(H) dependences according to the relation proposed for the MMR mechanism 23 : where α(T) is a temperature-dependent slope of MR(H) curve in the vicinity of zero field. The results of approximation are also presented in Fig. 6 (black solid lines). A perfect coincidence of the experimental and approximating MR(H) curves for the continuous Co/Pd MLs (Fig. 6a, b) proves that their spin-dependent MR is realized through the electron-magnon scattering mechanism. The experimental LF-MR curves of the porous Co/Pd MLs also demonstrate a good agreement with the corresponding approximation (Fig. 6c, d). Their main discrepancy lies in a delay of the MR signal drop (red dots) with respect to the reversal of magnetic moments at H = H C (blue dots and black line), with the latter process being more abrupt and nonlinear. Such a discrepancy relates to a complex origin of the MR signal. First of all, similarly to the magnetometry results, it reproduces static processes involving the magnetic moments, such as their misalignments, canting and reversal, which are reflected in the magnetization curves. However, it reveals also the sensitivity to high-frequency excitations of spins, with the corresponding MR signal being almost linear with the applied field 23 , since the number of excited or suppressed magnons is proportional to the H value. The latter contribution increases the linearity of the MR(H) curves.
Importantly, the porous structure and complex relief does not prevent spin waves propagation in the studied Co/Pd MLs. Indeed, they contain quite large inter-pore regions of tens of nanometers in length and demonstrate higher uniformity of Co and Pd mixing than the continuous film, according to the XRD data (Fig. 2). In addition, a significantly lager effect of negative MR is characteristic of the porous Co/Pd MLs as compared to the continuous counterparts (almost two-fold difference in H = 10 kOe, Fig. 6a, c). This can even indicate more intense spin waves in the porous system, which correlates with its larger Bloch constant estimated from the magnetization curves.

conclusions
We have carried out a detailed analysis of the role of surface morphology in magnetically ordered Co/Pd MLs with pronounced PMA (H A = 25 kOe) deposited onto the porous Ti/TiO 2 and Si/TiO 2 templates with significantly different surface relief. The morphology of the Co/Pd films is found to reflect the features of the surface of the templates used. As a result, a more homogeneous and smoothed relief is characteristic of the film deposited on the Si/TiO 2 template that provides a distinct PMA with high M r /M S ratio reaching 0.85 at RT. The film on the Ti/TiO 2 template contains pores with larger diameter (~ 40 nm) and microscale surface imperfections and undulations, which are responsible for the inhomogeneous magnetic ordering in the film and the occurrence of a soft-magnetic or superparamagnetic component. This component of the film is formed on the areas of the template with high surface curvature, like pore edges and surface convexities, and/or inside the pores. This partly deteriorates the PMA of the film, decreasing its M r /M S ratio down to 0.65, but provides the maximal coercive field H C reaching 2.4 kOe at RT due to enhanced pinning effects. At low temperature, a significant H C increase (up to 3.5 kOe at 2 K) and a noticeable growth of M S (10%) occurs mainly due to the reduction of thermally activated magnon population and the magnetic polarization of Pd by adjacent Co atoms, which strengthens the ferromagnetic coupling in the films.
The magnetization reversal in the porous films obeys mainly the Stoner-Wohlfarth rotational mechanism, with the double-step shape being characteristic of the corresponding magnetization curves due to the separate magnetization reversal of magnetically hard and soft regions. The ratio between these contributions is found to depend strongly on the film morphology.
A comparative analysis of the field dependences of magnetoresistance MR(H) and magnetization M(H) reveals the effect of spin waves propagation in both continuous and porous films and allows an identification of the dominant mechanism of magnetoresistance as coming from the electron scattering on magnons. The pronounced effect of spin waves in the films studied is consistent with a substantial intermixing of Co and Pd layers accompanied by the formation of CoPd ferromagnetic alloy. An increased negative MR effect and higher Bloch constant observed for the porous Co/Pd MLs, as compared to the continuous counterpart, indicate a www.nature.com/scientificreports/ strengthening of spin wave effects in the porous system. The effect is possibly related to their propagation in the undulated film, additionally modified with a quite regular array of pores.

Methods
Templates of nanoporous TiO 2 were fabricated by anodization of Ti film in 0.3% ammonium fluoride solution in ethylene glycol with 2 vol% of water at low temperature of electrolyte 24 . Two types of Ti films were used for anodization-(1) Ti foil with the thickness of 50 μm and (2) Ti film of 0.3 μm deposited onto Si wafer 46 . The anodization voltage was linearly increased from zero to 45-60 V with the rate of 1 V/s and then kept constant for the total anodization time, which was no longer than 35 min. The end of the anodization process was defined as the drop of the anodic current density below 30% of its maximum value 24,33,46 . Subsequent ion-plasma etching (Ar) was applied for additional smoothening of the surface relief. The etching time was varied from 60 min for TiO 2 on Ti foil 46 to 100 min for the templates fabricated over Si wafers 33,46 . Co/Pd multilayers with nominal composition of Ta 5 nm /Pd 15 nm /[Co 0.5 nm /Pd 1.0 nm ] x5 /Pd 3 nm /Ta 5 nm were deposited on anodized TiO 2 templates. Continuous MLs of the same composition were also deposited on Si (Si/SiO 2 ) wafers to serve as reference samples. All multilayers were fabricated using an ultra-high vacuum magnetron sputtering system (AJA International, Inc., USA) according to the procedure described previously 13,33,46 . The bilayers of Pd/Ta and Ta/Pd were used as seed and capping layers for promoting the (111) texture and for preventing the oxidation of the multilayers, respectively. The layer thicknesses were determined from the deposition time and calibrated deposition rates. Surface morphology and cross-sectional microstructure of the templates and the films deposited on them was analyzed using a HITACHI S-4800 scanning electron microscope (SEM) at a voltage of 15 kV. The structures and phase compositions of the Co/Pd films were examined by X-ray diffraction (XRD) using an Empyrean PANalytical diffractometer with Cu Ka radiation (λ = 0.15418 nm). Experimental data were collected at a grazing incidence of 5° with respect to the sample surface, with the detector scanning the 2θ space from 10° to 120°. The experimental data were analyzed with HighScore Plus software and fitted with the FullProf program 47 based on the Rietveld method.
The magnetic properties of the continuous and porous Co/Pd films were characterized using an alternating gradient magnetometer (AGM) and the vibrating sample magnetometer (VSM) option of a Quantum Design Physical Property Measurement System (PPMS) with external magnetic fields H up to 10 kOe applied along the film normal and up to 90 kOe applied in the film plane direction in the temperature T range of 2-300 K. The linear contribution of diamagnetic signal from the films substrates was subtracted from the experimental field dependences of magnetization M(H). Measurements of the field dependences of resistance R(H) were carried out using the resistivity option of the PPMS at T = 2-300 K. A linear press four-contact assembly was used for resistance R measurement using a square-wave excitation current with a frequency of 8.3 Hz applied parallel to the film surface. A magnetic field of up to 90 kOe was applied along the film normal.

Data availability
The data obtained and analyzed within this study are available from the corresponding author on reasonable request.