Abstract
A series of Co nanoclusterassembled films with cluster sizes ranging from 4.5 nm to 14.7 nm were prepared by the plasmagascondensation method. The sizedependent electrical transport properties were systematically investigated. Both of the longitudinal resistivity (\({\rho }_{xx}\)) and saturated anomalous Hall resistivity (\({\rho }_{xy}^{A}\)) continuously increased with the decrease of the cluster sizes (d). The \({\rho }_{xx}\) firstly increased and then decreased with increasing the temperature for all samples, which could be well described by involving the thermally fluctuationinduced tunneling (FIT) process and scattering. The tunneling effect was verified to result in the invalidation of classical anomalous Hall effect (AHE) scaling relation. After deducting the contribution from tunneling effect to \({\rho }_{xx}\), the AHE scaling relation between \({\rho }_{xy}^{A}\) and the scattering resistivity (\({\rho }_{S}\)) by varying the temperature was reconstructed. The value of scaling exponent γ increased with increasing Co cluster sizes. The size dependence of γ might be qualitatively interpreted by the interface and surfaceinduced spin flip scattering. We also determined the scaling relation between \({\rho }_{xy}^{A}\) and \({\rho }_{S}\) at 5 K by changing the Co cluster sizes, and a large value of γ = 3.6 was obtained which might be ascribed to the surface and interfacial scattering.
Introduction
Magnetic granular film, as a class of functional materials, is very attractive due to its rich fundamental phenomena and opening a new route for potential novel applications^{1,2,3}. The AHE in ferromagnets, arising from several origins, is one of the most prominent phenomena. For the present theories in homogeneous magnetic materials, it is generally accepted that the skew scattering (γ = 1)^{4}, sidejump (γ = 2)^{5}, and intrinsic (γ = 2)^{6} mechanisms account for the AHE, which gives an expression of \({\rho }_{xy}^{A}\propto {\rho }_{xx}^{\gamma }\). Therefore, one can parse the microscopic mechanisms of AHE by determining the scaling relation experimentally. However, large number of the theoretical and experimental results revealed that the AHE scaling relation in heterogeneous material was counterintuitive, especially in multilayer film and granular film^{7,8,9}. Song et al. studied the AHE in Fe/Cr multilayers and observed a large scaling exponent (γ = 2.6) which resulted from the interfacial scattering^{8}. Guo et al. discovered a large scaling exponent in Co/Pd multilayer films (γ = 5.7) which was also ascribed to the interfacial scattering^{10}. In addition, Zhang et al. observed a large enhancement of \({\rho }_{xy}^{A}\) in Co/Pt multilayers by inserting the MgO/CoO hybrid bilayers^{11}. Afterwards, Guo et al. also obtained a large enhancement of \({\rho }_{xy}^{A}\) in Co/Pd multilayers by modifying the interfacial structures^{12}. These results gave a strong indication that the interfacial scattering could significantly enhance the AHE. The AHE in granular films also have received extensive attention because of their abundant surface/interface and controllable microstructure^{13,14,15}. The microstructure in granular films can be effectively adjusted by governing the experiment parameters. Xiong et al. studied the size dependence of \({\rho }_{xy}^{A}\) and \({\rho }_{xx}\) in CoAg granular films by changing the annealing temperature, and the scaling exponent of γ = 3.7 was obtained at 4.2 K^{9}. They also found that the \({\rho }_{xy}^{A}\) increased with the decrease of Co grain sizes. The size dependence of \({\rho }_{xy}^{A}\) was also observed in CoCu granular films^{16}. These experimental observations implied that the grain size had a crucial effect on AHE. Nevertheless, the annealing affected the microstructure of the granular system by a complicated way^{17}. In this case, it was difficult to accurately demarcate the contribution of grain size, interface and interparticle distance to AHE. In the aspects of theoretical research, Granovsky et al.^{18} and Vedyaev et al.^{19} also suggested that the decrease of the grain sizes would effectively improve the \({\rho }_{xy}^{A}\) and the value of γ displayed obvious sizedependent in granular films. Unfortunately, the experimental evidence is still very scarce. The most critical factor is that it is difficult to individually control the grain size and interparticle distance by conventional preparation techniques. In this case, the sizedependent AHE remains an open question. Consequently, it is necessary and interesting to develop a more effective preparation method and study the sizedependent AHE in uniform single phase magnetic granular system.
In this paper, the uniform Co nanoclusterassembled granular films with different Co cluster sizes by plasmagascondensation (PGC)type cluster beam deposition apparatus. With this method, we successfully realized the individual control of cluster size. And then we systematically studied the Co cluster sizes dependence of \({\rho }_{xx}\) and \({\rho }_{xy}^{A}\) in uniform Co nanoclusterassembled films. Both of the \({\rho }_{xx}\) and \({\rho }_{xy}^{A}\) increased with the decrease of cluster sizes which could be attributed to the increase of surface and interfacial scattering. Furthermore, the sizedependent γ were investigated and corresponding physical mechanisms were discussed. Our results provide unequivocal experimental evidences for the effect of cluster size on the AHE.
Results and Discussion
The Lowmagnification TEM images and the corresponding size distribution of the Co nanoclusters are displayed in Fig. 1. The statistical results showed that the average size of clusters decreased from 14.7 nm to 6.5 nm as the Ar flow rate reduced from 600 sccm to 380 sccm, and further decreased to 4.5 nm when the 300 sccm He and 300 sccm Ar were simultaneously injected into deposition chamber [Fig. 1(a)]. The narrow size distribution meant that the size of Co clusters for all samples were very uniform. Additionally, the Co clusters were almost cubic geometry at d = 14.7 nm while gradually turned into sphericallike with the decrease of Co cluster sizes due to the highsurfaceenergy and small size effect. Hence, the size and geometry of Co clusters could be adjusted by tuning the Ar and He flow rates.
Figure 2(a) displays the SAED pattern of Co nanoclusterassembled film for d = 14.7 nm. The diffraction rings 2, 3, 5 and 6 corresponded to the {111}, {200}, {220} and {311} planes of metastable fcc Co. The presence of the diffraction rings 1 and 4 were attributed to {111} and {220} planes of fcc CoO, which was possibly originated from slight oxidization when the samples were exposed to the ambient atmosphere. The highresolution TEM observation of the Co clusters is exhibited in Fig. 2(b). The lattice fringe of 0.205 nm belonged to {111} interplanar spacing of metastable fcc Co. While the lattice fringes of 0.250 nm corresponded to {111} interplanar spacing of fcc CoO, which agreed well with the observation in Fig. 2(a). The adjacent Co clusters connected with each other, forming threedimensional (3D) effective conductive paths. Figure 2(cd) show the planarview and crosssectional SEM images of the Co clusterassembled film for d = 14.7 nm. These results demonstrated that a porous structure and the randomly stacking of the Co cluster were obtained in granular films.
Figure 3 plots the variation in \({\rho }_{xx}\) with the temperature for the four representative samples. In all cases, the \({\rho }_{xx}\) first decreased and then increased with the increase of temperature, resulting in a minimum value at a certain temperature (\({T}_{\min }\)). In the high temperature region (\(T > {T}_{\min }\)), all samples exhibited a positive temperature coefficient of resistance (TCR). Nevertheless, a negative TCR was observed in the low temperature range (\(T < {T}_{\min }\)). It was worth mentioning that the atom distribution at the Co clusters surface and interface was highly disorder and slightly oxidized [Fig. 2(ab)]. In this case, the interface between adjacent Co clusters could be considered as mesoscopic tunnel junctions and the barrier height was low enough. Under the circumstances, the negative TCR observed in our samples could be attributed to tunneling effect suggested by FIT process^{20, 21}. As can be seen from Fig. 3(d), the value of \({\rho }_{xx}\) for d = 14.7 nm at 300 K was far larger than the reported value in Co epitaxial thin films^{22}, which was attributed to the strong surface/interfacial scattering and tunneling effect in our sample. Guo et al. studied the electrical transport properties in polycrystalline Ni films and suggested that the total resistivity could be written as the superposition of tunneling effect and scattering^{23}. Hence, the temperaturedependent \({\rho }_{xx}\) in our samples might also be given as:
Here, the first term represents the resistivity dominated by FIT process and the residual terms are the contribution from temperaturedependent scattering^{21, 24,25,26}. The T ^{2} term includes the contribution from magnetic scattering, surfaceinduced scattering, and electronelectron scattering. The T ^{3} and T ^{5} terms are mainly ascribed to the contribution from phonon scattering in the framework of the BlochWilson and BlochGr€uneisen formula, respectively^{21}. The coefficient of B, C, D and \({\rho }_{0}\) are constant. \({T}_{1}\) and \({T}_{0}\) are characteristic parameters depending on mesoscopic tunnel junctions, which can be further expressed as^{20}:
and
Here, ω is the junction width, A is the junction area, and \({V}_{0}\) is the barrier height (See Supplementary Fig. S1). m represents the electronic mass, ε _{0} is the permittivity of vacuum and ћ is reduced Planck’s constant. As can be seen from Fig. 3, the experimental results for all samples agreed well with the theoretically predicted by Eq. (1). This gave a clear indication that the \({\rho }_{xx}\) originated form the superposition of tunneling effect and scattering, and scattering dominated the \({\rho }_{xx}\) in the high temperature range, while FIT process gradually became important with the decrease of temperature. The fitting parameters are displayed in Table 1.
To further clarify the physical mechanism in Co nanoclusterassembled granular films, we reconstructed the Eqs (2) and (3). The expression of \({T}_{1}/{T}_{0}\propto \omega {V}_{0}^{1/2}\) was obtained. According to the definition in FIT model, the decay length of the tunneling electron wave function inside the barrier is given as \(\xi =\hslash /\sqrt{2m{V}_{0}}\). Hence, the \({T}_{1}/{T}_{0}\) can be further written as \({T}_{1}/{T}_{0}\propto \omega /\xi \). This signifies that a lower value of \({T}_{1}/{T}_{0}\) corresponds to a higher electron tunneling probability. As can be seen from Table 1, the value of \({T}_{1}/{T}_{0}\) decreased with increasing the Co cluster sizes, suggesting a higher electron tunneling probability between adjacent Co clusters. Such a behavior revealed that the contribution from tunneling effect decreased with increasing Co cluster sizes. Meanwhile, a higher electron tunneling probability indicated a lower barrier height at interface between adjacent Co clusters. This scenario revealed that the atom distribution disorder at interface decreased with the increase of Co cluster sizes. On the other hand, the number of Co clusters in unit volume deceased with the increasing Co cluster sizes. Hence, the amount of the interface and surface in in unit volume also deceased with the increase of Co cluster sizes, suggesting the decrease of interfacial and surface scattering. Hence, the \({\rho }_{xx}\) decreased monotonously with the increase of Co cluster sizes might mainly result from the less contribution from FIT process, interfacial and surface scattering.
The fielddependent Hall resistivity \({\rho }_{xy}\) for all the samples at 5 K are plotted in Fig. 4(a). Generally, the Hall resistivity is parameterized by \({\rho }_{xy}={\rho }_{xy}^{O}+{\rho }_{xy}^{A}={R}_{0}H+4\pi {R}_{S}M\) ^{27}. R _{0}, R _{s} and M are defined as ordinary Hall coefficient, anomalous Hall coefficient and magnetization, respectively. As shown in Fig. 4(a), the \({\rho }_{xy}\) sharply increased at low fields and gradually tended to saturation at high fields. The \({R}_{S}\) could be achieved by mathematical calculation based on the abovementioned definition formulas of \({\rho }_{xy}\) and the magnetization curves data (See Supplementary Fig. S2). The calculation results of \({R}_{S}\) at 300 K were 1.06 × 10^{−8} (Ω cm)/G, 3.37 × 10^{−9} (Ω cm)/G, 1.79 × 10^{−9} (Ω cm)/G and 1.15 × 10^{−9} (Ω cm)/G for 4.5 nm, 6.5 nm, 9.5 nm and 14.7 nm, respectively. It is worth noting that, the value of \({R}_{S}\) for 4.5 nm Co granular film was almost four orders of magnitude larger than the reported value in blocky singlecrystal Co^{28}. Such a significant enhancement of Hall coefficient was closely related to large amount of interface and surface. The saturate anomalous Hall resistivity was acquired by using \({\rho }_{xy}^{A}=4\pi {R}_{S}M\) at H = 5 T (M was measured by Quantum Design physical property measurement system). Referring to this method, the \({\rho }_{xy}^{A}\) with different temperature for the four representative samples are obtained and display in Fig. 4(b). It can be seen form this figure that the value of \({\rho }_{xy}^{A}\) increased continuously with increasing the temperature. Such a behavior was mainly ascribed to surface and interfacial scattering^{21}. However, based on the current experimental data, the contribution of intrinsic mechanism could not be ruled out. This behavior was well supported by the results in Co/Pd multilayers^{10}. Pay attention to this figure, the \({\rho }_{xy}^{A}\) increased monotonously with the decrease of Co cluster sizes. This was because, as mentioned above, the atom distribution disorder at surface and interface increased with the decrease of Co cluster sizes. It is well known that the AHE was closely related to spinorbit scattering of conduction electrons at disorder sites in ferromagnet^{29, 30}. In the Co nanoclusterassembled films, the amount of surface and interface increased with decreasing Co cluster sizes. These behaviors would effectively enhance the amount of scattering center in the samples. Therefore, the increase of the spinorbit scattering finally enhanced the \({\rho }_{xy}^{A}\). Such a behavior was supported by the observation in Co/Pd multilayers^{12} and Fe nanoclusterassembled films^{31}, which also indicated that surface and interfacial scattering made a significant contribution to improve the AHE. Moreover, this result provided an experimental evidence for the theoretic investigation from Granovsky et al.^{18} and Vedyaev et al.^{19}.
To further identify the AHE mechanism in Co nanoclusterassembled films, the \({\rho }_{xy}^{A}\) and \({\rho }_{xx}\) were compiled into a power law of \({\rho }_{xy}^{A}\propto {\rho }_{xx}^{\gamma }\). Figure 5(a) shows the scaling behavior of \({\rho }_{xy}^{A}\) vs \({\rho }_{xx}\) with different Co cluster sizes. It was clear that two distinct regions were observed in log\({\rho }_{xy}^{A}\) varying with log\({\rho }_{xx}\) for all samples and the demarcation point was the resistivity of \({T}_{\min }\). Fitting the data into straight line, a negative γ was observed in the temperature range \(T < {T}_{\min }\), while a positive γ was found at higher temperature region (\(T > {T}_{\min }\)). The corresponding γ are exhibited in Fig. 5(b). Unfortunately, both of the negative and positive γ in our samples could not be explained by classical AHE scaling theory. Moreover, the value of γ clearly depended on the Co cluster size. There were some works indicated that the \({\rho }_{xx}\) and \({\rho }_{xy}^{A}\) dominated by different physical mechanisms and the tunneling effect had little effect on AHE^{32, 33}. It should be noted that the tunneling effect worked in the whole temperature range. Especially in the temperature range \(T < {T}_{\min }\), the \({\rho }_{xx}\) was principally governed by tunneling effect. Therefore, it was no wonder that the classical scaling relation between \({\rho }_{xy}^{A}\) and \({\rho }_{xx}\) was invalid in our systems even in higher temperature range (\(T > {T}_{\min }\)). To gain insight into the physical mechanisms of AHE in Co nanoclusterassembled films, tunneling effect should be removed from \({\rho }_{xx}\), and the scaling relation between \({\rho }_{xy}^{A}\) and the resistivity only deriving from scattering should be reconsidered.
It was worth mentioning that, as the temperature increased to be in a high limit, the tunneling effect can be neglected. In this case, the resistivity was only originated from scattering. Hence, the Eq. (1) can be rewritten as \({\rho }_{xx(T\to \infty )}={\rho }_{0}+{\rho }_{ST}\). Here, \({\rho }_{ST}\) is the temperaturedependent resistivity, which is given as \({\rho }_{ST}=\) \(B{T}^{2}+C{T}^{3}+D{T}^{5}\). \({\rho }_{0}\) is equivalent to residual resistivity which was originated from impurity or imperfection scattering. The scattering resistivity \({\rho }_{S}\) including residual resistivity \({\rho }_{0}\) and temperaturedependent scattering resistivity can be written as:
According to the fitting parameters from Eq. (1), we could effectively evaluate the contribution from \({\rho }_{0}\) and temperaturedependent scattering (\({\rho }_{ST}\)). In this case, the scattering resistivity with different temperature could be obtained. The \({\rho }_{S}\) − T curves with different Co cluster sizes are shown in Fig. 6. Different from the measuring results in Fig. 3, the \({\rho }_{S}\) for all samples continuously increased with increasing the temperature, indicating a behavior of a normal metal conduction characteristic. Moreover, the \({\rho }_{S}\) increased monotonically with decreasing Co cluster sizes. The phenomenon agreed well with the result presented in Fig. 4(b), which was ascribed to the increase of surface and interfacial scattering because of the raise of the amount of scattering center.
The AHE scaling between \({\rho }_{xy}^{A}\) and \({\rho }_{S}\) with different Co cluster sizes are exhibited in Fig. 7(a). Remarkably different from the observation in Fig. 5(a), the log\({\rho }_{xy}^{A}\) increased monotonously with increasing log\({\rho }_{S}\) in the whole temperature range. This observation gave an unambiguous indication that after deducting the contribution from tunneling effect the scaling relation was constructed successfully. By fitting the data to a straight line, the positive scaling exponent for all samples were observed but all of γ were larger than 2. The large scaling exponent observed in our samples could be qualitatively attributed to surface and interfacial scattering. The present results agreed with the previously reported in some other heterogeneous systems, such as Fe/Cr multilayers (γ = 2.6)^{8}, εFe_{3}N nanocrystalline films (γ = 17.6)^{34} and Fe/Au multilayers (γ = 2.7)^{35}. More importantly, as shown in Fig. 7(b), the scaling exponent γ increased with increasing Co cluster sizes. To some extent, the γ could be considered as a quantified criterion to evaluate how fast the \({\rho }_{xy}^{A}\) increased with the raise of \({\rho }_{S}\). In our samples, both of the \({\rho }_{xy}^{A}\) and \({\rho }_{S}\) approximately originated from three parts: bulk scattering, interface scattering and surface scattering^{21}. According to the previous report in Co epitaxial thin films^{22}, the contribution from bulk scattering was independent on thickness of film. Unlike the Co epitaxial film, there was lager amount of surface and interface in our samples, which would introduce additional scattering center. On the one hand, as mentioned above, the increasing scattering center would effectively increase both of the \({\rho }_{xy}^{A}\) and \({\rho }_{S}\). On the other hand, great scattering strength could cause the spin flip to randomize the spins^{10, 36, 37}, which would effectively reduce the spindependent scattering ratio but had a limited impact on \({\rho }_{S}\). To gain a deeper understanding of this behavior, the residual resistivity ratio [RRR = \({\rho }_{S}\)(300 K)/\({\rho }_{S}\)(5 K)] of all samples was studied. The RRR is considered as a qualitative method to identify degree of atomic disorder and lattice defect^{38}. It should be noted that, at 5 K, the contribution from temperaturedependent scattering could be nearly neglected. In this case, the scattering resistivity was approximately equivalent to residual resistivity [\({\rho }_{S}(5{\rm{K}})\approx {\rho }_{0}\)]. In analogy with RRR, we defined the residual saturate anomalous Hall resistivity ratio as RAR = \({\rho }_{xy}^{A}\)(300 K)/\({\rho }_{xy}^{A}\)(5 K). The size dependence of RRR and RAR are displayed in Fig. 7(c). Obliviously, the values of RRR decreased with the drop of Co nanocluster sizes, suggesting the improvement of degree of atomic disorder and lattice defect with decreasing cluster size. This conclusion reconfirmed the result mentioned above (\({T}_{1}/{T}_{0}\)). Furthermore, it was obvious that RAR shown a sharper decrease than RRR with the decrease of Co cluster sizes. This indicated that temperaturedependent \({\rho }_{xy}^{A}\) and \({\rho }_{S}\) were affected by different physical mechanisms, and the spin flip enhanced at high density of interface and surface. As a consequence, the sizedependent γ in the Co nanoclusterassembled films might be qualitatively interpreted by the enhancement of interface and surfaceinduced spin flip to randomize the spins. Such a behavior was in good accord with the experimental investigation in Co/Pd multilayers^{10} and the theoretical research from Granovsky et al.^{18} and Vedyaev et al.^{19}.
Nagaosa et al. proposed that the more proper test of the scaling relation was at low temperature by varying the defect concentration where the resistivity was dominated by impurity scattering because the interference from temperaturedependentscattering could be excluded^{27}. Hence, in order to further clarify the physical mechanism of AHE in our samples, we should exclude the effect from temperaturedependentscattering and tunneling effect and tested the scaling relation between \({\rho }_{S}\) and \({\rho }_{xy}^{A}\) at low temperature. The log\({\rho }_{xy}^{A}\) − log\({\rho }_{S}\) curve at 5 K is plotted [Fig. 7(d)]. The log\({\rho }_{xy}^{A}\) increased monotonically with the increase of log\({\rho }_{S}\), which followed a linear behavior. Carrying on the data fitting to the experimental results, the scaling exponent \(\gamma =3.6\pm 0.4\) was observed. Therefore, the value of \(\gamma =3.6\pm 0.4\) was related to surface and interfacial scattering. Recently, another interesting finding was that Nagaosa et al.^{27} proposed the unified theory of the AHE based on a large body of experimental results and theoretical study. The theory predicted that three broad regimes were distinguished as a function of longitudinal conductivity (\({\sigma }_{xx}\)). (i) \({\sigma }_{xx} > {10}^{6}\) S/cm (high conductivity regime), skew scattering mechanism dominates the Hall transport. (ii) 10^{4} S/cm <\({\sigma }_{xx}\)< 10^{6} S/cm (intrinsic regime) in which anomalous Hall conductivity \({\sigma }_{xy}^{A}\) becomes \({\sigma }_{xx}\) independent. (iii) \({\sigma }_{xx} < {10}^{4}\) S/cm (bad metal regime), where \({\sigma }_{xy}^{A}\propto {\sigma }_{xx}^{1.6}\) is predicted. The value of the \({\sigma }_{xy}^{A}\) and \({\sigma }_{xx}\) are estimated separately by \({\sigma }_{xy}^{A}\approx {\rho }_{xy}^{A}/{\rho }_{xx}^{2}\) and \({\sigma }_{xx}\approx 1/{\rho }_{xx}\) because of \({\rho }_{xy}^{A} < < {\rho }_{xx}\) _{.} As shown in the inset of Fig. 7(d), apparently, all of our samples were in the bad metal regime. Fitting the experimental data into a straight line, \({\sigma }_{xy}^{A}\propto {\sigma }_{S}^{1.6}\) was obtained at 5 K (\({\sigma }_{S}\) represented the longitudinal conductivity originating from scattering), which disagreed with the universal character of the 1.6 scaling relation. This result gave a strong indication that our samples was inconsistent with the unified theory, which was mainly ascribed to the surface and interfacial scattering. The similar phenomenon also could be observed in εFe_{3}N nanocrystalline films^{34}.
In summary, the uniform Co nanoclusterassembled films with different Co cluster sizes were successfully prepared by the plasmagascondensation method. For all samples, the longitudinal resistivity could be very well fitted by the combination of FIT process and scattering in the whole temperature range. Both of \({\rho }_{xx}\) and \({\rho }_{xy}^{A}\) shown a decreasing function of the Co cluster sizes due to the drop of surface and interfacial scattering. The scaling relation of \({\rho }_{xy}^{A}\propto {\rho }_{xx}^{\gamma }\) could be divided into two parts while obeyed the same line relationship between \({\rho }_{xy}^{A}\) and \({\rho }_{S}\) in the whole temperature range, indicating that it was necessary to remove the tunneling effect in establishing the AHE scaling relation. The large scaling exponent (γ > 2) observed in our samples could be ascribed to the surface and interfacial scattering and the sizedependent scaling exponent were closely related to the interface and surfaceinduced spin flip scattering. The large anomalous Hall coefficient [R _{ s } ~ 1.06 × 10^{−8} (Ω cm)/G] observed d = 4.5 nm could be attributed to the large amount of surface and interface, which is especially valuable in practical application in Hall device applications.
Methods
The experimental apparatus of plasmagascondensation (PGC)type cluster deposition system was employed to prepare the samples. The apparatus was simply divided into three regions: a sputtering chamber, a cluster growth room and a deposition chamber^{39}. The nucleation and growth of Co clusters occurred mainly in the sputtering chamber. And then Co clusters were extracted twice in the cluster growth room to prevent further growth. Finally, the Co clusters entered into the deposition chamber and softly deposited onto substrate randomly. The DC power of 400 W was used to generate high density metal Co vapor. The argon gas (99.999%) and helium gas (99.999%) with different flow rates (Ar: 600 sccm, Ar: 500 sccm, Ar: 400 sccm, and Ar/He: 300 sccm/300 sccm) were injected continuously into sputtering chamber to control the Co cluster sizes. JEOL JEM2100 transmission electron microscope (TEM) was used to carry out transmission electron microscopy (TEM) analysis. The morphology and crystalline phase of Co clusters were determined by TEM images and the selected area electron diffraction (SAED) was used to identify crystalline phase. The surface micromorphology images of Co clustersassembled films were acquired by SU70 scanning electron microscope (SEM). The magnetic and electrical properties were performed on Quantum Design physical property measurement system (PPMS9) with temperatures ranging from 5 to 300 K and the magnetic field sweeping from −5 to 5 T. For each sample, the longitudinal and transverse voltage could be measured simultaneously because of the five contacts in Hall bar. The thickness of clusterassembled films (~700 nm) were determined by the surface profiler (AlphaStep D100).
References
 1.
Chadha, M. & Ng, V. Sequential sputtered CoHfO_{2} granular films. J. Magn. Magn. Mater 426, 302 (2017).
 2.
Sonntag, J. The Origin of the Giant Hall Effect in MetalInsulator Composites. Open Journal of Composite Materials 6, 78 (2016).
 3.
Bartov, D., Segal, A., Karpovski, M. & Gerber, A. Absence of the ordinary and extraordinary Hall effects scaling in granular ferromagnets at metalinsulator transition. Phys. Rev. B 90, 144423 (2014).
 4.
Smit, J. The spontaneous Hall effect in ferromagnetics I. Physica 21, 877 (1955).
 5.
Berger, L. Sidejump mechanism for the Hall effect of ferromagnets. Phys. Rev. B 2, 4559 (1970).
 6.
Karplus, R. & Luttinger, J. M. Hall Effect in Ferromagnetics. Phys. Rev. 95, 1154 (1954).
 7.
Canedy, C. L., Li, X. W. & Xiao, G. Large magnetic moment enhancement and extraordinary Hall effect in Co/Pt superlattices. Phys. Rev. B 62, 508 (2000).
 8.
Song, S. N., Sellers, C. & Ketterson, J. B. Anomalous Hall effect in (110) Fe/(110) Cr multilayers. Appl. Phys. Lett. 59, 479 (1991).
 9.
Xiong, P. et al. Extraordinary Hall effect and giant magnetoresistance in the granular CoAg system. Phys. Rev. Lett. 69, 3220 (1992).
 10.
Guo, Z. B. et al. Effects of surface and interface scattering on anomalous Hall effect in Co/Pd multilayers. Phys. Rev. B 86, 104433 (2012).
 11.
Zhang, J. Y. et al. Effect of interfacial structures on anomalous Hall behavior in perpendicular Co/Pt multilayers. Appl. Phys. Lett. 102, 102404 (2013).
 12.
Guo, Z. B., Mi, W. B., Li, J. Q., Cheng, Y. C. & Zhang, X. X. Enhancement in anomalous Hall resistivity of Co/Pd multilayer and CoPd alloy by Ga^{+} ion irradiation. Europhys. Lett. 105, 46005 (2014).
 13.
Wang, J. B., Mi, W. B., Wang, L. S., Zhang, Q. F. & Peng, D. L. Enhanced anomalous Hall effect in Fe nanocluster assembled thin films. Phys. Chem. Chem. Phys. 16, 16623 (2014).
 14.
Wang, J. B. et al. Anomalous Hall effect in monodisperse CoOcoated Co nanoclusterassembled films. J. Magn. Magn. Mater. 401, 30 (2016).
 15.
Li, H. B. et al. Extraordinary Hall effect and universal scaling in Fe_{ x }(ZnO)_{1–x } granular thin films at room temperature. Appl. Phys. Lett. 106, 012401 (2015).
 16.
Wang, J. Q. & Kim, H. K. Effect of Annealing on Extraordinary Hall Effects in Sputtered Granular Cu_{80}Co_{20} Thin Films. IEEE T. Magn. 42, 3282 (2006).
 17.
Gerber, A. et al. Correlation between the extraordinary Hall effect and resistivity. Phys. Rev. B 69, 224403 (2004).
 18.
Granovsky, A., Brouers, F., Kalitsov, A. & Chshiev, M. Extraordinary Hall effect in magnetic granular alloys. J. Magn. Magn. Mater. 166, 193 (1997).
 19.
Vedyaev, A. V., Granovskii, A. B., Kalitsov, A. V. & Brouers, F. Anomalous Hall effect in granular alloys. JETP 85, 1204 (1997).
 20.
Sheng, P. Fluctuationinduced tunneling conduction in disordered materials. Phys. Rev. B 21, 2180 (1980).
 21.
Zhang, Q. F. et al. Electrical transport properties in Co nanoclusterassembled granular film. J. Appl. Phys. 121, 103901 (2017).
 22.
Hou, D. Z. et al. The anomalous Hall effect in epitaxial facecenteredcubic cobalt films. J. Phys. Condens. Matter 24, 482001 (2012).
 23.
Guo, Z. B. et al. Anomalous Hall effect in polycrystalline Ni films. Solid State Communications 152, 220 (2012).
 24.
Kamalakar, M. V., Raychaudhuri, A. K., Wei, X. Y., Teng, J. & Prewett, P. D. Temperature dependent electrical resistivity of a single strand of ferromagnetic single crystalline nanowire. Appl. Phys. Lett. 95, 013112 (2009).
 25.
Zhang, P., Cohen, R. E. & Haule, K. Effects of electron correlations on transport properties of iron at Earth's core conditions. Nature 517, 605 (2015).
 26.
Lal, K. et al. A low temperature study of electron transport properties of tantalum nitride thin films prepared by ion beam assisted deposition. Solid State Commun 131, 1 (2004).
 27.
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous hall effect. Rev. Mod. Phys. 82, 1539 (2010).
 28.
Kondorskii, E. N., Galkina, O. S., Ivanovskii, V. I., Cheremushkina, A. V. & Usarov, U. T. Anisotropy of galvanomagnetic effects in singlecrystal cobalt. Sov. Phys. JETP 38, 977 (1974).
 29.
Wu, S. B., Yang, X. F., Chen, S. & Zhu, T. Scaling of the anomalous Hall effect in perpendicular CoFeB/Pt multilayers. J. Appl. Phys. 113, 17C119 (2013).
 30.
Zhang, J. Y. et al. Effect of MgO/Co interface and Co/MgO interface on the spin dependent transport in perpendicular Co/Pt multilayers. J. Appl. Phys. 116, 163905 (2014).
 31.
Wang, J. B., Mi, W. B., Wang, L. S. & Peng, D. L. Interfacialscattering–induced enhancement of the anomalous Hall effect in uniform Fe nanoclusterassembled films. Europhys. Lett. 109, 17012 (2015).
 32.
Meier, H., Kharitonov, M. Y. & Efetov, K. B. Anomalous Hall effect in granular ferromagnetic metals and effects of weak localization. Phys. Rev. B 80, 045122 (2009).
 33.
Liu, H., Lee, F. K., Zheng, R. K., Zhang, X. X. & Tsui, O. K. C. Extraordinary Hall effect in (Ni_{80}Fe_{20})_{ x }(SiO_{2})_{1− x } thin films. Phys. Rev. B 70, 224431 (2004).
 34.
Cheng, Y. H., Zheng, R. K., Liu, H., Tian, Y. & Li, Z. Q. Large extraordinary Hall effect and anomalous scaling relations between the Hall and longitudinal conductivities in εFe_{3}N nanocrystalline films. Phys. Rev. B 80, 174412 (2009).
 35.
Zhang, Q. et al. Anomalous Hall effect in Fe/Au multilayers. Phys. Rev. B 94, 024428 (2016).
 36.
Wang, J. Q. & Xiao, G. Large finitesize effect of giant magnetoresistance in magnetic granular thin films. Phys. Rev. B 51, 5863 (1995).
 37.
Chen, J. & Hershfield, S. Effect of spinflip scattering on currentinplane giant magnetoresistance. Phys. Rev. B 57, 1097 (1998).
 38.
Imort, I.M., Thomas, P., Reiss, G. & Thomas, A. Anomalous Hall effect in the Cobased Heusler compounds Co_{2}FeSi and Co_{2}FeAI. J. Appl. Phys. 111, 07D313 (2012).
 39.
Wang, L. S. et al. Gasphase preparation and size control of Fe nanoparticles. Appl. Phys. A 103, 1015 (2011).
Acknowledgements
This work was partially supported by the National Natural Science Foundation of China (Grant Nos 51371154 and 51571167), the Fundamental Research Funds for the Central Universities (Grant No. 20720140547).
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D.L.P. and L.S.W. initiated the study. Q.F.Z., X.Z.W. and H.F.Z. prepared the samples by plasmagascondensation (PGC)type cluster deposition system. Q.F.Z. and J.X. performed the PPMS9 measurements. L.L., X.L., Y.L.Q. and Y.Z.C. performed the SEM and TEM measurements. All the authors contributed to discussion of the project.
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Correspondence to L. S. Wang or D. L. Peng.
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