Search tips
Search criteria 


Logo of scirepAboutEditorial BoardFor AuthorsScientific Reports
Sci Rep. 2017; 7: 11666.
Published online 2017 September 15. doi:  10.1038/s41598-017-11983-7
PMCID: PMC5601485

Size-dependent electrical transport properties in Co nanocluster-assembled granular films


A series of Co nanocluster-assembled films with cluster sizes ranging from 4.5 nm to 14.7 nm were prepared by the plasma-gas-condensation method. The size-dependent electrical transport properties were systematically investigated. Both of the longitudinal resistivity (ρxx) and saturated anomalous Hall resistivity (ρxyA) continuously increased with the decrease of the cluster sizes (d). The ρxx firstly increased and then decreased with increasing the temperature for all samples, which could be well described by involving the thermally fluctuation-induced 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 ρxx, the AHE scaling relation between ρxyA and the scattering resistivity (ρS) 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 surface-induced spin flip scattering. We also determined the scaling relation between ρxyA and ρS 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.


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 applications13. 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, side-jump (γ = 2)5, and intrinsic (γ = 2)6 mechanisms account for the AHE, which gives an expression of ρxyAρxxγ. 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 film79. Song et al. studied the AHE in Fe/Cr multilayers and observed a large scaling exponent (γ = 2.6) which resulted from the interfacial scattering8. Guo et al. discovered a large scaling exponent in Co/Pd multilayer films (γ = 5.7) which was also ascribed to the interfacial scattering10. In addition, Zhang et al. observed a large enhancement of ρxyA in Co/Pt multilayers by inserting the MgO/CoO hybrid bilayers11. Afterwards, Guo et al. also obtained a large enhancement of ρxyA in Co/Pd multilayers by modifying the interfacial structures12. 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 microstructure1315. The microstructure in granular films can be effectively adjusted by governing the experiment parameters. Xiong et al. studied the size dependence of ρxyA and ρxx in Co-Ag granular films by changing the annealing temperature, and the scaling exponent of γ = 3.7 was obtained at 4.2 K9. They also found that the ρxyA increased with the decrease of Co grain sizes. The size dependence of ρxyA was also observed in Co-Cu granular films16. 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 way17. 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 ρxyA and the value of γ displayed obvious size-dependent 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 size-dependent AHE remains an open question. Consequently, it is necessary and interesting to develop a more effective preparation method and study the size-dependent AHE in uniform single phase magnetic granular system.

In this paper, the uniform Co nanocluster-assembled granular films with different Co cluster sizes by plasma-gas-condensation (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 ρxx and ρxyA in uniform Co nanocluster-assembled films. Both of the ρxx and ρxyA increased with the decrease of cluster sizes which could be attributed to the increase of surface and interfacial scattering. Furthermore, the size-dependent 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 Low-magnification 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 spherical-like with the decrease of Co cluster sizes due to the high-surface-energy and small size effect. Hence, the size and geometry of Co clusters could be adjusted by tuning the Ar and He flow rates.

Figure 1
(ad) Low-magnification TEM images of Co nanoclusters with different size. The inset in (ad) are the corresponding size distribution.

Figure 2(a) displays the SAED pattern of Co nanocluster-assembled 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 high-resolution 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 three-dimensional (3D) effective conductive paths. Figure 2(c-d) show the planar-view and cross-sectional SEM images of the Co cluster-assembled 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 2
(a) SAED pattern, (b) high-resolution TEM image, (c) plan-view and (d) cross-sectional SEM images of the Co nanocluster-assembled film for d = 14.7 nm.

Figure 3 plots the variation in ρxx with the temperature for the four representative samples. In all cases, the ρxx first decreased and then increased with the increase of temperature, resulting in a minimum value at a certain temperature (Tmin). In the high temperature region (T > Tmin), all samples exhibited a positive temperature coefficient of resistance (TCR). Nevertheless, a negative TCR was observed in the low temperature range (T < Tmin). It was worth mentioning that the atom distribution at the Co clusters surface and interface was highly disorder and slightly oxidized [Fig. 2(a-b)]. 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 process20, 21. As can be seen from Fig. 3(d), the value of ρxx for d = 14.7 nm at 300 K was far larger than the reported value in Co epitaxial thin films22, 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 scattering23. Hence, the temperature-dependent ρxx 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 temperature-dependent scattering21, 2426. The T 2 term includes the contribution from magnetic scattering, surface-induced scattering, and electron-electron scattering. The T 3 and T 5 terms are mainly ascribed to the contribution from phonon scattering in the framework of the Bloch-Wilson and Bloch-Gr€uneisen formula, respectively21. The coefficient of B, C, D and ρ0 are constant. T1 and T0 are characteristic parameters depending on mesoscopic tunnel junctions, which can be further expressed as20:


Figure 3
ρxx  T curves for Co nanocluster-assembled films with different Co cluster sizes. The symbols are the experimental data. The short dash curves are the theoretical forecasting by Eq. (1).



Here, ω is the junction width, A is the junction area, and V0 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 ρxx originated form the superposition of tunneling effect and scattering, and scattering dominated the ρxx in the high temperature range, while FIT process gradually became important with the decrease of temperature. The fitting parameters are displayed in Table 1.

Table 1
Data for the fitting parameters attained from Eq. (1).

To further clarify the physical mechanism in Co nanocluster-assembled granular films, we reconstructed the Eqs (2) and (3). The expression of T1/T0ωV01/2 was obtained. According to the definition in FIT model, the decay length of the tunneling electron wave function inside the barrier is given as ξ=/2mV0. Hence, the T1/T0 can be further written as T1/T0 ∝ ω/ξ. This signifies that a lower value of T1/T0 corresponds to a higher electron tunneling probability. As can be seen from Table 1, the value of T1/T0 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 ρxx decreased monotonously with the increase of Co cluster sizes might mainly result from the less contribution from FIT process, interfacial and surface scattering.

The field-dependent Hall resistivity ρxy for all the samples at 5 K are plotted in Fig. 4(a). Generally, the Hall resistivity is parameterized by ρxy=ρxyO+ρxyA=R0H+4πRSM 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 ρxy sharply increased at low fields and gradually tended to saturation at high fields. The RS could be achieved by mathematical calculation based on the above-mentioned definition formulas of ρxy and the magnetization curves data (See Supplementary Fig. S2). The calculation results of RS 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 RS for 4.5 nm Co granular film was almost four orders of magnitude larger than the reported value in blocky single-crystal Co28. 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 ρxyA=4πRSM at H = 5 T (M was measured by Quantum Design physical property measurement system). Referring to this method, the ρxyA 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 ρxyA increased continuously with increasing the temperature. Such a behavior was mainly ascribed to surface and interfacial scattering21. 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 multilayers10. Pay attention to this figure, the ρxyA 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 spin-orbit scattering of conduction electrons at disorder sites in ferromagnet29, 30. In the Co nanocluster-assembled 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 spin-orbit scattering finally enhanced the ρxyA. Such a behavior was supported by the observation in Co/Pd multilayers12 and Fe nanocluster-assembled films31, 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.

Figure 4
(a) The Hall resistivity as a function of field at 5 K, and (b) ρxyA  T curves for the Co nanocluster-assembled films with different Co cluster sizes.

To further identify the AHE mechanism in Co nanocluster-assembled films, the ρxyA and ρxx were compiled into a power law of ρxyAρxxγ. Figure 5(a) shows the scaling behavior of ρxyA vs ρxx with different Co cluster sizes. It was clear that two distinct regions were observed in logρxyA varying with logρxx for all samples and the demarcation point was the resistivity of Tmin. Fitting the data into straight line, a negative γ was observed in the temperature range T < Tmin, while a positive γ was found at higher temperature region (T > Tmin). 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 ρxx and ρxyA dominated by different physical mechanisms and the tunneling effect had little effect on AHE32, 33. It should be noted that the tunneling effect worked in the whole temperature range. Especially in the temperature range T < Tmin, the ρxx was principally governed by tunneling effect. Therefore, it was no wonder that the classical scaling relation between ρxyA and ρxx was invalid in our systems even in higher temperature range (T > Tmin). To gain insight into the physical mechanisms of AHE in Co nanocluster-assembled films, tunneling effect should be removed from ρxx, and the scaling relation between ρxyA and the resistivity only deriving from scattering should be reconsidered.

Figure 5
(a) The logρxyA  logρxx curves for the Co nanocluster-assembled films with different Co cluster sizes. (b) The corresponding scaling exponent of AHE.

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 ρxx(T)ρ0ρST. Here, ρST is the temperature-dependent resistivity, which is given as ρST BT2CT3DT5. ρ0 is equivalent to residual resistivity which was originated from impurity or imperfection scattering. The scattering resistivity ρS including residual resistivity ρ0 and temperature-dependent scattering resistivity can be written as:


According to the fitting parameters from Eq. (1), we could effectively evaluate the contribution from ρ0 and temperature-dependent scattering (ρST). In this case, the scattering resistivity with different temperature could be obtained. The ρS  T curves with different Co cluster sizes are shown in Fig. 6. Different from the measuring results in Fig. 3, the ρS for all samples continuously increased with increasing the temperature, indicating a behavior of a normal metal conduction characteristic. Moreover, the ρS 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.

Figure 6
ρS  T curves for the Co nanocluster-assembled films with different Co cluster sizes.

The AHE scaling between ρxyA and ρS with different Co cluster sizes are exhibited in Fig. 7(a). Remarkably different from the observation in Fig. 5(a), the logρxyA increased monotonously with increasing logρS 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, ε-Fe3N 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 ρxyA increased with the raise of ρS. In our samples, both of the ρxyA and ρS approximately originated from three parts: bulk scattering, interface scattering and surface scattering21. According to the previous report in Co epitaxial thin films22, 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 ρxyA and ρS. On the other hand, great scattering strength could cause the spin flip to randomize the spins10, 36, 37, which would effectively reduce the spin-dependent scattering ratio but had a limited impact on ρS. To gain a deeper understanding of this behavior, the residual resistivity ratio [RRR = ρS(300 K)/ρS(5 K)] of all samples was studied. The RRR is considered as a qualitative method to identify degree of atomic disorder and lattice defect38. It should be noted that, at 5 K, the contribution from temperature-dependent scattering could be nearly neglected. In this case, the scattering resistivity was approximately equivalent to residual resistivity [ρS(5K) ≈ ρ0]. In analogy with RRR, we defined the residual saturate anomalous Hall resistivity ratio as RAR = ρxyA(300 K)/ρxyA(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 (T1/T0). Furthermore, it was obvious that RAR shown a sharper decrease than RRR with the decrease of Co cluster sizes. This indicated that temperature-dependent ρxyA and ρS were affected by different physical mechanisms, and the spin flip enhanced at high density of interface and surface. As a consequence, the size-dependent γ in the Co nanocluster-assembled films might be qualitatively interpreted by the enhancement of interface and surface-induced spin flip to randomize the spins. Such a behavior was in good accord with the experimental investigation in Co/Pd multilayers10 and the theoretical research from Granovsky et al.18 and Vedyaev et al.19.

Figure 7
(a) The plot of logρxyA  logρS curves for the Co nanocluster-assembled films with different sizes. (b) The scaling exponent, (c) the RRR and RAR as function of Co cluster sizes. (d) The logρxyA  log ...

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 temperature-dependent-scattering could be excluded27. Hence, in order to further clarify the physical mechanism of AHE in our samples, we should exclude the effect from temperature-dependent-scattering and tunneling effect and tested the scaling relation between ρS and ρxyA at low temperature. The logρxyA  logρS curve at 5 K is plotted [Fig. 7(d)]. The logρxyA increased monotonically with the increase of logρS, which followed a linear behavior. Carrying on the data fitting to the experimental results, the scaling exponent γ = 3.6 ± 0.4 was observed. Therefore, the value of γ = 3.6 ± 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 (σxx). (i) σxx > 106 S/cm (high conductivity regime), skew scattering mechanism dominates the Hall transport. (ii) 104 S/cm <σxx< 106 S/cm (intrinsic regime) in which anomalous Hall conductivity σxyA becomes σxx independent. (iii) σxx < 104 S/cm (bad metal regime), where σxyAσxx1.6 is predicted. The value of the σxyA and σxx are estimated separately by σxyAρxyA/ρxx2 and σxx ≈ 1/ρxx because of ρxyA<<ρxx . 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, σxyAσS1.6 was obtained at 5 K (σS 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 ε-Fe3N nanocrystalline films34.

In summary, the uniform Co nanocluster-assembled films with different Co cluster sizes were successfully prepared by the plasma-gas-condensation 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 ρxx and ρxyA shown a decreasing function of the Co cluster sizes due to the drop of surface and interfacial scattering. The scaling relation of ρxyAρxxγ could be divided into two parts while obeyed the same line relationship between ρxyA and ρS 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 size-dependent scaling exponent were closely related to the interface and surface-induced 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.


The experimental apparatus of plasma-gas-condensation (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 chamber39. 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 JEM-2100 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 micro-morphology images of Co clusters-assembled films were acquired by SU-70 scanning electron microscope (SEM). The magnetic and electrical properties were performed on Quantum Design physical property measurement system (PPMS-9) 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 cluster-assembled films (~700 nm) were determined by the surface profiler (Alpha-Step D-100).

Electronic supplementary material


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).

Author Contributions

Author Contributions

D.L.P. and L.S.W. initiated the study. Q.F.Z., X.Z.W. and H.F.Z. prepared the samples by plasma-gas-condensation (PGC)-type cluster deposition system. Q.F.Z. and J.X. performed the PPMS-9 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.


Competing Interests

The authors declare that they have no competing interests.


Electronic supplementary material

Supplementary information accompanies this paper at 10.1038/s41598-017-11983-7.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Contributor Information

L. S. Wang, nc.ude.umx@slgnaw.

D. L. Peng, nc.ude.umx@gnepld.


1. Chadha M, Ng V. Sequential sputtered Co-HfO2 granular films. J. Magn. Magn. Mater. 2017;426:302. doi: 10.1016/j.jmmm.2016.11.094. [Cross Ref]
2. Sonntag J. The Origin of the Giant Hall Effect in Metal-Insulator Composites. Open Journal of Composite Materials. 2016;6:78. doi: 10.4236/ojcm.2016.63008. [Cross Ref]
3. Bartov D, Segal A, Karpovski M, Gerber A. Absence of the ordinary and extraordinary Hall effects scaling in granular ferromagnets at metal-insulator transition. Phys. Rev. B. 2014;90:144423. doi: 10.1103/PhysRevB.90.144423. [Cross Ref]
4. Smit J. The spontaneous Hall effect in ferromagnetics I. Physica. 1955;21:877. doi: 10.1016/S0031-8914(55)92596-9. [Cross Ref]
5. Berger L. Side-jump mechanism for the Hall effect of ferromagnets. Phys. Rev. B. 1970;2:4559. doi: 10.1103/PhysRevB.2.4559. [Cross Ref]
6. Karplus R, Luttinger JM. Hall Effect in Ferromagnetics. Phys. Rev. 1954;95:1154. doi: 10.1103/PhysRev.95.1154. [Cross Ref]
7. Canedy CL, Li XW, Xiao G. Large magnetic moment enhancement and extraordinary Hall effect in Co/Pt superlattices. Phys. Rev. B. 2000;62:508. doi: 10.1103/PhysRevB.62.508. [Cross Ref]
8. Song SN, Sellers C, Ketterson JB. Anomalous Hall effect in (110) Fe/(110) Cr multilayers. Appl. Phys. Lett. 1991;59:479. doi: 10.1063/1.105414. [Cross Ref]
9. Xiong P, et al. Extraordinary Hall effect and giant magnetoresistance in the granular Co-Ag system. Phys. Rev. Lett. 1992;69:3220. doi: 10.1103/PhysRevLett.69.3220. [PubMed] [Cross Ref]
10. Guo ZB, et al. Effects of surface and interface scattering on anomalous Hall effect in Co/Pd multilayers. Phys. Rev. B. 2012;86:104433. doi: 10.1103/PhysRevB.86.104433. [Cross Ref]
11. Zhang JY, et al. Effect of interfacial structures on anomalous Hall behavior in perpendicular Co/Pt multilayers. Appl. Phys. Lett. 2013;102:102404. doi: 10.1063/1.4795331. [Cross Ref]
12. Guo ZB, Mi WB, Li JQ, Cheng YC, Zhang XX. Enhancement in anomalous Hall resistivity of Co/Pd multilayer and CoPd alloy by Ga+ ion irradiation. Europhys. Lett. 2014;105:46005. doi: 10.1209/0295-5075/105/46005. [Cross Ref]
13. Wang JB, Mi WB, Wang LS, Zhang QF, Peng DL. Enhanced anomalous Hall effect in Fe nanocluster assembled thin films. Phys. Chem. Chem. Phys. 2014;16:16623. doi: 10.1039/C4CP01493F. [PubMed] [Cross Ref]
14. Wang JB, et al. Anomalous Hall effect in monodisperse CoO-coated Co nanocluster-assembled films. J. Magn. Magn. Mater. 2016;401:30. doi: 10.1016/j.jmmm.2015.10.008. [Cross Ref]
15. Li HB, et al. Extraordinary Hall effect and universal scaling in Fex(ZnO)1–x granular thin films at room temperature. Appl. Phys. Lett. 2015;106:012401. doi: 10.1063/1.4905357. [Cross Ref]
16. Wang JQ, Kim HK. Effect of Annealing on Extraordinary Hall Effects in Sputtered Granular Cu80Co20 Thin Films. IEEE T. Magn. 2006;42:3282. doi: 10.1109/TMAG.2006.879744. [Cross Ref]
17. Gerber A, et al. Correlation between the extraordinary Hall effect and resistivity. Phys. Rev. B. 2004;69:224403. doi: 10.1103/PhysRevB.69.224403. [Cross Ref]
18. Granovsky A, Brouers F, Kalitsov A, Chshiev M. Extraordinary Hall effect in magnetic granular alloys. J. Magn. Magn. Mater. 1997;166:193. doi: 10.1016/S0304-8853(96)00494-5. [Cross Ref]
19. Vedyaev AV, Granovskii AB, Kalitsov AV, Brouers F. Anomalous Hall effect in granular alloys. JETP. 1997;85:1204. doi: 10.1134/1.558394. [Cross Ref]
20. Sheng P. Fluctuation-induced tunneling conduction in disordered materials. Phys. Rev. B. 1980;21:2180. doi: 10.1103/PhysRevB.21.2180. [Cross Ref]
21. Zhang QF, et al. Electrical transport properties in Co nanocluster-assembled granular film. J. Appl. Phys. 2017;121:103901. doi: 10.1063/1.4977957. [PMC free article] [PubMed] [Cross Ref]
22. Hou DZ, et al. The anomalous Hall effect in epitaxial face-centered-cubic cobalt films. J. Phys. Condens. Matter. 2012;24:482001. doi: 10.1088/0953-8984/24/48/482001. [PubMed] [Cross Ref]
23. Guo ZB, et al. Anomalous Hall effect in polycrystalline Ni films. Solid State Communications. 2012;152:220. doi: 10.1016/j.ssc.2011.10.039. [Cross Ref]
24. Kamalakar MV, Raychaudhuri AK, Wei XY, Teng J, Prewett PD. Temperature dependent electrical resistivity of a single strand of ferromagnetic single crystalline nanowire. Appl. Phys. Lett. 2009;95:013112. doi: 10.1063/1.3174918. [Cross Ref]
25. Zhang, P., Cohen, R. E. & Haule, K. Effects of electron correlations on transport properties of iron at Earth's core conditions. Nature517, 605 (2015). [PubMed]
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. 2004;131:1. doi: 10.1016/j.ssc.2004.05.003. [Cross Ref]
27. Nagaosa N, Sinova J, Onoda S, MacDonald AH, Ong NP. Anomalous hall effect. Rev. Mod. Phys. 2010;82:1539. doi: 10.1103/RevModPhys.82.1539. [Cross Ref]
28. Kondorskii EN, Galkina OS, Ivanovskii VI, Cheremushkina AV, Usarov UT. Anisotropy of galvanomagnetic effects in single-crystal cobalt. Sov. Phys. JETP. 1974;38:977.
29. Wu SB, Yang XF, Chen S, Zhu T. Scaling of the anomalous Hall effect in perpendicular CoFeB/Pt multilayers. J. Appl. Phys. 2013;113:17C119. doi: 10.1063/1.4801335. [Cross Ref]
30. Zhang JY, et al. Effect of MgO/Co interface and Co/MgO interface on the spin dependent transport in perpendicular Co/Pt multilayers. J. Appl. Phys. 2014;116:163905. doi: 10.1063/1.4900193. [Cross Ref]
31. Wang JB, Mi WB, Wang LS, Peng DL. Interfacial-scattering–induced enhancement of the anomalous Hall effect in uniform Fe nanocluster-assembled films. Europhys. Lett. 2015;109:17012. doi: 10.1209/0295-5075/109/17012. [Cross Ref]
32. Meier H, Kharitonov MY, Efetov KB. Anomalous Hall effect in granular ferromagnetic metals and effects of weak localization. Phys. Rev. B. 2009;80:045122. doi: 10.1103/PhysRevB.80.045122. [Cross Ref]
33. Liu H, Lee FK, Zheng RK, Zhang XX, Tsui OKC. Extraordinary Hall effect in (Ni80Fe20)x(SiO2)1− x thin films. Phys. Rev. B. 2004;70:224431. doi: 10.1103/PhysRevB.70.224431. [Cross Ref]
34. Cheng YH, Zheng RK, Liu H, Tian Y, Li ZQ. Large extraordinary Hall effect and anomalous scaling relations between the Hall and longitudinal conductivities in ε-Fe3N nanocrystalline films. Phys. Rev. B. 2009;80:174412. doi: 10.1103/PhysRevB.80.174412. [Cross Ref]
35. Zhang Q, et al. Anomalous Hall effect in Fe/Au multilayers. Phys. Rev. B. 2016;94:024428. doi: 10.1103/PhysRevB.94.024428. [Cross Ref]
36. Wang JQ, Xiao G. Large finite-size effect of giant magnetoresistance in magnetic granular thin films. Phys. Rev. B. 1995;51:5863. doi: 10.1103/PhysRevB.51.5863. [PubMed] [Cross Ref]
37. Chen J, Hershfield S. Effect of spin-flip scattering on current-in-plane giant magnetoresistance. Phys. Rev. B. 1998;57:1097. doi: 10.1103/PhysRevB.57.1097. [Cross Ref]
38. Imort I-M, Thomas P, Reiss G, Thomas A. Anomalous Hall effect in the Co-based Heusler compounds Co2FeSi and Co2FeAI. J. Appl. Phys. 2012;111:07D313. doi: 10.1063/1.3678323. [Cross Ref]
39. Wang LS, et al. Gas-phase preparation and size control of Fe nanoparticles. Appl. Phys. A. 2011;103:1015. doi: 10.1007/s00339-011-6383-3. [Cross Ref]

Articles from Scientific Reports are provided here courtesy of Nature Publishing Group