Crossover between weak anti-localization and weak localization by Co doping and annealing in gapless PbPdO2 and spin gapless Co-doped PbPdO2 S. M. Choo, K. J. Lee, S. M. Park, J. B. Yoon, G. S. Park, C.-Y. You, and M. H. Jung Citation: Applied Physics Letters 106, 172404 (2015); doi: 10.1063/1.4919452 View online: http://dx.doi.org/10.1063/1.4919452 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/106/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetic versus nonmagnetic ion substitution effects in gapless semiconductor PbPdO2 Appl. Phys. Lett. 106, 072406 (2015); 10.1063/1.4913301 Electronic structure of the spin gapless material Co-doped PbPdO2 J. Appl. Phys. 114, 103709 (2013); 10.1063/1.4821039 Annealing effect on surface morphology and electrical transport of PbPdO2 and Pb(Pd,Co)O2 J. Appl. 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Jung1,a) Department of Physics, Sogang University, Seoul 121-742, South Korea Department of Electrical and Computer Engineering and NUSNNI, National University of Singapore, Singapore 117576, Singapore Department of Physics, Inha University, Incheon 402-751, South Korea (Received 20 January 2015; accepted 20 April 2015; published online 30 April 2015) The magnetotransport properties of Pb(Pd,Co)O2 and PbPdO2 thin films were investigated. In magnetoconductance curves, we observed a crossover between weak anti-localization (WAL) and weak localization (WL) depending on the annealing and Co doping in PbPdO2 thin films. For the Pb(Pd,Co)O2 case showing WAL signals, the ex-situ annealing weakens the Pd-O hybridization by stabilizing Co3þ states and generating Pd1þ states, instead of Pd2þ, so that the spin-orbit coupling (SOC) strength is significantly reduced. It causes the dominant magnetotransport mechanism change from WAL to WL. This annealing effect is compared with the PbPdO2 case, which possesses WL signals. The annealing process stabilizes the oxygen states and enhances the Pd-O hybridization, and consequently the SOC strength is enhanced. Our experimental results are well explained by the Hikami-Larkin-Nagaoka theory in terms of two important physical parameters; C 2015 AIP Publishing LLC. SOC strength-related a and inelastic scattering length l/. V [http://dx.doi.org/10.1063/1.4919452] Gapless semiconductors,1,2 that have zero gap between the conduction and valence bands at the Fermi level, are exciting materials to show unique electronic properties caused by their exotic band structure. They are extremely sensitive to external influences such as chemical doping, lattice imperfection, temperature, and magnetic field.1,3–5 Recently, a theoretical prediction of a spin gapless semiconductor has been developed by inducing spin degree of freedom in gapless semiconductors.6–9 These spin gapless semiconductors attract more interest because of their possible applications in the spintronics.8,10 Additional spin degree of freedom will be a huge advantage in high-density information storage and to control the spin polarization. Furthermore, because of its high spin polarization, it is applicable to spin filters. Wang predicted that PbPdO2 is a gapless semiconductor and Co-doped PbPdO2 is a spin gapless semiconductor by the first principle calculation.8 Experimentally, it was reported that a bulk PbPdO2 exhibits a metal-insulator-like transition and a ferromagnetic-like behavior at low temperatures.11,12 The metal-insulator-like transition comes from the gapless electronic band structure, and the ferromagnetic-like behavior seems to be associated with oxygen vacancies and/or spinorbit coupling (SOC). More investigations on Co- and Mndoped PbPdO2 showed that the magnetic properties can be easily tuned to be either ferromagnetic or antiferromagnetic.13 In a thin film form of Co-doped PbPdO2, colossal electroresistance and giant magnetoresistance were proposed in a wide temperature range from 25 to 300 K.14 The magnetoresistance ratio changes the sign from positive to negative when the temperature is cooled to 27 K. This sign change within such a a) Author to whom correspondence should be addressed. Electronic mail: mhjung@sogang.ac.kr 0003-6951/2015/106(17)/172404/5/$30.00 narrow temperature range was described by sharp phase transition or sudden change of the band structure. Our recent study on both PbPdO2 and Co-doped PbPdO2 thin films showed that the ex-situ annealing process has a major influence on the electrical transport as well as the surface morphology.15 This infers that the oxygen in the ex-situ annealing process plays an important role in determining the physical properties. Especially, the magnetization of PbPdO2 shows ferromagnetic-like signal, despite there is no magnetic ion.11 The origin of the ferromagnetism seems to be oxygen vacancies and/or SOC. Thus, we need to study the role of oxygen and the SOC mechanism by varying the annealing time. We have observed a crossover between weak antilocalization (WAL) and weak localization (WL) in Pb(Pd,Co)O2 samples depending on ex-situ annealing. Since the SOC plays an important role in the magnetic and electric properties of gapless and spin gapless semiconductors, the observed crossover between WAL and WL provides clues to understanding the underlying physics. Such crossovers between WAL and WL have been widely observed in various systems. For example, Roulleau et al.16 reported the crossover in InAs nanowires by changing the nanowire diameter, and Sch€apers et al. also reported similar phenomena in GaInAs/InP nanowires where the crossover is explained by a confinementinduced effect for narrow nanowires.17 Recently, such crossovers have been found in topological insulators by changing magnetic impurity concentration, temperature, and magnetic field,5 or by controlling the Fermi level with gate voltage.18 More recently, Wang et al.19 have shown the crossover even in the bulk state of Bi2Se3 possessing strong SOC. Also in graphene systems, the crossover was reported due to the valley symmetry breaking in Fermi line,20 and the transition from WL to WAL was found when the carrier density decreases and 106, 172404-1 C 2015 AIP Publishing LLC V This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 137.132.123.69 On: Tue, 23 Jun 2015 01:17:27 172404-2 Choo et al. the temperature increases.21 Despite the variety of physical origin for the crossover, this study can call another way for better understanding of the crossover induced by the ex-situ annealing, especially in gapless semiconducting systems. The thin films of PbPdO2 and Pb(Pd,Co)O2 (herein, PbPd0.75Co0.25O2) were deposited by a pulsed laser deposition (PLD) technique. The targets for deposition were manufactured by solid state reactions.11,13 The samples were deposited on MgO (100) substrates. An excimer laser of COMPEX-102 model with a KrF(248 nm) source was used for the PLD system. A lab made optical setup with a high vacuum chamber was used in the PLD setup. The chamber was prepared with an initial vacuum condition of 10À6 Torr. The deposition temperature was 550 C which was reached in a rate of 10 C/min. The oxygen partial pressure during the deposition was 300 mTorr. The laser power was maintained at 0.19 W and the beam trace was fixed at a mm  mm area for each pulse with a pulse rate of Hz. After deposition the samples were ex-situ annealed in an air with PbO powders in a box furnace for 12 h and 24 h at 650 C which is the ex-situ annealing temperature. Note that according to our previous study,15 the optimal annealing conditions were 650 C and 12 h. The scanning electron microscope and X-ray diffraction were used for sample characterization. The film thicknesses of the Pb(Pd,Co)O2 and PbPdO2 films were 60 nm and 200 nm, respectively, which were optimal thickness with high crystallinity and smooth surface. The X-ray spectroscopy was measured to determine the Co valence state. The magneto-transport measurements were done using the Van de Pauw method. Several difference samples were made in separate annealing runs to check reproducible data. The magnetic fields were swept from À9 to T at low temperatures down to K. The physical property measurement system (PPMS-Quantum Design) was used to change the temperature and magnetic field. Figure shows the Hall resistivity qxy of as-grown and ex-situ annealed Pb(Pd,Co)O2 thin films. The slopes of all the Hall resistivity are positive, implying that the charge carriers are mostly holes. The carrier densities of the Pb(Pd,Co)O2 films are 19.02, 15.51, and 6.44  1019 cmÀ3 for the asgrown, 12 and 24 h-annealed samples, respectively. The carrier density decreases gradually by the increase of ex-situ FIG. 1. Hall resistivity qxy for as-grown, 12 and 24 h-annealed Pb(Pd,Co)O2 thin films at K. The inset shows the temperature dependence of electrical resistivity qxx for as-grown and 24 h-annealed Pb(Pd,Co)O2, respectively. Appl. Phys. Lett. 106, 172404 (2015) annealing time. The inset of Fig. shows the temperature dependence of electrical resistivity qxx. The resistivity of Pb(Pd,Co)O2 is semiconducting, where the resistivity increases as the temperature decreases, i.e., dqxx/dT < 0. However, we could not fit the data with the Arrhenius law, which is lnq $ À1/T. The mobilities are 9.33, 2.56, and 1.96 cm2 VÀ1 sÀ1 for as-grown, 12 and 24 h-annealed samples, respectively. The carrier mobility decreases by the increase of the ex-situ annealing time. As we reported previously, the carrier density and mobility of Pb(Pd,Co)O2 are strongly influenced by Pd-O hybridization and oxygen vacancies on ex-situ annealing.15 Now let us get to the main issue on the magnetotransport properties of Pb(Pd,Co)O2. In Fig. 2, we plot the magnetoconductance (MC) curves measured at K. For the Pb(Pd,Co)O2 case in Fig. 2(a), it is hard to compare the MC curves between the as-grown and ex-situ annealed samples because of their different behaviors. Here, we only focus on the low-field data between À1 and T. The as-grown Pb(Pd,Co)O2 sample shows a sharp negative MC cusp at low fields. This behavior is a finger print of WAL, which normally comes from strong SOC. The low-field MC curve of Pb(Pd,Co)O2 shows a change from negative to positive cusp by the ex-situ annealing. The annealed Pb(Pd,Co)O2 samples exhibit only positive MC cusps at low fields. Therefore, we speculate that the SOC is weakened by ex-situ annealing and thereby the WAL is changed to WL. For the PbPdO2 case in Fig. 2(b), the main features are the only positive MC cusp at low fields, which is different from the Pb(Pd,Co)O2 case. The results are in consistent with the bulk PbPdO2 samples.11,13 Since the PbPdO2 has no magnetic scattering source and shows similar positive MC behavior observed in the annealed Pb(Pd,Co)O2, the positive MC cusp in the PbPdO2 films can be interpreted as WL. In that sense, we discuss the WL and WAL contributions to the MC data. In order to explain the experimental MC data of WL and WAL, the Hikami-Larkin-Nagaoka (HLN) theory has been FIG. 2. MC curves for as-grown, 12 and 24 h-annealed (a) Pb(Pd,Co)O2 and (b) PbPdO2 films at K. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 137.132.123.69 On: Tue, 23 Jun 2015 01:17:27 172404-3 Choo et al. Appl. Phys. Lett. 106, 172404 (2015) widely used in the diffusive regime of 2-dimensional (2D) systems.22,23 Due to the layered crystal structure of Pb(Pd,Co)O2 and its 2D conduction path,24 it can be considered to be a quasi-2D system although the thickness of our films is 60 nm. The original HLN theory rigorously treated the localization problem including the spin-orbit interaction and the magnetic scattering by impurity spins because these interactions have different symmetries.23 We tried to fit our experimental MC data with this original HLN theory, but could not extract any physically meaningful parameters because of too many fitting parameters in one MC curve. Thus, we adopted the simplified empirical HLN theory with two fitting parameters a and l/, used in many other materials with strong spin-orbit coupling,5,25–29 given by drðBÞ ¼ rðBÞ À rð0Þ ae2 h h w þ À ln ; ¼ 2p h 4eBl2U 4eBl2U (1) where e is the electronic charge, h is the Planck’s constant, l/ is the inelastic scattering length, and w(x) is the digamma function. The a value should be either 0, 1, or À1/2. These three cases of a are distinguished by the main mechanism in the process of electronic transport.29,30 When a is 0, there is strong magnetic scattering so that all quantum phases are incoherent and disappear. If SOC and magnetic scattering are rather weak, WL is dominant due to the constructive interference of coherent quantum phases, so that a ¼ 1. If SOC is strong but magnetic scattering is weak, a is À0.5, because WAL is the main mechanism where the destructive quantum interference is dominant due to the strong SOC. If single mechanism is dominant, a should be one of the exact values of À0.5, 0, or 1. However, each mechanism competes each other so that a is an intermediate value between them in actual systems. It is well known that when a is positive, the MC curve tends to show a positive slope, and it is a characteristic of commonly observed WL.5 On other hand, a negative slope of MC curve is a signature of WAL, which originates from strong SOC. If a is an intermediate value, the mechanism in the magneto-transport is in a competing regime between WAL and WL.17,18,31–36 Now let us discuss the fitted results by the HLN theory for experimental MC data of Pb(Pd,Co)O2 and PbPdO2 thin films. Fig. shows the well fitted results by the HLN theory. We obtain intermediate a values for different ex-situ annealed conditions in the Pb(Pd,Co)O2 films. The fitted a value of the as-grown Pb(Pd,Co)O2 film is À0.15. This negative value suggests strong SOC, which means WAL is the dominant transport mechanism. As aforementioned, the negative a ( ¼ À0.5) value implies strong SOC. Thus, it is clear evidence of the strong SOC in the as-grown Pb(Pd,Co)O2 film. However, the a value becomes positive 0.013 and 0.0023 for the 12 and 24 h-annealed samples, respectively. The positive a implies that WL overcomes the WAL mechanism. In other word, the quantum interference is changed from destructive to constructive by the ex-situ annealing. This crossover can be explained by the Co state in Pb(Pd,Co)O2. The Co state in as-grown Pb(Pd,Co)O2 is trivalent, which was confirmed by previous x-ray absorption FIG. 3. Low-field MC data for as-grown, 12 and 24 h-annealed (a) Pb(Pd,Co)O2 and (b) PbPdO2 films at K. The red lines represent the fitted curves by the HLN theory. As for the fitted results, we obtain a ¼ À0.15, 0.013, 0.0023 and l/ ¼ 79, 297, 249 nm for the as-grown, 12 and 24 hannealed Pb(Pd,Co)O2 samples, respectively, and a ¼ 0.31, 0.20, 0.25 and l/ ¼ 33, 78, 74 nm for the as-grown, 12 and 24 h-annealed PbPdO2 samples, respectively. spectroscopy (XAS) experiments,37 then the trivalent Co forces the Pd state in Pb(Pd,Co)O2 to exist as Pd1þ. The Pd1þ state induced by the Co3þ state causes the Pd-O hybridization to be weaker by ex-situ annealing. The weakened PdO hybridization can result in the decrease of SOC, and finally the constructive quantum interference (i.e., WL) is achieved by annealing in the Pb(Pd,Co)O2 films. This result is supported by our previous report.15 On the other hand, for PbPdO2, the HLN theory may not be suitable because of the thick film thickness of 200 nm. However, we fit the MC data with a similar method to the Pb(Pd,Co)O2 case for simple comparison. The fitted results support the 3-dimensional (3D) transport mechanism in the PbPdO2 case, which will be discussed later. We obtain only positive a values (WL) for different ex-situ annealing conditions in the PbPdO2 films. The obtained a values are 0.31, 0.20, and 0.25 for the as-grown, 12 and 24 h-annealed samples, respectively. Since the a values are positive (closer to instead of À0.5), the origin of positive a is either due to strong magnetic scattering (where a is 0) or strong WL (where a is 1). However, in the PbPdO2 films, there is no magnetic scattering source. Thus, the origin of the positive MC curves is relatively weak SOC. Even though the strong SOC exists in the gapless PbPdO2 films, WL can be dominant when the spin flip time due to the SOC is relatively longer than the inelastic scattering time, or SOC scattering length is longer than inelastic scattering length l/. It means that the quantum interference between the time reversed trajectories are still constructive in spite of the existence of This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 137.132.123.69 On: Tue, 23 Jun 2015 01:17:27 172404-4 Choo et al. SOC. Similar phenomena were already reported in topological insulators by Wang et al.19 This is also consistent with the results of annealed Pb(Pd,Co)O2. The opposite annealing effect in PbPdO2, compared to Pb(Pd,Co)O2, can be explained by oxygen vacancies, which influence the Pd-O hybridization.29,30 As the samples are annealed, the oxygen vacancies are reduced and the Pd1þ states are reduced, unlike the Pb(Pd,Co)O2. This causes the Pd-O hybridization to be enhanced, which well agrees with the results of XAS and photo emission spectroscopy (PES) experiments.29 Also, in our previous paper,15 the carrier density of PbPdO2 is decreased after the ex-situ annealing and the mobility is increased due to the enhanced Pd-O hybridization. Then, the enhanced Pd-O hybridization can lead to the increase of SOC, and finally the a value decreases with the ex-situ annealing in PbPdO2. By fitting the MC data with the HLN theory, we can obtain another important parameter, the inelastic scattering length l/. If the inelastic scattering length is longer than the thickness of the sample, the transport mechanism can be treated by a 2D regime.22 For the as-grown, 12 and 24 hannealed Pb(Pd,Co)O2 films, the inelastic scattering lengths are 79, 297, and 249 nm, respectively. When we consider the thickness (¼60 nm) of the Pb(Pd,Co)O2 film, it implies that the transport mechanism is in the 2D regime because the l/ is longer than the sample thickness. This result is also reasonable when considering the relation between l/ and a.36 However, for the as-grown PbPdO2 films, the l/ is 33 nm which is shorter than the sample thickness. This hints that the transport mechanism is in the 3D regime, as aforementioned, where many scattering events occur in the out-ofplane direction of the film. However, by annealing for 12 and 24 h, the l/ increases to 78 nm and 74 nm, respectively. This increment of l/ suggests that the transport mechanism approaches the 2D transport regime. Considering the relation between l/ and a, this result is also reasonable. In order to analyze the WAL behavior (i.e., negative MC curve) of the as-grown Pb(Pd,Co)O2 film more closely, the temperature-dependent data of low-field MC have been measured as plotted in Figs. 4(a) and 4(b). It shows that the sharp negative cusp in MC gradually broadens as the temperature increases up to K, while it changes to a broad positive cusp above K. The fitted l/ decreases gradually as the temperature increases from K to K. The l/ is 80 nm at K and monotonically decreases to 20 nm at K, as shown in Fig. 5. Here, it is noticeable that the l/ at K is 50 nm that is near the thickness of Pb(Pd,Co)O2 film. This infers that the transport mechanism can be changed around K. Indeed, the a value changes from negative to positive with increasing temperature at K, as marked with green horizontal line in Fig. 5. As aforementioned, the l/ is closely associated with the a. The negative a means strong SOC below K, where we have larger l/ values than the sample thickness, and vice versa. Similar crossover due to the length scale has been reported in GaInAs/InP nanowire.17 They reported that the crossover between WAL and WL occurs when the spin relaxation length is suppressed by reducing the diameter of nanowires. Furthermore, the temperature dependence of l/ is wellknown to be scaled as l/ $ TÀp/2.25 In Fig. 5, we plot the l/ Appl. Phys. Lett. 106, 172404 (2015) FIG. 4. (a) Low-field MC data of as-grown Pb(Pd,Co)O2 film measured at various temperatures 2, 3, 4, 5, 8, and K. The red lines represent the fitted curves by the HLN theory. (b) Corresponding magnetoresistance (MR) data measured at various temperatures 2, 3, 4, 5, 7, 8, and K. data as a function of temperature in logarithmic scales. The data are well fitted with p ¼ 1.1 0.16 when T < K and p ¼ 2.2 0.44 when T > K The p value determines the collision type of inelastic scattering. When the electron-electron collision is dominant, p ¼ 1, while the electron-phonon collision is dominant, p ¼ 3. Our experimental data suggest that when temperature is below K, the phonon scattering is suppressed and electron-electron scattering prevails. For higher temperature, electron-phonon scattering starts to contribute. In our observation, when temperature is raised above K, three important changes occur simultaneously: (1) the MC mechanism (sign of a) is changed from WAL to WL, (2) the 2D nature is weakened (l/ < film thickness), and (3) the phonon scattering become important (p $ 2.2). We speculate that those three changes are mutually related each other. We observed WAL signals from the strong SOC in Pb(Pd,Co)O2 films. By ex-situ annealing, the SOC is weakened and the crossover from WAL to WL is observed. These results are compared with WL signals for PbPdO2. The different magneto-transport mechanism was interpreted in terms of a and l/ parameters based on the HLN theory, which are closely associated with the Pd-O hybridization of FIG. 5. Fitted l/ and a values as a function of temperature for as-grown Pb(Pd,Co)O2 film. The red and blue dashed lines are the cases with p ¼ and 3, respectively. The red and blue solid lines represent the linear fits from the experimental data for two temperature regimes, T < K and T > K, respectively. The green horizontal line indicates zero a. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 137.132.123.69 On: Tue, 23 Jun 2015 01:17:27 172404-5 Choo et al. the two films. This strong dependence of SOC associated with Pd-O hybridization by annealing process shows the potential of Pb(Pd,Co)O2 as a spintronics material. This work was supported by the National Research Foundation of Korea (NRF) (Nos. 2014R1A2A1A11050401, 2013R1A1A2011936, and 2012M2A2A6004261). I. M. Tsidilkovski, Electron Spectrum of Gapless Semiconductors (Springer, New York, 1996). X. L. Wang, S. X. Dou, and C. Zhang, NPG Asia Mater. 2, 31 (2010). Y. Li, Z. Zhou, P. Shen, and Z. Chen, ACS Nano 3, 1952 (2009). M. I. D’yakonov and A. V. Khaetskl, Zh. Eksp. Teor. Fiz. 82, 1584 (1982) [Sov. Phys. JETP 55, 917 (1982)]. M. Liu, J. Zhang, C.-Z. Chang, Z. Zhang, X. Feng, K. Li, K. He, L.-L. Wang, X. Chen, X. Dai, Z. Fang, Q.-K. Xue, X. Ma, and Y. Wang, Phys. Rev. Lett. 108, 036805 (2012). Y. Pan and Z. Yang, Phys. Rev. B 82, 195308 (2010). S. Ouardi, G. H. Fecher, and C. Felser, Phys. Rev. Lett. 110, 100401 (2013). X. L. Wang, Phys. Rev. Lett. 100, 156404 (2008). G. Z. Xu, E. K. Liu, Y. Du, G. J. Li, G. D. Liu, W. H. Wang, and G. H. Wu, EPL 102, 17007 (2013). 10 S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001). 11 K. J. Lee, S. M. Choo, J. B. Yoon, K. M. Song, Y. Saiga, C.-Y. You, N. Hur, S. I. Lee, T. Takabatake, and M. H. Jung, J. Appl. Phys. 107, 09C306 (2010). 12 T. C. Ozawa, T. Taniguchi, Y. Nagata, Y. Noro, T. Naka, and A. Matsushita, J. Alloys Compd. 388, (2005). 13 K. J. Lee, S. M. Choo, Y. Saiga, T. Takabatake, and M.-H. Jung, J. Appl. Phys. 109, 07C316 (2011). 14 X. Wang, G. Peleckis, C. Zhang, H. Kimura, and S. Dou, Adv. Mater. 21, 2196 (2009). 15 S. M. Choo, K. J. Lee, S. M. Park, G. S. Park, and M.-H. Jung, J. Appl. Phys. 113, 014904 (2013). 16 P. Roulleau, T. Choi, S. Riedi, T. Heinzel, I. Shorubalko, T. Ihn, and K. Ensslin, Phys. Rev. B 81, 155449 (2010). Appl. Phys. Lett. 106, 172404 (2015) 17 Th. Sch€apers, V. A. Guzenko, M. G. Pala, U. Z€ ulicke, M. Governale, J. Knobbe, and H. Hardtdegen, Phys. Rev. B 74, 081301(R) (2006). M. Lang, L. He, X. Kou, P. Upadhyaya, Y. Fan, H. Chu, Y. Jiang, J. H. Bardarson, W. Jiang, E. S. Choi, Y. Wang, N.-C. Yeh, J. Moore, and K. L. Wang, Nano Lett. 13, 48 (2013). 19 H. Wang, H. Liu, C.-Z. Chang, H. Zuo, Y. Zhao, Y. Sun, Z. Xia, K. He, X. Ma, X. C. Xie, Q.-K. Xue, and J. Wang, Sci. Rep. 4, 5817 (2014). 20 E. McCann, K. Kechedzhi, V. I. Fal’ko, H. Suzuura, T. Ando, and B. L. Altshuler, Phys. Rev. Lett. 97, 146805 (2006). 21 F. V. Tikhonenko, A. A. Kozikov, A. K. Savchenko, and R. V. Gorbachev, Phys. Rev. Lett. 103, 226801 (2009). 22 P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985). 23 S. Hikami, A. I. Larkin, and Y. Nagaoka, Prog. Theor. Phys. 63, 707 (1980). 24 S. W. Chen, S. C. Huang, G. Y. Guo, J. M. Lee, S. Chiang, W. C. Chen, Y. C. Liang, K. T. Lu, and J. M. Chen, Appl. Phys. Lett. 99, 012103 (2011). 25 R. Scherwitzl, S. Gariglio, M. Gabay, P. Zubko, M. Gibert, and J.-M. Triscone, Phys. Rev. Lett. 106, 246403 (2011). 26 J. Kim, S. Lee, Y. M. Brovman, M. Kim, P. Kim, and W. Lee, Appl. Phys. Lett. 104, 043105 (2014). 27 J. Hu, J. Y. Liu, and Z. Q. Mao, J. Phys.: Condens. Matter 26, 095801 (2014). 28 S.-P. Chiu and J.-J. Lin, Phys. Rev. B 87, 035122 (2013). 29 H.-T. He, G. Wang, T. Zhang, I.-K. Sou, G. K. L. Wong, J.-N. Wang, H.Z. Lu, S.-Q. Shen, and F.-C. Zhang, Phys. Rev. Lett. 106, 166805 (2011). 30 J. A. Kurzman, M.-S. Miao, and R. Seshadri, J. Phys.: Condens. Matter 23, 465501 (2011). 31 B. Y. Jin and J. B. Ketterson, Phys. Rev. B 33, 8797(R) (1986). 32 S. A. Studenikin, P. T. Coleridge, N. Ahmed, P. J. Poole, and A. Sachrajda, Phys. Rev. B 68, 035317 (2003). 33 I. Garate and L. Glazman, Phys. Rev. B 86, 035422 (2012). 34 H. Suzuura and T. Ando, Phys. Rev. Lett. 89, 266603 (2002). 35 J. B. Miller, D. M. Zumb€ uhl, C. M. Marcus, Y. B. Lyanda-Geller, D. Goldhaber-Gordon, K. Campman, and A. C. Gossard, Phys. Rev. Lett. 90, 076807 (2003). 36 H.-Z. Lu, J. Shi, and S.-Q. Shen, Phys. Rev. Lett. 107, 076801 (2011). 37 D. H. Kim, J. H. Hwang, E. S. Lee, K. J. Lee, S. M. Choo, M. H. Jung, J. Baik, H. J. Shin, B. J. Kim, K. Kim, B. I. Min, and J.-S. Kang, Appl. Phys. Lett. 104, 022411 (2014). 18 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 137.132.123.69 On: Tue, 23 Jun 2015 01:17:27 . Crossover between weak anti -localization and weak localization by Co doping and annealing in gapless PbPdO2 and spin gapless Co- doped PbPdO2 S. M. Choo, K. J. Lee,. http://scitation.aip.org/termsconditions. Downloaded to IP: 137.132.123.69 On: Tue, 23 Jun 2015 01:17:27 Crossover between weak anti -localization and weak localization by Co doping and annealing in gapless PbPdO 2 and spin. anti -localization (WAL) and weak localization (WL) depending on the annealing and Co doping in PbP dO 2 thin films. For the Pb(Pd ,Co) O 2 case showing WAL signals, the ex-situ annealing weakens the Pd-O