Anomalous Hall effect of Nd 0.7 Sr 0.3 MnO 3 films with large magnetoresistance ratio: Evidence of Berry phase effect

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1 PHYSICAL REVIEW B, VOLUME 64, Anomalous Hall effect of Nd 0.7 Sr 0.3 MnO 3 films with large magnetoresistance ratio: Evidence of Berry phase effect H. C. Yang Department of Physics, National Taiwan University, Taipei, Taiwan, Republic of China L. M. Wang Department of Electrical Engineering, Ta-Yei University, Chang-Hwa 515, Taiwan, Republic of China H. E. Horng Department of Physics, National Taiwan Normal University, Taipei, Taiwan, Republic of China Received 21 November 2000; revised manuscript received 5 July 2001; published 10 October 2001 The transverse Hall resistivity, xy, and magnetization, M, of 110 and 100 oriented epitaxial Nd 0.7 Sr 0.3 MnO 3 films with large magnetoresistance were measured as a function of temperature and applied magnetic field to study the ordinary and spontaneous Hall coefficients. In the ferromagnetic regime, 100 K T 200 K, ( R s /R o ) T was found to be proportional to exp( E c /k B T), where R s is the spontaneous Hall coefficient, R o is the ordinary Hall coefficient, and E c is the core energy of the magnetic dipole. In addition, R s 2 was found to be proportional to xx in the low-temperature regime (T 160 K) where the ordinary Hall coefficient, R o, is independent of temperature. A scaling behavior, R s xx was observed at high temperatures (T 160 K). Hall effects of 110 and 100 oriented films are compared to each other. The results are discussed in terms of the exiting theories. DOI: /PhysRevB PACS number s : m, h, i INTRODUCTION Strong interest in the transport and magnetic properties has been stimulated by the observation of colossal magnetoresistance CMR near T c. 1 4 Several groups measured the Hall resistivity of epitaxial films and single crystals of these CMR materials In Hall measurements, it was found that xy can be expressed as xy R o B 4 MR s 1 where R o is the ordinary Hall coefficient, B is the magnetic induction, M is the magnetization, and R s the spontaneous Hall coefficient. The R s becomes evident above 100 K, increases sharply around T c and peaks near T c, and decreases at high temperatures. Besides, the R s is proportional to the zero-field resistivity. It is surprising that the sign of R s is opposite to R o. Theories 14,15 have been proposed to clarify Hall effects. Recently, a Berry phase theory of the anomalous Hall effects and its implication to CMR has been proposed by Ye et al. 14 The theory shows that the Berry phase can in the presence of spin-orbital coupling give rise to an anomalous Hall effect. The theory predicts that the value of R s increases rapidly in magnitude as temperature is raised from zero through the ferromagnetic transition temperature, T c, peaks at temperature T max, which is higher than T c. In the low temperature regime, R s was found to be proportional to exp ( E c /k B T), where is a parameter and E c is the core energy of the magnetic dipole. In the high temperature regime, R s behaves as R s T 3. Most studies of Hall effects were done on samples with low magnetoresistance such as La 1 x Ca x MnO 3. Hall effects measured on samples with high magnetoresistance were seldom reported presumably because of complications in Hall measurement for samples with high resistivity. Recently, Poddar et al. 16 and Wagner et al. 17 have reported the Hall measurements on the bulk Nd 2/3 Sr 1/3 MnO 3 and Nd 0.5 Sr 0.5 MnO 3 films, respectively. However, in the work done by Poddar et al., anomalous temperature dependences of R s and R o associated with an opposite sign of Hall voltage to that observed in other manganites were presented. Thus a detailed temperature dependence of Hall coefficients of Nd 0.7 Sr 0.3 MnO 3 films is worthily studied. In this work we investigated the transverse Hall resistivity, xy, for 100 and 110 oriented Nd 0.7 Sr 0.3 MnO 3 films with high CMR ratio 1000%. We derived the temperature dependence of R s both at T T c and T T c. From the temperature dependence of R s, we want to study the effect of the Berry phase on the anomalous Hall effect. Our present R s data supply the evidences of the Berry phase effect on the anomalous Hall effect. EXPERIMENTS We prepared Nd 0.7 Sr 0.3 MnO 3 NSMO films by radio frequency magnetron sputtering Nd 0.7 Sr 0.3 MnO 3 target. The sputtering gas was a mixture of Ar and O 2 3 atm/7 atm. The substrate used was 100 and 110 oriented SrTiO 3 substrates. The films were grown at 680 C. The powder x-ray diffractometer was used to characterize the crystal orientation of grown films. A detailed description of the preparation and transport properties in magnetic fields is reported in Ref. 18. For magnetoresistance and Hall measurements, the films were patterned to a five-leads Hall geometry. Au film was evaporated onto the electrical leads to decrease the contact resistance. A magnetic field up to 7 T was applied to the sample and the applied current was 100 A /2001/64 17 / /$ The American Physical Society

2 H. C. YANG, L. M. WANG, AND H. E. HORNG PHYSICAL REVIEW B FIG. 1. X-ray diffraction pattern of a 110 and b 100 oriented Nd 0.7 Sr 0.3 MnO 3 film on the SrTiO and SrTiO substrates. RESULTS AND DISCUSSION Figure 1 shows the x-ray diffraction of Nd 0.7 Sr 0.3 MnO 3 films grown onto SrTiO 3 (100) and 110 substrates. The crystal structure of the Nd 0.7 Sr 0.3 MnO 3 films deposited onto SrTiO 3 (100) can be indexed with its 110 direction perpendicular to the surface of the film and with d 110 spacing of 3.87 Å. For Nd 0.7 Sr 0.3 MnO 3 films grown onto SrTiO 3 110, its 100 direction is perpendicular to the surface of the film and the d 100 spacing is 5.44 Å. Here an orthorhombic crystal structure for Nd 0.7 Sr 0.3 MnO 3 is taken into account. In Fig. 2 a we show the resistivity, xx, as a function of temperature in zero and 7 T for Nd 0.7 Sr 0.3 MnO 3 films. The magnetoresistance MR ratio xx (H 0) xx (H 7 T) / xx (H 7 T) was 1000% and 1200% respectively for 110 and 100 oriented films at T 220 K. The magnetization M as a function of applied field H at various temperatures for the 110 oriented film is shown in Fig. 2 b. The Curie temperature, T c, extrapolated from the linear temperature dependence of magnetic susceptibility, 1/, inthe paramagnetic state is T c 222 K for 110 and 100 oriented films as shown in the inset of Fig. 2 b. In the ferromagnetic state, as shown in Fig. 2 b, M initially increases linearly with H then goes to a saturated-like region with a finite slope in high fields. The slope of M versus H curves is temperature dependent both for the low-field and high-field regions. In FIG. 2. a xx as a function of temperature in zero and 7 T. The inset shows the magnetoresistance MR ratio xx (H 0) xx (H 7 T)/ xx (H 7 T). The MR ratio is 1000% and 1200% respectively for 110 and 100 oriented films at T 220 K. b Magnetization as a function of applied field for a 110 oriented film at various temperatures. The inset shows the 1/ as a function of temperature. the paramagnetic state, a linear field dependence of M is observed. In Figs. 3 a, 3 b, 3 c, and 3 d we show the magnetic field dependence of the transverse Hall resistivity xy for 100 and 110 oriented Nd 0.7 Sr 0.3 MnO 3 films at different temperatures. The solid or dashed lines are the guides to the eyes. In the low field regime xy is negative and linearly proportional to the applied magnetic field with a negative slope while in the high field regime xy is reverted to a linear behavior with a positive slope. The initial drop becomes larger when T is close to T c, and xy shows a profound concave upward feature near T c. For T above T c, a negative

3 ANOMALOUS HALL EFFECT OF Nd 0.7 Sr 0.3 MnO 3... PHYSICAL REVIEW B FIG. 3. Magnetic field dependence of xy for a, b 110 and c, d 100 oriented Nd 0.7 Sr 0.3 MnO 3 films at different temperatures. Hall effect was observed. The xy curves exhibit similar characteristics as those observed in other doped manganeseoxide perovskites The Hall resistivity is affected both by skew scattering and Lorentz scattering. In the skew scattering, the scattering of charge carriers from the local moment is asymmetric. The charge carrier has larger probability of being scattered from either towards the left or right with respect to the initial direction. The effect, known as the magnetic skew scattering, which occurred in addition to the Lorentz scattering is responsible for the extraordinary Hall coefficient. Therefore, in a magnetic system xy can be expressed as Eq. 1. Inthe high field regime where M is saturated, xy is a linear function of the applied H. In terms of Eq. 1, xy data may be decomposed into a positive term, R o B, and an anomalous term, 4 MR s, which is strongly dependent on temperature. The slope of the xy B curve above the saturation region gives R o. We noted that B H 4 (N 1)M, where N is the demagnetization factor, and N 1 when the applied field is perpendicular to the film. In our Hall geometry we set B H. To extract R s and R o accurately, we have measured M as a function of H in each value of magnetic field and temperature on the same samples as shown previously in Fig. 2 b. To subtract the large diamagnetic contribution of the substrate material, SrTiO 3, we also measured the blank substrate of almost similar size of each value of temperature and magnetic field. From the xy H curves and the M H curves, we can observe a linear field dependence of M(M H) and a linear field dependence of xy ( xy H) both in the low-field and high-field regimes. According to Eq. 1, this indicates that R 0 and R s must be H independent both in the low-field and high-field limits. In terms of Eq. 1, we consider the low-field and high-field slopes of dm/dh, and have

4 H. C. YANG, L. M. WANG, AND H. E. HORNG PHYSICAL REVIEW B FIG. 4. Temperature dependence of R o for a 110 and b 100 oriented Nd 0.7 Sr 0.3 MnO 3 films. The insets show the effective hole number per Mn as a function of temperature for both 110 oriented and 100 oriented films. and d xy /dh low R o 4 R s dm/dh low d xy /dh high R o 4 R s dm/dh high, where the subscripts of low and high denote the slopes of d xy /dh or dm/dh derived from the data in low-field and high-field regimes, respectively. Using Eqs. 2 and 3, we can determine R s and R o precisely. It was found that in the paramagnetic state, the field profile of M and xy shows linear behavior at low magnetic field. In the low field limit where H approaches zero, Eq. 1 remains valid, with M as the induced magnetization. Therefore, in the paramagnetic state (T 280 K), we can derive R s from the initial slopes using the formula R s (d xy /dh) low /(4 dm/dh) low.we 2 3 FIG. 5. Temperature dependence of R s for a 110 and b 100 oriented Nd 0.7 Sr 0.3 MnO 3 films. The insets show R s as a function of temperature for both 110 and 100 oriented films. have neglected correcting the value of R o as it is quite small compared with R s which has been mentioned by Ong et al. 5 In Fig. 4, we show temperature dependence of R o. R o is independent of temperature for T 160 K for both 110 and 100 oriented films. For T 160 K, the value of R o increases with temperature and reaches maximum at T 230 K. As T 230 K, the value of R o is decreased. The value of R o is about m 3 CatT 5 K for both samples. This corresponds to a carrier concentration of n H cm 3 or 1.0 holes per Mn site. Majumdar et al. 15 have calculated ordinary Hall coefficient as a function of the electron phonon coupling constant g, electron density n, and temperature T within the model of double exchange and Jahn-Teller coupling. The theory predicts a cusp-like behavior in the temperature dependence of R o for certain doping concentration, x, and coupling constant g. In the present work, the R o of Nd 0.7 Sr 0.3 MnO 3 films is

5 ANOMALOUS HALL EFFECT OF Nd 0.7 Sr 0.3 MnO 3... PHYSICAL REVIEW B FIG. 6. Arrhenius plot of ( R s /R o ) T versus T for 110 and 100 oriented Nd 0.7 Sr 0.3 MnO 3 films. The inset shows the corresponding data. independent of temperature for T 160 K. The R o grows in magnitude as the temperature increases above T 160 K. We observed a cusp near T c in the temperature dependence of R o. The R o data seem to follow qualitatively the temperature behavior predicted by Majumdar et al. The R o data support that the double exchange interaction and Jahn-Teller coupling should play a role in the behavior of R o. In Figs. 5 a and 5 b we showed the temperature dependence of R s for 100 and 110 oriented Nd 0.7 Sr 0.3 MnO 3 films. A cusp-like behavior was observed in the R s T curve near T c. As T 270 K, the temperature dependence of R s can be scaled as T 3.09 and T 3.16 respectively for 110 and 100 oriented films. The inset shows the R s T curve along with the zero-field xx T curve. Figure 6 shows the temperature dependence of ( R s /R o ) T for 100 and 110 oriented Nd 0.7 Sr 0.3 MnO 3 films in the ferromagnetic state for an Arrhenius plot. The temperature dependence of ( R s /R o ) T was found to be proportional to R exp( E c /k B T) at temperatures above 100 K, where R is a parameter in unit of kelvin and E c is the core energy of the magnetic dipole. The inset of Fig. 6 shows the ( R s /R o ) T versus T plot of the corresponding data. The values of R are and K while the values of E c are 1295 K and 1572 K respectively for 110 and 100 oriented films. According to Eq. 12 in Ref. 14, the spin-orbit interaction so can be roughly estimated by taking the charge of a monopole Q 1, the entropy per dipole 320, the carrier density 1 hole/mn, and the lattice constant 3.9 Å. We obtain so 0.5 and 1.5 K for 110 and 100 oriented films, respectively. The obtained values of so are near to the value of 5 K for La 1 x Ca x MnO 3 estimated by Ye et al. 14 Additionally, the obtained core energy E c of a dipole for 100 oriented film is larger than that for 110 oriented film. It is known that the core energy of a dipole FIG. 7. R s as a function of xx at different temperatures for 110 and 100 oriented Nd 0.7 Sr 0.3 MnO 3 films. separated by distance d is E c 4 s d, where s is the spin stiffness. The larger value of E c for 100 oriented film may be due to the larger distance d 5.4 Å, as seen in Fig. 1 b between dipoles in the 100 oriented film. Regarding the transport properties of the perovskite manganites, increase in resistivity near T c prompted us to suggest that the mechanism of the double exchange and the Jahn Teller coupling can be successfully applied in reproducing most qualitative feature of the resistivity data. On the other hand, concerning the mechanism of the anomalous Hall effect, it is not yet well established. Recently, Ye et al. 14 showed that the anomalous Hall effect in manganites is a manifestation of Berry phase effects caused by carrier hopping in a nontrivial spin background. The mechanism is based on the observation that a carrier moving in a topologically involved nontrivial spin background acquires a Berry phase which affect the motion of electrons in the same way as does the phase arising from the physical magnetic field The theory of Ye et al. predicts that R s increases rapidly in magnitude as temperature is raised from zero through the ferromagnetic transition temperature, T c, peaks at temperature where T max T c, and decays as a power of temperature. Besides, in the ferromagnetic regime, the temperature dependence of ( R s /R o ) T is proportional to R exp( E c /k B T). In the high temperature regime the temperature dependence of R s should scale as R s T 3. Hall measurements in this work show that the sign of R s is opposite to that of R o. The sign of R s is electron-like while the sign of the R o is hole-like. The value of R s increases with temperature with a peak observed at T 220 K then decreases as the temperature is increased above T c. We note that the temperature behaviors of R s are consistent with the theoretical prediction of Ye et al. for both T 200 K and T 270 K regimes. This very close correspondence experimentally seems to support the prediction of Ye et al. A close correspondence in the temperature dependence of the R s data

6 H. C. YANG, L. M. WANG, AND H. E. HORNG PHYSICAL REVIEW B has also been reported by Matl et al. 5 in La 0.7 Ca 0.3 MnO 3 films. We conclude that the possibility of the Berry phase contribution therefore can, in the presence of spin-orbit interactions, leads to the anomalous Hall effect. Chun et al. 13 presented Hall resistivity data on La 0.66 Ca 0.33 Pb MnO 3 single crystal and demonstrated that the data collapse to a single curve when plotted as a function of reduced magnetization. Moreover, they showed the quantal phase accumulated by hopping charge carrier, as a result of strong Hund s-rule requirement that outer-shell carriers follow the local configuration of the core spins and provide a new anomalous Hall effect in the inelastic hopping region. Figure 7 shows R s as a function of xx at different temperatures for 110 and 100 oriented Nd 0.7 Sr 0.3 MnO 3 films. R s was found to scale as 2 xx in the low temperature regime T 160 K. In this regime R o is independent of temperature. Above 160 K, R s displays a linear temperature dependence with R s xx. Regarding the scaling behavior of the R s xx curve, we discussed the data in terms of the model used in conventional ferromagnets. Karplus and Luttinger 25 first treated the anomalous Hall effect in itinerant ferromagnets from the viewpoint of band theory taking into account of the spin orbit interaction of d electrons. They showed R s 2 xx, where xx is the resistivity. The contribution from phonon scattering also gives similar relation as shown by Irkhin and Shavrov For 110 and 100 oriented Nd 0.7 Sr 0.3 MnO 3 films, R s xx n was observed for T 160 K. As T 160 K, R s xx with n 1 dominates its temperature-dependence behavior. Since phonon scattering should be pronounced only at high temperatures, it is not the main scattering mechanism at low temperatures. Therefore we infer that the magnetic scattering or the spin-disorder scattering governs the transport properties for 110 and 100 oriented Nd 0.7 Sr 0.3 MnO 3 films at low temperatures. CONCLUSION The Hall resistivity and magnetization of 100 and 110 oriented epitaxial Nd 0.7 Sr 0.3 MnO 3 films were measured. In the ferromagnetic regime 100 K T 200 K, ( R s /R o ) T scales as exp( E c /k B T) for both 110 and 100 oriented Nd 0.7 Sr 0.3 MnO 3 films. In the high temperature regime (T 270 K), R s scales as R s T ( ) for 110 and 100 oriented films. These results supply the evidences of the Berry phase effect on the anomalous Hall effect. Besides, R s 2 xx was found for T 160 K while R s xx was observed for T 160 K. This result suggests that magnetic scattering or the spin-disorder scattering should govern the transport properties at low temperature for 110 and 100 oriented Nd 0.7 Sr 0.3 MnO 3 films. ACKNOWLEDGMENTS The authors are grateful for the partial support of the National Science Council of the R.O.C. under Grant No. NSC M , and the partial support of the program of the Ministry of Education of the R.O.C. for promoting university academic excellence. 1 P. Matl, N. P. Ong, Y. F. Yan, Y. Q. Li, D. Studebaker, T. Baum, and G. Doubinina, Phys. Rev. B 57, J. D. M. Coey, M. Viret, and L. Ranno, Phys. Rev. Lett. 20, G. C. Xiang, Q. Li, H. L. Liu, R. L. Greene, and T. Venkatesan, Appl. Phys. Lett. 66, M. Jaime, H. Hardner, M. B. Salamon, M. Rubinstein, P. Dorsey, and D. Emin, J. Appl. Phys. 81, P. Matl, N. P. Ong, Y. F. Yan, Y. Q. Li, D. Studebaker, T. Baum, and G. Doubinina, Phys. Rev. B 57, P. Mandal, K. Bärner, L. Haupt, A. von Helmolt, A. G. M. Janson, and P. Wyder, Phys. Rev. B 57, J. C. Chen, S. C. Law, L. C. Tung, C. C. Chi, and Weiyan Guan, Phys. Rev. B 60, A. Asamitsu and Y. Tokura, Phys. Rev. B 58, S. H. Chun, M. B. Salamon, and P. D. Han, Phys. Rev. B 59, N. G. Bebenin, R. I. Zaǐnullina, V. V. Mashkautsan, A. M. Burkhanov, V. V. Ustinov, V. V. Vasil ev, and B. V. Slobodin, Sov. Phys. JETP 86, G. Jakob, F. Martin, W. Westerburg, and H. Adrian, Phys. Rev. B 57, G. Jeffrey, M. R. Beasley, T. H. Geballe, Ron Hiskes, and Steve DiCarolis, Appl. Phys. Lett. 69, S. H. Chun, M. B. Salamon, Y. Lyanda, P. M. Goldbart, and P. D. Han, Phys. Rev. Lett. 84, Jinwu Ye, Yong Bae Kim, A. J. Millis, B. I. Shraiman, P. Majumdar, and Z. Tašanović, Phys. Rev. Lett. 83, P. Majumdar, Steven Y. Simon, and Anivaon M. Segupta, Phys. Rev. B 59, A. Poddar, P. Muruguraj, R. Fischer, E. Gmelin, K. Barner, L. Haupt, P. Mandal, and G. H. Rao, Physica B 254, P. Wagner, I. Gordon, A. Vantomme, D. Dierickx, M. J. Van Bael, V. V. Moshchalkov, and Y. Bruynseraede, Europhys. Lett. 41, L. M. Wang, H. H. Sung, B. T. Su, H. C. Yang, and H. E. Horng, J. Appl. Phys. 88, A. J. Millis, P. B. Littlewood, and B. I. Shraiman, Phys. Rev. Lett. 74, A. J. Millis, B. I. Shraiman, and R. Mueller, Phys. Rev. Lett. 77, H. Roder, J. Zang, and A. R. Bishop, Phys. Rev. Lett. 76, H. J. Schulz, Phys. Rev. Lett. 65, L. B. Ioffe and A. I. Larkin, Phys. Rev. B 39, N. Nagaosa and P. A. Lee, Phys. Rev. Lett. 64, R. Karplus and J. M. Luttinger, Phys. Rev. 95, Yu. P. Irkhin and V. G. Shavrov, Sov. Phys. JETP 15,