Assessment of Variation in Zero Field Hall Constant of Colossal Magnetoresistive Manganites (Re1-x AxMnO3)

Transcription

1 ESSENCE - International Journal for Environmental Rehabilitation and Conservation Panwar & Kumar/VIII [2] 2017/ Volume VIII [2] 2017 [ ] [ISSN ] [ Assessment of Variation in Zero Field Hall Constant of Colossal Magnetoresistive Manganites (Re1-x AxMnO3) Panwar, Sunil and Kumar, Vijay Received: August 10, 2017 Accepted: October 31, 2017 Online: December 31, 2017 Abstract Magnetic perovskites (manganites) such as La 0.7 Sr 0.3 MnO3 have attracted as potential magnetoresistive sensors. An anomalous Hall constant has been observed in various rare earth manganites doped with alkaline earths namely Re 1-x Ax MnO3 which exhibit colossal magnetoresistance (CMR), metal- insulator transition and many other poorly understood phenomena. We show that this phenomenon of anomalous Hall constant can be understood using two band (l-b) model Hamiltonian, recently studied by us for manganites in the strong electron- lattice Jahn- Teller (JT) coupling regime. In this work, we use a variational method to study the temperature variation of Hall constant RH in these compounds. The variational method is the best suited method to describe the low temperature properties of these compounds. Using this method, we have recently done the calculation For Correspondence: Department of Applied Sciences, Faculty of Engineering & Technology, Gurukula Kangri University, Haridwar, Uttarakhand, India of zero-field electrical resistivity and magnetic susceptibility of doped CMR manganites. It explains much CMR Physics at low temperatures at least qualitatively. Further, we have observed the role of the model parameters like U, JH, JF & Vk on Hall constant RH of these materials. These model parameters are local Coulomb Repulsion U, Hund s Rule coupling JH between eg spins and t2g spins, ferromagnetic nearest neighbor exchange coupling JF between t2g core spins and hybridization Vk between l -polarons and d-electrons. Here, we find that RH shows a rapid initial increase, followed by a sharp peak at low temperature say 50 K in our case and a slow decrease at high temperatures. This behavior of RH resembles qualitatively with the key feature of many CMR compounds like LaBa MnO3. This anomaly (sharp peak) in RH at low temperatures becomes broader and shifts towards higher temperatures and even vanishes on increasing Vk or JH or doping x. Our results of anomalous Hall constant RH have the same qualitative behavior as the zero - field electrical resistivity. It may be due to the magnetic scattering processes which are 103

2 responsible for both longitudinal resistivity and extraordinary Hall effect through asymmetric spin- orbit coupling. Keywords: Colossal magnetoresistance Anomalous Hall constant Variational method Model parameters Introduction The magnetoresistive materials of mixed- valence manganites with perovskite structure have been studied for a long time, due to their significance for both fundamental research and practical application. The strong interplay between the structure, magnetism and electronic transport has generated a large variety of interesting properties in hole - doped manganese oxides Re 1 x A x MnO 3 (Re= rare- earth ions ; A = divalent ions such as Ca, Sr, Ba, Pb, etc.). A Colossal Magnetoresistance (CMR) effect in these manganites was explained by the so - called double- exchange (DE) interaction between Mn 3+ and Mn 4+ ions. Recent studies suggest that the local Jahn-Teller (JT) distortion plays a key role in these manganites. However, these materials became more complex due to various interactions among charge, spin and lattice and DE alone cannot explain the entire electrical transport behavior. Later on various theoretical models have been proposed by considering electron - lattice and spin - lattice interaction and even today there is no comprehensive model to explain transport phenomena in manganites. Recently, it has been found that manganese oxides display a rich phase diagram. Percolation based on phase separation has been proposed to explain magneto- transport properties in these systems. Basic Formulation Model Hamiltonian We use the two band model Hamiltonian suitable for the doped manganites which exhibit colossal magnetoresistrance (CMR) involving a broad spin - majority (eg - spins) conduction band (b - band) as well as nearly localized spin - minority (t2g - spins) electron states (l - band). Two band models involving itinerant and localized states were also suggested earlier by both experimentalists and theorists. In the model Hamiltonian, we consider the l-b hybridization as an extra mechanism in order to address the low temperature properties of manganites (e.g. resistivity, Hall effect). The Hamiltonian is given by H lb = t ij (b + iσ b jσ ) E jt l + iσ l iσ ij σ + U n l iσ S j iσ V K (l + kσ b kσ e g spin s i and the t 2g spin S i. JF is the net 104 iσ n b iσ J H s i S i J F S i i ij kσ + h. c. ) (1) corresponding destruction operator) and b + iσ creates broad band electron having mean energy zero & nearest neighbor effective hopping amplitude t ij. In Eq. (1), the l- polarons has energy ( Ejt), the b- electrons hop between nearest neighbor sites with an effective amplitude t ij. U is the local Coulomb repulsion between l- polarons and b- electrons of the same spin at a particular site i. JH is the strong ferromagnetic Hund s rule coupling between the

3 effective ferromagnetic nearest neighbor exchange coupling between the t 2g core spins X=0.1, J H = (Si, Sj ) and V k is the l-b hybridization between l- polarons and b-electrons of the same spin. V=0.1 Hall Constant V= The Hall constant due to intrinsic skew scattering is given by the expression [Fert formula (Ref. 14)] RH (T) = γ χ (T) ρ (T) (2) X=, J H = where χ (T) is the normalized magnetic susceptibility. χ (T) = χs(u, JF)/ C, ( C being the Curie constant) and γ ( Electronic specific heat coefficient ) = 02 J/ K 2 mol for a band of width 2.0 ev (Ref. 12). whereas electrical resistivity ρ (T) = 1/ σ(t). In this work, we use a variational method to study the temperature variation of Hall constant RH in these compounds. The variational method is the best suited method to describe the low temperature properties of these compounds. Using this method, we have recently done the calculation of zero-field electrical resistivity and magnetic susceptibility of doped CMR manganites. More recently Panwar and co- workers have reported a theoretical study of magneto transport properties like electrical resistivity & thermoelectric power and Hall constant in the presence of magnetic field for the manganites systems. We are not interested here in the absolute value of Hall constant R H but only in the variation of Hall constant (R H/ R 0) with temperature. V=0.1 V= Fig. 1: Variation of Hall constant (RH/ R0) with temperature at U = 5, Ejt =0.5, JF = 0.1 and J H = for different values of V with a) x=0.1, b) x= R H / R 0 X=0.1, V= 0.1 J H = J H =2.0 X=, V=0.1 J H = J H =2.0 Fig. 2: Variation of Hall constant (RH/ R0) with temperature at U = 5, Ejt =0.5, JF = 0.1 and V= 0.1 for different values of JH with a) x=0.1, b) x= 105

4 0.15 x=0.1 x= x=0.3 V=0.1, J H = x= x= x=0.1 x= x=0.3 V=0.1, J H =2.0 0 Fig. 3: Variation of Hall constant (RH/ R0) with temperature at U = 5, Ejt =0.5, JF = 0.1 and V= 0.1 for different values of x with a) JH =, b) JH = 2.0. Results and Discussion In our calculations, we have taken the unperturbed band of three dimensional solid represented by simple semicircular density of states N c σ (ϵk) = ( 2/π) (1 ϵk 2 ) (which is centered around zero energy ) with band width W=2.0eV, U=5.0,E jt =0.5,V= 0.1 and, F = -38 ev (for x =0.3) and J H = and 2.0eV. Doping concentration x is varied from 0.1 to 0.5. In Figs. 1-3, we have shown the temperature dependence of Hall constant RH (T) at H=0 for different values of parameter V, JH and doping x. Here Hall constant RH (T) is positive, increases rapidly in magnitude with temperature and reaches a maximum at T * 50 K [Fig.1(a)] beyond which it falls off resembling with the key feature of many CMR compounds like La Ba MnO3. This anomaly in RH becomes broader and shifts towards higher temperatures and even vanishes on increasing V or JH or doping concentration x. We get a " hole - like " RH for hole doped manganites, as observed at low temperature by Matle et al., can be obtained only when lattice distortions persist in the metallic state as T 0. Our results for RH have the same qualitative behavior as the zero field electrical resistivity but we have no argument for the very close correspondence found experimentally 20. It may be due to the magnetic scattering processes which are responsible for both longitudinal resistivity and extraordinary Hall effect through asymmetric spin- orbit coupling. We have seen that the results of the simple model considered here are in qualitative agreement with the experimental results of a broad class of hole doped CMR manganites. Conclusion From the study of Hall Constant RH (T), we tried to find the effect of model parameters like V, JH or x on the transport properties of these materials and discussed the transport mechanism using variational method. In this study, we find that RH (T) shows a rapid initial increase, followed by a sharp peak at low temperature say 50 K in our case and a slow decrease at high temperatures, resembling with the key feature of many CMR compounds like LaBa MnO3. This anomaly in RH becomes broader & shifts towards higher temperatures and even vanishes on increasing Vk or JH or doping x. Our results of anomalous Hall constant RH (T) 106

5 have the same qualitative behavior as the zero - field electrical resistivity. Moreover, RH (T) is positive throughout the temperature range of investigation there by representing that the charge carriers are holes. In future, we are observing the effect of magnetic field on other finite temperature properties e.g. specific heat & magnetic susceptibility using Eq. (2) for variational wave function. 5. Acknowledgements We would like to acknowledge our great appreciation to University Grants Commission (UGC), New Delhi (India) for the financial support. (Grant No. F /2013 (SR) dated ) Reference Coey, J. M.; Viret, M.; Ramno, L.; Qunadjela, K. (1995): Phys. Rev. Lett Golosov, D. I. et al. (2008): Europhys. Lett ; 2010 Phys. Rev. Lett Jaime, M. et al. (1999): Phys. Rev. B Jakob, G.; Martin, F.; Westerberg, W. and Adrian (1998): Phys. Rev. B Jin, S.; Tiefel, T. H.; McCormack, M.; Fastnacht, R. A.; Ramesh, R. and Chen, L. H. (1994): Science Mayr, M. et al. (2001): Phys. Rev. Lett Millis, A. J.; Littlewood, P. B.; Shraiman, B. I. (1995): Phys. Rev. Lett Moreo, A. et al. (1999): Science (Washington DC, U. S.) Panwar, S.; Kumar, V.; Chaudhary, A. and Singh, I. (2014): Mod. Phys. Letts. (B) 28 (24) Ramakrishnan, T. V. et al. (2004): Phys. Rev. Lett ; 2007 J. Phys. Condens Matt Ramakrishnan, T. V.; Krishnamurthy, H. R.; Hassan, S. R. and Pai, G. V. (2004): Colossal Magnetoresistive manganites [Kluwer Academic Publishers, Netherlands] edited by Chatterji, T. 10: 417. Tokura, Y. (2000): In Colossal Magnetoresistance Oxide. [Gordon and Breach, New York]. Uehara, M. et al. (1999): Nature (London) Zener, C. (1951): Phys. Rev