A variational theory of Hall effect of Anderson lattice model: Application to colossal magnetoresistance manganites (Re_1−x A_x MnO₃)

Highlights

• We use two band (ℓ-b) Anderson lattice model Hamiltonian alongwith (ℓ-b) hybridization recently studied by us for manganites in the strong electron-lattice Jahn-Teller (JT) coupling regime.

• We use a variational method in this work to study the temperature variation of Hall constant R_H (T) in these compounds.

• We find that the Hall constant R_H (T) reduces with increasing magnetic field parameters h&m and the metal-insulator transition temperature (T_ρ) shifts towards higher temperature region.

• We have also observed the role of the model parameters e.g. U, J_H, J_F and hybridization V_k between ℓ-polarons and d-electrons on Hall constant R_H (T) of these materials at different magnetic fields.

• Here we find that R_H (T) for a particular value of h and m 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 La_0.8Ba_0.2 MnO_3.

Abstract

An anomalous Hall constant R_H has been observed in various rare earth manganites doped with alkaline earths namely Re_1−x A_x MnO₃ (where Re = La, Pr, Nd etc., and A = Ca, Sr, Ba etc.) 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) Anderson lattice model Hamiltonian alongwith (ℓ-b) hybridization recently studied by us for manganites in the strong electron-lattice Jahn-Teller (JT) coupling regime an approach similar to the two – fluid models. We use a variational method in this work to study the temperature variation of Hall constant R_H (T) in these compounds. We have already used this variational method to study the zero field electrical resistivity ρ (T) and magnetic susceptibility of doped CMR manganites. In the present study, we find that the Hall constant R_H (T) reduces with increasing magnetic field parameters h&m and the metal-insulator transition temperature (T_ρ) shifts towards higher temperature region. We have also observed the role of the model parameters e.g. local Coulomb repulsion U, Hund’s rule coupling J_H between e_g spins and t_2g spins, ferromagnetic nearest neighbor exchange coupling J_F between t_2g core spins and hybridization V_k between ℓ-polarons and d-electrons on Hall constant R_H (T) of these materials at different magnetic fields. Here we find that R_H (T) for a particular value of h and m 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 La_0.8Ba_0.2 MnO₃.The magnitude of R_H (T) reduces and the anomaly (sharp peak) in $$R_H becomes broader and shifts towards higher temperature region on increasing V_k or J_H or doping x and even vanishes on further increasing these parameters. Our results of anomalous Hall constant (R_H) have same qualitative behavior as the zero-field electrical resistivity. Moreover Hall Constant (R_H) shows positive values indicating that the carriers in these manganites are holes.

Introduction

Hole – doped Mixed-valence manganites with perovskite structure ${\mathit{Re}}_{\mathit{1}-\mathit{x}}$ ${\mathit{A}}_{\mathit{x}}$ $\mathit{Mn}{\mathit{O}}_{\mathit{3}}$ (where Re = rare- earth ions ; A = divalent ions such as Ca , Sr, Ba, Pb, etc.) have attracted for a long time a large proportion of researchers from varied fields because of their interesting physical properties such as phase coexistence, metal-insulator transitions, Colossal Magnetoresistance (CMR) and other multiferroic properties [1]. These properties make these systems promising for magnetic sensor and reading head device applications. Observation of CMR phenomenon in pervoskite manganites has been intensively studied, due to their distinctive structural, electrical, thermal and magnetic properties [2]. A number of works has been devoted to study the interplay between structure and transport properties of these manganese oxides [3], [4], [5]. In these compounds, electrical resistivity decreases by orders of magnitudes upon influence of application of a magnetic field [1], [6]. In doped manganites, metallic ferromagnetic (FM), insulating paramagnetic (PM), antiferromagnetic (AFM) and charge/orbital ordered states are among the competing ground states [7]. To explain the CMR phenomenon, Zener has proposed the double-exchange (DE) mechanism [8]. Recent studies suggest that the local Jahn-Teller (JT) distortion plays a key role in these manganites [9].

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 [2], [9]. Recently, it has been found that manganese oxides display a rich phase diagram [10], [11]. Percolation based on phase separation has been proposed to explain magneto- transport properties in these systems [12].

To reveal the origin of these anomalous transport properties, researchers have performed further detailed experiments, including Hall measurements, which give information about the sign and density of mobile carriers and/or the correlation of spin and charge systems. Chun et al. [13] have reported on low-field magnetization and the Hall effect in La_2-2x Sr_1+2x Mn₂O₇ (x = 0.40) , where they show the occurrence of spin-glass like behavior in the magnetization measurements and an enhancement of the anomalous Hall coefficient at low temperatures. The origin of these phenomena has been interpreted as a mixture of ferromagnetic and antiferromagnetic clusters. For CMR materials, such as La_0.67 Ca_0.33 MnO₃ and Nd_2/3 Sr_1/3 MnO₃ , anomalous Hall effect is usually observed [14], [15]. The anomalous Hall coefficient depends on asymmetric electron scattering due to spin- orbit coupling.

A review on the detailed theoretical study of doped rare earth manganites ${\mathit{Re}}_{\mathit{1}-\mathit{x}}$ ${\mathit{A}}_{\mathit{x}}$ $\mathit{Mn}{\mathit{O}}_{\mathit{3}}$ has been reported earlier [16] where the authors presented a new model of coexisting localized JT polarons and broad band electrons for manganites and shown that it explains a wide variety of characteristic properties of manganites. The theory ignores the ℓ-b hybridization so it does not describe properly the low temperature behavior of manganites below T * ~ 100 K. We believe that a more general treatment of the model which includes ℓ-b hybridization can lead to a complete description of manganites as suggested by Ramakrishnan et al. (Ref. [16]) . Whereas Graziosi and co-workers [17] presented a polaron framework to account for transport properties in metallic epitaxial manganite films. They propose a model for the consistent interpretation of the transport behavior of manganese perovskites in both the metallic and insulating regimes.

Some time ago, Panwar et al. [18] have developed a variational method to study the ground state and thermodynamic properties of heavy fermion systems using Anderson lattice model. Recently, Panwar et al. had used this variational method in the study of the zero field electrical resistivity and Magnetic susceptibility of doped CMR manganites over a fairly wide temperature range [19], [20]. More recently Panwar and co-workers have reported a theoretical study of magneto transport properties like electrical resistivity and thermoelectric power in the presence of magnetic field for the manganites systems [21]. In the present paper, we have carried out a systematic study of Hall constant R_H (T) of hole doped CMR manganites using the variational method. The rest of the work is as follows. In Section 2, we give the basic formulation for R_H (T). In Section 3, we discuss our results and finally we conclude our findings in Section 4.