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Phonon, Magnon and Electron Contributions to Low Temperature Specific Heat in Metallic State of La0·85Sr0·15Mno3 and Er0·8Y0·2Mno3 Manganites

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Phonon, Magnon and Electron Contributions to Low Temperature Specific Heat in Metallic State of La0·85Sr0·15Mno3 and Er0·8Y0·2Mno3 Manganites Bull. Mater. Sci., Vol. 36, No. 7, December 2013, pp. 1255–1260. c Indian Academy of Sciences. Phonon, magnon and electron contributions to low temperature specific heat in metallic state of La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3 manganites DINESH VARSHNEY1,∗, IRFAN MANSURI1,2 and E KHAN1 1Materials Science Laboratory, School of Physics, Devi Ahilya University, Khandwa Road Campus, Indore 452 001, India 2Deparment of Physics, Indore Institute of Science and Technology, Pithampur Road, Rau, Indore 453 331, India MS received 19 June 2012; revised 21 August 2012 Abstract. The reported specific heat C (T) data of the perovskite manganites, La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3, is theoretically investigated in the temperature domain 3 ≤ T ≤ 50 K. Calculations of C (T) have been made within the three-component scheme: one is the fermion and the others are boson (phonon and magnon) contributions. Lattice specific heat is well estimated from the Debye temperature for La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3 manganites. Fermion component as the electronic specific heat coefficient is deduced using the band structure calculations. Later on, following double-exchange mechanism the role of magnon is assessed towards spe- cific heat and found that at much low temperature, specific heat shows almost T3/2 dependence on the temperature. The present investigation allows us to believe that electron correlations are essential to enhance the density of states over simple Fermi-liquid approximation in the metallic phase of both the manganite systems. The present numerical analysis of specific heat shows similar results as those revealed from experiments. Keywords. Oxide materials; crystal structure; specific heat; phonon. 1. Introduction many properties are attributed to ‘electron–phonon’ interac- tion. As electron–phonon interaction is one of the most rele- The colossal magnetoresistance (CMR) manganites are com- vant contributions in determining the conduction mecha- pounds of chemical formula, R1−x DxMnO3, with R being nism in these materials (Goto et al 2004;Dabrowskiet al the rare-earth materials and D the doping materials such as 2005). The strong coupling between the electron and lattice alkaline earth, transition metals or non-metals, etc. CMR is affected by the ratio between trivalent and divalent ions at effect is caused by the temperature dependent phase transi- A site or the average ionic radius of the ions on A site. Thus, tion from a paramagnetic insulator to a ferromagnetic metal. thermal properties of this material may be taken as a starting Thus, for temperature slightly above this phase transition, point to a consistent understanding of more complex physical an applied magnetic field not only restores the magnetic properties of the doped compounds. order as it does in all types of ferromagnetic materials but Specific heat measurements are understood to be an also gives rise to metallic conductivity. The coincidence of instructive probe in describing low temperature properties of the ferromagnetic– paramagnetic phase transition with the the materials. Among various manganites, hole-doped sys- metal–insulator transition is generally believed to be associ- tem are widely analysed experimentally due to different elec- ated with the double-exchange mechanism. Besides a tech- tronic and magnetic structure with carrier density. The spe- nological interest in CMR effect, doped manganites are fas- cific heat for La1−x SrxMnO3-doped system reflects the first- cinating materials in that they exhibit a wide variety of order phase transition and the phase transition are observed unusual physical properties, which makes them considerably below Curie temperature. Based on the temperature and field more complex than conventional transition metal ferromag- dependent measured specific heats, it affected the two basic nets (Tokura and Nagosa 2000; Salamon and Jaime 2001; thermodynamic parameters, one being the magneto-caloric Das and Dey 2007). effect, i.e. the adiabatic change in temperature and the other, The systematic study of thermodynamic properties of isothermal change in entropy, induced by the change in solids has become one of the fascinating fields of condensed external magnetic field. The magnetic transition from low- matter physics in the recent years. Thermodynamics play an temperature ferromagnetic to the paramagnetic phase was important role in explaining the behaviour of manganites, as clearly observed (Szewczyk et al 2005). The observed specific heat hump near TC is associated with magnetic ordering and broadening of the peak is pre- sumably due to magnetic inhomogeneities and/or chemi- ∗ Author for correspondence ([email protected]) cal disorders in the half-doped La0·5−x LnxCa0·5−ySry MnO3 1255 1256 Dinesh Varshney, Irfan Mansuri and E Khan (Ln = Pr, Nd, Sm) samples (Mansuri et al 2011). The spe- structure calculations in order to estimate the electronic spe- cific heat of the divalent-doped manganites is also reported cific heat. In the case of manganites, separation of spin- and it has argued that the phase transition is of second order wave contribution from the lattice effect is difficult without and can be well modelled as a Peierls transition in a dis- an accurate estimation of the Debye temperature. Also, it ordered material. The heat capacity data shows two transi- is worth to seek the possible role of phonons and magnons tions with the transition at higher T exhibiting a much larger in the low temperature specific heat of manganites that has change in entropy than the lower transition. The magnetiza- immediate important meanings to reveal the phenomenon of tion data infers FM transition at higher temperature and AFM colossal magnetoresistance. transition at lower temperature (Cox et al 2007). The present investigation is organized as follows. In On the other hand, for the strongly correlated system, there § 2, we introduce the model and sketch the formalism may be another contribution arising from the renormalization applied. As a first step, we estimate the Debye temperature of the effective e–e interactions, which can modify density of following the inverse-power overlap repulsion for nearest- states at the Fermi energy. In order to get more insight into neighbour interactions in an ionic solid. We follow the Debye e–e interaction, Xu et al 2006 tried to separate its contribu- method to estimate the specific heat contributions of phonons tion from the specific heat for La2/3Ca1/3MnO3 manganite. and magnons. Within this scheme for phonons, electrons and The unique transport behaviour in manganites at low tem- magnons specific heat, we have computed the low tempe- perature can be understood by taking into account both e–e rature specific heat of La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3 interaction and weak spin disorder scattering including the manganites. In § 3, we return to a discussion of results spin polarization and grain boundary tunneling. This kind of obtained by way of heat capacity curves. A summary of the electron–electron interaction is a general characteristics and results is presented in § 4. We believe in giving detailed infor- verifies the strong correlated interaction between electrons in mation on physical parameters in correlated electron system, manganites (Xu et al 2006). as manganites can be understood by low temperature specific Subsequently, heat capacity of La0·78Pb0·22MnO3 in the heat behaviour. temperature range 0·5 ≤ T ≤ 25 K is measured and found that samples having ferromagnetic insulating or antiferro- magnetic ordering exhibits spin-wave signature in specific 2. Lattice specific heat heat data (Ghivelder et al 2001). Salient features of the reported specific heat measurements include a linear term The acoustic mode frequency shall be estimated in an ionic Ze =− e (γT) at low temperature. The contribution to electronic model using a value of effective ion charge 2 .The term (γT) was extracted from the total heat capacity and is Coulomb interactions among the adjacent ions in an ionic argued that this contribution is mainly due to the electronic crystal in terms of inverse-power overlap repulsion is given heat capacity and emphasized that the specific heat can be as (Varshney et al 2002) resolved into a γT contribution with a finite value of γ and 1 f a lattice contribution. (r) =−(Ze)2 − , (1) r rs On the theoretical side, explanation of specific heat behaviour for a wide doping concentration range has, there- where f being the repulsion force parameter between the ion fore, been of considerable interest. The motivation is two- cores. The elastic force constant κ is conveniently derived fold: (i) to reveal the importance of the Coulomb correlations from (r) at the equilibrium inter-ionic distance r0 following which is significant in controlling the transport properties in ∂2 s − 1 manganites and (ii) to understand the role of magnons as κ = = (Ze)2 . (2) ∂r2 r3 well as electron–phonon in specific heat of the ferromagnetic r0 0 metal or insulator. It is indeed essential to find out if these Here, s is the index number of the overlap repulsive poten- novel materials get their metal to insulator transition from tial. Then we use acoustic mass, M = (2 M+ + M−) [Mn an extremely strong interaction within the double-exchange (O) is symbolized by M+(M−)], κ∗=2κ for each direc- mechanism and electron-lattice interaction or if any entirely tional oscillation mode to get the acoustic phonon frequency new excitation has to be invoked. as No systematic theoretical efforts addressing the issues of Coulomb correlations, spin wave impact and lattice contri- ω = 2κ ∗ , D M bution as well as the competition among these processes (3) have been made so far, and in the present investigation, we = (Ze) (s−1) 1 . 2 M r3 try to understand them and retrace the reported specific heat 0 behaviour. We begin with the assumptions and motivate them In most of manganites, the specific heat is dominated by by simple physical arguments before taking up details of quantized lattice vibrations (phonons) and is well estimated numerical results obtained.
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