First principal calculation and Monte Carlo simulations of the Magnetocaloric effect, Electronic and Magnetic properties in perovskite oxide Pr 0.65Sr 0.35MnO 3

We have used the first principal calculation and Monte Carlo simulations (MCS) to investigate the magnetocaloric effect, electronic and magnetic properties of Pr 0.65Sr 0.35MnO 3 (PSMO) perovskite. The exchange-correlation potential was treated with the generalized gradient approximation (GGA) for the electronic and magnetic properties. The ferromagnetic phase of PSMO is half metallic with 100% spin polarization, which is important in the relation to the colossal magnetoresistance properties of this compound. The magnetic moment is obtained. The thermal variation of magnetization of PSMO has been obtained. The temperature dependence of the magnetic entropy change and the adiabatic temperature are obtained by MCS. The Curie temperature of PSMO has been deduced. The field dependence of relative cooling power PSMO has been obtained.


Introduction
The search for energy-efficient technologies for developing new refrigerator appliances has made the magnetocaloric effect a field of current scientific interest [1]. At present, there are several interesting groups of magnetocaloric materials, which are good candidates for active regenerator material used in the room temperature cooling devices. The first group of materials is hydrogenated as well as cobalt doped lanthanum based La(Fe,Si)13 intermetallic compounds. The second one is related to the manganese-based compounds, mainly Fe2P type compounds such as (Mn,Fe)2(P,X) [X = Ge, Si, As] [2][3][4][5]. Magnetic as well as calorimetric measurements have been performed on single crystal samples of Pr0.6Sr0.4MnO3 and Nd0.6Sr0.4MnO3 to develop a complete critical behavior study of the paramagnetic to ferromagnetic transition in both manganites [6]. Previously, the development of a new magnetic refrigeration (MR) technology, based upon the magnetocaloric effect (MCE) [7], has brought an alternative to the conventional gas compression (CGC) technique [8,9]. A thorough understanding of the magnetocaloric properties of existing magnetic refrigerant materials has been an important issue in magnetic refrigeration technology. This paper reviews a new class of magnetocaloric material that is, the ferromagnetic perovskite manganites (R1-xMxMnO3, where R =La, Nd, Pr and M= Ca, Sr, Ba, etc.) [10][11][12]. The different research activities can be gathered in the major following axes:  Study of MCE and research of new materials with high magnetocaloric effect [13][14];  Study and modeling of thermodynamic cycles [15];  Design and realization of magnetic refrigeration device with its magnetic source [16][17][18]. In this spirit, an oxide expected to show promising magnetocaloric properties around room temperature Pr0.65Sr0.35MnO3 was produced in large scale and shaped in order to build a regenerator [19]. on other hand, the perovskite type manganite systems, LnSrMnO (Ln=La, Pr, Nd, Sm, and Gd; 0x0.5) were studied as the electrode materials for solid oxide fuel cells from the viewpoint of applications to the co-firing process of the electrolyte and electrode at a higher temperature [20]. In previous works [21][22], the magnetocaloric effect on SmFe1-xMnxO3 and La0.67Ba0.22Sr0.11MnO3 perovskites has been investigated using the Monte Carlo simulations. In this work, both approaches First principal calculations and Monte Carlo simulations are used to study the Pr0.65Sr0.35MnO3 perovskite. The electronic structure are studied. The thermal of the magnetic entropy change and the adiabatic temperature are determined. The Curie temperature of Pr0.65Sr0.35MnO3 and the field dependence of relative cooling power Pr0.65Sr0.35MnO3 has been obtained.

Figure 1.
The structure of PrMnO3 A Sr / Pr substitution in the supercell of the total atom of 13 Pr leads to a composition Pr0.65Sr0.35MnO3 ( Figure 1), which is even of the composition Pr0.65Sr0.35MnO3 prepared experimentally [19]. The energy of separation between the valence and core states is -9.0 Ry. The valence wave functions inside the muffin-tin spheres are expanded in terms of spherical harmonics up to lmax = 10. The muffin-tin (MT) radii of Pr, Sr, Mn and O were chosen to be 2.45, 2.23, 1.95 and 1.68 respectively. Both the muffin-tin radius and the number of k-points were varied to ensure total energy convergence. To reduce the calculation time for structural alignment, we based on a distance cutoff 16.281 Bohr.

Model and Monte Carlo simulation
The Ising model of Pr0.65Sr0.35MnO3 perovskite is given by: with Jij is the first, second and third exchange interactions and h is the external magnetic field. The values of J1=+42.0, J2=+39.0 and J3=+36.0 are found from the mean field theory [29]. The spin moment of Mn 3+ is S=2. The Pr0.65Sr0.35MnO3 perovskite such as given in Figure 1 is assumed to reside in the unit cells and the system consists of the total number of spins N=896. Cyclic boundary conditions on the lattice were applied and the configurations were generated by sequentially traversing the lattice and making single-spin flip attempts. Our data were generated with 10 5 Monte Carlo steps IOP Publishing doi:10.1088/1757-899X/1160/1/012010 3 per spin, discarding the first 10 4 Monte Carlo simulations. Starting from different initial conditions, we performed the average of each parameter and estimate the MCSs, averaging over many initial conditions. The different parameters who calculate are given by the following equations: The internal energy per site is: Magnetizations of material are: Magnetic entropy is: ΔSm can be calculated indirectly from the experimental magnetization curves by using Maxwell relation [30]: The adiabatic temperature change is given by: The relative cooling power (RCP) described as an area under the dependence of Sm(T) on temperature, is a compromise between the magnitude of the magnetic entropy change and the width of the peak is given by: where Tc and Th are the cold and the hot temperatures corresponding to both ends of the halfmaximum value of max S m  ,respectively.

Results and discussion
In Figure 2a, we present the total DOS of Pr0.65Sr0.35MnO3 between -7 eV and 5eV as a function of energy. The presence of gap energy close to the Fermi level for spin down shows that this compound has a half metallic character. The summation of the total density of spin up and spin down greater than zero emphasizes that this compound has ferromagnetic behavior. To understand the bonding mechanisms between the atoms, the analysis of partial density of states (PDOS) has been performed Figure 2b. The atoms Mn and O have a significant contribution of the total density in the vicinity of the Fermi level. While Pr has a strong contribution from energy range -0.53eV to 0.85 eV. The contribution from Sr to the total DOS near Fermi level is negligible. Moreover, the Mn atom is dominant by the 3d orbital, and the O atom is dominant by the 2p orbital. Therefore, the strong contribution of Mn-d is due to the hybridization occurring with O(p) states [31]. This suggests that the half-metallicity and the magnetic spin moment are mainly due to the 2p (O) -3d (Mn) coupling. From the Mn-d orbital projected density of states (PDOS) (Figure 2c , where N is the density of states at EF for spin up ↑or spin down ↓ [32,33]. It is found that this system present 100% spin polarization. The calculated Mn spin magnetic moment is 3.37µB calculated by GGA-PBE (Table  1). Table 1. the values of magnetic moment of Mn, and spin polarization (SP)

Compound
Magnetic moment (μB) SP (%) Pr0.65Sr0.35MnO3 3.37617 100% We have presented in Figure 3 the thermal magnetization obtained by Monte Carlo simulations. From this curve, we deduce that the Curie temperature is equal to TC=294 K. This value is in good agreement with the experimental one in ref [19] (see Table 2). The magnetization curve shows a classical phase transition of the 2 nd order at C (ferromagnetic / paramagnetic).    Table 2). The large magnetic entropy change peak, which would be different if the sample is either measured with increasing or decreasing magnetic field. This change in peak is not associated with the intrinsic properties of the sample but to a wrong application of Maxwell relation.  Table 2).  Figure 5. The adiabatic temperature change Tad (a) and heat specific CP(b) for h=1 T. We give in Figure 6, the variation of relative cooling power with the magnetic field for Pr0.65Sr0.35MnO3 using Monte Carlo simulations. RCP varies linearly with magnetic field h. The maximum value of RCP is 17557 J/kg is given for h=5T.  Figure 6. The field dependence of relative cooling power for Pr0.65Sr0.35MnO3. It is very interesting to note here that usually, this type of giant magnetocaloric effect and large RCP is observed for samples possessing heavier rare-earth elements whose magnetic moments are large [34]. Finally, we have given in Figure 7, the thermal dependence of relative cooling power for

Conclusion
We investigated the magnetocaloric effect, electronic and magnetic properties of Pr0.65Sr0.35MnO3 by using first principle studies and Monte Carlo simulation. The spin polarization for Pr0.65Sr0.35MnO3 show half metallic ground state with the ferromagnetic coupling of Mn spin. The transition temperature has been obtained from the variation of magnetization versus the temperatures for a fixed value of magnetic field. The obtained values of TC=294 K using Monte Carlo simulations are comparable with that obtained by Ref. [19]. The obtained results of magnetic entropy change and heat specific for Monte Carlo simulations are comparable with that obtained by Ref. [19]. The maximum of magnetic entropy change is situate at the transition temperature and increase with increasing the magnetic field. The transition temperature of Pr0.65Sr0.35MnO3 is obtained and it is comparable with that found by experiment results. The adiabatic temperature and heat specific are obtained. The maximum of curves are situated at the transition temperature. The variation of RCP values versus the magnetic fields and temperatures values are found. The RCP values increase with increasing the magnetic field.