Spin Density for Intermetallic Compounds

: We first performed a pure spin-polarized calculation on Nd 2 Fe 14 B using the self-consistent Full Potential Linearized Augmented Plane Wave (FPLAPW). The total charge density and the spin density calculated by taking the sum or the difference of spin-up and spin-down charge densities, respectively. In this paper, we present the spin and charge density contours for rare-earth transition metal compounds e


Introduction
The discovery of the new performance permanent magnet based on rare earth (R), iron and born have been revolutionized the magnetic industry.As a result of its high energy storage/conversion efficiency, Nd2Fe14B is a base material for permanent magnetic devices and open a new horizon for further research in magnetic materials [1].Recently, neutron-Diffraction and magnetic elastic measurements were considered to be highly sophisticated techniques to obtain more definitive information on R2Fe14B [2][3][4][5].Spin and charge densities contours were reported, only for some rare-earth transition metal compounds R2T14B and other systems [6][7][8][9][10].Nd2Fe14B is the most important alloy in terms of practical applications.In this paper, we discuss the spin and charge density maps of Nd2Fe14B by using the first-principles spin polarized.These systems with large Nd-4f and Fe-3d orbitals undergoes magnetic coupling that persists the ordering of atoms in stabilizing the structure well above the room temperature.Nd2Fe14B crystallize in tetragonal structure with lattice parameters 'a' = 'b' = 8.707Å and 'c' = 2.203Å [11].A permanent magnet based on Nd2Fe14B alloy exhibit an important magnetic property, a high coercivity.The high coercivity is due to the presence of rare-earth (RE) ions which are immune to demagnetizing fields (coercivity) has resulted in their stable, permanent magnet, widely used in a broad spectrum of modern technologies [10,12].The high value of coercivity was described by the interfacial microstructure [13][14][15][16].However, previously the properties of permanent magnetism in Nd2Fe14B was mostly look into the defect-born pinning centers to enhance the coercivity, due to the interaction of the 4f orbital of RE ions with the electron clouds of the crystal electric field (CEF) of surrounding charges [17,18].This interaction was associated with the spin-orbit coupling which aligns the moment of RE ions along a specific crystalline direction.The magneto-crystalline anisotropy (MCA) energy plays a crucial role in disturbing this orientation that provides resistance to demagnetizing fields, resulting from a higher coercivity.The research on the magnetic materials is mounting year by year around the globe.Various research groups are working on to improve the efficiency of magnetic properties as well as the quality of its stoichiometry by substituting the impurities [19][20][21][22][23].The methods of the preparation and the method of calculation have been modified year after year.A magnetic nano-crystal of Nd-Fe-B called exchange-coupled nano-crystalline composite hard magnetic materials were prepared from the rapid quenching of the liquid method [13][14][15][16].Despite of technology progress in Nd2Fe14B as a permanent magnet, our basic understanding regarding the interaction in its atomistic scale is still limited.To understand the basis of permanent magnetism in Nd2Fe14B and it is important to study the ordering of constituent elements in forming the stability and their orbital interaction in an atomistic scale from first principles calculation.

Method of Calculations
The Nd2Fe14B crystal is a tetragonal unit cell with a space group P42/mnm, structure No. 136 [see Ref. 24,25] .We used the lattice constants and the fourteen atomic position parameters for Nd2Fe14B at 77K [26].The experimental values used in our calculations are a= 8.802, c= 12.179 A 0 [27,28].The Generalized Gradient Approximation (GGA) of Perdew, Burke , and Ernzerhof [29,30] used for correlations and exchange potentials as implemented in the Wien2k code [31].
Self-Consistent calculations performed with 30 k-points in the irreducible Brillouin zone.We used the muffin tin (MT) sphere radii R MT Nd =2.5 a.u, R MT Fe = 2.09 a.u, R MT B =1.85 a.u and the cut-off energy parameters RKmax and Gmax of 7 and 14 respectively.

Result and discussion
The charge and spin densities on the basal and {110} planes were presented in Figures (1b, 1c) and Figures (2b, 2c) respectively.There are two crystallographic planes in the tetragonal cell of Nd2Fe14B: basal plane (z=0) which contains the two R, B, and Fe(c) sites as shown in Fig. (1a), [13,14] and the (110) plane which is parallel to the c axis and contains Fe(e) and Fe(j1) sites in addition to B and R sites as shown in Figure (2a) [13,14].The spin and charge densities of Nd2Fe14B calculated from the difference between spin-up and spin-dn for spin density and sum between spin-up and spin-dn for charge density have been plotted in the (001) and (110) planes .
The charge of the occupied f electrons have been included .The spin density is from the Fe sublattice alone.The Nd(g) and Nd(f) sites show different charge and spin densities distributions.We calculated the spin and charge densities contours for rare-earth transition metal compounds e.g., Nd2Fe14B using spin-polarized.The contours used in the plots with an interval of 0.1.

Conclusion
We performed a systematic ab initio calculation on Nd2Fe14B using spin-polarized.The LDA + U scheme has been used and available in the Wien2k code.The spin and charge density contours show a strong dependence on the scheme used.Presentation of charge and spin density maps on the basal and {110} planes reveal some intricate details about the structure, bonding, and magnetic interactions in Nd2Fe14B alloys.Formation of multicenter bonds involving the B atom in the trigonal prism contributes to the stability of the tetragonal structure.
Figure (1b)  displays the charge density contours in a portion of the (001) plane containing two Nd(g) , two Nd(f), four Fe(c) and two B(g).Figure(1c) display the spin density contours in a portion of the (001) plane containing two Nd(g) , two Nd(f), four Fe(c) and disappear the two B(g).The charge density contours in a portion of the (110) plane containing two Nd(g) , two Nd(f), four B(g), six Fe(e), four Fe(j2) and four Fe(j1) as shown in (Fig.2b).But the spin density contours in a portion of the (110) plane containing two Nd(g) , two Nd(f), six Fe(e), four Fe(j2) and four Fe(j1) and disappear the four B(g) as shown in Figure( 2c).