⇦Chinese Physics Letters, 2018, Vol. 35, No. 3, Article code 036401 Spin and Orbital Magnetisms of NiFe Compound: Density Functional Theory Study and Monte Carlo Simulation R. Masrour1**, A. Jabar1, E. K. Hlil2, M. Hamedoun3, A. Benyoussef3,4, A. Hourmatallah5, K. Bouslykhane6, A. Rezzouk6, N. Benzakour6 Affiliations 1Laboratory of Materials, Processes, Environment and Quality, Cady Ayyed University, National School of Applied Sciences, Safi 63 46000, Morocco 2Institut Néel, CNRS et Université Grenoble Alpes, BP 166, F-38042 Grenoble Cedex 9, France 3Institute of Nanomaterials and Nanotechnologies, MAScIR, Rabat, Morocco 4Hassan II Academy of Science and Technology, Rabat, Morocco 5Equipe de Physique du Solide, Laboratoire LIPI, Ecole Normale Supérieure, BP 5206, Bensouda, Fes, Morocco 6Laboratoire de Physique du Solide, Université Sidi Mohammed Ben Abdellah, Faculté des Sciences DharMahraz, BP 1796, Fes, Morocco Received 6 October 2017, online 25 February 2018 **Corresponding author. Email: rachidmasrour@hotmail.com Citation Text: Masrour R, Jabar A, Hlil E K, Hamedoun M and Benyoussef A et al 2018 Chin. Phys. Lett. 35 036401 Abstract The self-consistent ab initio calculations based on the density functional theory approach using the full potential linear augmented plane wave method are performed to investigate both the electronic and magnetic properties of the NiFe compound. Polarized spin within the framework of the ferromagnetic state between magnetic ions is considered. Also, magnetic moments considered to lie along (001) axes are computed. The Monte Carlo simulation is used to study the magnetic properties of NiFe. The transition temperature $T_{\rm C}$, hysteresis loop, coercive field and remanent magnetization of the NiFe compound are obtained using the Monte Carlo simulation. DOI:10.1088/0256-307X/35/3/036401 PACS:64.70.K-, 02.60.Pn, 75.60.Ej © 2018 Chinese Physics Society Article Text Ni-Fe alloys have been extensively studied in recent years because of their electrical, catalytic and magnetic properties as well as their potential technological applications in catalysis, sensors, electromagnetic shielding, absorbing materials, and so on.[1,2] The magnetic and electrical properties of Ni-Fe alloys with various morphologies have been investigated.[3] Properties of magnetic metal thin films, applied as electrodes, should have a significant effect on the spin injection efficiency.[4] Phase and magnetic studies of the high-energy alloyed Ni-Fe have been presented.[5] The Fe-Ni alloys are used in recording applications, transformers, sensors, inductive devices, etc.[6] Especially the permalloy, such as NiFe, attracts interest in design of new materials due to its high magnetic permeability. The magnetic properties of the NiFe nanoparticles were measured at room temperatures using a vibrating sample magnetometer in an external magnetic field ranging from $-$13 kOe to +13 kOe.[7] The electronic property of Ni-Fe amorphous alloys has also been studied and reported in Refs. [8,9] using density functional theory. First-principles calculations of the energy of various crystal structures of Fe, Ni and ordered Fe-Ni compound with different stoichiometries have been performed by the linearized augmented plane wave method in the generalized gradient approximation.[10] Previously, the electronic structure, magnetic properties and half-metallicity of the CaMnO$_{3}$/BaTiO$_{3}$ superlattices are investigated by employing the first-principle calculation.[11] Moreover, the mixed spin Ising ferrimagnetic models have been studied using the effective-field theory with correlations and Monte Carlo simulation.[12-14] In this work, self-consistent ab initio calculations and Monte Carlo simulations are used to calculate the electronic and magnetic properties of NiFe compound. Firstly, FLAPW calculations based on density functional theory principle are performed on NiFe. Appropriate polarized spin as well as ferromagnetic state are considered. The variation of the magnetization with the temperature is obtained. Finally, the hysteresis loop is obtained for different values of temperatures. We use the full augmented plane wave (FLAPW) method,[15] which performs DFT calculations with the generalized gradient approximation (GGA). The Kohn–Sham equation and energy functional are evaluated consistently. For this performance, the space is divided into the interstitial and the non-overlapping muffin-tin spheres are centered on the atomic sites. The employed basis function inside each atomic sphere is a linear expansion of the radial solution of a spherical potential multiplied by spherical harmonics. In the interstitial region, the wave function is taken as an expansion of plane waves and no shape approximation for the potential is introduced in this region, consistently with the full potential method. The core electrons are described by atomic wave functions, which can be solved relativistically using the current spherical part. Spin polarized potential as well as the ferromagnetic state is considered for our calculations. The FLAPW calculations are performed using $a=0.381$ nm as the lattice parameter. In this lattice, the Fe atom occupies the (000) whereas the site (1/2, 1/2, 1/2) is fully occupied by the Ni atom. We consider the cubic NiFe ferromagnetic system as depicted in Fig. 1. Each site on the figure is occupied by Ising spins of Ni$^{2+}$ and Fe$^{2+}$ ($S_{\rm Ni}^{2+}=\pm1$, 0 and $\sigma_{\rm Fe}^{2+}=\pm2$, $\pm$1 and 0). Each spin is connected to the nearest neighbor spins with exchange interactions. The spin Ising system described by the Hamiltonian includes exchange interactions, and the external magnetic field is given by $$\begin{alignat}{1} H=\,&-J_{\rm NiNi} \sum\limits_{\langle i,j\rangle} S_i S_j -J_{\rm FeFe} \sum\limits_{\langle n,m\rangle} \sigma _n \sigma _m\\ &-J_{\rm NiFe} \sum\limits_{\langle i,n\rangle} {S_i \sigma _n} -h\Big(\sum\limits_i S_i +\sum\limits_n {\sigma _n}\Big),~~ \tag {1} \end{alignat} $$ where $\langle i,j\rangle$, $\langle n,m\rangle$ and $\langle i,n\rangle$ stand for the first nearest neighbor sites ($i$ and $j$), ($n$ and $m$) and ($i$ and $n$), respectively, $h$ is the external magnetic field, while $J_{\rm NiNi}$, $J_{\rm FeFe}$ and $J_{\rm NiFe}$ are the exchange-interaction parameters among NiNi, FeFe and NiFe, respectively. The values of $|J_{\rm FeFe}|=+1$ K, and $J_{\rm NiNi}/|J_{\rm FeFe}|=51$ are obtained using the mean field theory.[16]
cpl-35-3-036401-fig1.png
Fig. 1. The NiFe compound used for the calculations.
The NiFe compound formed by the ferromagnetic spin Ising model is assumed to reside in the unit cells, and the system consists of the total number of spins $N=N_{\rm Ni}+N_{\rm Fe}=250$ with $N_{\rm Ni}=125$ and $N_{\rm Fe}=125$, which are the number sites of $\sigma$ and $S$ spins. We apply a standard sampling method to simulate the Hamiltonian given by Eq. (1). Cyclic boundary conditions on the lattice are imposed and the configurations are generated by sequentially traversing the lattice and making single-spin flip attempts. The flips are accepted or rejected according to a heat-bath algorithm under the Metropolis approximation. Our data are generated with 10$^{5}$ Monte Carlo steps per spin, discarding the first 10$^{4}$ Monte Carlo simulations. Starting from different initial conditions, we perform the average of each parameter and estimate the Monte Carlo simulations, averaging over several initial conditions. Our program calculates the following parameters. The internal energy per site $E$ is given by $$\begin{align} E=\frac{1}{N_{\rm Fe} +N_{\rm Ni}}\langle H \rangle.~~ \tag {2} \end{align} $$ The magnetizations of Ni$^{2+}$ and Fe$^{2+}$ are given by $$\begin{align} M_{\rm Ni} =\,&\Big\langle {\frac{1}{N_{\rm Ni}}\sum\limits_i {S_i}}\Big\rangle,~~ \tag {3} \end{align} $$ $$\begin{align} M_{\rm Fe} =\,&\Big\langle {\frac{1}{N_{\rm Fe}}\sum\limits_i {\sigma _i}}\Big\rangle.~~ \tag {4} \end{align} $$ The total magnetization of NiFe is given by $$\begin{align} M=\frac{N_{\rm Ni} M_{\rm Ni} +N_{\rm Fe} M_{\rm Fe}}{N_{\rm Ni} +N_{\rm Fe}}.~~ \tag {5} \end{align} $$ The magnetic susceptibilities of Ni$^{2+}$and Fe$^{2+}$ are given by $$\begin{align} \chi_{_{\rm Ni}}=\beta(\langle {M_{\rm Ni}^2}\rangle-\langle {M_{\rm Ni}} \rangle ^2),~~ \tag {6} \end{align} $$ $$\begin{align} \chi_{_{\rm Fe}}=\beta ({\langle {M_{\rm Fe}^2}\rangle-\langle {M_{\rm Fe}} \rangle ^2}),~~ \tag {7} \end{align} $$ where $\beta =1/k_{_{\rm B}}T$ with $T$ being the absolute temperature and $k_{_{\rm B}}$ the Boltzmann constant. The total average magnetic susceptibility is given by $$\begin{align} \chi =\frac{N_{\rm Ni} \chi _{\rm Ni} +N_{\rm Fe} \chi _{\rm Fe}}{N_{\rm Ni} +N_{\rm Fe}}.~~ \tag {8} \end{align} $$ The density of state (DOS) of NiFe deduced from band structure calculations is reported in Fig. 2. Here the Fermi level is taken as reference. This DOS is originated from the contributions of Ni and Fe atoms taking place in both occupied states at negative energies and unoccupied states localized at positive energies. As seen, this DOS is not symmetrical with respect to the energy axis, pointing out that magnetic moments carried by Fe and Ni atoms are ferromagnetically ordered.
cpl-35-3-036401-fig2.png
Fig. 2. Total DOS of NiFe from FLAPW calculations.
The $l$-decomposed DOSs of $d$ like-states of Ni and Fe provide a more detailed picture and allow that both Ni and Fe contributions have mainly a character of the $3d$ band. The presence DOS at the Fermi level points out to the metallic character of our compound. This character is also confirmed by the band structure calculations performed for spin-up along high symmetry directions of the Brillouin zone in our cubic NiFe (Fig. 3). Magnetic moments of Ni and Fe are computed as well and are equal to 0.59 and 2.6$\mu_{\rm B}$, respectively. The obtained value of magnetic moment is $(0.59+2.61)/2=1.6$ and is superior to 0.85$\mu_{\rm B}$ given in Ref. [14] and 1.5$\mu_{\rm B}$.[17]
cpl-35-3-036401-fig3.png
Fig. 3. The calculated electronic structures for spin up along high symmetry directions of the Brillouin zone in cubic NiFe.
cpl-35-3-036401-fig4.png
Fig. 4. The variations of the total ($M_{\rm tot}$) and partials ($M_{\rm Fe}$ and $M_{\rm Ni}$) magnetizations versus the temperature for $|J_{\rm FeFe}|=+1$ K, $J_{\rm NiNi}/|J_{\rm FeFe}|=72$, $J_{\rm NiFe}/|J_{\rm FeFe}|=51$ and $h/|J_{\rm FeFe}|=20$.
cpl-35-3-036401-fig5.png
Fig. 5. The magnetic hysteresis curves for $J_{\rm FeFe}=-1$ K, $J_{\rm NiNi}/|J_{\rm FeFe}|=72$, $J_{\rm NiFe}/|J_{\rm FeFe}|=51$ with different temperatures $k_{_{\rm B}}T/|J_{\rm FeFe}|=500$, 600 and 700.
The magnetic properties of the NiFe compound are investigated using the Monte Carlo simulations. The magnetizations $M_{\rm Fe}$, $M_{\rm Ni}$ and the total magnetization versus the temperatures are presented in Fig. 4. The thermal magnetic susceptibilities of Ni, Fe and NiFe are also plotted in the same figure for $|J_{\rm FeFe}|=+1$ K, $J_{\rm NiNi}/|J_{\rm FeFe}|=51$ and $h/|J_{\rm FeFe}|=72$, $J_{\rm NiFe}/|J_{\rm FeFe}|=20$. The maximum of magnetic susceptibilities is situated in the transition temperature. The obtained value is 600 K. This value agrees nicely with the experimental results given in Refs. [18,19]. The magnetic hysteresis curves of NiFe are given in Fig. 5 for $|J_{\rm FeFe}|=+1$ K, $J_{\rm NiNi}/|J_{\rm FeFe}|=72$, $J_{\rm NiFe}/|J_{\rm FeFe}|=51$ with different temperatures $k_{_{\rm B}}T/|J_{\rm FeFe}|=500$, 600 and 700, and $|J_{\rm FeFe}|=1$ K with different temperatures $T < T_{\rm C}$, $T\approx T_{\rm C}$ and $T > T_{\rm C}$. At high temperature, the system displays a soft magnet characteristic with a small hysteresis loop.[19,20] Similar hysteresis curve behaviors have been observed for nanostructure systems in both theoretical[21-24] and experimental[25] frameworks. The saturation of the magnetization value of the NiFe compound depends on the temperatures. The saturation of magnetization decreases when the temperature increases. Similar behavior is observed in the magnetic properties of NiFe$_{2}$O$_{4}$ nanoparticles.[26] The magnetic calculations show that the NiFe compound has a superparamagnetic behavior transition temperature. A similar compositional dependence of the coercivity was also observed in CoPt and CoO nanoparticles synthesized using the reverse micelle method.[27,28] In summary, magnetic moments carried by Fe and Ni atoms in FeNi are computed and used as input data for Monte Carlo simulations. The magnetic properties of NiFe are investigated using Monte Carlo simulation. The transition temperature is obtained for a fixed value of exchange interactions. The obtained value is comparable with the experimental data. A superparamagnetic behavior of the NiFe compound is concluded from our calculations at $T\approx T_{\rm C}$. References Preparation, characterization and microwave absorbing properties of FeNi alloy prepared by gas atomization methodSynthesis of iron–nickel nanoparticles via a nonaqueous organometallic routeControlled synthesis of magnetic Ni–Fe alloy with various morphologies by hydrothermal approachPhase and magnetic studies of the high-energy alloyed Ni–FeMagnetic materialsSynthesis of monodisperse and high moment nickel–iron (NiFe) nanoparticles using modified polyol processDensity Functional Theory Study on Electronic Property of Cluster NixFe and NiFex (x=1–5)Ab initio investigation of the structural and electronic differences between active-site models of [NiFe] and [NiFeSe] hydrogenasesPhase stability in the Fe–Ni system: Investigation by first-principles calculations and atomistic simulationsStudy of the electronic structure and half-metallicity of CaMnO3/BaTiO3 superlatticePhase transition and magnetization of a hexagonal prismatic nanoisland with a ferrimagnetic spin configurationMagnetic properties of a hexagonal prismatic nanoparticle with ferrimagnetic core–shell structureMagnetic behaviors and multitransition temperatures in a nanoislandApplication of the Weiss molecular field theory to the B-site spinelThe influence of mechanical milling on structure and soft magnetic properties of NiFe and NiFeMo alloysThe heat capacity of Ni3Fe: experimental data from 300 to 1670 KMagnetic properties of core-shell catalyst nanoparticles for carbon nanotube growthTheoretical investigations of magnetic properties of ferromagnetic single-walled nanotubesAn effective-field theory study of hexagonal Ising nanowire: Thermal and magnetic propertiesThermal transport through a one-dimensional quantum spin-1/2 chain heterostructure: The role of three-site spin interactionMagnetic hysteresis dynamics of thin Co films on Cu(001)Room temperature ferromagnetism in Mn+-implanted Si nanowiresMagnetic properties of nanoparticles produced by a new chemical methodStructural characteristics and magnetic properties of chemically synthesized CoPt nanoparticlesPreparation and Magnetic Properties of Oxide-Coated Monodispersive Co Cluster Assembly
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