The article information
 Hao Aimin, Bai Jing, Luo Shaohua, Qi Xiwei
 郝爱民, 白静, 罗绍华, 齐西伟
 First Principles Investigation of Electronic Property and High Pressure Phase Stability of SmN
 SmN晶体的电子结构和高压相变的第一性原理
 Chinese Journal of Chemical Physics, 2016, 29(2): 219222
 化学物理学报, 2016, 29(2): 219222
 http://dx.doi.org/10.1063/16740068/29/cjcp1507143

Article history
 Dated: Received on July 7, 2015
 Accepted on October 8, 2015
Anomalous physical properties of the rareearth nitrides (RENs) have attracted numerous attentions for several decades. The emergence of the spintronics field provides new interest in this class of materials because of their unique magnetic and electronic properties [1, 2].
There have been a lot of theoretical and experimental studies on the electronic structures of the RENs. Aerts et al. systematically studied the electronic structures of the RENs using ab initio selfinteraction corrected local spin density approximation (LSDA),results showed that these materials had a broad range of electronic properties including forming a various class of halfmetallic magnets [3]. Preston et al. investigated the electronic structures of DyN and SmN using LSDA+$U$ method,results showed that the band gap of SmN was zero [4]. Larson et al. investigated the electronic structures of the RENs in B1 structure using density functional theory calculations within the LSDA+$U$ method and found that the early members of the RENs before GdN (with the exception of NdN) are halfmetals,while the later members after GdN have a small indirect gap [5].
SmN is reported to be antiferromagnetic with a very small net moment below 25 K,which is the earliest magnetic investigation of SmN [6]. Subsequently,a neutron scattering study suggested a ferromagnetic phase with near cancellation between the spin and orbital moment [7]. Very recently,Anton et al. experimentally and theoretically investigated spin/orbit magnetic property. Their results show that SmN is ferromagnetic with its net magnetic moment of 0.03 $\mu_\textrm{B}$ per formula unit [8]. The nearzero moment is a result of the nearly equal and opposing spin and orbital moments in the ground state of Sm$^{3+}$ ion.
The pressureinduced structure transition of the RENs has been an interesting topic for the last two decades. Vaitheeswaran et al. investigated the structural phase stability of LaN,and it was predicted that LaN undergoes a transition from B1 to B2 structure at 27 GPa [9]. CeN was theoretically predicted to transform from B1 to B$_2$ structure at 62 GPa [10]. The structural and elastic properties of CeN and TbN under high pressure have been investigated using two body inter ionic potential theory,result showed that CeN and TbN exhibited a structural phase transition from B1 to B2 structure at 88 and 136 GPa,respectively [11]. The pressureinduced structure transformation of PmN was studied using firstprinciples tightbinding linear muffintin orbital method,and it was predicted a structural phase transformation from B1 to B2 structure at 3.4 GPa [12]. Jakobsen et al. experimentally and theoretically investigated high pressure behavior of TbN [13]. Ciftci et al. theoretically investigated the elastic and thermodynamic properties of LaN [14]. Hao et al. studied the elastic properties of NdN using firstprinciples calculations [15]. Elastic properties and hardness of lanthanide nitrides in B1 structure were investigated using firstprinciples calculations [16, 17]. The result reveals that the ligand field stabilization energy and lanthanide contraction play an important role in determining the hardness of lanthanide nitrides in B1 structure.
To the best of our knowledge,the pressureinduced structure transition of SmN has not been investigated up to now. In this work,we discuss the electronic property and high pressure phase stability of SmN.
Ⅱ. COMPUTATIONAL DETAILSThe calculations were performed using the planewave pseudopotential method as implemented in the CASTEP code [18]. For all calculations in the present work,the normconserving pseudopotential was employed to model the ionelectron interaction. The exchangecorrelation functional was treated by the generalized gradient approximation (GGA) of PerdewBurkeErnzerhof (PBE) [19]. The energy cutoff of the planewave basis was set to 770 eV. Integration in the Brillouin zone was performed using the Monkhorst method with 4$\times$4$\times$4 [20]. The chosen planewave cutoff and numbers of $k$ points were carefully checked to ensure good convergence.
The selfconsistent convergence accuracy was set to be 5.0$\times$10$^{6}$ eV/atom. The convergence criterion for the maximal force between atoms was 0.01 eV/Å. The maximum displacement was 5.0$\times$10$^{4}$ Å,and the stress was set to be 0.02 GPa. For a given external hydrostatic pressure,lattice constants and internal coordination were fully relaxed.
Ⅲ. RESULTS AND DISCUSSION A. Electronic propertySmN is a strongly correlated system with 4f electrons. 4f bands are generally very narrow,which significantly differs from the bands dominated by s,p,and d states. Therefore there exist strong onsite Coulomb repulsions among the highly localized f electrons [21]. In the process of electronic structure calculations,the GGA+$U$ ($U$=6.0 eV) method is used to correct the strong onsite Coulomb repulsion of Sm 4f states.
We have carried out spinpolarized electronic structure calculations of SmN in B1 structure. The result is shown in Fig. 1. It can be seen that an overlap of the majorityspin bands and an energy gap of 0.9 eV of the minorityspin bands coexist at Fermi level,indicating that SmN is a half metal. A striking feature of a half metal is that the minorityspin band structure has a semiconductor gap straddling the Fermi level,whereas the majorityspin band structure has metallic intersections [22]. Our results are in good agreement with those of Aerts et al. [3] and Larson et al. [5].
Figure 2 presents the partial density of states (DOS) of SmN in B1 structrue. Just below the Fermi level $E_\textrm{F}$,the bands are predominantly due to N2p states with a substantial hybridization with Sm 5d and 4f states. Sm4f majorityspin electrons create an exchange filed that leads to a N2p small spin splitting of 0.2 eV [23]. Above $E_\textrm{F}$ are mainly Sm pf states with a substantial hybridization with N s and p states. It was found that pf hybridized states play a main role in the electronic bonding.
The occupied majorityspin f bands fall below N2p bands and push Sm5p bands lower in energy. The unoccupied majorityspin f bands sit just above $E_\textrm{F}$. There are two Sm f peaks between 5.0 and 8.0 eV,which are the unoccupied minorityspin bands.
A very large splitting of about 13.0 eV between Sm4f majorityspin and minorityspin states is responsible for the spin magnetic moments. A small spin splitting of Sm5d states implies that it has a weak contribution to the spin magnetic moments. It is the occupancy of the highly localized 4f states that determines the magnetic properties,while other electronic properties are principally determined by the itinerant sd electrons [24].
B. High pressure phase stabilityHere,we calculated the phase transition pressure of SmN. Our computational approach is based on constantpressure static quantum mechanical calculations at $T$=0 K. The relative stability of different phases can be deduced from the pressure dependence of the enthalpy instead of the Gibbs free energy [25, 26]. The pressure corresponding to $\Delta H$=$H$$$$H_{\textrm{B1}}$ approaching zero is the phase transition pressure ($P_\textrm{t}$). At a pressure higher than the predicted transition pressure,B1 phase becomes thermodynamically unstable while B2 phase becomes thermodynamically stable. The result shows that the transition pressure is 117 GPa,as shown in Fig. 3.
C. Elastic constants and phonon spectraTo check the mechanical stability,we calculated the elastic constants of SmN at 0 GPa using the "volumeconserving technique". The results are presented in Table Ⅰ. As can be seen from Table Ⅰ,our result is in reasonable agreement with the previous calculations [16].
The mechanical stability criteria (Born conditions) for a cubic crystal system are given by [27]:
$ C_{11} > 0,{}C_{44} > 0,C_{{\rm{11}}} > \left {C_{12} } \right,({C_{11} + 2C_{12}}) > 0 $ 
From Table Ⅰ,it can be seen that the elastic constants of SmN in B1 structure at 0 GPa satisfy Born conditions,indicating that B1 structure is mechanically stable at 0 GPa. While the elastic constants of B2 structure at 0 GPa do not satisfy Born conditions,indicating that B2 structure is not mechanically stable at 0 GPa.
To check the dynamic stability,we calculated the phonon spectra of SmN in B1 and B2 structures at 0 GPa. The result is shown in Fig. 4. It can be seen from Fig. 4(a) that there is not any imaginary frequency in the phonon spectra of SmN in B1 structure at 0 GPa. Therefore,our result shows that B1 structure is dynamically stable,which is in agreement with the result of elastic constants. From Fig. 4(b),it can be seen that there are several imaginary frequencies in the phonon spectra of B2 structure,indicating that B2 structure is dynamically unstable at 0 GPa.
Ⅳ. CONCLUSIONA computational study of the electronic property and pressureinduced structure transition of SmN is reported. The result of electronic structure shows that an overlap of the majorityspin bands and an energy gap of 0.9 eV of the minorityspin bands coexist at Fermi level,indicating that SmN is a half metal. The result of relative enthalpy versus pressure indicates that SmN undergoes a pressureinduced phase transition from B1 to B2 structure. The transition pressure is determined to be 117 GPa. Our result reveals that the elastic constants of B1 structure satisfy Born conditions,indicating that B1 structure is mechanically stable at 0 GPa. There is not any imaginary frequency in the phonon spectra of B1 structure,indicating that B1 structure is dynamically stable at 0 GPa. This conclusion is in agreement with that derived from elastic constants.
Ⅴ. ACKNOWLEDGMENTSThis work was supported by the Natural Science Foundation of Hebei Province (No.A2014501010 and No.E2013501135),the Program for New Century Excellent Talents in University (No.NCET100304),and the Special Fund for Basic Scientific Research of Central Colleges,Northeastern University (No.N100123003 and No.N120523001).
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