Solid State Communications 151 (2011) 1903–1906

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Solid State Communications

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Pressure dependence of electronic structure and magnetic properties in Fe16N2

Yifei Chen a,b,∗, Wenbo Mi b, Qinggong Song a, Huiyu Yan a, Tong Wei aa College of Science, Civil Aviation University of China, Tianjin, 300300, People’s Republic of Chinab Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Institute of Advanced Materials Physics and Faculty of Science, Tianjin University, Tianjin,300072, People’s Republic of China

a r t i c l e i n f o

Article history:Received 23 February 2011Received in revised form6 September 2011Accepted 27 September 2011by F. PeetersAvailable online 4 October 2011

Keywords:A. Fe16N2B. First-principlesD. Electronic structureD. Magnetic moment

a b s t r a c t

The electronic structures and magnetic properties of Fe16N2 system and their pressure dependence wereinvestigated byusing first-principles calculations based on the density functional theory. It has been foundthat the total magnetic moment in Fe16N2 system decreases monotonically as increasing pressure from0 to 14.6 GPa. A phase transition from ferromagnetic (FM) to non-magnetic (NM) occurs with a volumecollapse of around 0.008 nm3 at 14.6 GPa, The lattice constants a and c for magnetic results decreasemonotonically as pressure increasing from 0 to 14.6 GPa, at 14.6 GPa, the lattice constant a decreasessharply, on the contrary, the lattice constant c increases abruptly.We think that the change ofmicroscopicstructure of Fe16N2 is responsible for the phase transition from FM to NM.

© 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The key requirements for high-densitymagnetic recordingheadmaterials in the future are high saturationmagnetization (Ms), lowcoercivity and good corrosion resistance. The saturation momentof Fe is as high as 2.2 µB [1], but Fe is liable to corrode in air.Thus, its practical application in the field of magnetic recordingis limited. Iron nitrides have attracted considerable attention byvirtue of their excellent magnetic properties in combination withhigh corrosion and wear resistance. Especially, the α′′-Fe16N2phase exhibits a large Ms that is higher than α-Fe. Since the firstreport on the giant magnetic moment of the α′′-Fe16N2 phase byKim and Takahashi [2] in 1972, many researchers have done theirbest to reproduce the data on theα′′-Fe16N2 phase, to obtain a giantmagnetic moment, which is helpful to understand the physicalmechanisms and for practical applications. Various fabricationmethods have been applied to synthesize this compound, suchas ion implantation [3], molecular beam epitaxy (MBE) [4,5] andreactive magnetron sputtering [6–9]. However, the results on thesaturationmagnetization of theα′′-Fe16N2 phase are controversial,which is in the range from 2.3 to 2.9 µB [10,11].

After that, many discussions on whether or not Fe16N2 has alarge magnetic moment were reported. In order to clarify this

∗ Correspondence to: College of Science, Civil Aviation University of China,Tianjin, 300300, People’s Republic of China.

E-mail addresses: yfchen@cauc.edu.cn, yifei_chen@163.com (Y. Chen).

0038-1098/$ – see front matter© 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.ssc.2011.09.030

problem, many theoretical calculations have been performed onthe α′′-Fe16N2 phase. These calculation results [12–17] indicatethat the calculated averagemagnetic moment per Fe atom is about2.3–2.6 µB, which is much smaller than that reported by Sugitaet al. [18]. However, Lai et al. [15] took the on-site Coulombinteraction into consideration in their calculations and used thegeneralized gradient approximation to improve the accuracy oflocal spin density approximation. By adding these modifications,their calculations revealed a giant magnetic moment of 2.85 µBper Fe atom. Recently, Coey et al. [19] have reviewed the roleof nitrogen in enhancing the iron moment and raising the Curietemperature for magnetic nitrides and revealed that interstitialmodification of 3d metals and 3d–4f intermetallic compounds bynitrogenation leads to a dilation of the crystal lattice and changesin the electronic structure which produce significant changes inthe intrinsic magnetic properties of the iron based materials. Theytend to become strong ferromagnetswith increasedmagnetizationand Curie temperature. However, there is no consensus in favorof the average iron moments in excess of the Slater–Paulingextrapolation, although certain siteswith a low 3d electron densitymay havemoments as high as 3µB. Very recently, Ji et al. [20] haveproposed a new model for the ferromagnetism associated withpartially localized electron states in the Fe16N2 system, showingthat giant saturation magnetization can be achieved at sufficientlylarge Hubbard U values, and the feature of the coexistence ofthe localized and itinerant electron states plays a key role in theformation of giant saturation magnetization.

Up until now, whether Fe16N2 has a large magnetic momentor not is still remaining under debate both experimentally and

1904 Y. Chen et al. / Solid State Communications 151 (2011) 1903–1906

theoretically. Due to such inconsistent and poorly reproduciblereports, Fe16N2 has been regarded a mystery in magneticcommunity. Recently, Okamoto et al. [21] have pointed out thatthe magnetic moment has a strong correlation with the unit cellvolume of α′′-Fe16N2. Meanwhile, pressure dependence of thestructural and magnetic properties in γ ′-Fe4N has been studiedand it has been found that Fe4N undergoes a second-orderphase transition from the ferromagnetic state to a paramagneticstate [22–24]. However, no experimental and theoretical worksdeal with the magnetization under pressure on Fe16N2. All of theabove expression motivates us to focus on the effect of pressureon the electronic structures and magnetic properties of Fe16N2. Inthiswork,we investigated systematically the pressure dependenceof unit cell volume, electronic structure and magnetic propertiesof Fe16N2 system. It is found that a phase transition from FMto NM occurs at 14.6 GPa. In addition, it also has been foundthat the lattice constants a and c for magnetic results decreasemonotonically as pressure increasing from 0 to 14.6 GPa, at14.6 GPa, the lattice constant a decreases sharply, on the contrary,the lattice constant c increases abruptly.

2. Computational methods

All of the calculations were performed with the Cambridge Se-rial Total Energy Package (CASTEP) code, based on the densityfunctional theory (DFT) using ultrasoft pseudopotentials [25] anda plane-wave expansion of the wave function [26]. The general-ized gradient approximation with the Perdew–Burke–Ernzerhofscheme [27] was adopted for the exchange-correlation poten-tial. The valence-electron configurations for the Fe and N atomswere chosen as 3d64s2 and 2s22p3, respectively. The electronwave function was expanded in plane waves with a cutoff energyof 420 eV, and a Monkhorst–Pack grid [28] with parameters of9 × 9 × 9 was used for irreducible Brillouin zone sampling. Thelattice structure and the atomic coordinates were fully relaxedwithout any restriction when pressure is applied by using theBroyden–Fletcher–Goldfarb–Shanno method [29]. In the geome-try optimization process, the energy changes, as well as the max-imum tolerances of the force, stress, and displacement were setas 5 × 10−6 eV/atom, 0.01 eV/Å, 0.02 GPa, and 0.0005 Å, respec-tively. The test calculations with higher cutoff energies and denserk-point grids were also performed, and the overall results re-mained unchanged. Then the electronic structures were calculatedon the basis of the optimized supercells.

In this work, two types of calculations were considered atthe ambient pressure. The difference between the two types ofcalculations (called magnetic and non-magnetic, respectively) iswhether one takes into account the spin degree of freedom or not.

3. Results and discussion

The basic structure of Fe16N2 can be described as a 2 × 2 × 2supercell ofα-Fe dopedwith twoNatoms on interstitial octahedralpositions, in which there are three types of Fe atoms: Fe I atomssurround the N atom are in the up and down corners of theoctahedron, Fe II atoms are in the horizontal directions of the Natoms, and Fe III atoms are not directly connected with the Natoms, as shown in Fig. 1. Table 1 lists the positions of Fe and Nsites, as well as the space group of Fe16N2.

The calculated lattice constants (a = 5.65 Å, c = 6.23 Å) areslightly smaller than the experimental ones (a = 5.72 Å, c = 6.29Å), indicating that the calculation parameters are reasonable. Forcomparison,we first focus on the electronic structure andmagneticproperties of Fe16N2 at 0 GPa. Fig. 2 presents the total density ofstates (DOS) of Fe16N2. One can see that the total DOS of the up anddown spins are significantly different near the Fermi level. A peak

Fig. 1. (Color online) Body-centered tetragonal unit cell of Fe16N2 . Lattice constantsof a and c axes are 5.72 and 6.29 Å, respectively.

Table 1The positions of Fe and N sites, as well as space group of Fe16N2 .

Space group 14/ mmm

Atom Site x y z

N 2a 0 0 0Fe I 4e 0 0 0.293Fe II 8h 0.243 0.243 0Fe III 4d 0 0.5 0.25

Fig. 2. Total DOS of Fe16N2 . The positive (negative) channel represents the up(down) spin, respectively. The Fermi level is set to 0 eV.

in the down-spin channel appears but no peak in the up-spin bandsabove the Fermi level can be observed. More localized unoccupiedbands exist in down-spin channel than those in up-spin channel inthis area. The asymmetrical DOS between the up- and down-spinchannels near the Fermi level suggests that the Fe16N2 system isferromagnetic. The calculated total magnetic moment is 19.5µB inthe Fe16N2 primitive cell. Namely, the average magnetic momentis 2.44 µB per Fe atom, which is in good agreement with the valuereported by Sakuma [30], but it is much smaller than the value of3.2 µB reported by Sugita et al. [18].

It is well known that Fe atom has an electronic configurationof 3d64s2 and an atomic magnetic moment of 4 µB. However, dueto the broadening of 4s and 4p bands in the periodic structure, 4sand 4p band populations decreased while the 3d band populationincreased, resulting in a small magnetic moment. For instance, forFe atoms in α-Fe, the 4s and 4p band occupation number was quitesmall as 0.57 and 0.55, respectively. On the contrary, the 3d bandoccupation was raised to 6.88, resulting in an atomic moment ofonly 2.2 µB [31]. The local magnetic moment of each Fe atomin Fe16N2 is considerably sensitive to the site. The Fe I and Fe IIatoms, which directly connect to N atoms, lost their outer shellelectron to N. Nevertheless, their 3d electrons remained almostunchanged, so that the atomic magnetic moment was similar tothat of α-Fe. On the other hand, the Fe III atoms, which do notdirectly connect to N atoms, have high 4s and 4p band occupations

Y. Chen et al. / Solid State Communications 151 (2011) 1903–1906 1905

Table 2Mulliken population analysis of atom and magnetic moment for Fe16N2 at 0 GPa.

Atoms s electrons p electrons d electrons Total Moment (µB)

N 1.69 4.02 0.00 5.70 −0.08Fe I 0.56 0.69 6.62 7.88 2.16Fe II 0.52 0.73 6.62 7.88 2.36Fe III 0.58 0.88 6.55 8.02 2.84

Fig. 3. The total energies of FM and NM for the Fe16N2 system as a function of unitcell volume and the common tangent construction (straight line).

Fig. 4. (Color online) Total enthalpies as a function of pressure for magnetic andnon-magnetic results.

Fig. 5. Unit cell volume as a function of pressure for the magnetic and non-magnetic results.

and low 3d occupation leading to a giant magnetic moment, ascan been seen in Table 2, which is in good agreement with theresult in Ref. [32]. This giant magnetic moment can be attributedto the electron transfer among the bands [33]. As more spacesare vacated, the 4s and 4p electrons of Fe III atoms, which do notdirectly connect with N atoms, have more space to occupy. Theincrease in the occupation number gives rise to the decrease in its3d band occupation, resulting in a giant magnetic moment.

In order to explore the effect of pressure on the electronicstructure and magnetic properties of Fe16N2 system, a series ofdifferent hydrostatic pressures are applied to the primitive cell ofFe16N2. The total energy, unit cell volume and magnetic momentwere calculated for the Fe16N2 system under different pressures.

Fig. 6. Totalmagneticmoment for the ferromagnetic case as a function of pressure.

Fig. 7. Magnetic moments of Fe atoms directly connected to N in the Fe16N2 as afunction of the Fe–N distance.

Fig. 3 presents the total energies of FM and NM for Fe16N2 asa function of unit cell volume. It is well known that the phasetransition would occur at a pressure when the Gibbs energies ofthe two structures are equal. On the common tangent line of Fig. 3,the Gibbs free energies of the two curves are equal. Since all ourcalculations are performed at T = 0 K, the Gibbs free energybecomes the enthalpy H = E + PV (here, H, E, P and V stand forenthalpy, total energy, pressure and unit cell volume, respectively),so the common tangent line to the total energies versus unitcell volume curves for FM and NM indicates the phase transitionpressure. The calculated phase transition pressure from the slopeof the common tangent to the total energy versus volume curves isabout 14.6 GPa. In addition, we also determine the phase transitionpressure by comparing the Gibbs free energy as a function ofpressure. As debated above, at T = 0 K, the Gibbs free energy isequal to enthalpy H . The intersection between the two enthalpycurves (as shown in Fig. 4) also gives phase transition pressureof 14.6 GPa, which is in good agreement with the above resultin terms of the common tangent rule. Fig. 5 presents the unitcell volume as a function of pressure for the magnetic and non-magnetic results. One can see that the unit cell volumeof Fe16N2 formagnetic and non-magnetic results with pressure shows a similarvariation trend, i.e., the unit cell volume decreases monotonicallyas pressure increasing from 0 to 14.6 GPa, and the FM to NM phasetransition is accompanied by a volume collapse of 0.008 nm3. Fig. 6presents the total magnetic moment for the FM case as a functionof pressure. One can see that the total magnetic moment decreasesmonotonically with the increase of pressure from 0 to 14.6 GPaand the total magnetic moment becomes zero at 14.6 GPa, whichresults in a phase transition from FM to NM.

To understand the pressure dependence of total magneticmoment for the Fe16N2 system, the Fe–N distance dependenceof the magnetic moments for Fe atoms directly connected toN in the Fe16N2 is given in Fig. 7. The magnetic moment ofFe atom increases with the increase of Fe–N distance. Theexistence of N atoms can affect the charge transfer betweenthe 4s, 4p and 3d bands of Fe atoms, which is responsible for

1906 Y. Chen et al. / Solid State Communications 151 (2011) 1903–1906

Fig. 8. Pressure dependence of lattice constants for magnetic and non-magneticresults.

the change of magnetic moments. In order to achieve a betterunderstanding for the pressure dependence of total magneticmoment in Fe16N2 system, Fig. 8 presents the lattice constantsas a function of pressure for magnetic and non-magnetic results.One can see that the pressure dependence of lattice constantsfor non-magnetic results is monotonic in all the pressure range,while the pressure dependence of lattice constants for magneticresults is nonmonotonic. The lattice constants a and c for magneticresults decrease monotonically as pressure increasing from 0 to14.6 GPa, a sudden jump occurs at 14.6 GPa, the lattice constant adecreases sharply, on the contrary, the lattice constant c increasesabruptly, above which themagnetic calculation results completelycoincide with the nonmagnetic ones. In addition, we also foundthat the value of c/a keeps a constant of 1.414 for non-magneticresults in all the pressure range, while the value of c/a increasesmonotonically as pressure increasing from 0 to 14.6 GPa formagnetic results, a sudden jumpoccurs at 14.6 GPa, and then keepsa constant of 1.414. As we know, the local environment plays animportant role in determining themagneticmoment of Fe atoms inthe Fe16N2 system. Hence, based on the above discussion, we thinkthat the change of microscopic structure of Fe16N2 is responsiblefor the phase transition from FM to NM.

4. Conclusion

The electronic structure andmagnetic properties of Fe16N2 sys-tem, as well as their pressure dependence have been investigatedsystematically by using first-principles calculations based on DFT.It has been found that the total magnetic moment in Fe16N2 sys-tem decreases monotonically with the increase of pressure from 0to 14.6 GPa. At 14.6 GPa, a phase transition from FM to NM occurswith a volume collapse of around 0.008 nm3. The pressure depen-dence of lattice constants for non-magnetic results is monotonic inall the pressure range, while the lattice constants a and c for mag-netic results decrease monotonically with the increase of pressurefrom 0 to 14.6 GPa, at 14.6 GPa, the lattice constant a decreasessharply, on the contrary, the lattice constant c increases abruptly,above which the magnetic calculation results completely coincide

with the non-magnetic ones. In addition, we also found that thevalue of c/a keeps a constant of 1.414 for non-magnetic results inall the pressure range, while the value of c/a for magnetic resultsincreases monotonically as pressure increasing from 0 to 14.6 GPa,a sudden jump occurs at 14.6 GPa, and then keeps a constant of1.414. Based on the above discussion, we think that the phase tran-sition from FM to NM should be attributed to the change of micro-scopic structure of Fe16N2.

Acknowledgments

This research has been financially supported by the NationalNatural Science Foundation of China (Grant No. 60979008 and No.51102277) and Science Foundation of Civil Aviation University ofChina (Grant No. yk0528s). The authors are grateful to Prof. H.L. Baifor helpful discussion.

References

[1] A. Kano, N.S. Kazama, H. Fujimori, J. Appl. Phys. 53 (1982) 8332.[2] T.K. Kim, M. Takahashi, Appl. Phys. Lett. 20 (1972) 492.[3] H. Shinno, K. Saito, Surf. Coat. Technol. 103–104 (1998) 129.[4] Y. Sugita, H. Takahashi, M. Komuro, K. Mitsuoka, A. Sakuma, J. Appl. Phys. 76

(1994) 6637.[5] M. Komuro, Y. Kozono, M. Hanazono, Y. Sugita, J. Appl. Phys. 67 (1990) 5126.[6] D.C. Sun, C. Lin, E.Y. Jiang, J. Phys.: Condens. Matter 7 (1995) 3667.[7] X.Z. Ding, F.M. Zhang, J.S. Yan, H.L. Shen, X. Wang, X.H. Liu, D.F. Shen, J. Appl.

Phys. 82 (1997) 5154.[8] S.R. Kappaganthu, Y. Sun, Surf. Coat. Technol. 167 (2003) 165.[9] Y.F. Chen, E.Y. Jiang, Z.Q. Li, W.B. Mi, P. Wu, H.L. Bai, J. Phys. D: Appl. Phys. 37

(2004) 1429.[10] M. Takahashi, H. Shoji, H. Takahashi, H. Nashi, T. Wakiyama, J. Appl. Phys. 76

(1994) 6642.[11] H. Takahashi, H. Shoki, M. Komuro, Y. Sugita, J. Appl. Phys. 73 (1993) 6060.[12] S. Ishida, K. Kitawatase, S. Fujii, S. Asano, J. Phys.: Condens. Matter 4 (1992)

765.[13] A. Sakuma, J. Appl. Phys. 79 (1996) 5570.[14] K. Umino, H. Nakajima, K. Shiiki, J. Magn. Magn. Mater. 153 (1996) 323.[15] W.Y. Lai, Q.Q. Zheng, W.Y. Hu, J. Phys.: Condens. Matter 6 (1994) L259.[16] H. Nakajima, Y. Ohashi, K. Shiiki, J. Magn. Magn. Mater. 167 (1997) 259.[17] R. Coehoorn, G.H.O. Daalderop, Phys. Rev. B 48 (1993) 3830.[18] Y. Sugita, K.Mitsuoka,M. Komuro, H. Hoshiya, Y. Kozono,M. Hanazono, J. Appl.

Phys. 70 (1991) 5977.[19] J.M.D. Coey, P.A.I. Smith, J. Magn. Magn. Mater. 200 (1999) 405.[20] N. Ji, X. Liu, J.P. Wang, New J. Phys. 12 (2010) 063032.[21] S. Okamoto, O. Kitakami, Y. Shimada, J. Magn. Magn. Mater. 208 (2000)

102.[22] N. Ishimatsu, H. Marurama, N. Kawamura, M. Suzuki, Y. Ohishi, M. Ito, S. Nasu,

T. Kawakami, O. Shimomura, J. Phys. Soc. Japan 72 (2003) 2372.[23] M. Ogura, H. Akai, Hyperfine Interact. 158 (2004) 19.[24] E.L. Peltzer Y Blancá, J. Desimoni, N.E. Christensen, H. Emmerich, S. Cottenier,

Phys. Status Solidi B 246 (2009) 909.[25] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892.[26] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark,

M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717.[27] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.[28] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188.[29] B.G. Pfrommer, M. Cote, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997)

233.[30] A. Sakuma, J. Magn. Magn. Mater. 102 (1991) 127.[31] D. Li, Y.S. Gu, Z.R. Nie, B. Wang, H. Yan, J. Mater. Sci. Technol. 22 (2006) 833.[32] J.M.D. Coey, J. Appl. Phys. 76 (1994) 6632.[33] D. Li, J.W. Roh, K.J. Jeon, Y.S. Gu, W. Lee, Phys. Status Solid B 245 (2008)

2581.