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A first-principle study of the magnetic, electronic and elastic properties of the hypothetical YFe5 compound
Physica B 407 (2012) 2486–2489
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
A first-principle study of the magnetic, electronic and elastic properties of the hypothetical YFe5 compound Fatema Alzahraa Mohammad a,n, Sherif Yehia b, Samy H. Aly a a b
Department of Physics, Faculty of Science, Mansoura University, Damietta Branch, Mansoura University, New Damietta, Damietta 34517, Egypt Department of Physics, Faculty of Science, Helwan University, Cairo, Egypt
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 September 2011 Received in revised form 14 March 2012 Accepted 17 March 2012 Available online 30 March 2012
We present a DFT-based study of the magnetic properties, electronic structure and bulk modulus of YFe5 at ambient and higher hydrostatic pressures. The LSDA and GGA approximations, as implemented in the electronic structure code FPLO-09, are used throughout the scalar relativistic calculation in this work. Charge and spin density maps using the WIEN2k are also reported for the equilibrium lattice constants. Our study shows that the magnetic phase of this hypothetical compound is more stable than the nonmagnetic phase, and that the application of pressure on magnetic YFe5 has a prominent effect on its magnetic and electronic properties, e.g. the reduction of the magnetic moment and finally the disappearance of ferromagnetism. & 2012 Elsevier B.V. All rights reserved.
Keywords: YFe5 compound Electronic properties Magnetic properties Elastic properties DFT FPLO-09
1. Introduction Iron, one of the most important metals, has been the subject of extensive experimental and theoretical research for many years. Many ab initio calculations of the magnetic, elastic and electronic properties of Fe have been reported [1–4]. Iron compounds are of vital importance in condensed matter physics in general, and in magnetism in particular. RT5 compounds have attracted much attention because of their permanent magnetic properties. These intermetallic compounds crystallize in the hexagonal CaCu5-type structure with space group P6/mmm No. 191. In this structure Y, or a rare-earth atom, occupies the 1a(0,0,0) site and transition metal atoms occupy two crystallographically different sites 2c (1/3, 2/3,0) and 3g(1/2, 0,1/2). Some RT5 and YFe5 compounds with the hexagonal CaCu5-type structure do not exist in stable bulk form; however SmFe5 for example has been stabilized by RF sputtering in thin film form as reported in Refs. [5,6]. The lattice constant and magnetic moment for YFe5 are usually obtained by extrapolating the lattice constants of Y(T1 xFex)5, where T¼Co or Ni [7]. A similar work on R(Ni1 xFex)5 where R¼ Y or Gd with 0rxr1 has been reported by Nagai et al. [8]. The magnetic anisotropy dependence on Fe concentration in Y(Co1 xFex)5 pesudobinary compounds has been reported, for low
n
Corresponding Author. Tel.: þ 200572403980; fax: þ 20572403868. E-mail addresses: [email protected] (F. Alzahraa Mohammad), [email protected] (S. Yehia). 0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.03.050
Fe concentrations, by Steinbeck et al. [9]. The spin and orbital magnetic moments, for x ¼0, 0.4, 0.6 and 1, were also reported by the same reference, where LSDA has been used within the framework of Density Functional Theory (DFT). Larson et al [10] have reported on the magnetic anisotropy and magnetic moment of YCo5 xFex using the FLAPW methods in the range x¼0–5. Self consistent ab initio band structure calculations on the hypothetical YFe5 compound and other Y–Fe compounds, using the augmented–spherical–plane wave method (ASPW), have been reported by Coehoorn [11]. In the present study, we report a DFT-based [12–15] ab initio calculation on YFe5 using both the Local Spin Density Approximation (LSDA) and the Generalized Gradient Approximation (GGA) as implemented in the electronic structure code FPLO-09 [16]. Our purpose is to investigate the effect of these two approximations on the equilibrium volume, magnetic moment, bulk modulus and density-of-states (DOS), and to study to what extent the application of a hydrostatic pressure could change the elastic, electronic and magnetic properties of YFe5. The charge and spin density maps in the (0 0 1) plane are calculated using the WIEN2k package [17].
2. Theory and computation Our calculation is scalar relativistic within the LSDA and GGA approximation schemes of the FPLO-09 code, where the Perdew and Zunger [18] and the Perdew, Burke and Ernzerhof 96 [19]
F. Alzahraa Mohammad et al. / Physica B 407 (2012) 2486–2489
potentials are used for the LSDA approximation and GGA approximations, respectively. We have not considered taking spin–orbit coupling in the present calculation. We have used the same set of parameters to ensure an unbiased comparison between the results obtained from the LSDA and GGA approximations. The parameters are the k-mesh subdivision: 24 24 24, and the accuracies of the density and total energy are 10 6 and 10 8 Hartree respectively. The space group is P6/mmm, No. 191 and the atomic positions are 1a(0, 0, 0) for Y, and 3g(1/2, 0, 1/2) and 2c(1/3, 2/3, 0) for Fe. One formula unit of YFe5 is present in the conventional unit cell. At first, we make a geometrical optimization i.e. determine the equilibrium volume Vo of the crystal structure at hand from the calculated volume dependence of energy E(V). The chosen c/a ratio was calculated in the following manner: for a fixed volume, we perform total energy calculation for different c/a ratios. The value at the energy minimum is the one we chose. Next we fit the E(V) data to the Birch–Murnaghan equation-of-state [20]. The fitting parameters Bo (the bulk modulus), B (the pressure dependence of Bo), and Vo are consequently used to determine the volume dependence on the hydrostatic pressure P. The DOS and magnetic moment are calculated at either ambient pressure (P¼0) and equilibrium volume Vo, or at higher pressures. 3. Results and discussion Our geometrical optimization calculation showed that the magnetic phase of YFe5 is more stable than the nonmagnetic phase using either the LSDA or GGA approximation. The equili˚ and 77.5 A˚ 3 brium cell volumes are 85 A˚ 3 (a ¼5.03, c ¼ 3.87 A), ˚ for the GGA and LSDA approximations, (a¼4.88, c¼ 3.76 A) respectively in the magnetic phase. F. Maruyama et al. [7] have reported on a ¼5.03, c¼4.17 A˚ (V¼91.4 A˚ 3 ) by extrapolating the value of a and c to x¼1 for Y(T1 xFex)5 compounds. The relative percentage error, in the cell volume, between our GGA approximation (V¼85 A˚ 3) and that reported by Maruyama (V¼91.4 A˚ 3)
Total M.M. [µB]
14.0 12.0
LSDA Total M. M.
10.0
GGA Total M. M.
8.0 6.0 4.0 2.0 0.0
42
52
62
72
Volu me
82
92
[Å3]
Fig. 1. Dependence of the total magnetic moment on the cell volume for magnetic YFe5 using GGA and LSDA, approximations.
2487
is 7%. This relative error is only 1.4% off the value reported by Coehoorn (V¼86.2 A˚ 3) using interpolation between YFe3 and Y2Fe17 [11]. The overall decrease of the magnetic moment with decreasing unit cell volume is a feature of itinerant electron magnetic systems. This feature is demonstrated clearly by both of the GGA and LSDA calculations (Fig. 1). As the volume is reduced, the magnetic moment vanishes completely rendering this hypothetical compound as nonmagnetic i.e. having no microscopic magnetic moments. It is to be noted that the moment of the Fe(3g) site is affected relatively stronger, by volume reduction, than that at the 2c site. The calculated total and partial magnetic moments of our work together with the results of extrapolation from experimental data [7,8], and interpolation from ab initio calculated data [11] are presented in Table 1. The main features of this table are the negative small value of the Y moment and the relatively large moment at the Fe(2c) site as compared to the 3g site. In order to obtain the pressure dependence on volume i.e. P(V) of the hypothetical YFe5 compound, we have fitted the energy vs. unit cell volume, for the magnetic phase in the GGA and LSDA data, to the Birch–Murnaghan equation of state [20]. We have used the following expressions for the Birch– Murnaghan equation of state and its associated pressure dependence on volume: 8" #3 9Bo V 0 < V o 2=3 EðVÞ ¼ Eo þ 1 Bo’ 16 : V " " 2=3 #) V 0 2=3 V0 2 þ 1 64 V V " #) " 53 #( 7=3 3B0 Vo Vo 3 " V o 2=3 PðVÞ ¼ 1 1 þ ðBo 4Þ 4 2 V V V The result of fitting our data to the Birch–Muranghan equation of state is shown in Fig. 2 for the magnetic phase in the LSDA approximation. The bulk modulus Bo and its first pressure derivative B’ are reported in Table1. Our GGA value is close to 150 GPa calculated using the augmented-spherical-plane wave method (ASPW) reported by Coehoorn [11]. The pressure dependence of the partial magnetic moments of Y(1a), Fe(3g), Fe(2c) and the total magnetic moment of YFe5 using the GGA approximation are shown in Fig. 3. The compound loses its magnetic moment for pressures in excess of E250 GPa for this approximation. The total and partial DOS of the magnetic YFe5 at the equilibrium volume of 85 A˚ 3, in the GGA approximation, are shown in Fig. 4. The DOS structure, for the Fe 2c and 3g sites, shows that the total DOS is dominated by 3d electrons; the contribution of 4d electrons, however, is negligible. Fig. 5(a) and (b) displays the charge and spin density maps respectively, for YFe5 in (0 0 1) plane as calculated by WIEN2k. ˚ c ¼3.87 A. ˚ The maps are calculated for a crystal with a ¼5.03 A,
Table 1 Compilation of data from the present work and other references on experimental and theoretical investigations on ferro magnetic and nonmagnetic YFe5. References are ˚ V in A˚ 3 and the magnetic moment in mB. given in brackets. Lattice constants a and c are in A, Method
Phase
a, c, V, c/a
LSDA
mag nonmag mag nonmag mag [7] mag [8] mag nonmag
4.88, 4.83, 5.03, 4.93, 5.03, 4.99, 4.97, 4.89,
GGA By experimental extrapolating [7,8] By interpolation [11]
3.76, 3.72, 3.87, 3.80, 4.17, 4.20, 4.03, 3.97,
77.5, 0.77 75.0, 0.77 85.0, 0.77 79.9, 0.77 91.4, 0.83 90.56, 0.84 86.2, 0.81 82.5, 0.81
ltot
lY(1a)
lFe(2c)
lFe(3g)
B (GPa)
B’
7.4 – 9.6 – 8.0 8.6 7 0.2
0.2 – 0.47 –
1.8
1.3 – 2.0 – 1.60 1.6 7 0.1
185 222 148 187
3.30 2.16 4.42 5.55
8.4 ————
0.24 ————
1.53 ————
150 200
——
2.05 – 1.60 1.9 70.1 2.00
2488
F. Alzahraa Mohammad et al. / Physica B 407 (2012) 2486–2489
Fig. 2. Energy vs. cell volume in the LSDA approximation fitted to the Birch– Murnaghan equation for magnetic YFe5.
Fe
12.0 GGA. Total M.M. GGA. M. M. of Fe(2c) GGA. M. M. of Fe(3g) GGA. M. M. of Y(1a)
10.0
M.M. [µB]
8.0 6.0
Fe
Fe
Fe
4.0 2.0 0.0 -2.0 0
40
80
120
160
200
240
280
Pressure [GPa]
4. Conclusions
Fig. 3. Pressure dependence of the partial magnetic moments of Y(1a), Fe(3g), Fe(2c) and the total Magnetic moment of YFe5 in the GGA approximation.
Total Spin- up
20.0
Total Spin- down Fe (2c) Spin- up
15.0
DOS [States/eV]
Fe (2c)Spin- down
10.0
Fe (3g) Spin- up Fe (3g) Spin- down
5.0
Fig. 5. (a) Charge density map in the (0 0 1) plane of YFe5 at V ¼85 A˚ 3 in the GGA approximation by using WIEN2k package. (b) Spin density map in the (0 0 1) plane of YFe5 at V ¼ 85 A˚ 3 in the GGA approximation by using WIEN2k package.
We have performed a first-principle calculation, using the FPLO-09 and WIEN2k electronic structure codes, of the magnetic, electronic and elastic properties of the hypothetical YFe5 compound. Our calculation, using the GGA and LSDA approximations, showed that the magnetic phase is more stable than the nonmagnetic phase. The application of hydrostatic pressure reduces the magnetic moment until ferromagnetism ceases to exist and a truly nonmagnetic state on the microscopic level exists. Our results agree fairly well with available theoretical studies, and with extrapolated experimental data on related compounds.
0.0
Acknowledgment
-5.0 -10.0 -15.0 -8.0
-6.0
-4.0
-2.0
0.0
2.0
4.0
Energy [eV] Fig. 4. Total and partial DOS’s of the magnetic YFe5 at the equilibrium volume of 85 A˚ 3, in the GGA approximation.
The charge density maps display charge contours around both of the Y and Fe atoms, and at the Fe–Fe bond. However, less charge density may be seen at the interstitial Y–Fe space. The spin maps, on the other hand, show clearly the absence of any spin contours at the location of Y atoms indicating the null spin magnetic moment of Y. Further studies are underway to investigate, in more detail, the reasons for the hypothetical nature of YFe5, in particular its enthalpy of formation, and interatomic bonding.
The authors wish to thank their families, the staff of the Physics Department, Damietta branch at Mansoura University, and the FPLO team members for their help and encouragement in one way or another. References [1] D. Bagayoko, J. Callaway, Phys. Rev. B 28 (1983) 5419. [2] I. Schnell, G. Czycholl, R.C. Albers, Phys. Rev. B 68 (2003) 245102. [3] N.C. Bacalis, D.A. Papaconstantopous, M.J. Mehl, M. Lanch-hab, Physica B 296 (2001) 125. [4] W. Zhong, G. Overney, D. Tomanek, Phys. Rev. B 47 (1993) 95. [5] F.J. Cadieu, T.D. Cheung, S.H. Aly, L. Wickramasekara, R.G. Pirich, J. Appl. Phys. 53 (1982) 8338. [6] F.J. Cadieu, T.D. Cheung, L. Wickramasekara, S.H. Aly, J. Appl. Phys. 55 (1984) 2611. [7] F. Maruyama, H. Nagai, Y. Amako, H. Yoshie, K. Adachi, Physica B 266 (1999) 356. [8] H. Nagai, T. Ishii, Y. Amako, H. Yoshie, K. Adachi, J. Magn. Magn. Mater. 226 (2001) 596. [9] L. Steinbeck, M. Richter, H. Eschrig, Phys. Rev. B 63 (2001) 184431.
F. Alzahraa Mohammad et al. / Physica B 407 (2012) 2486–2489
[10] P. Larson, I.I. Mazin, D.A. Papaconstantopoulos, Phys. Rev. B 69 (2004) 134408. [11] R. Coehoorn, Phys. Rev. B 39 (1989) 13072. [12] R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, NewYork, 1989. [13] R.M. Dreizler, E.K.U. Gross, Density Functional Theory, Springer Verlag, Berlin, 1990. [14] Kieron Burke and friends, Department of Chemistry, The ABC of DFT, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854, April 7, 2003; /http:// dft.rutgers.edu/kieron/betaS.
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[15] S. Cottenier, Density Functional Theory and the Family of (L)APW-methods: a step-by-step Introduction, ISBN 90-807215-1-4, Instituut Voor Kern-en Stralingsfysica, K.U. Leuven, Belgium, 2002. [16] K. Koepernik, H. Eschrig, Phys. Rev. B 59 (1999) 1743. [17] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2k (Vienna University of Technology) (2001). [18] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. [19] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [20] F.D. Murnaghan, The compressibility of media under extreme pressure, The Proceedings of The National Academy of Science 30 (1944) 244.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
A first-principle study of the magnetic, electronic and elastic properties of the hypothetical YFe5 compound Fatema Alzahraa Mohammad a,n, Sherif Yehia b, Samy H. Aly a a b
Department of Physics, Faculty of Science, Mansoura University, Damietta Branch, Mansoura University, New Damietta, Damietta 34517, Egypt Department of Physics, Faculty of Science, Helwan University, Cairo, Egypt
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 September 2011 Received in revised form 14 March 2012 Accepted 17 March 2012 Available online 30 March 2012
We present a DFT-based study of the magnetic properties, electronic structure and bulk modulus of YFe5 at ambient and higher hydrostatic pressures. The LSDA and GGA approximations, as implemented in the electronic structure code FPLO-09, are used throughout the scalar relativistic calculation in this work. Charge and spin density maps using the WIEN2k are also reported for the equilibrium lattice constants. Our study shows that the magnetic phase of this hypothetical compound is more stable than the nonmagnetic phase, and that the application of pressure on magnetic YFe5 has a prominent effect on its magnetic and electronic properties, e.g. the reduction of the magnetic moment and finally the disappearance of ferromagnetism. & 2012 Elsevier B.V. All rights reserved.
Keywords: YFe5 compound Electronic properties Magnetic properties Elastic properties DFT FPLO-09
1. Introduction Iron, one of the most important metals, has been the subject of extensive experimental and theoretical research for many years. Many ab initio calculations of the magnetic, elastic and electronic properties of Fe have been reported [1–4]. Iron compounds are of vital importance in condensed matter physics in general, and in magnetism in particular. RT5 compounds have attracted much attention because of their permanent magnetic properties. These intermetallic compounds crystallize in the hexagonal CaCu5-type structure with space group P6/mmm No. 191. In this structure Y, or a rare-earth atom, occupies the 1a(0,0,0) site and transition metal atoms occupy two crystallographically different sites 2c (1/3, 2/3,0) and 3g(1/2, 0,1/2). Some RT5 and YFe5 compounds with the hexagonal CaCu5-type structure do not exist in stable bulk form; however SmFe5 for example has been stabilized by RF sputtering in thin film form as reported in Refs. [5,6]. The lattice constant and magnetic moment for YFe5 are usually obtained by extrapolating the lattice constants of Y(T1 xFex)5, where T¼Co or Ni [7]. A similar work on R(Ni1 xFex)5 where R¼ Y or Gd with 0rxr1 has been reported by Nagai et al. [8]. The magnetic anisotropy dependence on Fe concentration in Y(Co1 xFex)5 pesudobinary compounds has been reported, for low
n
Corresponding Author. Tel.: þ 200572403980; fax: þ 20572403868. E-mail addresses: [email protected] (F. Alzahraa Mohammad), [email protected] (S. Yehia). 0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.03.050
Fe concentrations, by Steinbeck et al. [9]. The spin and orbital magnetic moments, for x ¼0, 0.4, 0.6 and 1, were also reported by the same reference, where LSDA has been used within the framework of Density Functional Theory (DFT). Larson et al [10] have reported on the magnetic anisotropy and magnetic moment of YCo5 xFex using the FLAPW methods in the range x¼0–5. Self consistent ab initio band structure calculations on the hypothetical YFe5 compound and other Y–Fe compounds, using the augmented–spherical–plane wave method (ASPW), have been reported by Coehoorn [11]. In the present study, we report a DFT-based [12–15] ab initio calculation on YFe5 using both the Local Spin Density Approximation (LSDA) and the Generalized Gradient Approximation (GGA) as implemented in the electronic structure code FPLO-09 [16]. Our purpose is to investigate the effect of these two approximations on the equilibrium volume, magnetic moment, bulk modulus and density-of-states (DOS), and to study to what extent the application of a hydrostatic pressure could change the elastic, electronic and magnetic properties of YFe5. The charge and spin density maps in the (0 0 1) plane are calculated using the WIEN2k package [17].
2. Theory and computation Our calculation is scalar relativistic within the LSDA and GGA approximation schemes of the FPLO-09 code, where the Perdew and Zunger [18] and the Perdew, Burke and Ernzerhof 96 [19]
F. Alzahraa Mohammad et al. / Physica B 407 (2012) 2486–2489
potentials are used for the LSDA approximation and GGA approximations, respectively. We have not considered taking spin–orbit coupling in the present calculation. We have used the same set of parameters to ensure an unbiased comparison between the results obtained from the LSDA and GGA approximations. The parameters are the k-mesh subdivision: 24 24 24, and the accuracies of the density and total energy are 10 6 and 10 8 Hartree respectively. The space group is P6/mmm, No. 191 and the atomic positions are 1a(0, 0, 0) for Y, and 3g(1/2, 0, 1/2) and 2c(1/3, 2/3, 0) for Fe. One formula unit of YFe5 is present in the conventional unit cell. At first, we make a geometrical optimization i.e. determine the equilibrium volume Vo of the crystal structure at hand from the calculated volume dependence of energy E(V). The chosen c/a ratio was calculated in the following manner: for a fixed volume, we perform total energy calculation for different c/a ratios. The value at the energy minimum is the one we chose. Next we fit the E(V) data to the Birch–Murnaghan equation-of-state [20]. The fitting parameters Bo (the bulk modulus), B (the pressure dependence of Bo), and Vo are consequently used to determine the volume dependence on the hydrostatic pressure P. The DOS and magnetic moment are calculated at either ambient pressure (P¼0) and equilibrium volume Vo, or at higher pressures. 3. Results and discussion Our geometrical optimization calculation showed that the magnetic phase of YFe5 is more stable than the nonmagnetic phase using either the LSDA or GGA approximation. The equili˚ and 77.5 A˚ 3 brium cell volumes are 85 A˚ 3 (a ¼5.03, c ¼ 3.87 A), ˚ for the GGA and LSDA approximations, (a¼4.88, c¼ 3.76 A) respectively in the magnetic phase. F. Maruyama et al. [7] have reported on a ¼5.03, c¼4.17 A˚ (V¼91.4 A˚ 3 ) by extrapolating the value of a and c to x¼1 for Y(T1 xFex)5 compounds. The relative percentage error, in the cell volume, between our GGA approximation (V¼85 A˚ 3) and that reported by Maruyama (V¼91.4 A˚ 3)
Total M.M. [µB]
14.0 12.0
LSDA Total M. M.
10.0
GGA Total M. M.
8.0 6.0 4.0 2.0 0.0
42
52
62
72
Volu me
82
92
[Å3]
Fig. 1. Dependence of the total magnetic moment on the cell volume for magnetic YFe5 using GGA and LSDA, approximations.
2487
is 7%. This relative error is only 1.4% off the value reported by Coehoorn (V¼86.2 A˚ 3) using interpolation between YFe3 and Y2Fe17 [11]. The overall decrease of the magnetic moment with decreasing unit cell volume is a feature of itinerant electron magnetic systems. This feature is demonstrated clearly by both of the GGA and LSDA calculations (Fig. 1). As the volume is reduced, the magnetic moment vanishes completely rendering this hypothetical compound as nonmagnetic i.e. having no microscopic magnetic moments. It is to be noted that the moment of the Fe(3g) site is affected relatively stronger, by volume reduction, than that at the 2c site. The calculated total and partial magnetic moments of our work together with the results of extrapolation from experimental data [7,8], and interpolation from ab initio calculated data [11] are presented in Table 1. The main features of this table are the negative small value of the Y moment and the relatively large moment at the Fe(2c) site as compared to the 3g site. In order to obtain the pressure dependence on volume i.e. P(V) of the hypothetical YFe5 compound, we have fitted the energy vs. unit cell volume, for the magnetic phase in the GGA and LSDA data, to the Birch–Murnaghan equation of state [20]. We have used the following expressions for the Birch– Murnaghan equation of state and its associated pressure dependence on volume: 8" #3 9Bo V 0 < V o 2=3 EðVÞ ¼ Eo þ 1 Bo’ 16 : V " " 2=3 #) V 0 2=3 V0 2 þ 1 64 V V " #) " 53 #( 7=3 3B0 Vo Vo 3 " V o 2=3 PðVÞ ¼ 1 1 þ ðBo 4Þ 4 2 V V V The result of fitting our data to the Birch–Muranghan equation of state is shown in Fig. 2 for the magnetic phase in the LSDA approximation. The bulk modulus Bo and its first pressure derivative B’ are reported in Table1. Our GGA value is close to 150 GPa calculated using the augmented-spherical-plane wave method (ASPW) reported by Coehoorn [11]. The pressure dependence of the partial magnetic moments of Y(1a), Fe(3g), Fe(2c) and the total magnetic moment of YFe5 using the GGA approximation are shown in Fig. 3. The compound loses its magnetic moment for pressures in excess of E250 GPa for this approximation. The total and partial DOS of the magnetic YFe5 at the equilibrium volume of 85 A˚ 3, in the GGA approximation, are shown in Fig. 4. The DOS structure, for the Fe 2c and 3g sites, shows that the total DOS is dominated by 3d electrons; the contribution of 4d electrons, however, is negligible. Fig. 5(a) and (b) displays the charge and spin density maps respectively, for YFe5 in (0 0 1) plane as calculated by WIEN2k. ˚ c ¼3.87 A. ˚ The maps are calculated for a crystal with a ¼5.03 A,
Table 1 Compilation of data from the present work and other references on experimental and theoretical investigations on ferro magnetic and nonmagnetic YFe5. References are ˚ V in A˚ 3 and the magnetic moment in mB. given in brackets. Lattice constants a and c are in A, Method
Phase
a, c, V, c/a
LSDA
mag nonmag mag nonmag mag [7] mag [8] mag nonmag
4.88, 4.83, 5.03, 4.93, 5.03, 4.99, 4.97, 4.89,
GGA By experimental extrapolating [7,8] By interpolation [11]
3.76, 3.72, 3.87, 3.80, 4.17, 4.20, 4.03, 3.97,
77.5, 0.77 75.0, 0.77 85.0, 0.77 79.9, 0.77 91.4, 0.83 90.56, 0.84 86.2, 0.81 82.5, 0.81
ltot
lY(1a)
lFe(2c)
lFe(3g)
B (GPa)
B’
7.4 – 9.6 – 8.0 8.6 7 0.2
0.2 – 0.47 –
1.8
1.3 – 2.0 – 1.60 1.6 7 0.1
185 222 148 187
3.30 2.16 4.42 5.55
8.4 ————
0.24 ————
1.53 ————
150 200
——
2.05 – 1.60 1.9 70.1 2.00
2488
F. Alzahraa Mohammad et al. / Physica B 407 (2012) 2486–2489
Fig. 2. Energy vs. cell volume in the LSDA approximation fitted to the Birch– Murnaghan equation for magnetic YFe5.
Fe
12.0 GGA. Total M.M. GGA. M. M. of Fe(2c) GGA. M. M. of Fe(3g) GGA. M. M. of Y(1a)
10.0
M.M. [µB]
8.0 6.0
Fe
Fe
Fe
4.0 2.0 0.0 -2.0 0
40
80
120
160
200
240
280
Pressure [GPa]
4. Conclusions
Fig. 3. Pressure dependence of the partial magnetic moments of Y(1a), Fe(3g), Fe(2c) and the total Magnetic moment of YFe5 in the GGA approximation.
Total Spin- up
20.0
Total Spin- down Fe (2c) Spin- up
15.0
DOS [States/eV]
Fe (2c)Spin- down
10.0
Fe (3g) Spin- up Fe (3g) Spin- down
5.0
Fig. 5. (a) Charge density map in the (0 0 1) plane of YFe5 at V ¼85 A˚ 3 in the GGA approximation by using WIEN2k package. (b) Spin density map in the (0 0 1) plane of YFe5 at V ¼ 85 A˚ 3 in the GGA approximation by using WIEN2k package.
We have performed a first-principle calculation, using the FPLO-09 and WIEN2k electronic structure codes, of the magnetic, electronic and elastic properties of the hypothetical YFe5 compound. Our calculation, using the GGA and LSDA approximations, showed that the magnetic phase is more stable than the nonmagnetic phase. The application of hydrostatic pressure reduces the magnetic moment until ferromagnetism ceases to exist and a truly nonmagnetic state on the microscopic level exists. Our results agree fairly well with available theoretical studies, and with extrapolated experimental data on related compounds.
0.0
Acknowledgment
-5.0 -10.0 -15.0 -8.0
-6.0
-4.0
-2.0
0.0
2.0
4.0
Energy [eV] Fig. 4. Total and partial DOS’s of the magnetic YFe5 at the equilibrium volume of 85 A˚ 3, in the GGA approximation.
The charge density maps display charge contours around both of the Y and Fe atoms, and at the Fe–Fe bond. However, less charge density may be seen at the interstitial Y–Fe space. The spin maps, on the other hand, show clearly the absence of any spin contours at the location of Y atoms indicating the null spin magnetic moment of Y. Further studies are underway to investigate, in more detail, the reasons for the hypothetical nature of YFe5, in particular its enthalpy of formation, and interatomic bonding.
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