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Effect of Si substitution on structural, electronic and optical properties of YNi4Si-type DyNi5−xSix (x=0, 1, 2) compounds
Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
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Effect of Si substitution on structural, electronic and optical properties of YNi4Si-type DyNi5 xSix (x¼ 0, 1, 2) compounds Dinesh Kumar Maurya, Sapan Mohan Saini n Department of Physics, National Institute of Technology Raipur, Raipur, Chhattisgarh, India
art ic l e i nf o
a b s t r a c t
Article history: Received 19 February 2016 Received in revised form 16 March 2016 Accepted 6 May 2016 Available online 7 May 2016
We employed first principle calculations for investigation of structural, electronic and optical properties of YNi4Si-type DyNi5 xSix (x ¼ 0, 1, 2) compounds. These properties are studied first time on YNi4Si-type DyNi5 xSix compounds. The exchange and correlation potential is treated by the Coulomb corrected local spin density approximation (LSDAþU) method for better accounting of the correlation between the 4f electrons. The optimized lattice constants and internal cell parameters are in agreement with the available data. Self consistence band structure calculations show that Ni-3d states remains in valance band and dominant below the EF, while Dy-5d and 4f states mainly contributes above Fermi Energy (EF) in DyNi5 xSix (x ¼0, 1, 2) compounds. We also find that when silicon for nickel substitution takes place (DyNi4Si), there is a gradual hybridization of Ni-3d and Si-3p states results, nickel moments decrease rapidly in agreement with the experiment. Optical spectra shows the main absorption peak around 4 eV depends on the substituent concentration and could be due to transition from hybridized band (Ni-3d and Si-3p), below EF to free Dy-4d states. Frequency-dependent refractive index, n(ω), and the extinction coefficient, k(ω), of DyNi5 xSix (x ¼ 0, 1, 2) are also calculated for the radiation up to 14 eV. & 2016 Elsevier B.V. All rights reserved.
Keywords: Structural properties Density of states Optical properties LSDA þU approximation YNi4Si-type DyNi5 xSix (x¼ 0, 1, 2) compounds
1. Introduction Rare earth (R) intermetallic compounds of the CaCu5-type RNi5 are prominent in the large variety of their magnetic structures and electronic characteristics. The potential characteristics of these compounds motivate their engineering prospective as functional materials for permanent magnets and magnetothermal applications, as well as for devices based on magnetostriction and magnetoresistive effects [1–3]. The explicit features in the magnetic and electronic properties of the RNi5 intermetallic compounds are associated with the Ni-3d bands being practically fully occupied by 5d electrons of the outer shells of R atoms, which make the contribution of nickel atoms to the spontaneous magnetic moment weak. Significant change in the physical properties of the RNi5 compounds take place when nickel is substituted for by atoms of other d or p metals as a results of the strong effect an impurity exerts on the parameters of the electronic structure, crystal field, and exchange interaction. It has been established in the past that an increase in the number of electrons in the conduction band in CaCu5-type pseudobinary RNi5–xMx alloys (x r3 ) with M ¼(M ¼Al, Cu, Fe, Co) alloys, leads to significant changes in the physical properties and exhibit nonmonotonic concentration dependences n
Corresponding author. E-mail address: [email protected] (S.M. Saini).
http://dx.doi.org/10.1016/j.jmmm.2016.05.020 0304-8853/& 2016 Elsevier B.V. All rights reserved.
of the crystalline, electronic, magnetic, and thermodynamic characteristics [4–6]. Numerous experimental [7–10] and theoretical [11–13] studies of electronic and magnetic properties have been reported on these CaCu5 – type pseudobinary rare earth alloys in the past. Bajorek et al. [7,8] measured the magnetic susceptibility, electrical resistivity, crystal and electronic structure for GdNi5 xCux system and observed that when nickel is substituted for copper atoms the cell volume increases and Curie temperature is weakly dependence on concentration x. Optical properties of intermetallic isostructural compounds LaNi5 xCux (x¼ 0, 0.6, 1, 1.2) have been studied in the spectral range from 0.22 to 15 m using the ellipsometry method by Knyazev et al. [9] and found that the substitution of copper for nickel leads to local changes in the optical conductivity spectra. Lukoyanov and Knyaz [11] performed Magnetic measurements and XPS studies on RNi5 xAlx and RNi5 xCux (R¼La, Nd, Tb, Dy) compounds. They observed that the nickel moments, in low temperature range, decrease when increasing aluminum or copper content and are practically nil for x 41. Miletic et al. [14] prepared DyNi5 xGax alloys and studied by X-ray powder diffraction. A single phase region has been observed and it exists up to the composition DyNi2Ga3 in the DyNi5 xGax system. They also observed a decrease in the hydrogen capacity and the equilibrium pressure with increasing gallium content. Burzo et al. [15] studied on the magnetic properties and electronic structures of DyNi5 xAlx compounds. Analysis of the experimental data was
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D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
Table 1 Atomic positions for the 2a, 4i, 2c and 4f sites of the YNi4Si-type DyNi5 xSix (x¼ 0,1,2) compounds. DyNi5
Site
x/a
Dy Ni1 Ni2 Ni3
2a 4i 2c 4f
0 0 0 1/4
a
y/b
z/c
DyNi4Si
Site
x/a
0 yNi1 1/2 1/4
0 0 1/2 1/2
Dy Ni1 Si Ni3
2a 4i 2c 4f
0 0 0 1/4
a
y/b
z/c
DyNi3Si2
Site
x/a
y/b
z/c
0 yNi1 1/2 1/4
0 0 1/2 1/2
Dy Si Ni2 Ni3
2a 4i 2c 4f
0 0 0 1/4
0 ySi 1/2 1/4
0 0 1/2 1/2
a
yNi1 ¼0.3343 (DyNi5), yNi1 ¼ 0.3411 (DyNi4Si), ySi ¼0.3404 (DyNi3Si2).
done in correlation with computed band structures and found that when replacing nickel with aluminum there is a gradual hybridization of Ni 3d and Al 3p bands, and as a result the nickel moments at 0 K decrease and are nil for x 42. The refractive (n) and absorption (k) indices of intermetallic DyNi5 xAlx compounds (x ¼0, 0.5, 1, 1.5, 2) have been measured by Knyazev et al. [16] using ellipsometry at room temperature in the spectral range of 0.22–15 μm. They observed that the three-peak structure of the optical conductivity spectra for DyNi5 is gradually modified with an increase in x and has a single wide peak for the DyNi3Al2 ternary compound. Recently Morozkin et al. [17,18] have made modification of the CaCu5-type rare earth compound via solid solution and established the new YNi4Si-type structure of RNi4Si (R¼Y, La, Ce, Sm, Gd-Ho) compounds. The YNi4Si structure is a new structure type, which is an orthorhombic derivative of CaCu5 structure. They observed the order ferromagnetic nature of GdNi4Si and DyNi4Si compounds at 25 and 19 K, respectively and calculated the magnetocaloric effect of YNi4Si-type RNi4Si in terms of isothermal magnetic entropy change. In our earlier study [19], we reported the structural, electronic and optical properties of new YNi4Si-type RNi4Si (R¼La and Gd) compounds using self-consistent full-potential augmented plane wave (FP-LAPW) [20,21] method. Analysis of the calculated band structure of LaNi4Si and GdNi4Si compounds suggest that Ni-3d states mainly contribute to density of states (DOS) from 5.0 eV to the Fermi level which is consistent with experiment and previously reported result by Kowalczyk et al. [22] having hexagonal CaCu5 structure. In order to study the structural, electronic and optical properties of YNi4Si-type DyNi5 xSix (x ¼0, 1, 2) compounds first principle calculations are performed. To author's knowledge theoretical and experimental study on electronic and optical properties of YNi4Si-type DyNi5 xSix compounds have not been addressed. The present study would also explore the role of substitutional change of silicon in place of nickel on structural, electronic and optical properties as well as encourage the measurement of these properties on YNi4Si-type DyNi5 xSix (x ¼0, 1, 2) compounds.
2. Computational details Self-consistent FP-LAPW [20,21] calculations on DyNi5 xSix were carried out using WIEN2k code [23]. We considered a number of basic functions up to RMT Kmax ¼7, where RMT is the
minimum radius of the muffin-tin spheres and Kmax gives the magnitude of the largest K vector in the plane wave basis, to achieve an adequate exchange between accuracy and cost. In order to keep the same degree of convergence, we kept the values of the sphere radii and Kmax constant over all the crystal geometries considered. The muffin-tin radii RMT for Dy, Ni and S to be 2.5, 2.32 and 1.84 bohr, respectively, have been selected and the APW þ lo basis set [24], with additional 5s and 5p local orbitals for the rare earth atom is used. Additionally, the valence wave functions inside muffin-tin spheres are expanded up to lmax ¼ 10. The LSDA functional is used for exchange and correlation effects. For better accounting of the correlation between the 4f electrons, Anisimov et al. [25] introduced the self consistent LSDA þ U method. This method explicitly includes the on-site Coulomb interaction term in the conventional Hamiltonian. Harmon et al. [26] determined the numerical values of the parameters of the direct Coulomb (U¼6.7 eV) and exchange (J ¼0.7 eV) interaction for Gd. These numerical values of the parameters have been used to perform the calculations. The dependence of the energy on the number of k points in their reducible wedge of the Brillouin zone (IBZ) has been checked, and the size of the mesh has been set to 12 12 12 Monkhorst and Pack [27] k-point mesh, which yields 301 k-points in the IBZ. We considered the self-consistency to be reached when the total energy difference between successive iterations is o105 Ry per formula unit. The convergence was also checked with a refined mesh in the IBZ with no appreciable change in energy or properties. The modified tetrahedron method [28] has been used to perform the k space integration. We used a broadening of 0.1 eV to simulate the experimental finite lifetime effects. The Crystal arrangement of DyNi5 xSix (x ¼0, 1, 2) compounds is YNi4Si-type structure with space group Cmmm. In DyNi5 compound nickel atoms are located at three non equivalent positions. Rare earths occupy the 2a site (0, 0, 0) and Ni1 is located in the 4i site (0, yNi1, 0), where internal cell parameter (yNi1)¼ 0.3415 [17]. Ni2 and Ni3 atoms are statistically distributed over 2c site (0, 1/2, 1/ 2) and 4f site (1/4, 1/4, 1/2), respectively. Site occupation by Dy and Ni atoms in DyNi5 xSix (x ¼1, 2) is similar to the DyNi5, except 2c and 4i site which is doped with silicon atoms in DyNi4Si and DyNi3Si2, respectively. The Wyckoff positions and unit cell data are presented in Tables 1 and 2, respectively. We have performed calculations for the ferromagnetic phase, as DyNi5 xSix compounds are ferromagnetic at low temperatures. The electronic structure of DyNi5 xSix compounds is studied within the ab initio approach.
Table 2 Equilibrium lattice parameters (a, b, c, b/a and c/a) (in a.u.), internal cell parameters (yNi1/ySi), cell volume V (in a.u.3), bulk modulus B0 (in GPa), and its pressure derivative B0′ for DyNi5 xSix (x ¼0, 1, 2) at 0 GPa and 0 K (This work) and at 0.1 GPa and 298 K [17].
DyNi5 DyNi4Si DyNi3Si2
This work Expt. [17] This work Expt. [17] This work
a
b
c
b/a
c/a
yNi1/ySi
Vol
B0
B0′
9.24380 9.21354 9.42427 9.53914 9.42126
16.01076 15.95835 15.31007 15.49669 15.30520
7.52172 7.49710 7.37433 7.46422 7.37199
0.812586 0.813704 0.808758 0.782483 0.679411
1.734751 1.732053 1.564982 1.624536 1.818965
0.3343 0.3333 0.3411 0.3415 0.3404
556.60900 551.16164 531.82690 551.70089 531.45988
142.3509
2.8986
180.2626
5.3110
175.5218
4.8594
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
-39504.362
-39504.370
DyNi5
-39504.364
-39504.372
-39504.368
-39504.373
-39504.370
-39504.374
-39504.372
-39504.375
-39504.374
-39504.376
-39504.376
-39504.377
-39504.378 0.76 -37045.895
0.78
0.80
0.82
0.84
DyNi4 Si
0.86
0.88
-39504.378 1.60 -37045.860 -37045.870
-37045.900
Energy / Cell [ Ry ]
DyNi5
-39504.371
-39504.366
91
1.65
1.70
1.75
1.80
1.85
DyNi4Si
-37045.880
-37045.905
-37045.890 -37045.910 -37045.900 -37045.915
-37045.910
-37045.920
-37045.920
-37045.925 -37045.930 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 -34587.750 -34587.760
-34587.750
DyNi3Si 2
DyNi3 Si 2
-34587.760
-34587.770 -34587.770
-34587.780 -34587.790
-34587.780
-34587.800
-34587.790
-34587.810 -34587.800
-34587.820
-34587.830 -34587.810 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95
C/A
B/A
Fig. 1. Energy as a function of c/a ratio (left panel) and b/a ratio (right panel) of DyNi5 xSix (x ¼0,1,2) at 0 GPa and 0 K.
92
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
3. Results and discussions
-39504.290
3.1. Structure optimization
-39504.300
3.2. Band structure
-39504.310 -39504.320 Vp = 556.6090
-39504.330 -39504.340 -39504.350 -39504.360 -39504.370 -39504.380
LSDA+U 460 480 500 520 540 560 580 600 620 640
-37045.870
DyNi4Si
-37045.875 -37045.880
Energy / Cell [ Ry ]
To determine the structural properties in the ground state, such as the lattice parameters (a, b, c, b/a and c/a), bulk modulus (B0 ), and its pressure derivative B0′ of DyNi5 xSix (x ¼0, 1, 2) compounds in the orthorhombic YNi4Si type structure, we first optimized the value of the internal cell parameter (yNi1) of nickel at the 4i site of DyNi5 xSix (x¼0, 1) and ySi1 of silicon at 4i site of DyNi3Si2 structure so that the forces on each atom is o2 mRy per au by using experimental values [17]. The optimization was done with 105 k-points in the IBZ. Our optimized values of internal cell parameters are in good agreement with the experiment [17] and listed in the Table 2. To optimize the equilibrium volume, we adopted the experimental lattice parameters, c/a and b/a ratios to create a multitude of volumes around the experimental volume, and optimized the equilibrium volume with sequential minimization of internal cell parameters. For determination of optimized equilibrium c/a and b/a ratios, we followed the same minimization method as pointed out earlier for free internal cell parameters and used the experimental c/a and b/a ratios and volume to get optimized equilibrium c/a and b/a ratios. The Energy (E) vs. c/a and b/a curves and the E vs. volume (V) curves of DyNi5 xSix (x ¼0, 1, 2) so obtained are shown in Fig. 1 and Fig. 2, respectively. The lattice constants, the equilibrium cell volumes, B0 and B0′ for DyNi5 xSix (x ¼0, 1, 2) compounds at 0 GPa and 0 K are summarized in Table 2 and the values of equilibrium structural parameters obtained from present work are in good agreement with the corresponding experimental values [17]. The total energies versus unit cell volume are fitted to the Murnaghan's equation of state (EOS) [29] to determine the B0 and B0′ of DyNi5 xSix (x ¼ 0, 1, 2) compounds. Our LSDA (not listed here) and LSDA þU methods yields a deviation of 5% and 1%, respectively, of the lattice parameters with respect to the experimental data, for DyNi5 xSix (x¼ 0, 1, 2) compounds which shows strong correlation effect of 4f electrons has to be considered for a correct explanation of these rare earth compounds.
DyNi5
-37045.885 -37045.890
Vp = 531.8269
-37045.895 -37045.900 -37045.905 -37045.910 -37045.915 -37045.920 -37045.925
LSDA+U 480
500
520
540
560
580
600
620
-34587.730
DyNi3Si2
-34587.735 -34587.740
The spin polarised band structures (BSs) along the symmetry points of the Brillouin zone of the DyNi5 xSix (x¼ 0, 1, 2) compounds, within the LSDA þ U framework, are shown in Fig. 3(a)–(c). Number of energy bands cross the Fermi level indicates the metallic ground state of the DyNi5 xSix (x¼ 0, 1, 2) compounds. The BSs of spin up states is similar to that for spin down states except that the spin-up Dy-4f bands are occupied and lie well below the EF and the spin-down Dy-4f bands are unoccupied and lie well above EF. We find that occupied Dy-4f bands are centred around 8 eV below EF, while spin down unoccupied Dy-4f bands lie about 2 eV above EF. The LSDA þU enhances the exchange splitting of the f bands noticeably from 5 eV in LSDA (not presented for brevity) to 10 eV in LSDA þ U, by pushing the 4f spin-up states much below EF and 4f spin down states well above the EF. This shifting also explains why the results for DOS and magnetic moment obtained by using LSDA [30,31] when f states are treated as part of core or as pseudo core, are closer to those from LSDA þ U. The valence band region of the DyNi5 band structure is about 9.0 eV wide, which turn into 12 eV in DyNi3Si2, due to hybridization of Dy-4f and Si-3s states. Wideness of conduction band is almost similar and is about 7.0 eV in all DyNi5 xSix (x ¼0, 1, 2) compounds because of insignificance contribution of Si-3s and 3p states in conduction band. We also find that the valence bands are more dispersive in comparison to the conduction bands in these compounds. A comparison of BSs of DyNi5 xSix (x¼0,1,2) compounds
-34587.745 -34587.750
Vp = 531.4598
-34587.755 -34587.760 -34587.765 -34587.770 -34587.775 -34587.780 -34587.785
LSDA+U 480
500
520
540
560
580
600
620
3
Volume [ a.u ] Fig. 2. Energy as a function of primitive unit cell volume of DyNi5 xSix (x¼ 0,1,2) at 0 GPa and 0 K.
reveals that filled spin-up and unfilled spin-down Dy-4f states retain their position below and above EF, respectively and that the lowest band (Dy-5p) (not shown in the figure) moves away from EF as one moves from DyNi5 ( 21 eV) to DyNi3Si2 ( 23 eV). The large depth from EF ensures that these bands retain atomic character and do not attain the conventional large band-width as
EF
Energy (eV)
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0 -11.0 -12.0 -13.0 -14.0
Γ
Δ
H
Energy (eV)
Energy (eV)
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
N Σ
Γ
Λ
P
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0 -11.0 -12.0 -13.0 -14.0
93
EF
Γ
Δ
H
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0 -11.0 -12.0 -13.0 -14.0
N Σ
Γ
Λ
P
EF
Γ
Δ
H
N Σ
Γ
Λ
P
Fig. 3. Band structure of (a) DyNi5, (b) DyNi4Si and (c) DyNi3Si2 compounds using LSDA þU for spin up (solid lines) and spin down (dotted lines) states. The EF is at 0 eV.
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D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
Fig. 4. DOS of DyNi5 xSix (x¼ 0, 1, 2) compounds using LSDA þ U approximation. Solid (dotted) lines represent the majority (minority) states. The EF is at 0 eV.
Fig. 5. Partial DOS of DyNi5 xSix (x¼ 0, 1, 2) compounds using LSDA þ U approximation. Solid (dotted) lines represent the majority (minority) states. The EF is at 0 eV.
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
is associated with conduction bands. 3.3. Density of states In order to understand clearly the electronic structure and the differences in the magnetic properties between DyNi5 xSix (x ¼0,1,2), the total DOS and partial DOS of all the compounds are calculated using LSDA þ U approximation and shown in Fig. 4 and Fig. 5, respectively. From the partial DOS, we are able to identify the angular momentum character of the states. Although there are some general similarities, the structures of total DOS for substitution of silicon in place of nickel differ from each other. The broad valance band is constituted by Ni-3d states and located in a range from 5 eV to the EF in DyNi5 xSix (x ¼0, 1, 2) compounds. The spin-down states of 3d electrons are filled more completely as compared to the spin-up states, since the spin-down states are energetically more favoured for the 3d electrons because of the mutually opposite directions of spin magnetic moments of the 3d and R subsystems [32]. Another group of bands located from 5 eV to 11 eV, is characterized by Si-s states with some amount of Si-3p states. Replacement of Ni atoms by Si results in a rather independent Si-3s, 3p band centred at around 8 eV below the EF for the compounds with x¼ 1, 2. These Si-3s states lie around 9.5 eV below EF in DyNi4Si remains unhybridized and lie slightly lower around 10.5 eV below EF and hybridized with Dy-4f states in DyNi3Si2. The Si-3p states show gradual hybridization with Ni-3d states in compounds (x ¼1, 2). The band width of Si-3p states is considerably smaller with respect to the Ni-3d states. The intense and pronounced peaks of 4f states also present in the valence band lie at around 8.0 eV in DyNi5 and remain unhybridized, while for the compounds (x ¼1, 2) we found slight larger band width of 4f states due to the hybridization with Si-3s and Si-3p states. The position of Dy-4f states ( 8.0 eV) from this way is fairly consistent with the x-ray photoemission spectroscopy (XPS) results [15] of DyNi5 xAlx as well as with other theoretical results for dysprosium compounds [33]. It shows that Dy-4f states retain their elemental character in these compounds. On the other hand spin down 4f states are completely unoccupied and constitute the conduction band. The energy bands from 15 to 20 eV consist of Dy-5p states. The position of the Dy-5p states is different in these DyNi5 xSix (x ¼0, 1, 2) compounds. These Dy-5p states are located far below the EF at 21 eV in DyNi5 and lie around 22 eV and 23 eV below EF in DyNi4Si and DyNi3Si2 compounds, respectively and not shown in the figure. Above EF, the energy band is constituted by Dy-5d and 4f states. The bottom of the conduction band and the top of valence band are formed from the hybridized Dy-5d states and 3d states of Ni atoms. We found that Ni-3d states remains in valance band in DyNi5 xSix (x ¼0, 1, 2) show that substitution of silicon in place of nickel atom does not give significant change in DOS near EF. The partial DOS for DyNi5 xSix (x ¼0, 1, 2) shows that, the 3d- states of Ni atoms are dominant below the EF, while the Dy-4f states peak stands tall in comparison to the small contributions made by the Dy-3d states above EF in these compounds. A comparison of DOS of DyNi5 xSix (x ¼0,1,2) compounds reveals that the total DOS width becomes
95
larger after silicon substitution as compared with that in DyNi5. Simultaneously, The DOS at the EF is gradually reduced with the increase of silicon concentration. The value of magnetic moment (m), density of states at Fermi level N(EF), and the coefficient of electronic specific heat (γ) from this work and those obtained by various workers [18,34,35] are listed in Table 3. Our spin polarized LSDA þU calculations yield 7.34167 mB, 5.0629 mB and 5.13746 mB magnetic moment for DyNi5 xSix (x¼ 0, 1, 2) compounds, respectively. The calculated total magnetic moment of DyNi5 is in agreement with experiment [34] and for x ¼1, 2 it decreases because of the decrease of the moment of the 3d subsystem. When silicon for nickel substitution takes place (DyNi4Si), nickel moments decrease rapidly (0.00965 mB/atom) while the dysprosium moment increases slightly (5.01542 mB). The anti parallel orientation of dysprosium and nickel moments is also revealed, in agreement with other theoretical and experimental study [15,19,22]. As silicon for nickel substitution proceeds (DyNi3Si2), the dysprosium moment increases slightly and has the value of 5.02040 mB, while the nickel moments 0.01714 mB /atom but now the orientation of nickel moments is parallel to that of dysprosium moment similar to the calculations on DyNi5 xAlx compounds [36]. This behaviour can be attributed to hybridization effects and reduction of electron correlations between d electrons and also from that an antiparallel alignment of dysprosium and nickel moments. On the other hand magnetic moment of the dysprosium ion remains close to 5 mB for all DyNi5 xSix compounds. When orbital angular momentum L¼ 5 of the dysprosium ion is taken in to account by the analogy with [37], we obtained the total effective magnetic moment of dysprosium is of the order of 9.96 mB in DyNi5, which is in agreement with the experimental value of 10.33 [38]. The value of magnetic moment at the dysprosium site in DyNi5 xSix compounds (x¼ 0, 1, 2) showing 7%, 6% and 5% drop, respectively in comparison to pure dysprosium (10.645 mB) [40] by use of similar analogy [37]. On the other hand nickel shows even stronger impact dropping by 28%, 96% and 94% in comparison to elemental Ni (0.60 mB) [39] for DyNi5 xSix (x¼ 0,1,2) compounds, respectively. This suggests that the inter-atomic interaction in these compounds is much strong and affect the Ni atoms. This is due to the filling of the minority-spin d bands of Ni atoms by the conduction electrons from dysprosium atoms explaining the reduction of the nickel magnetic moment compared to that in pure nickel. The calculated N(EF) is increasing from the value of 1.65 in DyNi5 to 2.16 states/Ry/spin/unit cell in DyNi3Si2 due to a more complete filling of the 5d band of dysprosium. The value of electronic specific heat (γ) for this work is 31.56 mJ mol 1 K 2 for DyNi5 is in agreement with the experimental value [35]. There are no experimental or theoretical results for the value of γ for DyNi4Si and DyNi3Si2 compounds. We obtained the value of γ is 28.74 and 25.68 mJ mol 1 K 2 for both compounds, respectively. 3.4. Optical properties The optical properties of matter can be described by the complex dielectric function e(o), which represents the linear response
Table 3 Total and partial magnetic moment m (in mB), density of states at the Fermi level N(EF) (in states/Ry/spin/unit cell) and coefficient of electronic specific heat γ (in mJ mol 1 K 2) for DyNi5 xSix (x¼ 0, 1, 2) compounds.
DyNi5 DyNi4Si DyNi3Si2
This work Exp. This work Exp. This work
Total l (in mB)
lDy
lNi1
lSi/Ni
lNi3
N(EF) (states/Ry/spin/unit cell)
γ (mJ mol 1 K 2)
7.34167 7.19 [34] 5.0629 7.7 [18] 5.13746
4.96653
0.89359
0.19425
0.19690
1.65
5.01542
0.0095
0.0013
0.0097
1.88
31.56 36 [35] 28.74
5.02040
0.01189
0.0033
0.02239
2.16
25.68
96
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
Fig. 6. The Calculated (LSDA þU) and experimental optical conductivity of DyNi5 xSix (x¼ 0, 1, 2) compounds.
of a system to an external electromagnetic field. It can be expressed as ε (ω) = ε1 (ω) + ε2 (ω), where ε1 (ω) and ε2 (ω) are the real and imaginary components of the dielectric function, respectively. The imaginary part ε2 (ω) is directly related to the electronic band structure and it can be computed by summing up all possible transitions from the occupied to the unoccupied states, taking into account the appropriate transition dipole matrix elements. The real part ε1 (ω) can be derived from the imaginary part using the familiar Kramers–Kronig transformation [40]. The optical conductivity σ (ω) is related to the dielectric function ε (ω) as 4πiσ (ω) ε (ω) = 1 + ω . All optical properties are calculated at the theoretical equilibrium lattice constant using LSDA þ U approximation for the energy up to 16 eV. Lorentzian broadening is taken to be 0.1 eV. This is the first calculation on the optical conductivity of DyNi5 xSix (x¼0, 1, 2) compounds in YNi4Si-type structure. Since the anisotropy in these compounds is negligibly small; hence only the diagonal component of optical conductivity perpendicular to the c-axis, has been presented. Experimental data for optical conductivity of DyNi5 xSix is not available. The experimental optical conductivity data for parental compound DyNi5 [16] has been used to compare and conform our results. Fig. 6 shows the optical conductivity of DyNi5 xSix compounds (x ¼0, 1, 2) using LSDA þ U approximation. Three pronounced peaks at the energies around 1 and 1.8 and 3.5 eV, respectively are shown in the experimental data for the optical conductivity of DyNi5. A similar trend is also found in our calculated spectra, but with twice the magnitude. As mentioned earlier we have used a broadening of 0.1 eV to bring out the structures in the optical properties. For significantly larger values, the calculated optical conductivity spectra agree with experiment magnitude wise but the structures are lost. This relatively larger magnitude could be due to high reactivity of the surface of the rare earth compounds [41–43]. The comparison of the measured and calculated optical conductivity spectra of CaCu5 type - DyNi5 xAlx have also been shown by Knyazev et al. [16] but in the arbitrary units. We found the most prominent features are broad and structured peaks present around 0.8 eV, 1.6 eV and at 3.2 eV in DyNi5. Peaks below 4 eV could be due to the transition from hybridized bands of Ni-3d and Si-3p atoms below EF to free Dy-4d states. These are found to shifts slightly to lower energy as compared to the experiment [16]. Upon substitution of nickel by silicon, the intensity of the first two maximum significantly drops as well as shifted towards lower energy from DyNi5 to DyNi3Si2. One can also note that second peak appears significantly in the conductivity spectrum of binary DyNi5, seen as a small shoulder (x¼ 1) and then (х ¼2) this spectral feature almost disappears similar to the experiment [16]. Experiment is performed up to 6 eV. In the high energy range (above the 6 eV) prominent absorption peak at 6 eV in (x ¼ 0, 2) appears at around 5.8 eV in (x ¼1). Further, peak at 7.2 eV in DyNi4Si is slightly shifted towards higher energy at 7.4 eV in DyNi3Si2 is completely absent in
Fig. 7. The Calculated (LSDA þU) refractive index n(ω) (bottom panel) and extinction coefficient k(ω) (top panel) of DyNi5 xSix (x¼ 0, 1, 2) compounds.
DyNi5 showing the effect of silicon substitution at nickel site which could be due to transitions between occupied 3d states of Ni atoms hybridized with Si-p and unoccupied spin down Dy-f states. It should be noted that, for all compounds, the specific features associated with the 3s electrons of Si are weakly pronounced in the spectra of optical conductivity, although the corresponding bands are represented by significant maxima in the DOS (Fig. 4). The calculated refractive index n(ω) and extinction coefficient k (ω) of DyNi5 xSix (x ¼0, 1, 2) compounds are displayed in Fig. 7. Corresponding experimental data are not available for these compounds. The static refractive index n(0) are fairly large, 13.1 for DyNi5 and 13.8 for DyNi3Si2. The magnitude of n(ω)and k(ω) are larger in the 0–3 eV range, reflecting the dominating nature of the transitions in this energy range. We find that the n(ω)and k(ω) decreases sharply from 4.5 to 2.5 in the energy range 2.5 eV to 6.5 eV. In high energy range, n(ω) continuously decreases up to the value of 0.9 in all DyNi5 xSix (x ¼0, 1, 2) compounds. On the other hand extinction coefficient k(ω) reaches maximum value of 7.2 at around 0.5 eV in DyNi3Si2 and 6.5 at 1.1 eV in DyNi5. At intermediate energies small humps appear and vanishing curves in high energy range. One can notice that the relation k 4n is satisfied for DyNi5 xSix (x¼ 0, 1, 2) compounds almost in the entire spectral region, except for the low energy region, which is as a rule typical of the media with metallic conductivity, while the non monotonic behaviour of these parameters in the low energy region is a manifestation of interband absorption. Almost continuously decreases value in energy range 2.5 eV to 6.5 eV imply that the incident electromagnetic waves with energies in this range will be propagate inside material with continuously losses its signal
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
strength. As a result, it seems to suggest that for visible radiations, the DyNi5 xSix (x ¼0, 1, 2) compounds are highly sensitive to the frequency of the radiations.
4. Conclusions Spin polarized full potential calculations of structural, electronic and optical properties of YNi4Si–type DyNi5 xSix (x¼0, 1, 2) compounds have been performed using LSDA þU approximations with partial substitution of nickel by silicon. The calculated equilibrium lattice parameters are in good agreement with the available experimental results. The electronic BS and DOS of the DyNi5 xSix (x¼ 0, 1, 2) exhibit metallic behaviour. Partial DOS reveals that Dy-4d and spin down Dy-4f states are present in the conduction bands while Ni-3d, Si-3s and spin up Dy-4f states are present in the valence bands. When nickel is replaced by the silicon, moment at nickel site decreases sharply. Our calculated BS shows that the replacement of nickel with silicon leads to gradual filling of the 3d band, as a result of which N(EF) increases from the value of 1.65 in DyNi5 to 2.16 (states/Ry/spin/unit cell) in DyNi3Si2. Frequency dependent optical spectra of DyNi5 xSix compounds are similar with the experimental data on the parental DyNi5 compound. Main absorption peak around 4 eV depends on the substituent concentration and could be due to transition from hybridized band (Ni-3d and Si-3p), below EF to free Dy-4d states. Our calculation also suggest that the most prominent peak around 7 eV could be due to transition from 3d states of nickel atoms hybridized with Si-3p and unoccupied spin down Dy-4f states. The results on refractive index suggest that for the optical radiations in the energy range 2.5–6.5 eV, DyNi5 xSix (x ¼0, 1, 2) are very sensitive to the frequency of the radiations.
Acknowledgements The work was financially supported by the CCOST project, Raipur (C.G), India, through sanction no. 2161/CCOST/MRP/2013.
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Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Effect of Si substitution on structural, electronic and optical properties of YNi4Si-type DyNi5 xSix (x¼ 0, 1, 2) compounds Dinesh Kumar Maurya, Sapan Mohan Saini n Department of Physics, National Institute of Technology Raipur, Raipur, Chhattisgarh, India
art ic l e i nf o
a b s t r a c t
Article history: Received 19 February 2016 Received in revised form 16 March 2016 Accepted 6 May 2016 Available online 7 May 2016
We employed first principle calculations for investigation of structural, electronic and optical properties of YNi4Si-type DyNi5 xSix (x ¼ 0, 1, 2) compounds. These properties are studied first time on YNi4Si-type DyNi5 xSix compounds. The exchange and correlation potential is treated by the Coulomb corrected local spin density approximation (LSDAþU) method for better accounting of the correlation between the 4f electrons. The optimized lattice constants and internal cell parameters are in agreement with the available data. Self consistence band structure calculations show that Ni-3d states remains in valance band and dominant below the EF, while Dy-5d and 4f states mainly contributes above Fermi Energy (EF) in DyNi5 xSix (x ¼0, 1, 2) compounds. We also find that when silicon for nickel substitution takes place (DyNi4Si), there is a gradual hybridization of Ni-3d and Si-3p states results, nickel moments decrease rapidly in agreement with the experiment. Optical spectra shows the main absorption peak around 4 eV depends on the substituent concentration and could be due to transition from hybridized band (Ni-3d and Si-3p), below EF to free Dy-4d states. Frequency-dependent refractive index, n(ω), and the extinction coefficient, k(ω), of DyNi5 xSix (x ¼ 0, 1, 2) are also calculated for the radiation up to 14 eV. & 2016 Elsevier B.V. All rights reserved.
Keywords: Structural properties Density of states Optical properties LSDA þU approximation YNi4Si-type DyNi5 xSix (x¼ 0, 1, 2) compounds
1. Introduction Rare earth (R) intermetallic compounds of the CaCu5-type RNi5 are prominent in the large variety of their magnetic structures and electronic characteristics. The potential characteristics of these compounds motivate their engineering prospective as functional materials for permanent magnets and magnetothermal applications, as well as for devices based on magnetostriction and magnetoresistive effects [1–3]. The explicit features in the magnetic and electronic properties of the RNi5 intermetallic compounds are associated with the Ni-3d bands being practically fully occupied by 5d electrons of the outer shells of R atoms, which make the contribution of nickel atoms to the spontaneous magnetic moment weak. Significant change in the physical properties of the RNi5 compounds take place when nickel is substituted for by atoms of other d or p metals as a results of the strong effect an impurity exerts on the parameters of the electronic structure, crystal field, and exchange interaction. It has been established in the past that an increase in the number of electrons in the conduction band in CaCu5-type pseudobinary RNi5–xMx alloys (x r3 ) with M ¼(M ¼Al, Cu, Fe, Co) alloys, leads to significant changes in the physical properties and exhibit nonmonotonic concentration dependences n
Corresponding author. E-mail address: [email protected] (S.M. Saini).
http://dx.doi.org/10.1016/j.jmmm.2016.05.020 0304-8853/& 2016 Elsevier B.V. All rights reserved.
of the crystalline, electronic, magnetic, and thermodynamic characteristics [4–6]. Numerous experimental [7–10] and theoretical [11–13] studies of electronic and magnetic properties have been reported on these CaCu5 – type pseudobinary rare earth alloys in the past. Bajorek et al. [7,8] measured the magnetic susceptibility, electrical resistivity, crystal and electronic structure for GdNi5 xCux system and observed that when nickel is substituted for copper atoms the cell volume increases and Curie temperature is weakly dependence on concentration x. Optical properties of intermetallic isostructural compounds LaNi5 xCux (x¼ 0, 0.6, 1, 1.2) have been studied in the spectral range from 0.22 to 15 m using the ellipsometry method by Knyazev et al. [9] and found that the substitution of copper for nickel leads to local changes in the optical conductivity spectra. Lukoyanov and Knyaz [11] performed Magnetic measurements and XPS studies on RNi5 xAlx and RNi5 xCux (R¼La, Nd, Tb, Dy) compounds. They observed that the nickel moments, in low temperature range, decrease when increasing aluminum or copper content and are practically nil for x 41. Miletic et al. [14] prepared DyNi5 xGax alloys and studied by X-ray powder diffraction. A single phase region has been observed and it exists up to the composition DyNi2Ga3 in the DyNi5 xGax system. They also observed a decrease in the hydrogen capacity and the equilibrium pressure with increasing gallium content. Burzo et al. [15] studied on the magnetic properties and electronic structures of DyNi5 xAlx compounds. Analysis of the experimental data was
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Table 1 Atomic positions for the 2a, 4i, 2c and 4f sites of the YNi4Si-type DyNi5 xSix (x¼ 0,1,2) compounds. DyNi5
Site
x/a
Dy Ni1 Ni2 Ni3
2a 4i 2c 4f
0 0 0 1/4
a
y/b
z/c
DyNi4Si
Site
x/a
0 yNi1 1/2 1/4
0 0 1/2 1/2
Dy Ni1 Si Ni3
2a 4i 2c 4f
0 0 0 1/4
a
y/b
z/c
DyNi3Si2
Site
x/a
y/b
z/c
0 yNi1 1/2 1/4
0 0 1/2 1/2
Dy Si Ni2 Ni3
2a 4i 2c 4f
0 0 0 1/4
0 ySi 1/2 1/4
0 0 1/2 1/2
a
yNi1 ¼0.3343 (DyNi5), yNi1 ¼ 0.3411 (DyNi4Si), ySi ¼0.3404 (DyNi3Si2).
done in correlation with computed band structures and found that when replacing nickel with aluminum there is a gradual hybridization of Ni 3d and Al 3p bands, and as a result the nickel moments at 0 K decrease and are nil for x 42. The refractive (n) and absorption (k) indices of intermetallic DyNi5 xAlx compounds (x ¼0, 0.5, 1, 1.5, 2) have been measured by Knyazev et al. [16] using ellipsometry at room temperature in the spectral range of 0.22–15 μm. They observed that the three-peak structure of the optical conductivity spectra for DyNi5 is gradually modified with an increase in x and has a single wide peak for the DyNi3Al2 ternary compound. Recently Morozkin et al. [17,18] have made modification of the CaCu5-type rare earth compound via solid solution and established the new YNi4Si-type structure of RNi4Si (R¼Y, La, Ce, Sm, Gd-Ho) compounds. The YNi4Si structure is a new structure type, which is an orthorhombic derivative of CaCu5 structure. They observed the order ferromagnetic nature of GdNi4Si and DyNi4Si compounds at 25 and 19 K, respectively and calculated the magnetocaloric effect of YNi4Si-type RNi4Si in terms of isothermal magnetic entropy change. In our earlier study [19], we reported the structural, electronic and optical properties of new YNi4Si-type RNi4Si (R¼La and Gd) compounds using self-consistent full-potential augmented plane wave (FP-LAPW) [20,21] method. Analysis of the calculated band structure of LaNi4Si and GdNi4Si compounds suggest that Ni-3d states mainly contribute to density of states (DOS) from 5.0 eV to the Fermi level which is consistent with experiment and previously reported result by Kowalczyk et al. [22] having hexagonal CaCu5 structure. In order to study the structural, electronic and optical properties of YNi4Si-type DyNi5 xSix (x ¼0, 1, 2) compounds first principle calculations are performed. To author's knowledge theoretical and experimental study on electronic and optical properties of YNi4Si-type DyNi5 xSix compounds have not been addressed. The present study would also explore the role of substitutional change of silicon in place of nickel on structural, electronic and optical properties as well as encourage the measurement of these properties on YNi4Si-type DyNi5 xSix (x ¼0, 1, 2) compounds.
2. Computational details Self-consistent FP-LAPW [20,21] calculations on DyNi5 xSix were carried out using WIEN2k code [23]. We considered a number of basic functions up to RMT Kmax ¼7, where RMT is the
minimum radius of the muffin-tin spheres and Kmax gives the magnitude of the largest K vector in the plane wave basis, to achieve an adequate exchange between accuracy and cost. In order to keep the same degree of convergence, we kept the values of the sphere radii and Kmax constant over all the crystal geometries considered. The muffin-tin radii RMT for Dy, Ni and S to be 2.5, 2.32 and 1.84 bohr, respectively, have been selected and the APW þ lo basis set [24], with additional 5s and 5p local orbitals for the rare earth atom is used. Additionally, the valence wave functions inside muffin-tin spheres are expanded up to lmax ¼ 10. The LSDA functional is used for exchange and correlation effects. For better accounting of the correlation between the 4f electrons, Anisimov et al. [25] introduced the self consistent LSDA þ U method. This method explicitly includes the on-site Coulomb interaction term in the conventional Hamiltonian. Harmon et al. [26] determined the numerical values of the parameters of the direct Coulomb (U¼6.7 eV) and exchange (J ¼0.7 eV) interaction for Gd. These numerical values of the parameters have been used to perform the calculations. The dependence of the energy on the number of k points in their reducible wedge of the Brillouin zone (IBZ) has been checked, and the size of the mesh has been set to 12 12 12 Monkhorst and Pack [27] k-point mesh, which yields 301 k-points in the IBZ. We considered the self-consistency to be reached when the total energy difference between successive iterations is o105 Ry per formula unit. The convergence was also checked with a refined mesh in the IBZ with no appreciable change in energy or properties. The modified tetrahedron method [28] has been used to perform the k space integration. We used a broadening of 0.1 eV to simulate the experimental finite lifetime effects. The Crystal arrangement of DyNi5 xSix (x ¼0, 1, 2) compounds is YNi4Si-type structure with space group Cmmm. In DyNi5 compound nickel atoms are located at three non equivalent positions. Rare earths occupy the 2a site (0, 0, 0) and Ni1 is located in the 4i site (0, yNi1, 0), where internal cell parameter (yNi1)¼ 0.3415 [17]. Ni2 and Ni3 atoms are statistically distributed over 2c site (0, 1/2, 1/ 2) and 4f site (1/4, 1/4, 1/2), respectively. Site occupation by Dy and Ni atoms in DyNi5 xSix (x ¼1, 2) is similar to the DyNi5, except 2c and 4i site which is doped with silicon atoms in DyNi4Si and DyNi3Si2, respectively. The Wyckoff positions and unit cell data are presented in Tables 1 and 2, respectively. We have performed calculations for the ferromagnetic phase, as DyNi5 xSix compounds are ferromagnetic at low temperatures. The electronic structure of DyNi5 xSix compounds is studied within the ab initio approach.
Table 2 Equilibrium lattice parameters (a, b, c, b/a and c/a) (in a.u.), internal cell parameters (yNi1/ySi), cell volume V (in a.u.3), bulk modulus B0 (in GPa), and its pressure derivative B0′ for DyNi5 xSix (x ¼0, 1, 2) at 0 GPa and 0 K (This work) and at 0.1 GPa and 298 K [17].
DyNi5 DyNi4Si DyNi3Si2
This work Expt. [17] This work Expt. [17] This work
a
b
c
b/a
c/a
yNi1/ySi
Vol
B0
B0′
9.24380 9.21354 9.42427 9.53914 9.42126
16.01076 15.95835 15.31007 15.49669 15.30520
7.52172 7.49710 7.37433 7.46422 7.37199
0.812586 0.813704 0.808758 0.782483 0.679411
1.734751 1.732053 1.564982 1.624536 1.818965
0.3343 0.3333 0.3411 0.3415 0.3404
556.60900 551.16164 531.82690 551.70089 531.45988
142.3509
2.8986
180.2626
5.3110
175.5218
4.8594
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
-39504.362
-39504.370
DyNi5
-39504.364
-39504.372
-39504.368
-39504.373
-39504.370
-39504.374
-39504.372
-39504.375
-39504.374
-39504.376
-39504.376
-39504.377
-39504.378 0.76 -37045.895
0.78
0.80
0.82
0.84
DyNi4 Si
0.86
0.88
-39504.378 1.60 -37045.860 -37045.870
-37045.900
Energy / Cell [ Ry ]
DyNi5
-39504.371
-39504.366
91
1.65
1.70
1.75
1.80
1.85
DyNi4Si
-37045.880
-37045.905
-37045.890 -37045.910 -37045.900 -37045.915
-37045.910
-37045.920
-37045.920
-37045.925 -37045.930 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 -34587.750 -34587.760
-34587.750
DyNi3Si 2
DyNi3 Si 2
-34587.760
-34587.770 -34587.770
-34587.780 -34587.790
-34587.780
-34587.800
-34587.790
-34587.810 -34587.800
-34587.820
-34587.830 -34587.810 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95
C/A
B/A
Fig. 1. Energy as a function of c/a ratio (left panel) and b/a ratio (right panel) of DyNi5 xSix (x ¼0,1,2) at 0 GPa and 0 K.
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D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
3. Results and discussions
-39504.290
3.1. Structure optimization
-39504.300
3.2. Band structure
-39504.310 -39504.320 Vp = 556.6090
-39504.330 -39504.340 -39504.350 -39504.360 -39504.370 -39504.380
LSDA+U 460 480 500 520 540 560 580 600 620 640
-37045.870
DyNi4Si
-37045.875 -37045.880
Energy / Cell [ Ry ]
To determine the structural properties in the ground state, such as the lattice parameters (a, b, c, b/a and c/a), bulk modulus (B0 ), and its pressure derivative B0′ of DyNi5 xSix (x ¼0, 1, 2) compounds in the orthorhombic YNi4Si type structure, we first optimized the value of the internal cell parameter (yNi1) of nickel at the 4i site of DyNi5 xSix (x¼0, 1) and ySi1 of silicon at 4i site of DyNi3Si2 structure so that the forces on each atom is o2 mRy per au by using experimental values [17]. The optimization was done with 105 k-points in the IBZ. Our optimized values of internal cell parameters are in good agreement with the experiment [17] and listed in the Table 2. To optimize the equilibrium volume, we adopted the experimental lattice parameters, c/a and b/a ratios to create a multitude of volumes around the experimental volume, and optimized the equilibrium volume with sequential minimization of internal cell parameters. For determination of optimized equilibrium c/a and b/a ratios, we followed the same minimization method as pointed out earlier for free internal cell parameters and used the experimental c/a and b/a ratios and volume to get optimized equilibrium c/a and b/a ratios. The Energy (E) vs. c/a and b/a curves and the E vs. volume (V) curves of DyNi5 xSix (x ¼0, 1, 2) so obtained are shown in Fig. 1 and Fig. 2, respectively. The lattice constants, the equilibrium cell volumes, B0 and B0′ for DyNi5 xSix (x ¼0, 1, 2) compounds at 0 GPa and 0 K are summarized in Table 2 and the values of equilibrium structural parameters obtained from present work are in good agreement with the corresponding experimental values [17]. The total energies versus unit cell volume are fitted to the Murnaghan's equation of state (EOS) [29] to determine the B0 and B0′ of DyNi5 xSix (x ¼ 0, 1, 2) compounds. Our LSDA (not listed here) and LSDA þU methods yields a deviation of 5% and 1%, respectively, of the lattice parameters with respect to the experimental data, for DyNi5 xSix (x¼ 0, 1, 2) compounds which shows strong correlation effect of 4f electrons has to be considered for a correct explanation of these rare earth compounds.
DyNi5
-37045.885 -37045.890
Vp = 531.8269
-37045.895 -37045.900 -37045.905 -37045.910 -37045.915 -37045.920 -37045.925
LSDA+U 480
500
520
540
560
580
600
620
-34587.730
DyNi3Si2
-34587.735 -34587.740
The spin polarised band structures (BSs) along the symmetry points of the Brillouin zone of the DyNi5 xSix (x¼ 0, 1, 2) compounds, within the LSDA þ U framework, are shown in Fig. 3(a)–(c). Number of energy bands cross the Fermi level indicates the metallic ground state of the DyNi5 xSix (x¼ 0, 1, 2) compounds. The BSs of spin up states is similar to that for spin down states except that the spin-up Dy-4f bands are occupied and lie well below the EF and the spin-down Dy-4f bands are unoccupied and lie well above EF. We find that occupied Dy-4f bands are centred around 8 eV below EF, while spin down unoccupied Dy-4f bands lie about 2 eV above EF. The LSDA þU enhances the exchange splitting of the f bands noticeably from 5 eV in LSDA (not presented for brevity) to 10 eV in LSDA þ U, by pushing the 4f spin-up states much below EF and 4f spin down states well above the EF. This shifting also explains why the results for DOS and magnetic moment obtained by using LSDA [30,31] when f states are treated as part of core or as pseudo core, are closer to those from LSDA þ U. The valence band region of the DyNi5 band structure is about 9.0 eV wide, which turn into 12 eV in DyNi3Si2, due to hybridization of Dy-4f and Si-3s states. Wideness of conduction band is almost similar and is about 7.0 eV in all DyNi5 xSix (x ¼0, 1, 2) compounds because of insignificance contribution of Si-3s and 3p states in conduction band. We also find that the valence bands are more dispersive in comparison to the conduction bands in these compounds. A comparison of BSs of DyNi5 xSix (x¼0,1,2) compounds
-34587.745 -34587.750
Vp = 531.4598
-34587.755 -34587.760 -34587.765 -34587.770 -34587.775 -34587.780 -34587.785
LSDA+U 480
500
520
540
560
580
600
620
3
Volume [ a.u ] Fig. 2. Energy as a function of primitive unit cell volume of DyNi5 xSix (x¼ 0,1,2) at 0 GPa and 0 K.
reveals that filled spin-up and unfilled spin-down Dy-4f states retain their position below and above EF, respectively and that the lowest band (Dy-5p) (not shown in the figure) moves away from EF as one moves from DyNi5 ( 21 eV) to DyNi3Si2 ( 23 eV). The large depth from EF ensures that these bands retain atomic character and do not attain the conventional large band-width as
EF
Energy (eV)
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0 -11.0 -12.0 -13.0 -14.0
Γ
Δ
H
Energy (eV)
Energy (eV)
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
N Σ
Γ
Λ
P
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0 -11.0 -12.0 -13.0 -14.0
93
EF
Γ
Δ
H
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -7.0 -8.0 -9.0 -10.0 -11.0 -12.0 -13.0 -14.0
N Σ
Γ
Λ
P
EF
Γ
Δ
H
N Σ
Γ
Λ
P
Fig. 3. Band structure of (a) DyNi5, (b) DyNi4Si and (c) DyNi3Si2 compounds using LSDA þU for spin up (solid lines) and spin down (dotted lines) states. The EF is at 0 eV.
94
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
Fig. 4. DOS of DyNi5 xSix (x¼ 0, 1, 2) compounds using LSDA þ U approximation. Solid (dotted) lines represent the majority (minority) states. The EF is at 0 eV.
Fig. 5. Partial DOS of DyNi5 xSix (x¼ 0, 1, 2) compounds using LSDA þ U approximation. Solid (dotted) lines represent the majority (minority) states. The EF is at 0 eV.
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
is associated with conduction bands. 3.3. Density of states In order to understand clearly the electronic structure and the differences in the magnetic properties between DyNi5 xSix (x ¼0,1,2), the total DOS and partial DOS of all the compounds are calculated using LSDA þ U approximation and shown in Fig. 4 and Fig. 5, respectively. From the partial DOS, we are able to identify the angular momentum character of the states. Although there are some general similarities, the structures of total DOS for substitution of silicon in place of nickel differ from each other. The broad valance band is constituted by Ni-3d states and located in a range from 5 eV to the EF in DyNi5 xSix (x ¼0, 1, 2) compounds. The spin-down states of 3d electrons are filled more completely as compared to the spin-up states, since the spin-down states are energetically more favoured for the 3d electrons because of the mutually opposite directions of spin magnetic moments of the 3d and R subsystems [32]. Another group of bands located from 5 eV to 11 eV, is characterized by Si-s states with some amount of Si-3p states. Replacement of Ni atoms by Si results in a rather independent Si-3s, 3p band centred at around 8 eV below the EF for the compounds with x¼ 1, 2. These Si-3s states lie around 9.5 eV below EF in DyNi4Si remains unhybridized and lie slightly lower around 10.5 eV below EF and hybridized with Dy-4f states in DyNi3Si2. The Si-3p states show gradual hybridization with Ni-3d states in compounds (x ¼1, 2). The band width of Si-3p states is considerably smaller with respect to the Ni-3d states. The intense and pronounced peaks of 4f states also present in the valence band lie at around 8.0 eV in DyNi5 and remain unhybridized, while for the compounds (x ¼1, 2) we found slight larger band width of 4f states due to the hybridization with Si-3s and Si-3p states. The position of Dy-4f states ( 8.0 eV) from this way is fairly consistent with the x-ray photoemission spectroscopy (XPS) results [15] of DyNi5 xAlx as well as with other theoretical results for dysprosium compounds [33]. It shows that Dy-4f states retain their elemental character in these compounds. On the other hand spin down 4f states are completely unoccupied and constitute the conduction band. The energy bands from 15 to 20 eV consist of Dy-5p states. The position of the Dy-5p states is different in these DyNi5 xSix (x ¼0, 1, 2) compounds. These Dy-5p states are located far below the EF at 21 eV in DyNi5 and lie around 22 eV and 23 eV below EF in DyNi4Si and DyNi3Si2 compounds, respectively and not shown in the figure. Above EF, the energy band is constituted by Dy-5d and 4f states. The bottom of the conduction band and the top of valence band are formed from the hybridized Dy-5d states and 3d states of Ni atoms. We found that Ni-3d states remains in valance band in DyNi5 xSix (x ¼0, 1, 2) show that substitution of silicon in place of nickel atom does not give significant change in DOS near EF. The partial DOS for DyNi5 xSix (x ¼0, 1, 2) shows that, the 3d- states of Ni atoms are dominant below the EF, while the Dy-4f states peak stands tall in comparison to the small contributions made by the Dy-3d states above EF in these compounds. A comparison of DOS of DyNi5 xSix (x ¼0,1,2) compounds reveals that the total DOS width becomes
95
larger after silicon substitution as compared with that in DyNi5. Simultaneously, The DOS at the EF is gradually reduced with the increase of silicon concentration. The value of magnetic moment (m), density of states at Fermi level N(EF), and the coefficient of electronic specific heat (γ) from this work and those obtained by various workers [18,34,35] are listed in Table 3. Our spin polarized LSDA þU calculations yield 7.34167 mB, 5.0629 mB and 5.13746 mB magnetic moment for DyNi5 xSix (x¼ 0, 1, 2) compounds, respectively. The calculated total magnetic moment of DyNi5 is in agreement with experiment [34] and for x ¼1, 2 it decreases because of the decrease of the moment of the 3d subsystem. When silicon for nickel substitution takes place (DyNi4Si), nickel moments decrease rapidly (0.00965 mB/atom) while the dysprosium moment increases slightly (5.01542 mB). The anti parallel orientation of dysprosium and nickel moments is also revealed, in agreement with other theoretical and experimental study [15,19,22]. As silicon for nickel substitution proceeds (DyNi3Si2), the dysprosium moment increases slightly and has the value of 5.02040 mB, while the nickel moments 0.01714 mB /atom but now the orientation of nickel moments is parallel to that of dysprosium moment similar to the calculations on DyNi5 xAlx compounds [36]. This behaviour can be attributed to hybridization effects and reduction of electron correlations between d electrons and also from that an antiparallel alignment of dysprosium and nickel moments. On the other hand magnetic moment of the dysprosium ion remains close to 5 mB for all DyNi5 xSix compounds. When orbital angular momentum L¼ 5 of the dysprosium ion is taken in to account by the analogy with [37], we obtained the total effective magnetic moment of dysprosium is of the order of 9.96 mB in DyNi5, which is in agreement with the experimental value of 10.33 [38]. The value of magnetic moment at the dysprosium site in DyNi5 xSix compounds (x¼ 0, 1, 2) showing 7%, 6% and 5% drop, respectively in comparison to pure dysprosium (10.645 mB) [40] by use of similar analogy [37]. On the other hand nickel shows even stronger impact dropping by 28%, 96% and 94% in comparison to elemental Ni (0.60 mB) [39] for DyNi5 xSix (x¼ 0,1,2) compounds, respectively. This suggests that the inter-atomic interaction in these compounds is much strong and affect the Ni atoms. This is due to the filling of the minority-spin d bands of Ni atoms by the conduction electrons from dysprosium atoms explaining the reduction of the nickel magnetic moment compared to that in pure nickel. The calculated N(EF) is increasing from the value of 1.65 in DyNi5 to 2.16 states/Ry/spin/unit cell in DyNi3Si2 due to a more complete filling of the 5d band of dysprosium. The value of electronic specific heat (γ) for this work is 31.56 mJ mol 1 K 2 for DyNi5 is in agreement with the experimental value [35]. There are no experimental or theoretical results for the value of γ for DyNi4Si and DyNi3Si2 compounds. We obtained the value of γ is 28.74 and 25.68 mJ mol 1 K 2 for both compounds, respectively. 3.4. Optical properties The optical properties of matter can be described by the complex dielectric function e(o), which represents the linear response
Table 3 Total and partial magnetic moment m (in mB), density of states at the Fermi level N(EF) (in states/Ry/spin/unit cell) and coefficient of electronic specific heat γ (in mJ mol 1 K 2) for DyNi5 xSix (x¼ 0, 1, 2) compounds.
DyNi5 DyNi4Si DyNi3Si2
This work Exp. This work Exp. This work
Total l (in mB)
lDy
lNi1
lSi/Ni
lNi3
N(EF) (states/Ry/spin/unit cell)
γ (mJ mol 1 K 2)
7.34167 7.19 [34] 5.0629 7.7 [18] 5.13746
4.96653
0.89359
0.19425
0.19690
1.65
5.01542
0.0095
0.0013
0.0097
1.88
31.56 36 [35] 28.74
5.02040
0.01189
0.0033
0.02239
2.16
25.68
96
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
Fig. 6. The Calculated (LSDA þU) and experimental optical conductivity of DyNi5 xSix (x¼ 0, 1, 2) compounds.
of a system to an external electromagnetic field. It can be expressed as ε (ω) = ε1 (ω) + ε2 (ω), where ε1 (ω) and ε2 (ω) are the real and imaginary components of the dielectric function, respectively. The imaginary part ε2 (ω) is directly related to the electronic band structure and it can be computed by summing up all possible transitions from the occupied to the unoccupied states, taking into account the appropriate transition dipole matrix elements. The real part ε1 (ω) can be derived from the imaginary part using the familiar Kramers–Kronig transformation [40]. The optical conductivity σ (ω) is related to the dielectric function ε (ω) as 4πiσ (ω) ε (ω) = 1 + ω . All optical properties are calculated at the theoretical equilibrium lattice constant using LSDA þ U approximation for the energy up to 16 eV. Lorentzian broadening is taken to be 0.1 eV. This is the first calculation on the optical conductivity of DyNi5 xSix (x¼0, 1, 2) compounds in YNi4Si-type structure. Since the anisotropy in these compounds is negligibly small; hence only the diagonal component of optical conductivity perpendicular to the c-axis, has been presented. Experimental data for optical conductivity of DyNi5 xSix is not available. The experimental optical conductivity data for parental compound DyNi5 [16] has been used to compare and conform our results. Fig. 6 shows the optical conductivity of DyNi5 xSix compounds (x ¼0, 1, 2) using LSDA þ U approximation. Three pronounced peaks at the energies around 1 and 1.8 and 3.5 eV, respectively are shown in the experimental data for the optical conductivity of DyNi5. A similar trend is also found in our calculated spectra, but with twice the magnitude. As mentioned earlier we have used a broadening of 0.1 eV to bring out the structures in the optical properties. For significantly larger values, the calculated optical conductivity spectra agree with experiment magnitude wise but the structures are lost. This relatively larger magnitude could be due to high reactivity of the surface of the rare earth compounds [41–43]. The comparison of the measured and calculated optical conductivity spectra of CaCu5 type - DyNi5 xAlx have also been shown by Knyazev et al. [16] but in the arbitrary units. We found the most prominent features are broad and structured peaks present around 0.8 eV, 1.6 eV and at 3.2 eV in DyNi5. Peaks below 4 eV could be due to the transition from hybridized bands of Ni-3d and Si-3p atoms below EF to free Dy-4d states. These are found to shifts slightly to lower energy as compared to the experiment [16]. Upon substitution of nickel by silicon, the intensity of the first two maximum significantly drops as well as shifted towards lower energy from DyNi5 to DyNi3Si2. One can also note that second peak appears significantly in the conductivity spectrum of binary DyNi5, seen as a small shoulder (x¼ 1) and then (х ¼2) this spectral feature almost disappears similar to the experiment [16]. Experiment is performed up to 6 eV. In the high energy range (above the 6 eV) prominent absorption peak at 6 eV in (x ¼ 0, 2) appears at around 5.8 eV in (x ¼1). Further, peak at 7.2 eV in DyNi4Si is slightly shifted towards higher energy at 7.4 eV in DyNi3Si2 is completely absent in
Fig. 7. The Calculated (LSDA þU) refractive index n(ω) (bottom panel) and extinction coefficient k(ω) (top panel) of DyNi5 xSix (x¼ 0, 1, 2) compounds.
DyNi5 showing the effect of silicon substitution at nickel site which could be due to transitions between occupied 3d states of Ni atoms hybridized with Si-p and unoccupied spin down Dy-f states. It should be noted that, for all compounds, the specific features associated with the 3s electrons of Si are weakly pronounced in the spectra of optical conductivity, although the corresponding bands are represented by significant maxima in the DOS (Fig. 4). The calculated refractive index n(ω) and extinction coefficient k (ω) of DyNi5 xSix (x ¼0, 1, 2) compounds are displayed in Fig. 7. Corresponding experimental data are not available for these compounds. The static refractive index n(0) are fairly large, 13.1 for DyNi5 and 13.8 for DyNi3Si2. The magnitude of n(ω)and k(ω) are larger in the 0–3 eV range, reflecting the dominating nature of the transitions in this energy range. We find that the n(ω)and k(ω) decreases sharply from 4.5 to 2.5 in the energy range 2.5 eV to 6.5 eV. In high energy range, n(ω) continuously decreases up to the value of 0.9 in all DyNi5 xSix (x ¼0, 1, 2) compounds. On the other hand extinction coefficient k(ω) reaches maximum value of 7.2 at around 0.5 eV in DyNi3Si2 and 6.5 at 1.1 eV in DyNi5. At intermediate energies small humps appear and vanishing curves in high energy range. One can notice that the relation k 4n is satisfied for DyNi5 xSix (x¼ 0, 1, 2) compounds almost in the entire spectral region, except for the low energy region, which is as a rule typical of the media with metallic conductivity, while the non monotonic behaviour of these parameters in the low energy region is a manifestation of interband absorption. Almost continuously decreases value in energy range 2.5 eV to 6.5 eV imply that the incident electromagnetic waves with energies in this range will be propagate inside material with continuously losses its signal
D.K. Maurya, S.M. Saini / Journal of Magnetism and Magnetic Materials 416 (2016) 89–97
strength. As a result, it seems to suggest that for visible radiations, the DyNi5 xSix (x ¼0, 1, 2) compounds are highly sensitive to the frequency of the radiations.
4. Conclusions Spin polarized full potential calculations of structural, electronic and optical properties of YNi4Si–type DyNi5 xSix (x¼0, 1, 2) compounds have been performed using LSDA þU approximations with partial substitution of nickel by silicon. The calculated equilibrium lattice parameters are in good agreement with the available experimental results. The electronic BS and DOS of the DyNi5 xSix (x¼ 0, 1, 2) exhibit metallic behaviour. Partial DOS reveals that Dy-4d and spin down Dy-4f states are present in the conduction bands while Ni-3d, Si-3s and spin up Dy-4f states are present in the valence bands. When nickel is replaced by the silicon, moment at nickel site decreases sharply. Our calculated BS shows that the replacement of nickel with silicon leads to gradual filling of the 3d band, as a result of which N(EF) increases from the value of 1.65 in DyNi5 to 2.16 (states/Ry/spin/unit cell) in DyNi3Si2. Frequency dependent optical spectra of DyNi5 xSix compounds are similar with the experimental data on the parental DyNi5 compound. Main absorption peak around 4 eV depends on the substituent concentration and could be due to transition from hybridized band (Ni-3d and Si-3p), below EF to free Dy-4d states. Our calculation also suggest that the most prominent peak around 7 eV could be due to transition from 3d states of nickel atoms hybridized with Si-3p and unoccupied spin down Dy-4f states. The results on refractive index suggest that for the optical radiations in the energy range 2.5–6.5 eV, DyNi5 xSix (x ¼0, 1, 2) are very sensitive to the frequency of the radiations.
Acknowledgements The work was financially supported by the CCOST project, Raipur (C.G), India, through sanction no. 2161/CCOST/MRP/2013.
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