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Spintronic properties of the Ti 2 CoB Heusler compound by density functional
theory
Article in Solid State Communications · January 2011
DOI: 10.1016/j.ssc.2011.05.00
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Solid State Communications 151 (2011) 1162–1164
Contents lists available at ScienceDirect
Solid State Communications
journal homepage: www.elsevier.com/locate/ssc
Spintronic properties of the Ti2 CoB Heusler compound by density functional
theory
Selçuk Kervan ∗ , Nazmiye Kervan
Nevşehir University, Faculty of Arts and Sciences, Physics Department, 50300, Nevşehir, Turkey
article
info
Article history:
Received 4 April 2011
Received in revised form
29 April 2011
Accepted 10 May 2011
by F. Peeters
Available online 17 May 2011
Keywords:
A. Magnetically ordered materials
D. Electronic band structure
abstract
The electronic structure and magnetic properties of the Ti2 CoB Heusler compound with a high-ordered
CuHg2 Ti structure were investigated using the self-consistent full potential linearized augmented plane
wave (FPLAPW) method within the density functional theory (DFT). Spin-polarized calculations show that
the Ti2 CoB compound is half-metallic ferromagnetic with a magnetic moment of 2 µB at the equilibrium
lattice constant, a = 5.74 Å. The Ti2 CoB Heusler compound is ferromagnetic below the equilibrium lattice
constant and ferrimagnetic above the equilibrium lattice constant. A large peak in majority-spin DOS and
an energy gap in minority-spin DOS are observed at the Fermi level, yielding a spin polarization of 100%. A
spin polarization higher than 90% is achieved for a wide range of lattice constants between 5.6 and 6.0 Å.
© 2011 Elsevier Ltd. All rights reserved.
1. Introduction
2. Computational method
Half-metallic (HM) materials, which have a complete spin polarization at the Fermi level, attract increasing interest for their
potential spintronic device applications such as nonvolatile magnetic random access memories (MRAM) and magnetic sensors
[1–4]. Half-metallic properties have been observed in many
materials, for example Heusler compounds [5–10], ferromagnetic metallic oxides [11–13], dilute magnetic semiconductors
[14,15] and zincblende transition-metal pnictides and chalcogenides [16–20]. The Heusler compounds are ternary X2 YZ intermetallics, where X and Y are transition metals and Z is a main group
element [21]. The X2 YZ Heusler compounds crystallize in the cubic AlCu2 Mn-type structure with the space group Fm3m. In this
structure, X, Y and Z atoms are placed on the Wyckoff positions
8c (1/4, 1/4, 1/4), 4a (0, 0, 0) and 4b (1/2, 1/2, 1/2), respectively.
If the number of 3d electrons of Y atom is more than that of X atom,
CuHg2 Ti-type structure with the space group F 43m is observed. In
this structure, X atoms occupy the nonequivalent 4a (0, 0, 0) and
4c (1/4, 1/4, 1/4) positions, while Y and Z atoms are located on 4b
(1/2, 1/2, 1/2) and 4d (3/4, 3/4, 3/4) positions, respectively [7].
Although many Heusler compounds have been theoretically
predicted to be half-metallic [5–10,22–26], the electronic structure
calculations of the Ti2 -based Heusler compounds have not been
widely studied up to now. In the present paper, the electronic
structure and magnetism of the Ti2 CoB Heusler compound with
CuHg2 Ti-type structure are studied by means of the self-consistent
full potential linearized augmented plane wave (FPLAPW) method.
Electronic structure calculations were performed using the
self-consistent full potential linearized augmented plane wave
(FPLAPW) method [27] implemented in WIEN2K code [28] within
the density functional theory (DFT). The Perdew–Burke–Ernzerhof
generalized gradient approximation (GGA) [29,30] was used for
the exchange correlation correction. In this method, the space is
divided into non-overlapping muffin-tin (MT) spheres separated
by an interstitial region. The basis functions are expanded into
spherical harmonic functions inside the muffin-tin sphere and
Fourier series in the interstitial region. The muffin-tin sphere radii
were 2.15 a.u. for Ti and Co, 2.0 a.u. for B. The convergence of
the basis set was controlled by a cut off parameter Rmt Kmax = 7,
where Rmt is the smallest of the MT sphere radii and Kmax is the
largest reciprocal lattice vector used in the plane wave expansion.
The magnitude of the largest vector in charge density Fourier
expansion (Gmax ) was 12. The cutoff energy, which defines the
separation of valence and core states, was chosen as −6 Ry. We
select the charge convergence as 0.0001e during self-consistency
cycles. In these calculations, we neglected the effect of spin–orbit
coupling. For the Brillouin zone (BZ) integration, the tetrahedron
method [28] with 72 special k points in the irreducible wedge
(2000 k-points in the full BZ) was used to construct the charge
density in each self-consistency step.
3. Results and discussion
∗
Corresponding author. Tel.: +90 384 215 3900; fax: +90 384 215 3948.
E-mail address: selcuk.kervan@nevsehir.edu.tr (S. Kervan).
0038-1098/$ – see front matter © 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ssc.2011.05.008
The calculated total energy as a function of lattice constant for
both ferromagnetic and non-magnetic configurations is plotted
S. Kervan, N. Kervan / Solid State Communications 151 (2011) 1162–1164
Fig. 1. The calculated total energy as a function of lattice constant for the Ti2 CoB
Heusler compound.
Fig. 2. The spin-polarized total densities of states (DOS) and atom-projected DOS.
Fig. 3. The band structures of the Ti2 CoB compound for the spin-up and spin-down
electrons.
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Fig. 4. The dependence of the half-metallic state on the lattice constant.
in Fig. 1 for the CuHg2 Ti-type structure. It can be seen that the
ferromagnetic state is more stable. The equilibrium lattice constant
is 5.74 Å and there is no experimental or theoretical lattice constant
value to compare with our value. The energy difference between
the ferromagnetic and non-magnetic states increases slightly with
increasing lattice constant.
Fig. 2 presents the spin-polarized total densities of states
(DOS) and atom-projected DOS of Ti2 CoB at its equilibrium
lattice constant. The calculated total magnetic moment of Ti2 CoB
compound is 2 µB , while the atomic magnetic moments are 0.981
µB for Ti (1), 0.575 µB for Ti (2), 0.004 µB for Co and −0.023 µB
for B. It is clear that the majority-spin band is metallic, while the
minority-spin band shows a semiconducting gap around the Fermi
level. In minority-spin band, the valance band maximum is located
at −0.59 eV and the conduction band minimum is at 0.05 eV. The
energy gap for spin-down electrons at around the Fermi level is
0.64 eV. This energy gap in the minority-spin band gap leads to
100% spin polarization at the Fermi level, resulting in the halfmetallic behavior at equilibrium state. In the spin-down band, the
total density of states around the Fermi level are predominantly
due to Co-d, Ti(1)-d and Ti(2)-d electrons. The projected density of
states of Co atom lies mainly below the Fermi level and has the
main contribution to the total DOS. The spin-down densities of
states of Ti(1) and Ti(2) atoms lie mainly above the Fermi level. The
energy region between −9 and −7 eV consists mainly of s electrons
of B atoms.
The band structures of the Ti2 CoB compound for the spin-up
and spin-down electrons is plotted in Fig. 3. It is obviously seen
that the spin-up band structure has metallic intersections at the
Fermi level which is a sign of metallic nature. However, the spindown band structure has energy gap near the Fermi level. The
width of the energy gap can be calculated using the energies of the
highest occupied band at the Γ point and the lowest unoccupied
band at the L point. The Fermi level lies 0.59 eV above the highest
spin-down valance band. Therefore, spin-flip gap, which is the
minimum energy required to flip a minority-spin electron from
the valance band maximum to the majority-spin Fermi level, is
of 0.59 eV. The non-zero spin-flip gap indicates that the Ti2 CoB
compound is a true half-metallic ferromagnet (HMF). This spinflip gap is close to the spin-flip gap of the Co2 MnP compound
[25].
In order to investigate the dependence of the half-metallic
state on the lattice constant, the electronic structure calculations
were performed for the lattice parameters between 5.5 and 6.0
Å. It is clearly seen in Fig. 4 that the Ti2 CoB Heusler compound
has half-metallic nature above the lattice constant value of 5.65
Å. Therefore, the lattice expansion does not change half-metallic
behavior of the Ti2 CoB compound.
1164
S. Kervan, N. Kervan / Solid State Communications 151 (2011) 1162–1164
4. Conclusions
Using the first-principles full potential linearized augmented
plane waves (FPLAPW) method, the spintronic and magnetic
properties have been calculated for the Ti2 CoB Heusler compound.
The spin-polarized calculations show that the Ti2 CoB Heusler
compound is a half-metallic ferromagnet with a magnetic moment
of 2 µB at the equilibrium lattice constant. The Ti2 CoB Heusler
compound has half-metallic character above the lattice constant
value of 5.65 Å.
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Fig. 5. The calculated total magnetic moment, the magnetic moments of the Ti(1),
Ti(2) and Co atoms and the spin polarization as a function of lattice constant.
The calculated total magnetic moment, the magnetic moments
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function of lattice constant is given in Fig. 5. The calculated total
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moment of the Co atom decreases. The Ti2 CoB Heusler compound
is ferromagnetic up to the lattice constant value of 5.75 Å before
becoming ferrimagnetic. The Ti2 CoB Heusler compound maintains
the half-metallic character having 100% polarization above the
lattice constant value of 5.65 Å.
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