Computational Materials Science 81 (2014) 510–516

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Computational Materials Science

journal homepage: www.elsevier .com/locate /commatsci

The surface electronic properties of newly designed half-metallicferromagnets: GeKCa and SnKCa

0927-0256/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.commatsci.2013.08.061

⇑ Corresponding author. Fax: +82 32 872 7562.E-mail address: jilee@inha.ac.kr (J.I. Lee).

Beata Białek a, Jae Il Lee a,⇑, Miyoung Kim b

a Department of Physics, Inha University, Incheon 402-751, Republic of Koreab Department of Physics, Sookmyung Women’s University, Seoul 140-742, Republic of Korea

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 June 2013Received in revised form 28 August 2013Accepted 30 August 2013Available online 5 October 2013

Keywords:Half-metalFirst-principles calculationsHalf-Heusler alloySurface electronic structure

The electronic and the magnetic properties of the (001) surfaces of GeKCa and SnKCa with half-Heuslerstructure are studied with the use of a full-potential linearized augmented plane wave method. It isshown that although the two compounds are half-metals in their bulk structures, only the surfaces ter-minated with a carbon group atom retain the half-metallic properties. The magnetic properties of the sur-faces terminated with layers containing group 14 atoms are enhanced compared with the properties ofthe bulk. The calculated magnetic moments on the Ge atom in GeKCa are 0.38lB in the bulk and 0.97lB atthe (001) surface. In the SnKCa surface, the value of the magnetic moment on the Sn atom increases from0.28lB in the bulk to 0.75lB at the surface. In the Ge (Sn) terminated Ge(Sn)KCa surfaces, the metal atomsare also polarized. In addition to destroyed half-metallicity at the surfaces terminated with metal atomswe also find a strong demagnetization of the systems.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Half-metallic ferromagnets (HMFs) are characterized by a com-plete spin polarization of electrons at the Fermi level (EF) [1] evenin the ground state. Such materials are rare in nature, but nowa-days there are many known compounds possessing these proper-ties. Many of them were computer designed first and synthesizedlater. For example, Akinaga et al. synthesized CrAs in zinc-blende(ZB) structure by molecular beam epitaxy [2]. ZB CrSb thin filmswere also grown by that method [3], and epitaxial layers of ZB(Ga,Mn)As were deposited on the Si (001) surface [4]. Those exper-iments prove that it is possible to obtain materials of desired mag-netic properties, even though their crystal structure is not the moststable one.

The latest trend in search of new materials in the group of HMFsis studying substances that possess magnetic properties, in spite ofthe lack of a transition metal in their structure. For example,Kasukabe et al. reported p-electron magnetism in a ZB CaAs [5].The magnetic moment in the material appeared due to 4p elec-trons of As; 4p As orbitals transformed using a proper symmetrygroup so they could hybridize with the t2g d orbitals of Ca [5]. Thatfinding opened a possibility for materials design where the topol-ogy of p (or p) orbitals was a guiding principle.

Since then, many similar materials were proposed as candidatesfor application to spintronics; a vast group of them are compounds

of group 2 and group 14 or 15 elements. Gao et al. found p-electronhalf-metallic ferromagnetism in ZB CaSi and CaGe [6], and in rock-salt SrC and BaC [7], as well as in several other compounds (see forexample [8,9]). Recently, attention has also been drawn to poten-tial sp-electron HMFs of Heusler or half-Heusler structure. This ismainly because the Heusler-based materials have TC much higherthan the room temperature [10]. High TC is very important forapplication to spintronic devices since it stabilizes the half-metal-licity of the material through a small reduction of the spin polari-zation at room temperature. Unfortunately, the same compoundprepared in the form of a thin film no longer possessed the half-metallic properties of the bulk, which was attributed to a disorderin the crystal structure [11]. We surmise, however, that the alter-ation can also be attributed to surface effects, which destabilizethe properties of the bulk.

In an attempt to combine the desired properties of half-Heusleralloys and sp-electron HMFs, Chen et al. investigated a new groupof materials, i.e. GeKCa and the SnKCa in the half-Heusler structure[12]. Using the first-principles pseudopotential plane wave meth-od, they found that both the GeKCa and SnKCa are HMFs and theproperty is preserved even if their lattice constants are contractedby 10% (GeKCa) or 13% (SnKCa) of their equilibrium values, 7.58and 7.99 Å, respectively. These values are much larger than theones determined for the compounds containing 3d metals, suchas CoMnSb or NiMnSn [13,14]. Hence, it is likely that while appliedin the form of thin films, these new materials would preserve theirhalf-metallic properties at a wide range of temperatures.

B. Białek et al. / Computational Materials Science 81 (2014) 510–516 511

Even though sp-electron ferromagnetic solids have not yet beensynthesized, the challenge will most likely be addressed due to thepromising properties. Geshi et al. have already proposed a synthe-sis process of ferromagnetic nitrides, i.e. CaN and SrN, in RS struc-ture [15]. Alkaline earth carbides, such as CaC2, are synthesized in ahigh yield and with a high purity in monoclinic structure [16]. Inone of the possible methods, synthesis of the carbides involvessoaking highly oriented pyrolitic graphite in a Li–Ca melt [17]. Per-haps similar methods may be used in the future to synthesize thecompounds of K, Ca, and Ge or Sn as bulk materials. Thin films ofKCa compounds with Ge or Sn could form interfaces with othersp-electron magnetic materials, since they happen to have quitea large lattice constant; for example, the lattice constants of afew alkaline earth silicides in ZB structure range from 6.55 to7.55 Å [18].

In this paper, we present and discuss the results of calculationsof the electronic and magnetic properties of (001) surfaces of GeK-Ca and SnKCa in the half-Heusler structure carried out with the useof a first-principles method.

)nips.Ve/setats

(a) Ge-term

2. Computational method

In half-Heusler alloys the three elements constituting the com-pound form three interpenetrating face centered cubic sublattices.GeKCa and SnKCa form the most energetically stable configura-tions when group 14 atom (Ge or Sn) occupies the (0,0,0) positionwhile K and Ca occupy the ð14 ; 1

4 ;14Þ and ð34 ; 3

4 ;34Þ positions, respec-

tively [12]. The calculated equilibrium lattice constant of thehalf-Heusler GeKCa in the most stable arrangement is 7.58 Å andthat of the SnKCa is 7.99 Å [12]. We adapted the lattice constantsto the study of (001) surfaces of GeKCa and SnKCa.

The surfaces were simulated by repeated slabs consisting of 13atomic layers. A building block of these slabs is shown in Fig. 1. Theseparation between the slabs was twice the slab thickness, whichmade the interactions between the slabs negligible. We consideredtwo possible terminations of the surfaces. Fig. 1a illustrates the ter-mination with a carbon group atom, i.e. Ge in GeKCa and Sn inSnKCa. We refer to these terminations as Ge-term and Sn-term,respectively. In the other termination, illustrated in Fig. 1b, thetopmost layer consists of K and Ca atoms. We call this terminationKCa-term. Since the predicted half-metallicity of the materials intheir bulk structures is not sensitive to the lattice constant contrac-tion within 10% and 13% of their equilibrium values [12], the geo-metrical parameters were not optimized. All the calculations werecarried out with the use of a first-principle full potential linearizedaugmented plane wave (FLAPW) method [19,20] with the general-ized gradient approximation [21] to the exchange–correlation po-

(a) (b)Fig. 1. Arrangement of atoms in a building block of the MKCa (M = Ge, Sn) (001)surfaces (a) M-terminated and (b) KCa-terminated. Only half slabs are shown. Cdentoes the center layer, S – the topmost layer; S � n (n = 1, . . . , 5) numerate theother layers from the subsurface (n = 1) toward the bulk.

tential. Lattice harmonics with l 6 8 were employed to expand thecharge density, potential, and wave functions inside the muffin-tinradii (MT) of 2.50, 2.60, 3.70, and 3.00 a.u. for Ge, Sn, K, and Caatoms, respectively. The number of basis functions was about200 per atom. A plane wave cut-off of 16 Ry was employed. Inte-grations were performed over a 7 � 7 � 1 mesh of k-points insidethe irreducible three-dimensional Brillouin zone. All core electronswere treated fully relativistically, while valence states were treatedscalar relativistically. The self-consistent calculations were consid-ered to be converged only when the integrated charge differenceper formula unit between the input and the output charge densi-ties was less than 1 � 10�4.

3. Results and discussion

3.1. The total densities of states

As bulk materials, both GeKCa and SnKCa are HMFs with energygaps in the spin-up electron channels [12]. Cleaving the bulk struc-tures and exposing (001) planes results in slabs whose electronicproperties depend on surface termination. As seen in Fig. 2, inwhich the calculated total density of states (DOS) of the GeKCa sur-faces are presented, the half-metallic properties of the bulk aresustained only in the Ge-term surface. The calculated width ofthe energy gap in the spin-up electron channel in this system is0.80 eV, which is smaller than the reported 1.21 eV for the bulkstructure.

In the KCa-term surface, there are electronic states present at EF

in both spin channels. As discussed later, the new states at EF arecontributed by the electrons of surface and subsurface atoms.Polarization of electrons at EF is 70% and the exchange splittingof the spin-up and spin-down electronic states is small. The ferro-magnetic order of the bulk is supressed at the surface. In the half-metallic Ge-term GeKCa surface, the surface states are as near EF as0.04 eV. This distance in energy is called a half-metallic gap and is ameasure of the excitation energy for an electron in the top of thevalence band. The narrow half-metallic band gap may be disadvan-tageous from an application point of view, since the spin-up elec-

Energy (eV)

(setat

Sfo

ytisneDlato

T

(b) KCa-term

Fig. 2. The total spin-polarized density of states (DOS) calculated for GeKCa (001)surfaces of (a) Ge-term, and (b) KCa-term. The spin-down DOS values are multipliedby � 1, and the Fermi levels are set to zero.

Energy (eV)

)nips.

Ve/setats(set at

Sf

oytisne

Dl atoT

(b) KCa-term

(a) Sn-term

Fig. 3. The total spin-polarized density of states (DOS) calculated for SnKCa (001)surfaces of (a) Sn-term, and (b) KCa-term. The spin-down DOS values are multipliedby � 1, and the Fermi levels are set to zero.

512 B. Białek et al. / Computational Materials Science 81 (2014) 510–516

trons may be easily excited at operating temperatures, which inmodern electronic devices are often larger than 500 K. However,the position of EF may change because of imperfections or impuri-ties. Therefore, with a careful control of the growth process one cantailor the properties of the GeKCa (001) surface according to spe-cific needs.

Energy (eV)

)nips.Ve/setats(

setatS

foytisne

Ddetcejor

P-mot

A

(a) Ge-term

Fig. 4. Atom-projected DOSs calculated for the GeKCa (001) surface (a) Ge-term and (b) Kset to zero.

The total DOS calculated for the (001) surfaces of SnKCa areshown in Fig. 3. Qualitatively, DOS distribution in the SnKCa sur-faces, either Sn-term or KCa-term, is the same as in the corre-sponding GeKCa surfaces. However, the Sn-term SnKCa surface isat the verge of metallicity with the top of the valence band inthe spin-up electron channel nearly touching the Fermi level. Still,the electrons at EF are completely polarized and the calculated totalmagnetic moment (MM) of the system is integer and equals 10 lB.

3.2. Surface triggered evolution of density of states

Comparing the DOSs contributed by equivalent elements fromsubsequent layers, we can understand changes in the propertiesof the materials due to the broken periodicity. In Fig. 4, we put to-gether the plots of the atom-projected DOSs obtained for the Ge-term and the KCa-term GeKCa. In each panel DOS spectra projectedon the atoms from different layers of the slab are plotted. The DOSsin Fig. 4 are not l-decomposed. In the Ge-term GeKCa surface, thedifferences in DOSs start to appear only in the near-surface region.The occupied spin-up electronic states contributed by the Ge atomin the top layer are more delocalized than those of the Ge atoms inthe other layers. The spin-down electrons are more sensitive tobroken periodicity. The number of occupied spin-down states con-tributed by the Ge (S) atom is reduced nearly to zero. This is fol-lowed by a reduction in number of the states contributed by theK (S � 1) and Ca (S � 1) at EF. In the topmost layer a large exchangesplitting between spin-up and spin-down states results in a verylow number of available states for spin-down electrons of the Ge(S) atom at EF. The changes in the spin-down DOSs contributedfrom metal atoms in the subsurface layer, although less dramatic,mirror the interactions with the electrons of the Ge (S). Thesechanges must be reflected in charge and spin density distributions,which are presented below.

(b) KCa-term

Energy (eV)

Ca-term. The spin-down DOS values are multiplied by � 1, and the Fermi levels are

Energy (eV)

)nips.Ve/setats(

setatS

foytisne

DlacoL

(a) (b)

Energy (eV)

Fig. 5. l-decomposed atom-projected DOSs calculated for the Ge-term GeKCa (001) surface for (a) bulk-like atoms and (b) topmost and subsurface atoms. The spin-down DOSvalues are multiplied by � 1, and the Fermi levels are set to zero.

B. Białek et al. / Computational Materials Science 81 (2014) 510–516 513

From Fig. 4b it is evident that the break down of the half-metal-lic properties of the bulk is due to surface effects. In the Ca (S) andK (S) atoms delocalization of the occupied spin-up states is so largethat they spread over EF and the slab becomes metallic. The spin-up and spin-down DOSs contributed from the K (S) and Ca (S)atoms are nearly symmetric, which indicates demagnetization ofthe atoms. In Fig. 5, l-decomposed densities of states (LDOSs) cal-culated for the atoms in C, S � 5, S � 1, and S layers are shown.The plots show a predominant contribution of Ge p electrons tothe near-EF band structure of the GeKCa. There is 0.48 eV exchangesplitting between the spin-up and spin-down p electron states con-tributed by the Ge (C) atom. The spectra of DOSs contributed by pand d states of the K (S � 5) and Ca (S � 5) atoms reflect the inter-actions between their valence electrons and the strong interactionswith p electrons of the Ge (S). Hence, the pd hybridization isresponsible for the energy splitting. The DOSs calculated for thedeep layers do not change much until the S � 1 layer is reached.The evolved LDOSs are shown in Fig. 5b. At the surface, Ge p elec-trons become more delocalized. The valence band is formed mostlyby p" electron states of Ge. The number of occupied spin-downstates at EF and below is drastically reduced compared with thebulk layers. Similar depletion in the number of spin-down statesis noticed at the K (S � 1) and Ca (S � 1) sites.

Delocalization of the electron states is even stronger in the KCa-term surfaces. In Fig. 6, the calculated LDOSs are shown as obtainedfor the Ge, K, and Ca atoms of bulk-like, C and S-4, layers and oftopmost and subsurface, S � 1 and S, layers. In the KCa-term GeKCasurface, the metal atoms of the S layer form a compact structure.

The valence electrons not engaged in forming a bond with Geatoms become strongly delocalized, resembling free electrons ina simple metal. The strong delocalization of the K (S) and Ca (S)electrons results in the smoothing of the LDOSs curves in a wideenergy range around EF. The electrons of the Ge (S � 1) respondto the changes. Although there is still a distinguishable peak inthe DOS contributed by p electrons of Ge (S), delocalization ofthe states is large enough so the band crosses EF. All the atoms inthe two respective topmost layers are strongly demagnetized.

There are many similarities between the electronic properties ofthe GeKCa and SnKCa surfaces. Especially KCa-term surfaces seemto be electronically insensitive to the nature of the metalloids intheir structure. The DOS spectra calculated for the KCa-term SnKCasurface are nearly identical with those calculated for the GeKCasurface. In the Sn-term SnKCa, the differences between the surfaceand the Ge-term GeKCa one are visible in the part of the electronicstructure contributed by the atoms of the two respective topmostlayers. The valence p electrons of the Sn (S) atom are more weaklybound than those of the Ge (S) atom in the GeKCa. Therefore, at theboundary they are more likely to be delocalized. The number ofstates per energy unit in the valence band, formed mostly byspin-up electrons, is decreased, and the top of the band touchesthe Fermi level. Because of the interactions between the Sn (S) pelectrons and K (S � 1) p and d electrons, the contribution of thelatter to the valence band follows the changes in DOS projectedon the Sn (S). The evolution of spin-down DOSs calculated for theSnKCa surface is also qualitatively very similar to that discussedfor the GeKCa surfaces.

Energy (eV)

)nips.Ve/seta ts(

set atS

foyt isn e

Dlac oL

(a) (b)

Energy (eV)

Fig. 6. l-decomposed atom-projected DOSs calculated for the KCa-term GeKCa (001) surface for (a) bulk-like atoms and (b) topmost and subsurface atoms. The spin-downDOS values are multiplied by � 1, and the Fermi levels are set to zero.

Table 1l-Decomposed electrons within muffin-tin spheres on the atoms in the surface,subsurface, and center layers of the (001) surfaces of Ge-term GeKCa and Sn-termSnKCa together with the calculated values of the total magnetic moments (MMs).

Atom s "/; p "/; d "/; Total "/; MM (lB)

Ge-term GeKCaGe (C) 0.66/0.66 0.87/0.49 1.53/1.15 0.38Ge (S � 2) 0.66/0.66 0.87/0.49 1.53/1.15 0.38Ge (S) 0.70/0.70 1.05/0.09 1.75/0.78 0.97K (S � 5) 0.15/0.16 0.19/0.12 0.16/0.11 0.54/0.41 0.12K (S � 1) 0.16/0.14 0.20/0.09 0.18/0.07 0.59/0.32 0.27Ca (S � 5) 0.12/0.13 0.10/0.06 0.18/0.11 0.40/0.31 0.10Ca (S � 1) 0.13/0.13 0.10/0.04 0.22/0.06 0.46/0.24 0.22

Sn-term SnKCaSn (C) 0.58/0.58 0.70/0.42 1.28/1.00 0.28Sn (S � 2) 0.58/0.58 0.70/0.39 1.28/0.97 0.31Sn (S) 0.62/0.62 0.83/0.07 1.44/0.69 0.75K (S � 5) 0.13/0.14 0.16/0.11 0.13/0.08 0.45/0.35 0.10K (S � 1) 0.16/0.14 0.20/0.09 0.15/0.05 0.59/0.32 0.27Ca (S � 5) 0.12/0.13 0.09/0.06 0.17/0.09 0.38/0.28 0.10Ca (S � 1) 0.13/0.13 0.10/0.04 0.20/0.05 0.43/0.22 0.21

514 B. Białek et al. / Computational Materials Science 81 (2014) 510–516

3.3. The charge and the spin distributions at the surfaces

The l � decomposed electronic charges contributed by bothspin-up and spin-down electrons within muffin-tin spheres onthe atoms in C, S � 5, S � 2, S � 1, and S layers of the Ge-term GeK-Ca and the Sn-term SnKCa are collected in Table 1, and the chargescalculated for the KCa-term surfaces are collected in Table 2. Thecalculated values of the total MMs are also included in the tables.The valence electronic structures of Ge, Sn, K, and Ca are 4s2p2,5s2p2, 4s1, and 4s2, respectively. Since Ge and Sn atoms have com-pletely occupied d shells, there is no contribution to the chargedensity from their d electrons. In K and Ca atoms on the otherhand, the lowest in energy occupied orbital is 4s and the distancein energy to 3d and 4p is not large, so both 4p and 3d orbitals arebeing populated when the atoms are in a solid. In the Ge-termGeKCa and Sn-term SnKca surfaces, the s electrons of Ge and Snatoms are not polarized, no matter how near the surface the atomsare. The p electrons, however, become polarized, which contributesto the total MM calculated for Ge and Sn atoms in the slabs. In theGe-term GeKCa, the atoms in the deep layers have the properties ofthe atoms in the bulk which remain unaltered up to S � 2 layer.The calculated values of the MM on the Ge (C) atom in the Ge-termsurface is 0.38lB, exactly the value calculated by us for the half-Heusler GeKCa bulk. As shown in Fig. 5, due to the surface effectsthe number of occupied spin-down states is largely reduced inthe Ge (S) atom causing changes in distribution of electrons be-tween spin-up and spin-down states. Consequently, the numberof s electrons in the MT sphere of the Ge (S) atom is larger than thatin the other Ge atoms. Also, the population of p" electrons is in-creased. In contrast, 80% of the p; electrons of the Ge (S) atomare drained into other areas within the system leaving the Ge (S)

atom with MM of 0.97lB. Other atoms in the system are also polar-ized. The polarization of K is increased from 0.12lB in the bulk to0.27lB in the S � 1 layer. The electrons of Ca atoms in the S � 1layer become polarized, too. A transfer of electrons from spin-down to spin-up states is noticeable in K and Ca p and d orbitals,as well. In the Sn-term SnKCa, the picture is similar: s electronsare not polarized, but their number in the S layer is greater thanin the deeper layers; p electrons are polarized and the p; electronswithin the MT of the Sn (S) atom outnumber the electrons of Snatoms in other layers. Therefore, MM on the Sn (S) atom is0.47lB larger than the MM value on Sn (C) atom.

Table 2l-Decomposed electrons within muffin-tin spheres on the atoms in the surface,subsurface, and center layers of the (0 01) surfaces of KCa-term GeKCa and SnKCatogether with the calculated values of the total magnetic moments (MMs).

Atom s "/; p "/; d "/; Total "/; MM (lB)

KCa-term GeKCaGe (S � 5) 0.66/0.66 0.88/0.48 1.54/1.14 0.40Ge (S � 1) 0.66/0.66 0.73/0.64 1.39/1.30 0.09K (C) 0.15/0.16 0.19/0.12 0.16/0.11 0.54/0.41 0.13K (S � 2) 0.15/0.15 0.17/0.13 0.15/0.12 0.51/0.43 0.08K (S) 0.15/0.16 0.12/0.11 0.10/0.08 0.38/0.36 0.02Ca (C) 0.12/0.13 0.10/0.06 0.18/0.11 0.40/0.30 0.10Ca (S � 2) 0.12/0.12 0.09/0.07 0.16/0.12 0.38/0.32 0.06Ca (S) 0.15/0.15 0.06/0.05 0.13/0.11 0.35/0.31 0.04

KCa-term SnKCaSn (S � 5) 0.58/0.58 0.70/0.38 1.28/0.97 0.31Sn (S � 1) 0.58/0.58 0.58/0.53 1.16/1.10 0.05K (C) 0.14/0.14 0.16/0.10 0.13/0.08 0.45/0.34 0.11K (S � 2) 0.13/0.14 0.15/0.12 0.12/0.09 0.43/0.36 0.06K (S) 0.14/0.14 0.10/0.10 0.08/0.07 0.32/0.31 0.01Ca (C) 0.12/0.13 0.09/0.06 0.16/0.09 0.38/0.27 0.11Ca (S � 2) 0.12/0.12 0.08/0.07 0.15/0.11 0.36/0.30 0.06Ca (S) 0.15/0.15 0.06/0.05 0.12/0.10 0.33/0.30 0.03

B. Białek et al. / Computational Materials Science 81 (2014) 510–516 515

The charge distributions within the MT spheres of metal atomsin the Ge-term GeKCa and Sn-term SnKCa slabs are similar. Thepolarization of the K and Ca atoms comes from populating p andd orbitals due to the interactions with the electrons of the Ge(Sn) atoms. Even though there are two valence electrons per Caatom and only one valence electron per K atom, the total chargeon K atoms in the GeKCa and SnKCa surfaces is slightly larger thanthe population of electrons in the Ca valence orbitals. This is due toa smaller electronegativity of K compared with Ca. The s electronsof the K atoms are more easily donated to Ge (or Sn) orbitals of aproper symmetry. However, due to a bond creation with the car-bon group atom, some of the electronic charge density is movedback to the d orbitals of the alkali metal. Therefore, the populationon d orbitals of the K atoms is noticeably larger than the popula-tion on d orbitals of the Ca atoms.

In Table 2, l � decomposed electrons within MT spheres of thechosen atoms of the KCa-term surfaces are presented together withthe calculated values of MMs. The most striking property of theatoms in the S and S � 1 layers is a large reduction in their MMscompared to the atoms in the bulk. The values of the MMs calcu-lated for the atoms in the deep layers of the KCa-term surfacesare almost the same as those calculated for the inner layers inGe(Sn)-term surfaces. However, in the Ge-term surface MM onGe (S) atom is increased to 0.97lB, while in the KCa-term surfaceMM on the Ge (S � 1) atom is reduced to 0.09lB. The atoms ofthe S layer of the KCa-term surfaces are also demagnetized.

Two effects may be responsible for this behavior. First, there isthe strong delocalization of the states at the top layer of the KCa-term surface due to a spread of electrons into the vacuum region.Second, the nature of bonding between the metal and non-metalatoms changes at the boundary. For example, the total number ofelectrons within MT spheres of the Ge (S) and K (S � 1) in theGe-term surface are 2.53 and 0.91, respectively, while in theKCa-term surface, they are 2.69 and 0.63 within MT spheres ofthe Ge (S � 1) and K (S). For a comparison, in the deeper layersthe number of electrons within MT spheres of Ge and K does notdepend on surface termination. The differences indicate that inthe bulk and in the Ge(Sn)-term surfaces the bonding betweenthe metaloids and metal atoms is polar covalent, while at theboundaries of the surfaces terminated with KCa layers, the bondis in a large degree ionic. A covalent bond between simple metalatoms and carbon atom was also predicted in half-Heusler CCsBacompound [22]. Since the electronegativity of Ge is slightly larger

than Sn, there is greater difference between the population of elec-trons in the Ge and K (Ca) atoms in the GeKCa surface than be-tween the population of electrons in the Sn and K (Ca) atoms inthe SnKCa surface. Since at the surface there is a greater tendencyfor the electrons to be donated from K (Ca) atoms to the Ge (Sn)atoms, in the latter the spin-down states become populated to alarger degree, which causes the reduction of the magnetic moment.

4. Conclusions

We investigated the electronic and magnetic properties of(001) surfaces of GeKCa and SnKCa in the half-Heusler structure.Two terminations of the surfaces for both materials were consid-ered: Ge(Sn)-term and KCa-term. Although the two solids arehalf-metallic ferromagnets, we found that their (001) surfaces re-tain the property only when terminated with a layer of metalloidatoms. The surfaces terminated with a layer of K and Ca atomswere found to have metallic properties. The magnetic propertiesof the systems were enhanced at the half-metallic surfaces. Inthe Ge-term GeKCa, the value of the magnetic moment on the Geatom increased from 0.38lB in the bulk to 0.97lB at the topmostlayer. The magnetic moments of the metal atoms were also in-creased from 0.12lB and 0.10lB in the bulk to 0.27lB and 0.22lB

at the subsurface layer for the K and Ca atoms, respectively. Inthe Sn-term SnKCa surface the top of the conduction band in thespin-up channel is at the edge of the Fermi level, so the half-met-allicity of the surface may be unstable. The surface, however,exhibits magnetic properties similar to the Ge-term GeKCa. Thecalculated value of the magnetic moment on the Sn atom at thesurface is 0.75lB, and the magnetic moments on K and Ca atomsin the subsurface layer are nearly the same as those calculatedfor the atoms in the Ge-term GeKCa.

The surfaces terminated with a layer of metal atoms had metal-lic properties. The transition from half-metallic properties at thebulk to metallic properties of the surface was related to a strongdelocalization of electrons at the surfaces. In result, the magnetismof the atoms in the surface and subsurface layers was dramaticallyreduced; the magnetic moment on the Ge (Sn) atoms at the sub-surface layer was only 0.09 (0.05)lB and the magnetic momentson the K and Ca atoms at the topmost layer of Ge(Sn)KCa were0.02 (0.01) and 0.04 (0.03)lB.

GeKCa and SnKCa in their half-Heusler structure are possiblecandidates for application to spintronics. However, if the materialswere used in spintronic devices in the form of thin films, a specialcaution is necessary because of a strong dependence of their prop-erties on surface effects.

Acknowledgement

This work was supported by the Inha University research fund.

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