Table 2 Calculated lattice constants, formation energies, magnetic moments and energy differences between possible structures of quaternary CoX′Y′Si compounds.

From: New quaternary half-metallic ferromagnets with large Curie temperatures

Systems (Type-I)

Lattice constant (Å)

Formation energy (eV)

ΔE (eV/f.u.)

ΔE′ (eV/f.u.)

Structure type

M (μ B /f.u.)

CoYMnSi

6.30

−1.94

0.39

0.05

TI

4.55

CoZrMnSi

5.96

−2.23

1.14

0.82

TI

0.00

CoNbMnSi

5.85

−1.74

0.69

0.85

TI

1.00

CoMoMnSi

5.84

−1.90

−0.21

0.67

TII

2.33

CoTcMnSi

5.79

−3.14

−0.89

0.84

TII

3.00

CoRuMnSi

5.79

−2.70

−1.38

0.85

TII

4.00

CoRhMnSi

5.83 (5.8449)

−2.82

−1.46

0.81

TII

5.00 (5.0049)

CoPdMnSi

5.90

−2.06

−0.67

0.51

TII

4.90

CoAgMnSi

5.96

−0.38

0.05

0.28

TI

3.53

CoYFeSi

6.08

−2.14

0.91

0.81

TI

0.00

CoZrFeSi

5.96 (5.9721)

−3.33

1.19

1.24

TI

1.00 (1.0021)

CoNbFeSi

5.88

−2.31

0.77

1.06

TI

1.99

CoMoFeSi

5.84

−1.42

−0.05

0.39

TII

2.83

CoTcFeSi

5.80

−2.65

−0.67

0.49

TII

3.89

CoRuFeSi

5.78 (5.77314)

−3.12

−1.02

0.52

TII

4.66 (4.8014)

CoRhFeSi

5.80

−2.10

−0.78

0.21

TII

4.90

CoPdFeSi

5.86

−1.48

−0.23

0.06

TII

4.00

CoAgFeSi

5.88

−0.10

0.09

0.18

TI

2.71

  1. The energy differences between Type-II (T II ) and Type-I (T I ) structures are given by ΔE = \({{\rm{E}}}_{{{\rm{T}}}_{{\rm{II}}}}\) − \({{\rm{E}}}_{{{\rm{T}}}_{{\rm{I}}}}\). A positive ΔE implies T I as the ground state. The energy differences between Type-III (T III ) and Type-I or Type-II structures are given by ΔE′ = \({{\rm{E}}}_{{{\rm{T}}}_{{\rm{III}}}}\) − \({{\rm{E}}}_{{{\rm{T}}}_{{\rm{I}}}/{{\rm{T}}}_{{\rm{II}}}}\). For the systems which crystallise in Type-II (TII), ΔE′ = \({{\rm{E}}}_{{{\rm{T}}}_{{\rm{III}}}}\) − \({{\rm{E}}}_{{{\rm{T}}}_{{\rm{II}}}}\); for the systems which crystallise in Type-I (TI), ΔE′ = \({{\rm{E}}}_{{{\rm{T}}}_{{\rm{III}}}}\) − \({{\rm{E}}}_{{{\rm{T}}}_{{\rm{I}}}}\).