Fig. 1.
Three crystalline structures of CoNiMnSi.
Fig. 2.
Calculated total energy versus volume for CoNiMnSi.
Table 1.
Calculated equilibrium lattice parameters a0 (Å), bulk modulus B0 (GPa), its pressure derivative B′0 (GPa) and equilibrium energy E0 (Ryd) for the CoNiMnSi compound in the different structures considered in this work.
| Material | Structure | a0(Å) | B0 (GPa) | B′ | E0 (Ryd) |
|---|---|---|---|---|---|
| CoNiMnSi | Hg2CuTi-type | 5.6256 | 179.51 | 3.50 | −8726.0826 |
| Cu2MnAl-type | 5.6810 | 187.89 | 5.06 | −8726.1164 | |
| LiMgPbSb-type | 5.6787 | 187.6 | 4.81 | −8726.1177 | |
| Co2MnSi | Cu2MnAl-type | 5.633a | 212.8a | 4.68a | – |
| 5.634bb | 226bb | – | – | ||
| 5.639cc | 214cc | 4.674cc | – |
a [4]
a [4]
a [4]
bb [25]
bb [25]
cc [26]
cc [26]
cc [26]
Table 2.
Calculated single crystal elastic constants Cij (GPa), polycrystalline elastic modulus (GPa), shear modulus G (GPa), Young’s modulus E (GPa), Poisson’s ratio ν and shear anisotropic factor A for the CoNiMnSi compound.
| Material | C11 | C12 | C44 | G | E | ν | A |
|---|---|---|---|---|---|---|---|
| CoNiMnSi | 425.75 | 68.52 | 172.49 | 174.94 | 400.37 | 0.144 | 0.966 |
| Co2MnSi | 311.16a | 164.75a | 153.26a | – | – | – | – |
| 316bc | 174bc | 143bc |
a [4]
a [4]
a [4]
b [27]
c [28]
b [27]
c [28]
b [27]
c [28]
Table 3.
Calculated longitudinal, transverse and average sound velocity (v1, vt, and vm, in ms−1) and Debye temperature (θD, K) for the CoNiMnSi compound.
| (T = 0) Material | VS | V1 | Vm | θD |
|---|---|---|---|---|
| (P = 0) | [m/s] | [m/s] | [m/s] | [K] |
| CoNiMnSi | 4902.70 | 7604.25 | 5381.81 | 445.20 |
Fig. 3.
Total and partial densities of states (TDOS, PDOS) for CoNiMnSi in its stable structure types calculated using the GGA approximation.
Fig. 4.
Total and partial densities of states (TDOS, PDOS) for CoNiMnSi in its stable structure types calculated using the GGA + U approximation.
Fig. 5.
Charge density distribution in the (1 1 0) plane of the CoNiMnSi quaternary Heusler compound calculated using the GGA approximation.
Fig. 6.
Charge density distribution in the (1 1 0) plane of the CoNiMnSi quaternary Heusler compound calculated using the GGA + U approximation.
Table 4.
Total, interstitial and local magnetic moments.
| Compounds | μTotal (μB/Cell) | μinterstitial (μB/Cell) | μatomic (μB/Cell) | ||||
|---|---|---|---|---|---|---|---|
| Co1 | Ni/Co2 | Mn | Si | ||||
| CoNiMnSi | GGA | 4.69 | 0.038 | 1.036 | 0.458 | 3.18 | 0.022 0.038 |
| GGA+U | 5.99 | −0.03377 | 1.613 | 0.567 | 3.89 | ||
| Co2MnSi | 5.00abcd | – | – | – | – | – |
a [4]
b [25]
c [29]
d [26]
Table 5.
Calculated spin-polarization, exchange energy (∆E(FM−AFM), and Curie temperature (Tc).
| Compounds | ∆E(FM–AFM) (mRy/Atom) | TC (K) | Spin polarization ratio (%) |
|---|---|---|---|
| CoNiMnSi | −0.011 | 871.89 GGA | 56 % GGA |
| 1107.19 GGA + U | 100 % GGA+U | ||
| Co2MnSi | 928a | 100 % | |
| 985bc |
a [4]
b [27]
c [28]
Fig. 7.
The antiferromagnetic (AFM) configuration of CoNiMnSi.