Structural stability, electronic structure and magnetic properties of the new hypothetical half-metallic ferromagnetic full-Heusler alloy CoNiMnSi

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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	311.16 [4]	164.75 [4]	153.26 [4]	–	–	–	–
	316 [27] [28]	174 [27] [28]	143 [27] [28]

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	5.633 [4]	212.8 [4]	4.68 [4]	–
		5.634b [25]	226b [25]	–	–
		5.639c [26]	214c [26]	4.674c [26]	–

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		928 [4]	100 %
		985 [27] [28]

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

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		5.00 [4] [25] [29] [26]	–	–	–	–	–