Table 1 Calculated formation energy (\(E_f\)) in eV, magnetic energy differences: \(\Delta E_1 = E_{FM}-E_{FiM-I}\), \(\Delta E_2 = E_{FM}-E_{FiM-II}\), \(\Delta E_3 = E_{FM}-E_{FiM-III}\), and \(\Delta E_4 = E_{FM}-E_{FiM-IV}\) in meV, FiM ordering temperature (\(T_{C1}\)) in K, and energy band gap (\(E_g\)) in eV for \(\text {Lu}_2 \text {Ni}_{0.5} \text {TM}_{0.5} \text {IrO}_6\) (TM = Cr, Mn, and Fe) double perovskite oxides.

From: Insulator-to-half metal transition and enhancement of structural distortions in \(\text {Lu}_2 \text {NiIrO}_6\) double perovskite oxide via hole-doping

TM

\(E_f\)

\(\Delta E_1\)

\(\Delta E_2\)

\(\Delta E_3\)

\(\Delta E_4\)

\(T_{C1}\)

\(E_g\)

\(m_{tot.}\)/u.c.

\(m_{tot.}\)/f.u.

\(m_{Ni}\)

\(m_{TM}\)

\(m_{Ir1}\)

\(m_{Ir2}\)

\(m_{O1}\)

\(m_{O2}\)

\(m_{O3}\)

Undop.

28.3

25.5

17.8

17.5

219

0.20

1.90

0.95

1.66

1.66

− 0.54

− 0.54

− 0.01

− 0.03

− 0.02

Cr

− 0.52

37.7

35.5

33.3

31.9

292

HM

4.00

2.00

1.66

2.66

− 0.09

− 0.39

− 0.09

− 0.39

− 0.03

Mn

− 1.21

33.8

31.2

30.5

28.7

261

HM

5.00

2.50

1.69

3.80

− 0.16

− 0.41

− 0.16

− 0.41

− 0.02

Fe

− 1.65

30.5

29.2

28. 9

− 13.8

236

HM

6.00

3.00

1.67

4.11

− 0.05

− 0.42

− 0.06

− 0.42

− 0.09

  1. The “−” and “\(+\)” signs in \(E_f\) and \(\Delta E\) show that doped crystal structure and FiM spin ordering are energetically stable, respectively. Moreover, “ HM” in the \(E_g\) column represents the half-metallic nature of the system along with total spin moments per unit cell (\(m_{tot.}\)/u.c.) as well as per formula unit (\(m_{tot.}\)/f.u.) and partial spin moments on Ni (\(m_{Ni}\)), TM (\(m_{TM}\)), Ir (\(m_{Ir}\)), and O (\(m_{O}\)) ions.