Group 2: 6B/7B transition metal pair with Co, Cu and Ni

Fig.4.6

The Group 2 HM compounds Sr2BB′O6 of BB′ ion pairs on the periodic table.

Sr2BB′O6 (B = Co, Cu, and Ni; B′ = Mo, W, Tc, and Re, and BB′=FeTc)

Fig.4.6 shows the cyclical behavior of Group 2 HM compounds Sr2BB′O6 of BB′

ion pairs in the periodic table. Each pairs with the same color, for example, the red frame Co(Ni) pairs with the same color 6B and 7B element. And the blue frame Cu pairs with Tc and Re. Combining with the previous research, for the pairs of B=Cr and Fe (yellow frame) can be also classified in Group 2 HM compounds where our calculations agrees with previous experimental and theoretical investigations[3, 5-7, 16-18]. Thus, in this paper, we focus on B = Co, Cu, and Ni and no longer discuss the series of B=Cr and Fe, except Sr2FeTcO6, which has been less discussed in previous work.

During the self-consistent process, first, Sr2CuWO6 and Sr2NiTcO6 remain in their ideal cubic structure ( ) and others relax into the tetragonal structure ( ).

(Table 4.4) Second, the initial FM and FiM states converge into one of these states. For example, compounds of B = Cu converge into the FM state whereas compounds of B = Co converge into the FiM state. In the NM state, no spin polarization can be observed; thus, an absence of magnetic properties is obtained. Calculations that consider spin polarization are always more stable than those that do not. A self-consistent process with high convergence criteria is also performed to guarantee the accuracy of the calculation results. For brevity, we use [BB′] to indicate the chemical formula of the perovskites. For example, [FeTc] represents Sr2FeTcO6.

Table 4.4 Structural parameters in the fully optimized structure ( , no.139 and 3

Fm m I4 /mmm

4 /

I mmm

, no.255) where Sr(x,y,z) = (0, 0.5, 0.75), B (x,y,z) = (0, 0, 0), B′(x,y,z) = (0, 0, 0.5), favorable than their AF states in the GGA scheme (Table 4.5). The results match those of a previous study on [CoMo] [54-56], [CoRe] [54], [CoW][57, 58] and [NiRe][59]. The AF states of [CoTc] and [CoRe] are more stable than their FiM states, with energies of 93.7 and 76.4 meV/f.u., respectively. The energy differences of [CuMo], [CuW], [NiMo], [NiW], and [NiTc] are extremely small at –2.2, –1.3, 13.0, 3.8, and 13.7 meV, respectively; that is, the AF and FiM states in these compounds degenerate and can coexist. In the GGA+U scheme, the AF states of [CoMo] and [CoRe] are more stable than their FiM states, with an energy difference in the order of 10² meV/f.u. More specifically, the energy differences between the AF and FiM states of [CoMo], and [CoRe] are 596.1, and 61.9 meV/f.u., respectively. The energy difference between the AF and FiM states of [CoTc] in the GGA+U scheme is about 2.2 meV, which implies that the FM state coexists with the AF state. For the rest of the compounds in the GGA+U scheme, the stable magnetic state resulting from the energy difference remains the same as in the GGA scheme. The value of U eventually depends on the experiment where it only can be evaluated by an reasonable range of U, where different value of U can

Table 4.5

Calculated physical properties of possible HM of Sr2BB′O6 (B=Co, Cu and Ni; M=Mo, W, Tc and Re; and BB′=FeTc) in double perovskites structure in the full structural be observed through the band gaps at the spin-up channel and the integer total magnetic moments (mtot) listed in Table 4.5. [NiMo] and [NiW] appear to be ferromagnetic insulators (FM-Is), having band gaps at both spin states, but retain magnetic properties.

The valence electron configurations of Mo and W, as well as Tc and Re, are similar to

each other; thus, we only present the DOS of B′ = Mo and Tc in Fig. 4.7~4.8

Fig. 4.7 Calculated total, spin, and site-decomposed DOS of [FeTc], [CoMo], and [CoTc]

in the GGA scheme.

For B=Co and [FeTc], the hybridization between the Co(Fe) 3d and O 2p orbitals occurs mainly in the energy region from –7.0 eV to –1.0 eV in the spin-up channel and from –2.0 eV to 2.0 eV in the spin-down channel. Strong spin-splitting of the Co(Fe) eg

orbital at the EF yields half-metallicity. Around the EF, the 4(5)d orbital of B′ (Mo, W, Tc, and Re) hybridizes with the O 2p orbital in the energy region from –2.0 eV to 2.0 eV in the spin-down channel, where the Co(Fe) orbital extends through double-exchange interactions. This interaction constructs a bridge of Co(Fe)3d–O2p-B′4(5)d for the conductance of the spin-down electron. Based on the calculated electron populations, the following electron configurations are obtained: [FeTc] (Fe³⁺(3d⁵:t2g3eg2) at S = 5/2, Tc⁵⁺(4d²:t2g2eg0) at S = -1), [Co-Mo/W] (Co³⁺(3d⁶:t2g4eg2) at S = 2, Mo/W⁵⁺(4/5d¹:t2g1eg0) at S = -1/2), [Co-Tc/Re] (Co³⁺(3d⁶:t2g4eg2) at S = 2, Tc/Re⁵⁺(4/5d²:t2g2eg0) at S = -1).

The mechanisms of FiM stabilization and half-metallicity of compounds of B = Co and [FeTc] can be described by p-d hybridization, as proposed by Terakura et al. [63].

When a NM element is located between magnetic elements, such as Fe, the fully spin-polarized magnetic elements are denoted as d-states. By contrast, NM elements between spin-split d-states are denoted as the p-state as the EF goes through the p band.

During p-d hybridization, the d-state pushes the p-state upward (downward) at the spin-up (spin-down) channel. The electron population switches spin states, inducing the NM elements to contribute negative moments and stabilize the FiM state to achieve a common EF value in both spin states. If p-d hybridization is adequately strong, the p-state can be pushed above the EF to the conduction band at the spin-up channel. During double-exchange, the band is extended to the spin-down channel with the EF, producing half-metallicity in the FiM states. In the current work, compounds of B = Co and Fe represent the spin-split d-state of magnetic elements, while those of B′ = Mo (W) and Tc (Re) represent the p-state of the NM elements.

Fig. 4.8 Calculated total, spin, and site-decomposed DOS of [CuMo], [NiMo], and [NiTc]

in the GGA scheme

For compounds of B = Cu the DOS of the spin-up and spin-down channels are symmetrical, except for the orbitals around the E (Fig. 4). The spin-splitting of the Cu t

band with the band gap at the spin-up channel is the main reason causing the half-metallicity. The hybridization between Cu 3d and O 2p orbitals occurs mainly in the energy region from –7.0 eV to 1.0 eV. The double-exchange of Cu3d–O2p-Mo(W)4(5)d

bonding induces the spin-splitting of the Mo (W) t2g orbital near the Fermi level, which give a weak local magnetic moment for Mo (W) under 0.05µB and the total effect causes the half-metallicity. Based on the calculated electron population, the following electron configurations are obtained: [CuMo] (Cu²⁺(3d⁹:t2g6eg3) at S = 1/2, Mo⁶⁺(4d⁰:t2g0eg0) at S = 0) and [CuW] (Cu²⁺(3d⁹:t2g6eg3) at S = 1/2, W⁶⁺(5d⁰:t2g0eg0) at S = 0).

For compounds of B = Ni, [NiMo] and [NiW] appear to be FM-Is, while [NiTc]

and [NiRe] are FiM-HM. For compounds of B′ = Mo and W (Fig. 4.8), hybridization between the Ni 3d and O 2p orbitals occurs mainly in the energy region from –7.0 eV to 0.0 eV in the spin-up channel, as well as –7.0 eV to -1.0 eV and 1.0 eV to 2.0 eV in the spin-down channel. In the spin-up channel, the Ni t2g band drops along the EF, creating a band gap of 1.03 (1.81) eV with the Mo (W) eg orbital at the conduction band. In the spin-down channel, the Ni t2g band shows large spin-splitting and is pushed up above the EF, with the Ni eg orbital in the valence band; a band gap of 0.78 (0.93) eV can be observed. Thus, with two energy gaps at both sides of the spin state channels, [NiMo] and [NiW] appear to be FM-Is. Based on the calculated electron population, the following electron configurations are obtained: (Ni²⁺(3d⁸:t2g6eg2) at S = 1, Mo/W⁶⁺(3/4d⁰:t2g0eg0) at S = 0). According to the Goodenough-Kanamori rule [64-66], which states that the superexchange between two transition metal cations is ferromagnetic if the electron transfer is from a half-filled to an empty or a filled to a half-filled allows ferromagnetic potential exchange and involve the restriction of Pauli exclusion principle. For the High-Spin(HS)/Low-Spin(LS) state, electrons transfer from the half-filled HS Ni eg states to the Mo (W) via the O atoms in between, gives to a ferromagnetic nearest-neighbor interaction.

Given that the population of valence electrons of Tc (Re) is greater than that of Mo (W) by one, the EF shifts to a higher energy level, crossing the spin-down state of the Tc (Re) eg band. Only the band gap of the spin-up channel survives, yielding a HM compound. The valence electron population also affects the mtot; the difference in mtot of each compound of 1µB results from the difference of one valence electron between Mo (W) and Tc (Re). Based on the calculated electron population, the following electron

configurations are obtained: (Ni³⁺(3d⁷:t2g5eg2) at S = 3/2, Tc⁵⁺(4d²:t2g2eg0) at S = -1), Ni³⁺(3d⁷:t2g5eg2) at S = 3/2, Re⁵⁺(5d²:t2g2eg0) at S = -1), respectively.

4.3.3. Exchange Correlation Correction

Fig. 4.9 Calculated total, spin, and site-decomposed DOS of [FeTc], [CoMo], [CoTc], [CuMo], [NiMo], and [NiTc] in the GGA+U scheme.

When applying electron correlation correction (GGA+U), the U value is often based on experimental results; therefore, obtaining appropriate values of U to predict new materials is not easy. Adding an exchange correlation correction (GGA+U) generally enhances the localization of d orbitals and pushes unoccupied states into a higher energy level, thus increasing the energy gap and local magnetic moment. Fig. 4.9 shows DOS in the GGA+U scheme. All of the bands are strongly localized such that they accumulate at a narrow energy region. The spin-split effect in the t2g orbital of Fe (Co) grows larger such that the spin-up state is located in the energy region from –8 eV to –7 eV and the spin-down state is pushed up to a higher energy level. Thus, for example, the local magnetic moment of [FeTc] increases from –3.76µ to –4.19µ and its band gap increases

from 0.57 eV to 2.16 eV. Other compounds show the same behavior (Table 4.5).

The electron correlation correction affects the Fe (Co) band more than the Cu t2g

band. The main peak of the Cu (Ni) t2g spin-up band is pushed down to the energy region from –7 eV to –6 eV, while the Cu t2g spin-down band remains at the same location. By contrast, the Ni t2g spin-down band is pushed up to a higher energy level, similar to Fe (Co). Thus, the local magnetic moment of Cu is only slightly changed considering that the t2g spin-up band is always in the valence band (Table 4.5). The local magnetic moments of Ni increase from 1.56µB to 1.73µB, 1.58µB to 1.75µB, 1.43µB to 1.72µB, and 1.39µB to 1.75µB in [NiMo], [NiW], [NiTc], and [NiRe], respectively. These results are similar to those of Fe (Co). As the Mo (Tc) t2g orbital becomes more localized and is pushed up to a higher energy level, the band gaps of [CuMo], [CuW], [NiTc], and [NiTe]

widen, as do both spin states in [NiMo] and [NiW]. These results are shown in Table 4.5.

Fig. 4.10 The double exchange interaction configuration and schematic diagram of the DOS.

According to the electronic configuration and DOS, we suggest that the double exchange interaction plays an important role in these HM materials and magnetism in these materials. Fig.4.10 (a)~(e) shows the double exchange interaction configuration of the HM materials of Sr2BB′O6 (B = Co, Cu, and Ni; B′ = Mo and W). Except for Sr2NiMoO6 and Sr2NiWO6 where they are FM-Is and the super exchange is the main mechanism of the system. And with B′ = Tc and Re are similar to Mo and W where they had one additional valance electron than Mo and W. From (a), (b) and (c), as the number of the element increase, the valance election gains that fills the spin-up d orbital that can be observed by the total magnetic moment. The conducting spin-down channel refers to the double exchange interaction via Mo/W↓d-O↓2p-B↓d bonds. From (d), the Sr2NiMoO6

follows the GKA super exchange rule that the Ni eg orbital tend to be half-filled and t2g

orbital tend to be filled, thus, the valance electron of Mo(W) moved to Ni that makes the

d orbital of Mo(W) empty. From (e), Cu has one additional valance electron than Ni that breaks the super exchange interaction, which take the whole system back to double exchange. Form (f), as the number of the B element increases, the orbital energy decreases; that is, the density of the deg states (red peak) is shifted deep into the valence band. For B=Ni, the eg orbital is under the Fermi level that shows the compound to be a insulator; For B=Cu, although the eg orbital is under the Fermi level, but the the Fermi level crosses the spin polarized t2g band making the compound HM.