Electronic and Magnetic Properties of 5d1, 5d2, and 5d3 Double

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Electronic and Magnetic Properties of 5d1, 5d2, and 5d3 Double Perovskites Ba2MOsO6 (M = K, Ca, and Sc): Ab Initio Study Min Liu,†,‡ Cui-E Hu,*,§ and Xiang-Rong Chen*,† †

Institute of Atomic and Molecular Physics, College of Physical Science and Technology, Sichuan University, Chengdu 610064, China Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China § College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 400047, China ‡

ABSTRACT: We perform detailed investigations on the electronic and magnetic properties in double perovskites Ba2MOsO6 (M = K, Ca, and Sc), with formal valences of Os7+ (5d1), Os6+ (5d2), and Os5+ (5d3), respectively, using first-principles calculations. To understand the effects of Coulomb interaction (U), spin−orbit coupling (SOC), and magnetic order, we carry out different calculations within density functional theory. It is shown that SOC and U energy not only provide the magneto crystalline anisotropies but also significantly affect the size of the local moments and the magnetic structures in these compounds. The electronic configuration of 5d1 and 5d2 of Os in Ba2MOsO6 (M = K and Ca) have the metal−insulator transition (MIT) as the direction of the local moment changes, while the electronic structure of half-filled 5d3 orbitals of Os in Ba2ScOsO6 is insulator, independent of the local moment direction. Our results indicate that both SOC and U interactions are necessary in enlarging the band gaps and putting these compounds into the MIT correlated insulators. Os5+ (5d3) system, Sr2CrOsO6 is a semimetallic ferrimagnet.10 However, La2NaOsO6, also an Os5+ (5d3) system, is observed highly distorted due to incompatible radii.19 We here consider the 5d1, 5d2, and 5d3 cases of Ba2MOsO6 (M = K, Ca, and Sc). Ba2CaOsO6 has been investigated previously,20 but Ba2KOsO6 and Ba2ScOsO6 have not been investigated in theory yet. Hence, we perform detailed investigation on the electronic and magnetic properties in Ba2MOsO6 (M = K, Ca, and Sc). To understand the importance of U, SOC and magnetic order, we performed both GGA+U calculation and GGA+U+SOC calculation. Our results indicate that SOC efforts not only provide the magneto crystalline anisotropies, but also significantly affect the size of the local moment and the magnetic structures in these compounds.

1. INTRODUCTION Transition metal oxides containing 4d or 5d atoms with double perovskite structure are attracting more and more attentions recently, as they present an abundant kind of physical phenomena.1−6 The abundance of behaviors have been further expanded with recent observations in a few 5d-osmate (Os) based double perovskites.7−15 Especially, these crucial behaviors originating from large spin−orbit coupling (SOC) have attracted tremendous interests. SOC is often considered as a perturbation due to the relativistic effect. The atoms from 3d to 5d electrons in the periodic table present several competing trends. At first, from 3d to 5d, the orbitals have been much more spatial extension. Hence, the Coulomb interaction (U) is much weaker, and thereby the correlation effects will be decreased. However, from 3d to 5d, the SOC strength is enhanced by an order of magnitude at the same time. The SOC effect enhances the splitting between degenerate orbitals and bands, and in many cases the kinetic energy can be reduced.16 The SOC, crystal field (CF), bandwidths (W), and U effects usually have comparable characteristic energy scales in compounds with 5d atoms. Recently, the role of SOC in Os-5d oxides of double perovskites is gaining more and more interest. For example, the cubic double perovskite Ba2NaOsO6, within Os7+ (5d1) systems is ferromagnetic (FM) and has a small magnetic moment, which is found to be Dirac−Mott insulator,17 while the magnetic structures of the double perovskite Ba2LiOsO6 belong to antiferromagnetic (AFM) order, which also maintains a cubic structure.18 In the Os6+ (5d2) systems, the double perovskite Ba2CaOsO6 shows antiferromagnetic order.13 In a © XXXX American Chemical Society

2. CALCULATION METHOD The electronic structure calculations were performed by the full potential linearized augmented plane-wave (FP-LAPW) method,21 with augmented plane-wave (APW) plus local orbitals implementation22 in WIEN2k code.23 We adopted the GGA-PBE exchange correlation potential24 with effective Coulomb interaction Ueff ranging from 0 to 5 eV for Os by self-interaction correction method.25 The SOC was also included using scalar relativistic wave functions.26 Both SOC and U effects have been assessed within GGA+SOC, GGA+U, and GGA+U+SOC methods. The Muffin-tin radii (RMT) are taken as 2.50 au for Ba, 1.90 au for Os, 2.00 au for K/Ca/Sc, and 1.60 au for O, respectively. We set the parameter RMT × Kmax = 8.0, where Kmax is Received: January 12, 2018

A

DOI: 10.1021/acs.inorgchem.8b00085 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry cutoff wave vector; 1000 k-points are used over the first Brillouin zone during self-consistency. The lattice constants and ionic sites from experiments were used to perform the calculations.

experimental ones to perform all the calculations.13,27,28 The lattice parameters a of Ba2MOsO6 (M = K, Ca, and Sc) are 8.7234, 8.3462, and 8.1525 Å, respectively. The ionic positions are Ba (0.25, 0.25, 0.25), K/Ca/Sc (0.5, 0.5, 0.5), and Os (0.0, 0.0, 0.0). The O positions in Ba2MOsO6 (M = K, Ca, and Sc) are (0.21770, 0.00, 0.00), (0.22911, 0.00, 0.00), and (0.2618, 0.00, 0.00), respectively. We also performed structural relaxation, and the optimized lattice constants are all systematically overestimated by about 1% compare to experiments, which is a well-known limitation of GGA exchange-correlation functional. For Ba2CaOsO6 and Ba2ScOsO6, they both are type I antiferromagnetic ground state with TN at 50 and 93 K in experiment, respectively.13,28 To manifest the magnetic ground states, we here perform the FM and AFM order calculations. For Ba2KOsO6, AFM state has the lowest energy. The energy of FM is 6.37, 53.07, 2.83, and 18.90 meV higher than that of AFM in GGA, GGA+U, GGA+SOC, and GGA+U+SOC, respectively. In Ba2CaOsO6, AFM state is almost the state of lowest energy, but the energy of FM is 38.29 meV lower than the AFM one in GGA+U calculation, and the energy of FM is 19.99, 54.93, and 50.30 meV higher than that of AFM in GGA, GGA+SOC, and GGA+U+SOC, respectively. However, the energies of FM and AFM are equal to that of GGA in Ba2ScOsO6. The energy of FM is 184.96, 193.98, and 174.65 meV higher than the AFM one in GGA+U, GGA+SOC, and GGA+U+SOC. It is very important to consider CF, SOC, and U interactions for Ba2MOsO6 (M = K, Ca, and Sc), which are 5d1, 5d2, and 5d3 cases. For the 5d1 system, U plays a dominant role in determining the local spin and orbitals.29 For the 5d2 system, owing to the strong SOC interactions, the spin and orbital vectors forming an effective total momentum j = 2.30 For a 5d3 system, the freedom of orbital degree is quenched, and only the spin Hamiltonian is considered and may behave classically.31 In this work, we give a schematic model to explain the CF and

3. RESULT AND DISCUSSION 3.1. Structure and Crystal Field. The double perovskite compounds Ba2MOsO6 (M = K, Ca, and Sc) all have facecentered cubic structure (Fm3̅m) as shown in Figure 1a. In

Figure 1. (a) Schematic view of the unit cell of Ba2MOsO6 (M = K, Ca, and Sc). (b) OsO6 octahedra are highlighted by blue; (c) 5d level splitting by crystal field and SOC.

these 5d double perovskites, the MO6 octahedron share corners with the OsO6 octahedron (see Figure 1b). The ionic and cell parameters of Ba2MOsO6 (M = K, Ca, and Sc) are set to the

Figure 2. (a) Spin ms and orbital ml magnetization, (b) magnetization of Os mtot, and (c) band gap as a function of U in Ba2MOsO6 (M = K, Ca, and Sc). B


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Inorganic Chemistry

Table 1. Calculated Spin, Orbital, and Total (mtot = ms + ml) Moments (μB) of Os, the Spin Moments of M and O, Magnetocrystalline Anisotropy Energy (meV), and the Band Gap (meV) Presented in Four Spin Directions ([001], [100], [110], and [111]) in Ba2MOsO6 (M = K, Ca, and Sc)a method

a

ms(Os)

ml(Os)

GGA+U GGA+U+SOC(001) GGA+U+SOC(100) GGA+U+SOC(110) GGA+U+SOC(111)

0.574 0.515 0.507 0.517 0.516

N −0.408 −0.413 −0.390 −0.424


1.087 1.024 1.028 1.029 1.030

N −0.463 −0.463 −0.505 −0.450


1.632 1.577 1.581 1.581 1.580

N −0.138 −0.134 −0.129 −0.138

mtot(Os) Ba2KOsO6 0.574 0.107 0.094 0.127 0.092 Ba2CaOsO6 1.087 0.561 0.565 0.524 0.580 Ba2SsOsO6 1.632 1.439 1.447 1.452 1.442

m(M)

m(O)

ΔE

gap

0.0012 0.0002 0.0004 0.0005 0.0000

0.040 0.041 0.039 0.042 0.041

N 25.084 0.000 10.894 0.877

N N 155 45 188

0.0018 0.0029 0.0016 0.0014 0.0021

0.063 0.057 0.064 0.056 0.062

N 37.300 0.000 4.934 1.474

N N 260 204 369

0.0108 0.0104 0.0101 0.0102 0.0104

0.095 0.093 0.093 0.092 0.093

N 3.200 3.593 1.511 0.000

574 587 502 502 548

N means none.

three compounds is equal to zero, and the ms increases with U in GGA+U calculations. However, in GGA+U+SOC calculations, the sign of ms is always opposite to ml in all the three compounds (see Figure 2a). In most cases, ms is reduced by 3%−20% when SOC is included and it is almost independent of the direction of spin, which we will show in section 3.4 clearly. However, in Ba2KOsO6, the values of ms are a little larger in GGA+U+SOC calculations than that of GGA+U. It might be due to the strong hybridization of Os−O when SOC is included. The ml increases in Ba2KOsO6 and Ba2CaOsO6, while it is almost constant in Ba2ScOsO6 over all the range of U. Hence, for the 5d1 and 5d2 systems, it is very important to investigate the SOC effect. The total moment of Os (mtot) in all of these three compounds increase with U in GGA+U calculations. However, in GGA+U+SOC calculations, the mtot of Ba2KOsO6 is almost constant as U increases, because of the cancellation of ms and ml. For Ba2CaOsO6, the mtot changes slightly with the increasing of U, because of the large value of ml. However, for Ba2CaScO6, it has an obvious increasing trend over all the range of U, as the ml has a little value compare with the ms. The band gap has a large difference in these three compounds. For Ba2KOsO6 and Ba2CaOsO6, both of them are metal in GGA+U calculations. However, for Ba2ScOsO6, it is an insulator, and the value of band gap increases with U. Within GGA+U+SOC calculations, the values of band gap have the same trend. However, when U = 0 and only SOC effect is included, all of them are metal. It means that the insulating phase is the combined effect of SOC and U. As shown in Figure 2 and Table 1, with U = 3 eV, we can get the values of local magnetization for Os ions (mtot) 0.094, 0.565, and 1.442 μB, and the band gaps 0.155, 0.260, and 0.548 eV in Ba2MOsO6 (M = K, Ca, and Sc), respectively, consistent with the experiments.13,28 3.3. Electronic Structure. The band structures of Ba2MOsO6 (M = K, Ca, and Sc) from DFT calculations are shown in Figure 3. The octahedral CF OsO6 splits Os 5d orbitals into t2g and eg levels, stabilizing 5d1, 5d2, and 5d3 electronic configurations in Ba2MOsO6 (M = K, Ca, and Sc). In

SOC effects for Ba2MOsO6 (M = K, Ca, and Sc) as shown in Figure 1c. With Oh symmetry, 5d states of OsO6 octahedral (see Figure 1b) CF split into t2g and eg orbitals with CF energy equaling to 10 Dq. The CF splitting energies in these three compounds investigated are pretty large with the calculated values around 4.5 eV. The Os-t2g orbitals have a lower energy than the Os-eg orbitals. As Os-t2g orbitals are partially filled, Oseg orbitals are far above Fermi level and not occupied. Therefore, the U in GGA+U would not affect the energy of Oseg orbitals. However, GGA+U would lead to a splitting between Os-t2g orbitals due to the partial occupations. In contrast, the strong SOC in Ba2MOsO6 would also split the Os-t2g orbitals into j = 1/2 doublet and j = 3/2 quartet. The competition between SOC and U gives rise to interesting electronic properties in Ba2MOsO6. 3.2. SOC and Correlation Effects on Spin, Orbital Moments, and Band Gap. GGA usually underestimates the effects of electronic correlations in systems with d orbitals. When we calculate electronic properties within GGA+U method, it requires U and J two parameters, and J is always set to 0 eV. All of the magnetic spin polarized calculations are performed in the AFM order, and we vary the magnitude of the parameter U from 0 to 5 eV for the Os 5d-states. The standard spin-polarized GGA corresponds to U = J = 0 eV. In order to understand the interplay of the effects related to SOC and local U in Ba2MOsO6 (M = K, Ca, and Sc), GGA+U and GGA+U +SOC are performed as a function of different strengths of electronic correlations in Ba2MOsO6 (M = K, Ca, and Sc). In our GGA+U+SOC, the calculated properties of AFM states with spin quantization along the [001], [100], [110], and [111] directions are shown in Figure 2 for Ba2MOsO6 (M = K, Ca, and Sc), respectively. The spin (ms), orbital moments (ml), and local magnetization mtot of Os atoms and the band gap as functions of U are shown in Figure 2a−c. The Os−O hybridization reduces ms of Os in both GGA+U and GGA+U+SOC, which reduces from expected 3, 2, and 1 μB corresponding to S = 3/2, 1, and 1/2 for Ba2MOsO6 (M = K, Ca, and Sc), respectively. The ml of these C


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Inorganic Chemistry

5d2, and 5d3 states in Os. We note that the electron correlation and SOC might induce a band gap in Ba2KOsO6 and Ba2CaOsO6, which leading to the magnetic MIT, but for Ba2ScOsO6, it shows little difference with and without SOC effect. To further understand the SOC effect on these three different double perovskites, the associated densities of states (DOS) are presented in Figure 4. From GGA+U calculations, both Ba2KOsO6 and Ba2CaOsO6 are metals, but Ba2ScOsO6 is an insulator. The Os 5d and O 2p states lie in Fermi level, revealing that it has a strong hybridization with them in Ba2MOsO6 (M = K, Ca, and Sc). The occupations are t2g1 for Os in Ba2KOsO6, t2g2 for Os in Ba2CaOsO6, and t2g3 for Os in Ba2ScOsO6, indicating valence states of Os7+, Os6+, and Os5+, respectively. In our GGA+U+SOC calculations, we only present the results of [100], [100], and [111] directions for Ba2MOsO6 (M = K, Ca, and Sc), respectively. All of these double perovskites are insulators. The Os 5d and O 2p orbitals contribute almost equally in t2g bands, suggesting a very strong hybridization effect emphasized in GGA+U method before. 3.4. Magnetocrystalline Anisotropy. As we all known that the structure symmetry is lowered when SOC is included. The resulting symmetry is mainly dependent on the direction of magnetization, so it is very important to investigate the properties on the different directions of magnetization. In order to illuminate SOC and spin direction effects in these 5d double perovskites, we have performed GGA+U+SOC (U = 3 eV) calculations at [001], [100], [110], and [111] different spin directions. Our magnetocrystalline anisotropy energy calculations of these different directions are presented in Table 1. It is found that Ba2KOsO6 and Ba2CaOsO6 both have an [100] easy axis, and the [111] direction has the almost similar energy with that of [100]. However, Ba2ScOsO6 has an [111] easy axis. In addition, the direction of [110] has the similar energy with that of easy axis. We also perform the band structures in these four different spin directions (Figure 5). It shows that the band structures of Ba2KOsO6 and Ba2CaOsO6 depend strongly on the strong SOC effect. The obtained band gap is small, which is in agreement with the values of band gap (0.02−0.3 eV) by SOC driven insulator.32 Both of them are metal in [001] and are insulator in other spin directions. However, Ba2ScOsO6

Figure 3. Band structures calculated for Ba2MOsO6 (M = K, Ca, and Sc) using different methods. The cyan and red lines refer to the GGA +U and GGA+U+SOC, respectively.

our calculations, the spin-polarized GGA and GGA+SOC band structures calculated for the AFM state of Ba2MOsO6 (M = K, Ca, and Sc) all show metallicity. The t2g bands cross the Fermi level, which does not agree with the fact that Ba2CaOsO6 and Ba2ScOsO6 both are insulators in experiments.13,28 The failure of traditional GGA and GGA+SOC is owing to the ignoring of the on-site U. As W is smaller than the on-site U (3 eV), suggesting that the electron correlations are very important in Ba2MOsO6 (M = K, Ca, and Sc).17 We performed GGA+U calculations, which are present in Figure 3. All of these calculations give a metallic state in Ba2KOsO6 and Ba2CaOsO6. However, Ba2ScOsO6 is an insulator. In our GGA+U calculations, it does not change the general picture described above even with the larger U values up to 5 eV. The values of band gap are zero for Ba2KOsO6 and Ba2CaOsO6. However, for Ba2ScOsO6, it increases by increasing U. To investigate the effects of SOC and U on the electronic structure of Ba2MOsO6 (M = K, Ca, and Sc), we also performed GGA+U+SOC calculation. The band structures obtained for AFM states with the spin quantization along the [100], [100], and [111] directions are shown in Figure 3 for Ba2MOsO6 (M = K, Ca, and Sc), respectively. All of band calculations give insulating phase for Ba2MOsO6 (M = K, Ca, and Sc). It clearly shows 5d1,

Figure 4. DOS of Ba2MOsO6 (M = K, Ca, and Sc) obtained from the GGA+U and GGA+U+SOC, respectively. D


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Inorganic Chemistry

and Sc), respectively. Although the ml values of Ba2ScOsO6 are very small in different spin directions, it does not affect the mtot. The SOC occupations of 5d2 Ba2CaOsO6 are presented in four spin directions, i.e., [001], [100], [110], and [111] (Table 2). The largest SOC occupation in the table is 0.70, which can Table 2. 5d Orbital Specific Occupation for Ba2CaOsO6, Using Four Directions [001], [100], [110], and [111], Spin Up, Spin Down, and Orbital Occupations along with the Difference (Net Spin) Are Displayed direction [001] spin up spin down net spin direction [100] spin up spin down net spin direction [110] spin up spin down net spin direction [111]

Figure 5. Band structures computed using GGA+U+SOC in four directions of magnetization axis of Ba2KOsO6 (a−d), Ba2CaOsO6 (e− h), and Ba2ScOsO6 (i−l).

spin up spin down net spin

shows little change of these different spin directions, always presenting insulator with different spin direction. The origin of the different MIT depending on the spin direction in Ba2MOsO6 (M = K, Ca) and Ba2ScOsO6 is primarily due to the different orbital filling of Os-t2g orbitals in these compounds. In Ba2ScOsO6, the Os-t2g orbitals are halffilled. Even in the absence of SOC, it is an insulator due to the U, as shown in the upper row of Figure 4. Half of the Os-t2g orbitals with the same spin polarization are filled, while the other half with opposite spin polarization is empty. The splitting is purely due to U, and the gap increases with it. In Ba2MOsO6 (M = K and Ca), on-site U is unable to open a band gap without SOC (see upper row of Figure 4). Due to a smaller filling factor of Ba2MOsO6 (M = K and Ca), their Fermi levels locate in the lower half of the Os-t2g orbitals. Therefore, in Ba2MOsO6 (M = K and Ca), SOC plays a dominant role in opening the band gap. From Table 1, with formal charge of Os, the spin moment of Os ms increases, in accordance with the 5d1, 5d2, and 5d3 configurations of Ba2MOsO6 (M = K, Ca, and Sc). The values of ms are reduced by SOC, which may owe to the hybridization. However, for Ba2MOsO6 (M = K, Ca, and Sc) the orbital moment ml are almost invariant. The ml of Os in Ba2CaOsO6 is bigger than others as expected. However, the value of ml/ms is 81, 45, and 9% in the easy axis for Ba2MOsO6 (M = K, Ca, and Sc), respectively. It means Ba2KOsO6 maybe has the strongest SOC effect. Table 1 gives the calculated the total moment of Os (mtot) among 0.092−0.574, 0.52−1.087, and 1.44−1.63 μB for Ba2MOsO6 (M = K, Ca, and Sc), respectively, depending on the direction of spin. The full spin moments of the OsO6 cluster are around 0.328, 0.949, and 2.0 μB, which are also reduced by SOC from 1, 2, and 3 μB in Ba2MOsO6 (M = K, Ca,

ml

ml

ml

ml

−2

−1

0

+1

+2

sum

0.537 0.224 0.313

0.701 0.219 0.482

0.304 0.283 0.021

0.286 0.243 0.043

0.435 0.269 0.166

2.263 1.238 1.025

−2

−1

0

+1

+2

sum

0.398 0.253 0.145

0.579 0.224 0.355

0.303 0.282 0.021

0.579 0.224 0.355

0.398 0.253 0.145

2.257 1.236 1.021

−2

−1

0

+1

+2

sum

0.391 0.254 0.137

0.586 0.223 0.363

0.303 0.282 0.021

0.586 0.223 0.363

0.391 0.254 0.137

2.257 1.236 1.021

−2

−1

0

+1

+2

sum

0.411 0.255 0.156

0.567 0.221 0.346

0.303 0.283 0.020

0.567 0.221 0.346

0.411 0.255 0.156

2.259 1.235 1.024

be understood as full occupation. For the net spin moment, it is independent of spin direction. Comparing the 5d occupation numbers in different spin directions, the spin down occupations hardly change. However, the occupations of spin up channel do vary with spin direction. The two largest occupations almost do not change with spin direction except the direction of [001], shown in Table 2 in boldface. For [001], the two primary occupations are ML = −2, −1. However, for [100], [110], and [111], they all are ML = −1, 1.

4. CONCLUSIONS We have performed first-principles calculations on the electronic properties of B-site ordered double perovskites Ba2MOsO6 (M = K, Ca, and Sc) with 5d1, 5d2, and 5d3 configures. To understand the importance of U, SOC, and magnetic order, GGA+U and GGA+U+SOC are carried out to study the magnetic, electronic, and magnetocrystalline anisotropy properties. We note the electronic structure of half-filled 5d3 orbitals of Os in Ba2ScOsO6 is slightly affected by SOC, while the electronic configuration of 5d1 and 5d2 of Os in Ba2MOsO6 (M = K and Ca) responds differently to SOC, and both SOC and correlation effects are essential in enlarging the band gap, putting these compounds to the correlated insulator. Our magnetocrystalline anisotropy calculations show that Ba2KOsO6 and Ba2CaOsO6 both have an easy axis of [100]. However, the easy axis of Ba2ScOsO6 is [111] direction. The calculated band gaps are very small, which is in agreement with the values of band gap (0.02−0.3 eV) in SOC driven insulator, in which the rotation of the spin direction in magnetization produces a MIT through band overlap. In addition, To understand the nature of spin and orbital of Os, we study the E


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5d orbital occupation matrix of Ba2CaOsO6 through the GGA +U+SOC calculations. Our results indicate that the total occupation is independent of the spin direction.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Min Liu: 0000-0002-7674-7309 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Science Challenge Project (Grant No. TZ2016001) and the NSAF (Grant No. U1430117).

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REFERENCES

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