Two-Dimensional Metal–Organic Half-metallic Antiferromagnet

Article Cite This: J. Phys. Chem. C 2018, 122, 1846−1851

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Two-Dimensional Metal−Organic Half-metallic Antiferromagnet: CoFePz Haoqiang Ai, Xiaobiao Liu, Bo Yang, Xiaoming Zhang, and Mingwen Zhao* School of Physics & State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, Shandong, China S Supporting Information *

ABSTRACT: Half-metals are always accompanied by ferromagnetism with undesired stray magnetic field which may be harmful in highly integrated circuits. By contrast, halfmetallic antiferromagnets (HMAFMs) can achieve fully spin-polarized current without stray magnetic field, enabling spintronic filed sensing and magnetic memories. Using firstprinciples calculations, we demonstrated that the tantalizing HMAFM can be realized in a two-dimensional (2D) metal−organic framework (MOF) containing Co ions and octaamino-substituted iron-porphyrazines (CoFePz). The strong p−d exchange interaction between ions and ligands leads to an antiferromagnetic ground state with metallic features in one spin direction and semiconducting features in the opposite spin direction. Monte Carlo simulations based on the Ising model on an edge-centered square lattice indicate that the Néel temperature of the CoFePz (247 K) is much higher than the temperature of liquid nitrogen. Considering the huge number of MOFs, it is expected that the present findings can shed light on a new way to develop organic HMAFMs.

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INTRODUCTION Spintronics, based on the novel notch of spin degree of freedom of electrons, promises to be the next generation information technology with potential advantages of speeding up data processing, reducing power consumption, and increasing circuit integration density,1−3 in which fully spinpolarized carriers for pure spin generation and injection dominate the innovation of spintronics.4 With the concurrence of metallic conductivity in one spin channel and insulating or semiconducting state in the opposite spin orientation (Figure 1a), half-metallic ferromagnets (HMFs) may filter the current

spintronics devices are scaled to lower dimension, the stray magnetic fields increase in size, which disturb the spintronics field sensing and magnetic memories in highly integrated circuits.14,15 To eliminate the effects of stray magnetic fields, a subclass of half metals, namely, half-metallic antiferromagnets (HMAFMs), were proposed.16,17 Fully spin-polarized conduction electrons and exact cancellation of the local magnetic moments coexist in this new type of half-metals, which paved a new way to spintronics.5,17,18 In contrast to the conventional antiferromagnets in which the electron density of states of the two spin channels are occupied symmetrically (Figure 1b), HMAFMs have the antiparallel magnetic moments of the same magnitude residing on different sublattices of distinct symmetry (Figure 1c), leading to the nullification of magnetic moments and a perceptible exchange splitting between two spin channels.19 By elaborately selecting magnetic sublattices, several groups of inorganic materials have been theoretically predicted to be promising candidates for HMAFMs,20−31 and recently, the Mn2Ru0.5Ga compound has been experimentally identified as a possible HMAFM.32 However, the crystal structures of these HMAFMs are sophisticated18 and may transform into a ferrimagnetic state at finite temperatures due to different intrasublattice exchange interactions.33 The design of novel HMAFMs with zero magnetic moment and half-metallicity survive at high temperature remains challenging. Recently, organic spintronics is attracting growing attention because of their rich physics, low cost, and flexibility.13,34,35 In contrast to the inorganic materials used for spintronics, organic

Figure 1. Schematic diagram of the electron density of states n(E) as a function of energy E for (a) a half-metal, (b) a conventional antiferromagnetic semiconductor, and (c) an antiferromagnetic halfmetal. S1, S2 denote the two sublattices. The two spin channels are marked in red and blue, respectively.

into a single spin channel without any external operation and are expected to generate fully spin-polarized carriers.5,6 Until now, a great number of inorganic materials have been demonstrated to be HMFs.7−12 Among them, La0.67Sr0.33MnO3 has been successfully used for electrodes in spin valves.13 The main drawback of HMFs, however, is the stray magnetic field arising from the nonzero net magnetic moments. As the © 2017 American Chemical Society

Received: October 11, 2017 Revised: December 23, 2017 Published: December 29, 2017 1846

DOI: 10.1021/acs.jpcc.7b10051 J. Phys. Chem. C 2018, 122, 1846−1851

The Journal of Physical Chemistry C

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RESULTS AND DISCUSSION The 2D MOF considered in this work was constructed by joining the 2,3,9,10,16,17,23,24-octa-amino-substituted ironporphyrazine52 with Co ions, leading to a long-range planar square lattice, labeled as CoFePz, as shown in Figure 2. Akin to

counterparts are composed of lightweight elements and usually have a weaker spin−orbit coupling and hyperfine interaction, which facilitate longer spin relaxation time.35,36 Low-dimensional organic half-metals with a high magnetic phase transition temperature are quite promising for achieving spin-injection and spintronics device applications.34,37 First-principles calculations have demonstrated a number of 2D organic HMFs, such as a 2D manganese phthalocyanine (MnPc),38 a manganese bisdithiolene (Mn3C12S12) kagome lattice,39 and a 2D metal− organic framework (MOF) of NiMnPc.40 The Curie temperatures of these organic HMFs are in the range of 150−212 K. However, the 2D organic HMAFM has never been reported until now. We noticed that the Fe and Co ions in some dsp2 hybridized 2D MOFs have integer magnetic moments, two and one Bohr magneton (μB), respectively,40,41 and may couple antiferromagnetically via suitable ligands, which may facilitate the exact cancellation of the local magnetic moments. On the basis of this idea, we propose for the first time a candidate metal−organic HMAFM by using first-principles calculations. We demonstrated theoretically the coexistence of half-metallicity and antiferromagnetism in a 2D MOF of Co ions and octa-aminosubstituted iron-porphyrazines (CoFePz), which can be attributed to the unique p−d exchange interaction between ions and ligands. The Néel temperature (247 K) of the CoFePz evaluated from the Monte Carlo simulations based on the 2D Ising model42,43 is much higher than the temperature of liquid nitrogen, suggesting the thermal stability of the HMAFM state. The first candidate material for the 2D metal−organic HMAFMs opens an avenue for organic spintronics.

Figure 2. Schematic representation of the structures of octa-aminoiron porphyrazine (FePz) and two-dimensional (2D) metal−organic framework (MOF) of CoFePz. The primitive cell is denoted by the dashed rectangle.

the cases of NiMnPc40 and triphenylene-based 2D MOFs,53 the amino groups in the iron-porphyrazine may be replaced by imino groups after the deprotonation processes. Similar 2D MOFs (e.g., the polymeric Fe-phthalocyanine monolayer54) have been successfully synthesized and the planar Co coordination has been experimentally affirmed in the THTACo sheets,55 which strongly imply the plausibility of the 2D CoFePz. Structural optimization showed that the 2D CoFePz MOF has a planar configuration without any Jahn−Teller distortions, exhibiting a perfect 2D square lattice (space group: p4m). All the atoms are on the same plane without any distortional buckling. The lattice constant of the square lattice is about 13.439 Å, and the length of the Fe−N (Co−N) bond is about 1.909 Å (1.879 Å). To determine the magnetic ground state of CoFePz, three types of spin patterns in a unit cell were considered, namely, ferromagnetic (FM), ferrimagnetic (FiM), and antiferromagnetic (AFM) configurations for the spins of Fe and Co ions, as shown in Figure 3a. These spin patterns were obtained through self-consistent DFT calculations, starting from different initial spin distributions. The results are summarized in Table 1. Obviously, the AFM state is energetically most favorable. The high exchange energy (Eex ≡ EFM − EAFM) of about 143.4 meV per unit cell implies that AFM coupling is strongly preferred between nearest-neighbor magnetic moments, leading to a long-range AFM ordering at 0 K. The magnetic moments in the AFM state are totally compensated within a unit cell without any stray magnetic field. Other two states have nonzero integer total magnetic moments in one unit cell. The local magnetic moments originate preponderantly from the Fe and Co atoms with a small difference in magnitudes for the same ion in different magnetic orderings. The N and C atoms nearest to the transition-metal (TM) atoms carry tiny local magnetic moments (from −0.048 to 0.004 μB). The local magnetic moments of the Fe and Co ions are very close to 2 and 1 μB, respectively, consistent with the results of previous works.56−58 The magnitudes of the magnetic moments of Fe (2 μB) and Co (1 μB) ions could be explained by the 4 + 1 splitting scheme,56 as the Fe and Co are in the +2 charge state. The nonintegral

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COMPUTATIONAL METHODS Our first-principles calculations were performed on the basis of spin-polarized density functional theory (DFT) implemented in the plane wave basis Vienna ab initio simulation package (VASP) code.44−46 The electron−ion interactions were described by the projector augmented wave (PAW) method.47 The electron−electron interaction was treated within a generalized gradient approximation (GGA) in the form proposed by Perdew, Burke, and Ernzerhof (PBE) for the exchange-correlation functional.48 Because of deficiency for GGA in describing the strong Coulomb interaction between the partially filled 3d shells of the transition metals, the GGA +U method49 was adopted in our calculations. The values of correlation energy (U) and exchange energy (J) were set to 4.0 and 1.0 eV, respectively, as used in many previous studies.38−40,50 We also tested other U values and found that the antiferromagnetic ground state is robust (see Supporting Information). The supercell was repeated periodically along the x- and y-direction, while a vacuum region of about 20 Å was introduced in the z-direction to avoid spurious interactions between neighboring sheets and its periodic images. The energy cutoff employed for plane-wave expansion of electron wave functions and convergence criteria for energy and force were set to be 550 eV, 1 × 10−5 eV, and 0.005 eV/Å respectively. A √2 × √2 × 1 supercell was adopted to search for the stable magnetic ordering. For the unit cell and the √2 × √2 × 1 supercell, the Brillouin zone integrations were carried out by the Monkhorst−Pack k-points meshes51 of 7 × 7 × 1 and 5 × 5 × 1, respectively. The convergence of this strategy has been verified. All the atom positions and the lattice constants were fully optimized using a conjugate gradient (CG) algorithm. 1847

DOI: 10.1021/acs.jpcc.7b10051 J. Phys. Chem. C 2018, 122, 1846−1851

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Figure 3. (a) Top and side views of the spin density isosurfaces at absolute value of |Δρ| = 0.04 electrons per Å3 for three magnetic orderings: FM, FiM, and AFM. Red and blue isosurfaces correspond to positive and negative spin density, respectively. The primitive cell is denoted by the dashed rectangle. (b) Spin-resolved electronic band structure (left), partial electron density of states (middle), and total electron density of states (right) of the 2D AFM CoFePz framework near the Fermi level. The energy at the Fermi level was set to zero. The red and blue solid lines in the band structure represent the spin-up bands and spin-down bands, respectively. “Up” and “down” arrows denote the spin-up and -down polarization, respectively. Γ (0, 0, 0), X (0, 1/2, 0), and M (1/2, 1/2, 0) are highly symmetric points in reciprocal space.

Table 1. Calculated Total Energies Etot Relative to That of the AFM Configuration, Total Magnetic Moments per Unit Cell Mtot, Local Magnetic Moments of Fe (MFe) and Co (MCo), and Electronic Band Structures (EBS) of Three Magnetic Coupling Configurations Etot (meV) Mtot (μB) MFe (μB) MCo (μB) EBS a

FM

FiM

AFM

143.4 4 1.82 1.16 SCa

42.3 2 2.25 1.00/−1.18

0 0 2.26 −1.18 HMb

The electronic band structure of the CoFePz near the Fermi level in the AFM state along with the corresponding partial density of states (PDOS) and total density of states (DOS) are displayed in Figure 3b. (The band structure of the FM state is shown in Figure S3.) It is conspicuous that two spin-down bands cross the Fermi level, while the spin-up channel has a band gap of about 0.61 eV, suggesting the half-metallicity of the CoFePz. To understand the origin of local magnetic moment of TM atoms and the half-metallicity, the PDOS projected onto the 3d orbitals of Fe and Co atoms in a wider range of energy (Figure S4) has been analyzed. According to the crystal field theory, in a crystal-field environment with a square symmetry, the 3d orbitals of the Fe ions in CoFePz split into dz2, dxy, and dx2−y2 orbitals and a doubly degenerate dπ (dxz + dyz) orbitals. For the Co ion, the absence of the local square symmetry leads to five singly degenerate orbitals. The large spin-splitting existing in the dz2, dπ orbitals of Fe and dxz/dyz orbitals of Co renders them singly occupied, as shown in Figure 4a. The magnetic moments of Fe and Co ions calculated from these electron configurations are consistent with DFT calculations. From the PDOS plotted in Figure 3b and Figure S4, one can see that the electronic states near the Fermi level arise mainly from the dπ of Fe, dyz/dxz of Co, and π (i.e., pz) orbitals of C and N atoms. The hybridization of these atomic orbitals forms a π-conjugated framework and contributes to the two spindown bands crossing the Fermi level, akin to the cases in

Semiconductor. bHalf-metal.

local magnetic moments of the TM atoms can be attributed to the charge transfer.15,59 These features are more obvious in the isosurfaces of the spin density (Δρ = ρ↑ − ρ↓) of the three spin configurations shown in Figure 3a. It is evident that the spin density mainly appears on TM atoms, and the local magnetic moments of nearest-neighbor Fe and Co atoms are parallel or antiparallel, accompanied by spin-polarized electron density of the ligand moieties between them. We also employed a large √2 × √2 supercell with more spin patterns and obtained similar results (see Figure S2 and Table S2), confirming the AFM ground state of the 2D CoFePz. 1848

DOI: 10.1021/acs.jpcc.7b10051 J. Phys. Chem. C 2018, 122, 1846−1851

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Figure 4. (a) Schematic diagrams for the origin of magnetic moments of Fe and Co ions in the AFM CoFePz. “Up” and “down” arrows denote the spin-up and -down electron occupancies, respectively. (b) Top and side views of the band decomposed charge density (ρ = 0.01 electrons per Å3) of the two spin-down bands across the Fermi level in an energy range of −0.3 to 0 meV. (c) Schematic representation of the ground-state spin configuration in an edge-centered square lattice. (d) Variation of the heat capacity (Cv) of the system as a function of temperature.

NiMnPc.40 These features are further affirmed from the shape of the band decomposed charge density of the two spin-down bands across the Fermi level in an energy range of −0.3 to 0 meV, which is depicted in Figure 4b. The exact cancellation of the local magnetic moments in one unit cell of the CoFePz framework is closely related to the π orbitals of C and N atoms that act as an intermediary between the nearest-neighbor spin moments. Considering the long distance between the TM ions, the magnetic coupling between them can be understood in terms of a superexchange mechanism intermediated by the π orbitals of C and N atoms.40 The energy favorability of AFM over FM states is related to the electron occupations of Fe and Co ions whose 3d orbitals are more than half-filled. According to the superexchange mechanism, the exchange interaction between them via the ligands with close-shell nature will lead to an AFM ordering. In addition, there are obvious overlaps in both energy (the spin-down channel) and real space between dyz/dxz orbitals of TM atoms and π orbitals of C and N atoms, which prefer strong p−d exchange interaction between the nearest-neighbor magnetic moments. It is noteworthy that the magnetic phase transitions do not always exist in a 2D system. For example, the 2D isotropic spinS Heisenberg model with finite-range exchange interaction showed that magnetic order will be destroyed at any nonzero temperature.60 However, the existence of long-range magnetic ordering has been affirmed both theoretically and experimentally.40,42,43,61 This is related to the magnetic anisotropy of 2D materials which lifts the Mermin−Wagner restriction60 to stabilize long-range magnetic ordering even in a monolayer.61 We evaluated the magnetic anisotropy of CoFePz monolayer by taking the spin−orbit coupling (SOC) into account40 based on DFT+U method. The magnetic anisotropy energy (MAE) is defined as MAE ≡ E⊥ − E∥, where the E⊥ and E∥ are the energies of 2D CoFePz when the easy axis is perpendicular to or in the plane. The calculated MAE value is 0.236 meV per unit cell. This magnitude is of the same order as those of NiMnPc40 and 2D Fe2Si,62 confirming the magnetic anisotropy of the CoFePz monolayer.

Finally, we employed an Ising model to reveal the temperature-dependent magnetic ordering, which has been widely adopted in many previous theoretical works.38,39,62 In the absence of external fields, the Hamiltonian can be written as Ĥ = −J0∑i,jm̂ iFe·m̂ jCo, where m̂ iFe and m̂ jCo represent the local magnetic moments of a Fe ion at site i and a Co ion at site j, respectively. If only the nearest-neighbor exchange was considered, exchange parameter J0 can be estimated from the exchange energy (Eex) using the formula J0 = −Eex/(8mFemCo). For simplification, the local magnetic moments in Fe and Co ions were taken as integral values, mFe = |m̂ Fe| = 2 and mCo = | m̂ Co| = 1, which constitute an edge-centered square lattice as shown in Figure 4c. The estimated J0 is about −8.96 meV. Monte Carlo (MC) simulations based on the Ising Hamiltonian using this parameter were then performed to reveal the phase transition of magnetic orderings. The possible values of m̂ Fe were set to 2, 0, −2, while those of m̂ Co were 1 and −1 because the net spin states of Fe and Co ions are approximately 1 and 1 /2, respectively. A 50 × 50 2D square supercell containing 7500 local magnetic moments was employed and the calculation lasted for 3 × 108 loops at each temperature. In each loop, the magnetic moments on each site changed randomly according to the net spin states of TM atoms. The heat capacity (Cv) of the system was then calculated using the ΔE expression Cv = lim ΔTT , where ΔET is the change of the ΔT → 0

total energy of the system as the temperature is increased from T to T + ΔT.39 The temperature-dependent (Cv) curve (shown in Figure 4d) shows the magnetic phase transition with a critical temperature (Néel temperature) of about 247 K, which is much higher than the temperature of liquid nitrogen (78 K). This implies that the HMAFM features may survive at the temperature lower than 247 K. The Néel temperature in the 2D CoFePz is also higher than the Curie temperatures in some 2D organic HMFs.38,39

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CONCLUSIONS In conclusion, using first-principles calculations, we proposed a candidate 2D MOF, namely, CoFePz monolayer for half1849

DOI: 10.1021/acs.jpcc.7b10051 J. Phys. Chem. C 2018, 122, 1846−1851

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(7) Galanakis, I.; Dederichs, P. H.; Papanikolaou, N. Slater-Pauling Behavior and Origin of the Half-Metallicity of the Full-Heusler Alloys. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 66, 174429. (8) Kobayashi, K.-I.; Kimura, T.; Tomioka, Y.; Sawada, H.; Terakura, K.; Tokura, Y. Intergrain Tunneling Magnetoresistance in Polycrystals of the Ordered Double Perovskite Sr2FeReO6. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 11159−11162. (9) Kobayashi, K.-I.; Kimura, T.; Sawada, H.; Terakura, K.; Tokura, Y. Room-Temperature Magnetoresistance in an Oxide Material with an Ordered Double-Perovskite Structure. Nature 1998, 395, 677−680. (10) Schwarz, K. CrO2 Predicted as a Half-Metallic Ferromagnet. J. Phys. F: Met. Phys. 1986, 16, L211−L215. (11) Dedkov, Y. S.; Rüdiger, U.; Güntherodt, G. Evidence for the Half-Metallic Ferromagnetic State of Fe3O4 by Spin-Resolved Photoelectron Spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 064417. (12) Soulen, R. J., Jr; Byers, J. M.; Osofsky, M. S.; Nadgorny, B.; Ambrose, T.; Cheng, S. F.; Broussard, P. R.; Tanaka, C. T.; Nowak, J.; Moodera, J. S.; Barry, A.; Coey, J. M. D. Measuring the Spin Polarization of a Metal with a Superconducting Point Contact. Science 1998, 282, 85−88. (13) Sun, D.; Yin, L.; Sun, C.; Guo, H.; Gai, Z.; Zhang, X.-G.; Ward, T. Z.; Cheng, Z.; Shen, J. Giant Magnetoresistance in Organic Spin Valves. Phys. Rev. Lett. 2010, 104, 236602. (14) Ž ic, M.; Rode, K.; Thiyagarajah, N.; Lau, Y.-C.; Betto, D.; Coey, J. M. D.; Sanvito, S.; O’Shea, K. J.; Ferguson, C. A.; MacLaren, D. A.; Archer, T.; et al. Designing a Fully Compensated Half-Metallic Ferrimagnet. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 140202. (15) Nie, Y.-M.; Hu, X. Possible Half Metallic Antiferromagnet in a Hole-Doped Perovskite Cuprate Predicted by First-Principles Calculations. Phys. Rev. Lett. 2008, 100, 117203. (16) van Leuken, H.; de Groot, R. A. Half-Metallic Antiferromagnets. Phys. Rev. Lett. 1995, 74, 1171−1173. (17) de Groot, R. A. Half-Metallic Magnetism in the 1990s. Phys. B 1991, 172, 45−50. (18) Hu, X. Half-Metallic Antiferromagnet as a Prospective Material for Spintronics. Adv. Mater. 2012, 24, 294−298. (19) Chakraverty, S.; Yoshimatsu, K.; Kozuka, Y.; Kumigashira, H.; Oshima, M.; Makino, T.; Ohtomo, A.; Kawasaki, M. Magnetic and Electronic Properties of Ordered Double-Perovskite La2VMnO6 thin Films. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 132411. (20) Chen, S. H.; Xiao, Z. R.; Liu, Y. P.; Wang, Y. K. Investigation of Possible Half-Metallic Antiferromagnets on Double Perovskites LaABB′O6 (A = Ca,Sr,Ba; B,B′=Transition Elements). J. Appl. Phys. 2010, 108, 093908. (21) Ghimire, M. P.; Wu, L.-H.; Hu, X. Possible Half-Metallic Antiferromagnetism in an Iridium Double-Perovskite Material. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 134421. (22) Pardo, V.; Pickett, W. E. Compensated Magnetism by Design in Double Perovskite Oxides. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 054415. (23) Park, J. H.; Kwon, S. K.; Min, B. I. Half-Metallic Antiferromagnetic Double Perovskites: LaAVRuO6 (A = Ca,Sr, and Ba). Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 174401. (24) Pickett, W. E. Spin-Density-Functional-Based Search for HalfMetallic Antiferromagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57, 10613−10619. (25) Wang, Y. K.; Guo, G. Y. Robust Half-Metallic Antiferromagnets LaAVOsO6 and LaAMoYO6(A = Ca,Sr,Ba;Y = Re,Tc) from FirstPrinciples Calculations. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 064424. (26) Galanakis, I.; Ö zdoğan, K.; Şaşıoğlu, E.; Aktaş, B. Ab Initio design of Half-Metallic Fully Compensated Ferrimagnets: The Case of Cr2MnZ (Z = P, As, Sb, and Bi). Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 172405. (27) Gao, G. Y.; Yao, K.-L. Antiferromagnetic Half-Metals, Gapless Half-Metals, and Spin Gapless Semiconductors: The D03-Type Heusler Alloys. Appl. Phys. Lett. 2013, 103, 232409.

metallic antiferromagnets with zero net magnetic moments and half-metallic electronic band structure. The exact cancellation of the local magnetic moments in one unit cell arises from the antiferromagnetic ordering of the magnetic moments of Fe and Co ions in an edge-centered square lattice, which is understandable in terms of the indirect exchange mechanisms. The hybridization between the dxz/dyz orbitals of ions and the π orbitals of the ligand moieties leads to the strong p−d exchange interaction and consequently a stable AFM ordering. The CoFePz monolayer behaves like a metal in a one spin channel due to the finite density of states at the Fermi level, while as a semiconductor in the opposite spin channel with a gap of about 0.61 eV. The electron density of states near the Fermi level arises mainly from the dxz/dyz of TM atoms and pz orbitals of C and N atoms. The Monte Carlo simulations within an Ising model indicate that the Néel temperature is about 247 K, which is higher than the temperature of liquid nitrogen. The fully compensated spin moments and the half-metallic features of the 2D MOF are expected to shed light on a new way to design 2D organic HMAFMs, opening an avenue for spintronics applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b10051. Electronic structures with different U values; spin density isosurfaces and energies of the supercell with four spin patterns; the electronic band structure of FM CoFePz; the PDOS projected onto the 3d orbitals of Fe and Co atoms in the antiferromagnetic CoFePz (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Mingwen Zhao: 0000-0002-7583-9682 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Nos. 21433006 and 11774201) and the 111 project (No. B13029).

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REFERENCES

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DOI: 10.1021/acs.jpcc.7b10051 J. Phys. Chem. C 2018, 122, 1846−1851

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DOI: 10.1021/acs.jpcc.7b10051 J. Phys. Chem. C 2018, 122, 1846−1851