First-principles Calculations of Effects of Pressure on Paramagnetic, Ferromagnetic and Antiferromagnetic spin-web Cu3TeO6

The structure, electronic and magnetic properties have been investigated by the rst-principles calculations for paramagnetic, ferromagnetic and antiferromagnetic Cu 3 TeO 6 under pressure from 0 to 100 GPa. The calculated lattice parameters at 0 GPa are in excellent agreement with the available calculated and experimental values. With increasing pressure, the lattice parameters and volume decrease, but Cu 3 TeO 6 keep a stable cubic structure. The electronic calculations show that paramagnetic and ferromagnetic Cu 3 TeO 6 are metallic, and antiferromagnetic Cu 3 TeO 6 has the non-metallic nature with a direct band gap which decreases with the increasing pressure. Under the pressure, their non-locality of density of states enhances and the electrons becomes more active. Moreover, for antiferromagnetic Cu 3 TeO 6, the spin moments of Cu atoms are affected obviously by pressures, and Te atoms show nonmagnetic performance. The total magnetic moment which is mainly contributed by Cu, reaches the maximum at 20 GPa, and decreases with the increasing pressure. The knowledge of these properties will provide reference and guidance for the subsequent study of Cu 3 TeO 6 .


Introduction
Cuprates have a variety of exotic physical properties, such as high-temperature superconductivity [1], layered crystal structures, magnetic insulating state [2], hybridization of Cu-d and O-p orbitals [3], and they show effects of strong electronic correlations [4].Based on this wealth of fascinating properties, cuprates have attracted considerable attention both theoretically and experimentally [5][6][7][8][9][10], many researchers have done a lot of research on cuprates [11][12][13][14][15][16][17][18][19][20][21].With 3d 9 Cu 2+ ions, Cu 3 TeO 6 is a typical Te-based cuprate and exhibits an enormous diversity of magnetic structures [22][23][24][25] and variegated physical properties [2], displaying a long range antiferromagnetic order at TN ≈ 61 K [26][27][28].As early in 1968 [7], the crystal structure of Cu 3 TeO 6 was rst determined, and it was modi ed in 1978 [12].Herak et al. [7] identi ed the presence of a novel type of magnetic lattice which referred to as a 3D spin-web [22] by scrutinizing the neutron diffraction data crystal structure of Cu 3 TeO 6 .The existence of special manifestation attracts much interest to the study of Cu 3 TeO 6 .Moreover, in 2017, Li et al. [25] put forward that Dirac magnons may occur in Cu 3 TeO 6 .Yan et al. [2] predicted that the antiferromagnetic phase of Cu 3 TeO 6 may be Slater insulator by investigating the electronic and magnetic properties in 2019.Therefore, Cu 3 TeO 6 is a very interesting material due to the fascinating properties, which worthy further studies.But from the available studies on Cu 3 TeO 6 , the most researches have been carried out on it in the antiferromagnetic state, up to now no comprehensive researches on Cu 3 TeO 6 in other two magnetic (paramagnetic and ferromagnetic) states.On the other hand, the properties of materials will change in different degrees under different pressures.High-pressure studies of Cu 3 TeO 6 are important to understand its properties under pressure, and it is possible to nd new potential features of Cu 3 TeO 6 under high pressures.In above context, it is of great signi cance to study the effects of pressure on paramagnetic, ferromagnetic and antiferromagnetic spin-web Cu 3 TeO 6 .
In this paper, based on density functional theory, we systematically studied the crystal structures, electronic and magnetic properties of paramagnetic (PM), ferromagnetic (FM) and antiferromagnetic (AFM) Cu 3 TeO 6 under 0-100 GPa.We expect to ll in the blanks that studies about Cu 3 TeO 6 in three magnetic states under different pressure and provide some references in the search for new features of Cu 3 TeO 6 under pressures.This paper is organized as follows: we describe our rst-principles calculations details in the next Computational methods section.In results and discussion section, we present the calculated results concerning the structural, electronic and magnetic properties of PM, FM and AFM Cu 3 TeO 6 , and discuss their properties in comparison under 0-100 GPa, the summary of our work is given in the last section.

Computational Methods
As a prized technique in condensed-matter theory, rst-principles calculation has become one of the common research methods [29][30][31].It can be used to predict the structures and other physical properties of materials under high pressure theoretically, which can provide guidance for the research under high pressure [31].In our study, we used the rst-principles method based on density functional theory (DFT) [32,33] implemented in the Cambridge Sequential Total Energy Package (CASTEP) code [34].The calculations adopted the generalized gradient approximation (GGA) with the Perdew-Wang 1991 (PW91) functional [35] to deal with exchange-correlation functional.The GGA + U approach was used to calculate the electronic properties of three magnetic states.The calculation of paramagnetic Cu 3 TeO 6 was started without considering the spin polarization.The pseudoatomic calculations were performed on 3d 10 4s 1 , 4d 10 5s 2 5p 4 and 2s 2 2p 4 of Cu, Te and O atoms.In order to ensure the convergence of total energy, the cutoff energy of plane-wave was set to be 400 eV.The Brillouin zone integration was performed using the Monkhorst-Pack [36] method with a k-point grid of 2×2×2 for Cu 3 TeO 6 .We introduced the different pressures (0-100 GPa) during the geometry optimization (the different pressures were set using the CASTEP code) to study the effect of pressure on crystal structure, electronic and magnetic properties.

Crystal structures
In order to verify the reliability of the obtained results, the lattice parameters of antiferromagnetic Cu 3 TeO 6 at 0 GPa along with the available data [2,24,28,37] are shown in Table 1 for comparison.The results show that the lattice parameters are in good agreement with these values, showing the accuracy of the structural optimization.The crystal structure of Cu 3 TeO 6 at 0 GPa is shown in Figure 1, it is a cubic structure with the space group Ia3(-) [5].In this structure, each Te atom is surrounded by six O atoms, and they form a regular TeO 6 octahedra, [38] as shown in Figure 1(c).Per unit cell contains eight TeO 6 octahedras and twenty-four Cu 2+ ions [7,24].Six Cu atoms form a planar hexagon [24,25], surrounded by six O atoms, and they form a distorted octahedron [4,5,38], as shown in Figure 1(d).A regular TeO 6 octahedra is connected to irregular CuO 6 octahedras, forming a unique three-dimensional structure [27,39].There are two types of Cu-O bonds and Te-O bonds, resulting in the coupling of CuO 6 octahedrons and TeO 6 octahedrons [2].In three different magnetic states (paramagnetic, ferromagnetic and antiferromagnetic), Cu 3 TeO 6 crystals are all cubic structures with the space group Ia3(-) analyzing the optimization results.Table 1.Space group and calculated lattice parameters along with available experimental data.
To nd out the speci c differences in structure among three magnetic states under different pressures, the next step is to analyze the lattice parameter of three magnetic states from 0 to 100 GPa.The effects of pressure on lattice parameter and volume of Cu 3 TeO 6 are shown in Figure 2. It can be seen that these parameters have the similar change trend, namely, the lattice parameter and volume decrease monotonically with the increasing pressure and this is because the pressure compresses the crystal structures.In addition, it could be found that FM state possess greater lattice parameter and cell volume than other two states at the same pressure.With the increasing pressure, the lattice parameter and cell volume of AFM state are larger than that of PM state.

Electronic structures
The band structures of PM, FM and AFM states and the effect of pressure on band gaps of antiferromagnetic Cu 3 TeO 6 from 0-100 GPa are shown in Figure 3 and Figure 4.The vertical dashed line at 0 eV is the Fermi level.For FM and AFM band structures, the pink, yellow and purple lines represent the spin up.The blue, green and orange lines represent the spin down.The spin polarization of the PM state is not considered.From the calculated results of electronic structures, it can be observed that PM and FM band structures have no bandgap at 0 GPa, indicating that they are metallic [2].As shown in Figure 3(a) and Figure 3(b), with the increasing pressure, they retain their metallicity character.For AFM state, as in Figure 4(a) (only the important Brillouin points are shown in the abscissa), there is an insulation gap at the Fermi level, indicating that it has the non-metallic nature [23].The valence band maximum (VBM) and conduction band minimum (CBM) are both located at H point for AFM band structure, this indicates that the insulation gap of antiferromagnetic Cu 3 TeO 6 is direct band gap.The value of this direct band gap at 0 GPa is 1.784 eV and this result is basically consistent with that obtained in the literature [23].Figure 4(b) show the pressure dependence of the band gap of AFM state.Its band gap decreases monotonically with the increasing pressure, which means that its nonmetallic property is weakened.Moreover, in the low pressure section (0-50 Gpa), the band gap decreases fast with the increase of pressure; in the high pressure section (50-100 GPa), the band gap decreases slowly with the increase of pressure.
Next, we adopt the energy range from −25 eV to 25 eV to analyze the effects of pressure on total density of states (TDOS) of three states, as shown in the Figure 5. Comparing the total density of states at the Fermi level under different pressures, we discover that the peak at the Fermi level increases with the increasing pressure for PM state.This results show that its conductivity increases with the increasing pressure.For FM state and AFM state, the pressure has little effect on the total density of states at their Fermi level.From the whole, for three magnetic state states, the bandwidths of TDOS broaden and the TDOS dispersion increases with the increasing pressure.It indicates that the non-locality enhances and the electrons become more active under higher pressure.In other words, the hybridization is enhanced under pressures.
In order to analyze the electronic properties under pressure in detail, the partial density of states (PDOS) under pressure of 0, 40 and 80 GPa is plotted in Figure 6, which can well re ect the variation of PDOS with pressure.For PM state, the density of states at Fermi level originates predominantly from Cu-d and O-p states, and the density of states of Te atom orbits is approximately zero at Fermi level.When the density of each electron orbital is in the same energy range, it indicates that there is hybridization between them.Here, the hybridization is mainly generated by the Te-p and O-p states from −8.0 to -6.5 eV.There is a pseudo-gap between the peaks of O-p states to the left of the Fermi level.At 0 GPa, the density of states in the range of -19.3 eV to -17.4 eV originates predominantly from O-s states; in the range of 4.5 eV to 6 eV, it is predominantly contributed by Te-p states.With the increasing pressure, the peak of Cu-d states at -3 eV decreases and the pseudo-gap decreases.For FM state, there is no signi cant contribution of Te states around the Fermi level.The electrons from Cu-d and O-p states contribute little to the DOS near the Fermi level.At 0 GPa, the density of states in the range of -8 eV to -4 eV mainly consists of the Cu-d state.the Cu-d, Te-s, Te-p and O-s states have peaks around -5.4, -5.2, -6.5, and -17.5 eV, respectively.When pressure increases, the peaks of Cu-d, Te-s, Te-p and O-s states decrease and the bandwidths become broad.This implies that the electrons in these states are active under pressure [40].
For AFM state, it can be seen that the peak in the valence band near Feimi level is mainly contributed by Cu-d and O-p states, Te atom orbits is approximately zero at Fermi level [3].At 0 GPa, the density of states in the range of -8 eV to -3 eV originates predominantly from Cu-d and O-p states, which indicates that strong hybridization between Cu-d and O-p states [5,23].In addition, O-s states are mainly located between −19 and -18 eV, -16.7 and -14.4 eV.The Te-s and Te-p states also appear in these two ranges, respectively.This suggests that the hybridization between Te and O atoms [5].With the increasing pressure, the peaks of Cu-d, Te-s, O-s and O-p states decrease and the non-locality enhances.In summary, the pressure not only affects the crystal structures but also impact the electronic properties of Cu 3 TeO 6 in three states.

Magnetic properties
Because the ground state of Cu 3 TeO 6 is antiferromagnetic state [27], we analyze the magnetic properties of antiferromagnetic Cu 3 TeO 6 under different pressures.Figure 7 shows the spin moments dependence of pressure and the total magnetic moment dependence of pressure.In Figure 7(a), the spin magnetic moment of the Cu atoms at 0 GPa is 0.76 μ B , which is larger than experimental value of 0.64 μ B [7] and smaller than calculated value of 0.81 μ B in literature [23].The spin contribution of O atoms is small and Te atoms show nonmagnetic feature, Cu atom contributing the most to the total magnetic moment.With the increasing pressure, the spin contribution of Cu atoms decreases remarkably, and the spin moments have little change for Te and O atoms.This illustrates that the spin moment of Cu atoms is affected obviously by the pressure, while the spin moments of Te and O atoms are insensitive to pressures.In Figure 7(b), the total magnetic moment reaches the maximum at 20 GPa and decreases monotonously with increasing pressure from 20 to 100 GPa.
In order to get more information from the magnetic properties, the orbital projected DOS of Cu-d, O-p, Te-s and Te-p states under 0, 40 and 80 GPa are shown in Figure 8, the positive and negative values on the y axis stand for spin-up and spin-down, respectively.The calculated magnetic moments of O-s [23], Cu-s and Cu-p states are small and it is negligible, so they are not shown here.It can be seen that there are spin down states of Cu and O atoms around 2.5 eV, which indicates that strong hybridization between Cud and O-p states [5].For Cu-d states, most of the spin moments are totally occupied and a few spin moments are partially occupied, showing the high spin state of Cu ions in Cu 3 TeO 6 [5].The spin contribution of Te atoms is small because the distribution of the spin-up and spin-down densities are substantially symmetric for different orbital.Total magnetic moment is mainly from the spin down states of Cu-d and O-p states, and these results are in good agreement with previous results.For Cu and O atoms, the spin up states and spin down states are decreased with pressure.The spin up states and spin down states of Te atoms move sideways under the pressure.The total magnetic moment varies mainly with the spin contribution of Cu and O atoms.

Summary
Based on the density functional theory, we have studied the structural, electronic and magnetic properties of paramagnetic, ferromagnetic, and antiferromagnetic spin-web Cu 3 TeO 6 in pressure range 0-100 GPa.
The results of the calculations reveal that Cu 3 TeO 6 crystals are all cubic structures in three magnetic states, and their lattice parameters decrease monotonically with the increasing pressure.The calculated band structures show that PM and FM Cu 3 TeO 6 behave in a metal manner at all pressures of interest.For AFM state, it exhibits a non-metallic nature with a direct band gap, and its nonmetallic property is weakened with the increasing pressure.For the three states, the bandwidths of TDOS broaden obviously,