Conclusion• We studied the electronic structure of LiMVO4(M=Ni and Cu)from first-principles calculations. • We find the cubic ground-state structure causes the Li and Ni ions to randomly distribute in LiNiVO4.Antiferromagnetic structure was found to be ground state of magnetism for LiNiVO4 at low temperature. • Semiconductor bands with a band gap of 1.5eV are obtained for LiCuVO4 under this noncollinear magnetic structure. To obtain this noncollinear ground state, both the on-site Coulomb interaction and the spin-orbit coupling need to be employed in the calculations. The most stable xy orbit can rationalize why the spin of Cu2+ ions rotates only along xy plane after the spin-obit coupling is considered. •References[1] B.J.Gibson, R.K.Kremer et al. Incommensurate antiferromagnetic order in the S=1/2 quantum chain compound LiCuVO4 Physica B 350(2004)e253-256[2] C.Gonzalez,M.Gaitan et al. Structure and magnetic properties of LiMVO4(M=Co,Ni,Cu) spinels Journal of Materials Science 29 (1994) 3458-3460[3] R.S.Liu, Y.C.Cheng, et al. Crystal and electronic structures of inverse spinel-type LiNiVO4 Materials Research Bulletin 36(2001)1479-1486[4] H.J.Xiang and M.-H. Whangbo Density-Functional Characterization of the Multiferroicity in Spin Spiral Chain Cuprates PhysRevLett.99.257203

Special electronic structures of inverse spinels LiMVO4(M=Ni and Cu): a first-principles study

S.Li (李晟 ) and Z.Q.Yang (杨中芹 )Department of Physics, Fudan University, Shanghai 200433, China

MotivationRecently, LiMVO4(M=Ni and Cu) are typical inverse spinels which have attracted considerable attention due to their abundant and fantastic properties, such as long-range orbital ordering and multiferroicity. LiNiVO4 and LiCuVO4 have completely different magnetic behaviors due to random distribution of Li and Ni in LiNiVO4 and ordered Li and Cu in LiCuVO4. But there was no investigation on the mechanisms of the disorder/order of those cations in the compounds yet. We would like to study the electronic structures of them systematically from first-principles calculations.

Since Li 2S electron is almost lost in both LiNiVO4 and LiCuVO4, it mainly occupies above EF. It was not shown in the DOS figure. When U is not considered, there generates a gap of 0.4eV near the EF, which is formed mainly by the energy interval of the occupied and unoccupied Ni 3d states near the EF.

After U is added into the cal-culations, the gap is widened to 2.3eV since the occupied and unoccupied Ni 3d states both move away from the EF with U considered.

LiCuVO4 NM FM AFMNCM

A B C D E

GGA 246.4 72.4 70.4 15.4 13.7 0 0 0

Fig.4 Different types of NCM structures considered for LiCuVO4. For each case, the left Cu line corresponds to line(I) marked in the right panel in Fig.1,while the right Cu line,line(II)

Table-2 Total energies(in meV) for different magnetic structures for LiCuVO4

based on GGA calculations without U or SOC considered.

Calculation Methods and Models

Fig.2 Total energy per unit cell versus lattice constant for LiNiVO4 and LiCuVO4Fig.1Crystal structure of LiMVO4(the left is LiNiVO4 and the other is LiCuVO4

Results and Discussion

Calculation method: The density functional theory calculations using VASP code. Valence electrons were described by a plane wave basis set with the energy cutoff of 460 eV and valence-core electron interactions were treated with projector augmented wave(PAW) method at the level of generalized-gradient approxiamtion (GGA).16x16x16 k-point grids were used for the calculations with primitive unit cell. To improve the converge in the eigenstates at the Fermi level(EF), a Gaussian smearing of sigma=0.01 eV was applied. The on-site Coulomb interactions were considered for Ni and Cu 3d states with the parameters of U=6.0eV and J=0.8eV. Only commensurate(collinear or noncollinear) magnetic ordering was considered in our calculations.

LiCuVO4(NCM) A B C D E

GGA+SOC 37.3 0.6 0.0 0.0 0.7GGA+U 26.3 19.2 17.2 17.2 17.2

GGA+U+SOC 9.2 2.0 2.6 2.5 0.0

Fig.3 Calculated total and partial densities of states for AFM LiNiVO4 within GGA and GGA+U methods, respectively.

Energy(eV) Space group Li/M M/Li

LiNiVO4Fd3mImma

-97.720-94.556

-97.720-96.441

LiCuVO4Fd3mImma

-93.644-93.974

-93.644-92.763

The total energies of LiMVO4(M=Ni and Cu) with different geometric structures. “Li/M” →“M/Li” means Li ions exchange positions with M in the lattice. The bold space group in Table I gives the ground state of the compound.

It is the stable cubic structure of LiNiVO4 that gives rise to random distribution of Li/Ni ions in the lattice. It is expected that Li/Cu may also occupy randomly when LiCuVO4 takes cubic structure at certain conditions.

Table-1 energy difference between two structures of LiMVO4

Table-3 Total energies(in meV) for the five NCM structures shown in Fig.4 for LiCuVO4.The lowest energies in the cases with U and without U are set as zero.

Fig.5 Calculated total and partial densities of states for LiCuVO4 corresponds to the ground state of NCM-(e) within GGA and GGA+U methods, respectively.Our calculation show that when the on-site Coulomb interaction and the SOC, which play a very important role in the electronic structures of such kind of inverse spinels. are considered together, the correct NCM-(e) ground state can be produced in calculations.