Ⅲ-2. Atomic & Solid State Physics (Muon)
RIKEN
Accel. Prog. Rep. 56 (2023)

RIKEN Accel. Prog. Rep. 56 (2023)

DFT investigations on magnetic properties with Muon in La2 CuO4
using LSDA + U functional
S. Charoenphon,∗1,∗2 P. Reunchan,∗1 and I. Watanabe∗2Lanthanum cuprate (La2 CuO4 , LCO) is a typical
Mott insulator exhibiting a strong covalent state of Cu3d with O-2p within the two-dimensional (2D) CuO2
plane. In a previous study, LCO has been well investigated experimentally and theoretically; however, questions regarding electromagnetic states remain unanswered. The primary concern is the on-site Coulomb
potential, U, and the covalent state of the electronic
orbitals of Cu. The muon spin resonance technique(µSR) can provide information on local magnetic ﬁelds
at the muon site. However, obtaining the muon effect in the structure.5) In this study, we apply thedensity functional theory (DFT) + U to comprehensively investigate the electronic structure surrounding
the muon. Our attempt to solve the problem within
the DFT framework has yielded mixed results. Notably, most studies have attempted to correct the antiferromagnetic (AFM) ground state model of LCO andhave failed to provide a handle on the key experimentally observed properties of LCO. More speciﬁcally,
the local-spin-density approximation (LSDA) incorrectly predicts LCO to be nonmagnetic (NM) metals
in complete disagreement with the experimental value.
The generalized gradient approximation (GGA) produces a weak AFM. Thus, the development of methods
that have stronger electron correlations to stabilize theAFM ground state is necessary. DFT + U is a methodthat was proposed to improve the strong correlationsystem.6) Among the most implemented methods inthe DFT + U realm is the LSDA + U method.
The DFT calculation was performed using theRIKEN-integrated HOKUSAI Supercomputing Facility. Ab initio calculations were performed in the Vienna ab initio simulation package (VASP) with an energy cutoﬀ of 400 eV for the plane-wave basis set. We
employed the Hubbard parameter U = 4.87 eV.4) We
use a 28-atoms primitive cell with a 6×6×3 Γ -centeredk-point mesh for the Brillouin zone integrations to calculate the fundamental properties of LCO shown inFig. 1(a). In addition, a supercell structure containing
252 atoms (3 × 3 × 1 unit cell) was adopted for a calculation to consider the eﬀect of the relaxation of muonposition.
The lattice parameters calculated based on LSDA+ U, band gap, and magnetic moment are listed inTable 1. The experimental values. The calculated
bandgap was obtained as 1.15 eV, slightly higher thanthe experimental value of 1 eV.3) Next step, the LSDA+ U was conducted, including the muon, to repro∗1∗2

RIKEN Nishina Center
Department of Physics, Kasetsart University- 131 -Fig. 1. (a) Crystal structure of LCO in the LTO phase withcopper, oxygen, and lanthanum atom indicated as blue,red, and green spheres, respectively. (b) Schematic ofa CuO6 octahedral showing the O apical site and Cu,
O in the planar site. (c) Electrostatic potential calculation result. The grey sphere indicates three localminimum potential positions as candidates for initialmuon-stopped positions.

Table 1. Calculation of structural parameter, band gap,and magnetic moment of a unit cell of LCO.
Function

The bandMagnetica

Lattice parameterbcgap (eV)moment (µB)

Exp.

5.35715.406113.1431130.48 ± 0.152

LSDA+U

5.196

5.246

12.903

1.15

0.469

duce the µSR results. We estimate the initial positionof muon injection in LCO obtained from the electrostatic potential. There are three possible local minimum potential positions that the muons can stop ina structure: M1, M2, and M3 as shown in Fig. 1(c),compared with muon spin resonance technique µSR results.4,5) Our method is fundamentally similar to theGGA functional method4) except for the diﬀerence inthe functional. This is important for investigating theeﬀect of the diﬀerence in the functional in the previousresult.
The ﬁnal muon position and local deformations of
the crystal structure estimated from our LSDA + U +µ calculations are shown in Fig. 2. We calculated themagnetic moment of Cu without muon to be 0.450 µB .
Following relaxation, the magnetic moment calculationof Cu changed to 0.414, 0.453, and 0.449 µB for M1,M2, and M3, respectively.

Ⅲ-2. Atomic & Solid State Physics (Muon)

RIKEN Accel. Prog. Rep. 56 (2023)

Fig. 2. (a) Structure of LCO without muon. The ﬁnal
muon position after relaxation for (b) M1, (c) M2, and(d) M3, respectively. The Grey spheres indicate theinitial position. The black spheres indicate the ﬁnal
position of the muon after relaxation.

In conclusion, the role of muon perturbation was
found to deform the local crystal structure in the immediate vicinity of the muon. This eﬀect resulted in aslight reduction in the magnetic moment surrounding
the muon. Moreover, a new result is that LSDA + U
is clearly proven to be not suitable for describing theelectronic state of a strongly correlated system, particularly LCO.
References
1) M. Reehuis et al., Phys. Rev. B 73, 144513 (2006).
2) D. Vaknin et al., Phys. Rev. Lett. 58, 2802 (1987).
3) S. Uchida et al., Phys. Rev. B 43, 7942 (1991).
4) R. Ramadhan et al., Phys. Rev. R 4, 033044 (2022).
5) J. S. Möller et al., Phys. Scr. 88, 068510 (2013).
6) M. Yu et al., npj Comput. Mater. 6, 180 (2020).

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