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

RIKEN Accel. Prog. Rep. 51 (2018)

Study of Implanted Muons in YBa2 Cu3 O6
I. Ramli,∗1,∗2 S. S. Mohd-Tajudin,∗3 S. Sulaiman,∗3 M. I. Mohamed-Ismail,∗3 and I. Watanabe∗1,∗2Since the discovery of cuprate-based high-Tc superconductivity, enormous eﬀorts in both experimental
and theoretical studies have invested to understand its
superconductivity mechanism. However, this mechanism is still unclear and debatable. YBa2 Cu3 O6(YBCO6 ) is one of the mother compunds of cupratebased high-Tc superconductors. This system shows
antiferromagnetic (AF) ordering with TN = 350 K.1)
The AF ordering of this system disappears by doping, YBa2 Cu3 O6+x , and superconductivity appears.2)
We study the magnetic and electronic properties ofYBCO6 by using the muon-spin resonance (µSR) technique. This technique is extremely sensitive to probe
local magnetism but has a limitation, because muonsites in the lattice and perturbation by muons to thehost system are unknown.3)
Therefore, we have been developing the method toestimate muon sites in YBCO6 by using density functional theory (DFT) which is implemented in Vienna
Ab-initio Simulation Package (VASP). Based on theµSR experimental data of YBCO6 below TN , threemuon-spin precession components are observed, indicating the presence of three diﬀerent kinds of muonsites in this system.
We ﬁrst calculate the density of state and the band
structure to conﬁrm the insulator state in this system. Considering strong electron correlation among
cuprate ions in this system, we optimize the exchangecorrelation function and the value of Hubbard parameter (U). The second step is to calculate the potentials
in this system under the same condition as that in theﬁrst step. In the calculation of the potential, the pseudopotential for hydrogen is used, because a muon isconsidered to be a light isotope of a proton. As a muon
has a positive charge, it prefers to be located at sitesof the local minimum of the potential. Thus the local
minimum site can be regarded as the initial muon site.
We found three kinds of muon sites (marked M1-M3)
in YBCO6 as shown in Fig. 1.
To investigate the eﬀect of the presence of a muonin the system, we performed calculation by placing amuon at the initial site in the 4x4x2 supercell and allowing the lattice to be relaxed. Then, we got the ﬁnal
site of the muon, the change of local electronic statesand spatial spin distributions.
We are also developing the program to calculate internal ﬁelds at the muon stopping sites. In this program, we considered zero point energy (ZPE) vibration of a muon because the muon is a light particle.
∗1∗2∗3RIKEN Nishina Center
Department of Condensed Matter Physics, Hokkaido University
School of Distance Education, University Sains Malaysia- 199 -Fig. 1. Possible muon sites in YBCO6 estimated from ourDFT calculations. Yellow area indicates the isosurface
at 500 meV.

The density distribution of the muon extends over theamplitude of the ZPE vibration. The density distribution of muon was calculated by solving the Schrödinger
equation for the wave function of muon around thelocal minimum of potential in the range up to 1.5
angstrom. By taking all those results into account,
we calculated the internal ﬁelds at each kind of muonsite to be 116 G for the M1, 335 G for the M2, and446 G for the M3 sites.
From previous µSR measurements for the antiferomagnetic phase of YBCO, Brewer et al. found one
muon spin precession frequency in YBCO6.2 which corresponds to the internal ﬁeld 300 G4) and Nishida et al.
found two additional muon spin precession frequencies
which correspond to the internal ﬁelds of 100–150 Gand 1.8 kG. The amplitude of muon spin precession for
the 1.8 kG is less than 1%.5) The calculated values on
the internal ﬁelds for the M1 and M2 sites are compatible with the experimental results, 100–150 G and300 G, respectively. However, the calculated value for
the M3 site is not compatible. To clarify the origin of
this discrepancy in the values for the M3 site, the µSR
measurement for the high-quality YBCO single crystal
and further checking the calculation for the M3 site arestill ongoing
References
1) N. Nishida et al., Jpn. J. Appl. Phys. 26, L1856 (1987).
2) Y. Koike et al., J. Phys. Soc. Jpn. 85, 091006 (2016).
3) P. Bonfa et al., J. Phys. Soc. Jpn. 85, 091014 (2016).
4) J. W. Brewer et al., Phys. Rev. Lett. 60, 1073 (1988).
5) N. Nishida et al., Hypefine Interaction 63, 183–197(1990).