Supplemental Information: Depinning of the ferroelectric domain wall in congruent LiNbO3

Donghwa Lee, Venkatraman Gopalan and Simon R. Phillpot

Computational Methodology

All the calculations are performed with density functional theory (DFT)1 using the generalized

gradient approximation (GGA)2 for exchange and correlation. Monkhorst-Pack3 k-point sampling with

a grid of up to 2x8x4 is used. The projected augmented wave (PAW) method4 implemented in Vienna

Ab Initio Simulation Package (VASP) code5 is used for pseudo-potential approaches.6 The Li 2s1, Nb

4p64d45s1, and O 2s22p4 are treated as valence electrons. An energy cutoff of up to 500 eV is used for

the plane-wave representation of the wavefunctions. Atomic structures are relaxed until all Hellman-

Feynman forces are below 0.01 eV/Å. The residual minimization scheme-direct inversion in the

iterative subspace (RMM-DIIS) algorithm7 is used to optimize several individual energy bands at the

same time. To avoid the interaction between a defect and its mirror image through periodic boundary

condition, the origin of the k-point mesh has been shifted from Γ point to (0.5, 0.5, 0.5).8 The nudged

elastic band (NEB) method9,10 with 10 images is employed in order to estimate the energy barrier for

the Y-wall motion.

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Figure S1. Change in potential energy of NbLi as a function of distance from the Y-wall.

We perform multiple calculations by putting a single MgLi at various distances from a Y-wall, next to

which a NbLi is positioned. Figure S1 shows the change in formation energy of the MgLi with

respect to that of the maximum at the middle of two Y-walls; two Y-walls are formed by periodic

boundary conditions (PBCs). This energy analysis shows that the MgLi preferentially sits either next

to the NbLi or near by the other Y-wall in the simulation supercell, which doesn’t include the NbLi .

Figure S2. Potential energy profile along the migration pathway of the NbLi , when system is doped

with either a MgLi or a ZnLi. The MgLi dopant cases are shown as red with square, while the ZnLi

case is drawn as green with circle. Empty points represent the results from the dopant sitting next to

the NbLi , while filled point represent the results, when the dopant sits far away from the NbLi .

2

Figure S2 shows the potential energy profile along the migration pathway of the NbLi when either a

MgLi or ZnLi sits is either close by or far away. When both of dopants are far away, the reductions in

the migration barrier for the NbLi are identical; the migration barrier is reduced from 3.44 eV to 3.15

eV. When the dopant is sitting next to the NbLi , the reduction in the migration barrier of the NbLi

obtained by the MgLi is slightly larger than that with the ZnLi; the barrier is reduced to 3.26 eV for

MgLi and 3.29 eV for ZnLi.

References

1 W. Kohn and L. J. Sham, Phys. Rev. 140 (4A), A1133 (1965).2 J. P. Perdew and W. Yue, Phys. Rev. B 33 (12), 8800 (1986).3 H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13 (12), 5188 (1976).4 P. E. Blochl, Phys. Rev. B 50 (24), 17953 (1994).5 G. Kresse and J. Furthmuller, Phys. Rev. B 54 (16), 11169 (1996).6 David Vanderbilt, Phys. Rev. B 41 (11), 7892 (1990).7 P. Pulay, Chem. Phys. Lett. 73 (2), 393 (1980).8 C. G. Van de Walle and J. Neugebauer, J. Appl. Phys. 95 (8), 3851 (2004).9 H. Jónsson, G. Mills, and K. W. Jacobsen, Nudged Elastic Band Method for Finding

Minimum Energy Paths of Transitions. (World Scientific, 1998).10 G. Henkelman, B. P. Uberuaga, and H. Jonsson, J. Chem. Phys. 113 (22), 9901 (2000).

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