Supplementary Information
Interlocked chiral/polar domain walls and large optical rotation in Ni3TeO6
Xueyun Wang1, Fei-Ting Huang1, Junjie Yang2,a), Yoon Seok Oh1,3, and SangWook Cheong1,2,b)
1
Rutgers Center for Emergent Materials and Department of Physics and Astronomy, Rutgers University, Piscataway,
New Jersey 08854, USA
2
Laboratory for Pohang Emergent Materials and Max Plank POSTECH Center for Complex Phase Materials, Pohang
University of Science and Technology, Pohang 790-784, Korea
3 Department
of Physics, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Korea
Section 1
Ni3TeO6 is a rare antiferromagnet that crystallizes in a polar and chiral structure as shown in
Fig. S1. One unit cell of Ni3TeO6 consists of three building blocks while 3NiO6+TeO6 form each
building block as shown with a bracket in Fig. S1 (as well as in Fig. 1a in the main text). Three
building blocks are linked through face sharing of TeO6 (gray) and Ni(i)O6 (orange) octahedra.
Note the presence of 120 rotation of adjacent building blocks.
FIG. S1. Ni3TeO6 crystallographic structure. One unit cell consists of three [NiO6+TeO6] building
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blocks. Gray and orange/yellow/purple spheres represent Te and three Ni cations, respectively,
while (light) green spheres represent oxygen anions.
Section 2
The concept of CCM (continuous chirality measure) was given in order to provide an exact
quantitative scale of chirality, rather than labeling objects as being either chiral or achiral. It
estimates the minimal distances that all vertices of a shape must move to attain the nearest achiral
symmetry [see Ref 16 in the main text]. Figure S2a demonstrate that the magnitude of chirality in
the 2 dimensional triangles gives: (a) > (b) > (c), and (c) is actually achiral. The CCM value is
related with how far to achieve an achiral structure as shown in Fig. S2a red dashed isosceles ones.
In a way that triangle-a is far more away from its achiral shape than triangle-b, comparing with
achiral triangle-c, so magnitude of chirality for triangle-a is the largest.
FIG. S2a. (a-b) Two scalene triangles (black) and their nearest achiral triangles (red dashed).
(c) An achiral triangle [new Ref 17 in the main text].
Fig. S2b shows three types of corundum-related hexagonal ABO3 structure where A and B
cations have six-fold coordination, instead of, e.g., 7-12-fold coordination in ABO3 perovskite.
The corundum structure of -Al2O3 or Cr2O3 is centrosymmetric, but due to the size mismatch of
A and B site ions, oxygen cages around cations are highly distorted in LiNbO3 and Ni3TeO6,
resulting in polar structures (R3c and R3, respectively). Blue and red triangles, which are part of
the first and second honeycomb layers, respectively, are labelled with bond lengths. Red and blue
helixes are shown by tracking the rotation of the shortest (bold) bond in the corresponding-color
triangle along the c axis. Note that red and blue helixes rotate in an opposite fashion. Importantly,
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the net chirality with red and blue helices exists if two different-color triangles are not identical as
illustrated in Fig. S2a. For example, in the case of Ni3TeO6, red scalene triangle has bond lengths
of 2.78, 2.88 and 3.2 Å and bond angles of 68.82o 54.16o and 57.02o while the values are 3.15 Å,
3.11 Å and 2.61 Å with bond angles of 49.2o, 66.2o and 64.6o in blue ones. Here we emphasize
that the chirality in Ni3TeO6 is mainly induced by non-cancelled components in both x and y
directions due to different asymmetric triangles and c-lattice doubling is not needed. Though
LiNbO3 has scalene triangle in red and blue chains but the effect has been cancelled out by identical
red and blue triangles, thus it is not-chiral (or antiferro-chiral), but Ni3TeO6 is chiral (or ferrichiral).
FIG. S2b. The unit cells of corundum (-Al2O3, Cr2O3), LiNbO3 and Ni3TeO6 structures in
different polar and chiral states. A/B cations are shown with large spheres, and oxygen anions by
red small spheres. -Al2O3 and Cr2O3 are centrosymmetric, LiNbO3 is polar, and Ni3TeO6 is chiral
and polar. The structures can be readily distinguished in terms of the different nature of oppositechirality helices.
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Section 3
In order to check the switchability of polarization, we carried out electric polarization vs. electric field,
P(E), hysteresis loop measurements on a 10 m-thick Ni3TeO6 single crystal at room temperature in silicon
oil. The electric fields at the frequency of 636 Hz were applied along the c axis using a programmable
function generator (Stanford Research DS340) and a high voltage amplifier (Trek 609E-6), and the current
density vs. E data J(E) were recorded using an oscilloscope (Tektronix TDS1010). Polarization was
obtained from integrating J(E) with respect to time.
Fig. S3 shows our experiment data of P(E) (red line) and J(E) (black line) of a Ni3TeO6 single crystal.
J(E) doesn’t exhibit any sharp current spike that corresponds to switching current. P(E) loop appears to
exhibit a polarization of 0.7 C cm-2 at 3.9 MV cm-1; however, the square shape is primarily due to a
relatively large RC time constant of this specimen (0.2 ms), compared with the measuring frequency (636
Hz). Therefore, polarization of Ni3TeO6 does not switch even at 3.9 MV cm-1, which is 20 times larger than
the coercive field of LiNbO3 (185 kV cm-1). Therefore, Ni3TeO6 is pyroelectric, rather than ferroelectric.
From P(E) and J(E) data, dielectric constant and electric resistivity at room temperature are estimated to
be  = 2.4 and ~1 G∙cm, respectively.
FIG. S3. Electric Polarization (red line) and corresponding current density (black line) as a
function of electric fields, applied on a 10 m-thick Ni3TeO6 crystal along the c-axis at room
temperature.
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