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66
Appendix A
Monoclinic SrIrO3
A.1
Introduction
Monoclinic SrIrO3 has a three dimensional network of IrO6 octahedra connecting each other at corner or face (Fig. A.1). Ir atoms align in the ab plane
like the triangular lattice. Such the layers stack along the c direction with
six-fold periodicity. The structure is almost hexagonal but slightly distorted
to monoclinic. This structure is called as 6H or 6M by taking the periodicity
along the c direction and the symmetry. The space group of the structure is
No. 15 (C 1 2/c 1). The lattice parameters are given as a = 5.60401(29) ˚
A,
b = 9.6256(4) ˚
A, c = 14.1834(7) ˚
A and β = 93.202(4)◦ [48].
Band calculation predicts that monoclinic SrIrO3 will have Dirac nodes at
A and M points on the boundary of the Brillouin zone (Fig. A.2) [49].
Polycrystalline bulk of monoclinic SrIrO3 is paramagnetic, and shows semimetallic resistivity [49]. These results are consistent with the band calculation.
For thin film, there is a study which reported realization of monoclinic SrIrO 3
as epitaxial thin films on SrTiO3 (111) substrates [50]. However, to our knowledge, there is no previous report which investigated electric transport properties
of monoclinic SrIrO3 thin films.
Figure A.1: Crystal structure of monoclinic SrIrO3 [48]. Lime balls: Sr. Yellow
balls: Ir. Red balls: O.
67
(a) Notation of k-space.
(b) Band dispersion.
Figure A.2: LDA calculation of band structure of 6M SrIrO3 with spin orbit
coupling. The figures are quoted from T. Takayama et al. (2019) [49].
A.2
Methods
We synthesized epitaxial thin films of SrIrO3 on SrTiO3 (111) substrates by
pulsed laser deposition. We performed X-ray diffraction and X-ray reflectivity
measurements for evaluation of crystal structure. We investigated transport
properties of the samples. These methods are similar to those for perovskite
iridates explained in the main article. For electric transport measurements of
monoclinic SrIrO3 / STO(111) samples, we used 5 mm × 2.5 mm samples with
edges parallel to [211] and [011] directions and printed the single Hall bar pattern
(Fig. 2.6a) on it. Thus, current is parallel to [211] or [011], but not controlled1 .
A.3
A.3.1
Results
Crystal structure
Fig. A.3 shows a result of XRD 2θ-θ scan of a SrIrO3 thin film sample fabricated
on SrTiO3 (111) plane. Two sharp peaks at 2θ = 40◦ and 86◦ correspond to 111
and 222 reflections of the SrTiO3 substrate. Peaks from the SrIrO3 film show
roughly three-fold periodicity of SrTiO3 nnn reflections, which are identified as
0 0 2n reflections of the monoclinic phase of SrTiO3 . The out-of-plane lattice
constant of the SrTiO3 film is estimated as 14.17(1) ˚
A and agrees with the bulk
value (c sin(β) = 14.16 ˚
A [48]).
To investigate the epitaxial relationship between the film and the substrate,
we conducted XRD reciprocal mapping around 231 and 131 SrTiO3 diffraction
spots (see Fig. A.4.). Film peaks around 231STO are identified as 2 0 12, 1 3 12,
1 3 12 and 2 0 12, while ones around 131STO are 2 2 11, 0 4(4) 11 and 2 2 11,
though overlapping of the peaks makes it difficult to determine their precise
positions. Therefore, relationship of crystalline orientation between film and
substrate is summarized as below:
a × b || [111] and
a || [011] or
a || [101]
or
a || [110] )
(A.1)
1 We should have controlled it, but we did not notice inequivalence of [211] and [011] when
we did the experiments.
68
10
STO 222
SIO 0 0 12
10
SIO 006
SIO 004
10
SIO 0 0 10
10
6M SrIrO3 / SrTiO3(111)
SIO 008
STO 111
10
SIO 002
XRD Intensity (cps)
10
10
20
40
60
80
100
2q (degree)
Figure A.3: XRD 2θ-θ scan of monoclinic (6M) SrIrO3 / SrTiO3 (111) film.
0.92
0.82
6M SrIrO3
6M SrIrO3
-1
0.88
2 0 12
0.86
0.84
0.82
0.80
1 3 12
1 3 12
2 0 12
0.78
0 4 11
2 2 11
0.76
0.74
STO 131
0.72
6M SrIrO3 / SrTiO3(111)
6M SrIrO3 / SrTiO3(111)
0.32
2 2 11
0.80
STO 231
q[111] (Å )
-1
q[111] (Å )
0.90
0.36
0.70
0.40
0.36
-1
0.40
0.44
0.48
-1
q[011] (Å )
- q[121] (Å )
(a) Around 231STO .
(b) Around 131STO .
Figure A.4: XRD reciprocal space mapping of monoclinic (6M) SrIrO3 /
SrTiO3 (111) film. Markers: calculated from bulk lattice constants.
The in-plane lattice of SrIrO3 is not fixed to that of STO, but lattice parameters
of film along [011]STO direction shrinks by ∼ 0.2 - 0.5 % from bulk. Distances
in reciprocal space between plus-minus pairs of diffractive points like 2 2 11 SIO
and 2 2 11SIO shrink from estimation from bulk lattice constants, which suggests
that the lattice constant β of SrIrO3 becomes closer to 90◦ .
A.3.2
Semimatallic properties
Fig. A.5 shows experimental results of temperature-dependent resistivity of
monoclinic SrIrO3 thin films. Resistivity gradually decreases as temperature
decreases, similarly to bulk [49]. This temperature-dependence supports the
semimetallic electronic state.
Fig. A.6 displays measured Hall coefficients of monoclinic SrIrO3 film samples. The results show V-shaped temperature-dependence and large sampledependence. The temperature-dependence of RH suggests existence of three
kinds of conducting carriers: (1) hole-type carriers which has positive contribution on RH at low temperature (< 10 K), (2) electron-type carriers which
has negative contribution on RH at moderate temperature (∼ 50 K), and (3)
69
1.4
(mΩcm)
1.2
1.0
0.8
#12
#14
#13
#01
0.6
0.4
0.2
6M SrIrO3 / SrTiO3(111)
0.0
100
200
300
T (K)
Figure A.5: Temperature-dependent resistivity of monoclinic (6M) SrIrO 3 /
SrTiO3 (111) films.
hole-type carriers which have positive contribution on RH at high temperature
(> 150 K). Since low temperature properties are determined by band structure
very near the Fermi level EF , (1) indicates a hole band crossing with the Fermi
level. If several band crosses with the Fermi level, the one with highest mobility
will be hole-type. On the other hand, (2) suggests that an electron band with
higher mobility than hole (1) is located a few milli-electron volts above EF .
Therefore, (1) and (2) suggest the existence of Dirac nodes a few milli-electron
volts above EF . Positive Hall coefficient (3) comes from a non-Dirac hole band
with large carrier density. Large sample-dependence of RH indicates that carrier balance is strongly affected by sample quality, probably lattice relaxation
or degree of oxygen deficiency.
Fig. A.7a shows magnetoresistance (MR) of monoclinic SrIrO3 film and
Fig. A.7b shows field direction-dependence of MR. MR takes its maximum value
when the field is parallel to the current, indicating orbital contribution. MR
is positive and linear-like. These features may be attributed to the linear MR
at quantum limit which is often observed in semimetals with small Fermi surfaces [31], like Dirac semimetals.
A.4
A.4.1
Discussion
Crystal structure
As mentioned in the main article, AIrO3 hosts a variety of crystalline polytypes,
and the monoclinic (6M) perovskite structure is a stable structure for bulk
SrIrO3 at ambient pressure. The orthorhombic perovskite phase is realized
at high pressure and high temperature. In our experiments, SrIrO3 grown on
STO(111) realizes the monoclinic phase, while SrIrO3 on STO(100) forms the
perovskite phase. Reasons of the selective growth of the crystalline polytypes
are attributed to characters of (001) and (111) planes, not strengths of epitaxial
strain. We suggest two factors which will enable this selective growth.
70
2.0
6M SrIrO3 / SrTiO3(111)
1.0
0.5
-3
RH (x10 cm /C)
1.5
0.0
-0.5
#12
#14
#13
#01
-1.0
-1.5
4 6
4 6
10
100
4 6
1000
T (K)
Figure A.6: Temperature-dependent Hall coefficient of monoclinic (6M) SrIrO 3
/ SrTiO3 (111) films.
(1) Similarity of crystal structures. The orthorhombic perovskite structure of SrIrO3 has only corner-sharing connections between IrO6 octahedra
and can be obtained by lattice distortions from cubic perovskite structure
of SrTiO3 . Therefore both (001) and (111) planes of SrTiO3 will allow
continuous connection to orthorhombic perovskite SrIrO3 . On the other
hand, the monoclinic SrIrO3 has both corner- and face-sharing connections between IrO6 octahedra. The direction of face-sharing connections
is along the c axis of monoclinic SrIrO3 unit cell, and IrO6 octahedra align
in the ab plane like the (111) plane in cubic perovskite. However, one cannot find a crystalline plane in monoclinic SrIrO3 which has square-like
periodicity like the (001) plane of cubic perovskite. This analysis supports the experimental results that the monoclinic SrIrO3 phase grows
not on (001)STO but on (111)STO .
(2) In-plane lattice fixing The XRD results show that the in-plane lattice of
perovskite SrIrO3 is fixed to the substrate while that of monoclinic SrIrO3
is partially relaxed. This means that perovskite SrIrO3 on STO(001)
receives stronger compressive strain than monoclinic SrIrO3 on STO(111),
which is consistent with the bulk phase diagram in which perovskite SrIrO 3
is located at high pressure. The reason for this difference of in-plane lattice
fixing is still an open question.
We suggest a hypothesis that different charge ordering patterns of SrTiO 3 ’s
surfaces may allow this difference of in-plane lattice fixing. When the [001]
direction is defined as the stacking direction, the surface plane contains either [Sr2+ O2− ] or [Ir4+ (O2− )2 ] ions. Therefore, the SrTiO3 (001) plane has
both positive and negative ions and will make a fluctuating potential for
deposited particles. On the other hand, when the [111] direction is defined
as the stacking direction the surface plane contains either [Sr2+ (O2− )3 ] or
[Ir4+ ] ions. These planes are more homogeneous than (001) planes in terms
of variation of the charges of the ions which the planes include. Therefore,
the SrTiO3 (111) plane will cause a more moderately changing potential
71
1.0
6M SrIrO3 / SrTiO3(111)
MR (%)
0.8
2K
5K
10K
20K
40K
80K
0.6
0.4
0.2
0.0
-10
-5
10
B (T)
(a) Transverse magnetoresistance.
(mΩcm)
0.4685
6M SrIrO3 / SrTiO3(111)
0.4680
0.4675
2K
9T
0.4670
90
180
270
360
Angle (degree)
(b) Dependence of direction of external field. B || [111] ⊥ I for 0◦ . B || [110] || I for
90◦ .
Figure A.7: Magnetoresistance of monoclinic (6M) SrIrO3 / SrTiO3 (111) film.
72
on the surface than the SrTiO3 (001) surface. This difference of the ordering patterns of charges in SrTiO3 ’s surfaces may explain the difference of
in-plane lattice fixing depending on (001) or (111) surfaces.
A.4.2
Semimetallic properties
Monoclinic SrIrO3 films have large sample-dependency in Hall effect, which
indicates semimetallic states with both electrons and holes. The scales of
carrier density and mobility are roughly estimated as n ∼ +1021 cm−3 and
µ ∼ +1 cm2 V−1 s−1 using a single carrier model. Na´ıvely speaking, these values, relatively large carrier density and small mobility, have least “Dirac-ness”
in the three materials investigated in this study. Probably the electrons and
holes in this material, generated by the two distinct Dirac nodes, will have comparable densities and mobilities, and their cancellation may pretend small Hall
coefficient |RH |.
73
Appendix B
Data for Hall effect of Sn
doped CaIrO3
Fig. B.1 shows Hall resistivity of Sn doped CaIrO3 films.
74
100
CaIr0.99 Sn0.01 O3
/ SrTiO3(001)
(µΩcm)
I || [100]STO
B || [001]STO
FC(9T)
-50
80K
120K
160K
200K
2K
5K
10K
20K
40K
yx
yx
(µΩcm)
50
-5
CaIr0.98 Sn0.02 O3 / SrTiO3(001)
20
I || [100]STO
B || [001]STO
FC(9T)
10
-10
2K
5K
10K
20K
40K
-20
-30 [ryx(B, down) - ryx(-B, up)] / 2
[ryx(B, down) - ryx(-B, up)] / 2
-100
-10
30
10
-10
-5
B (T)
(a) x = 0.01.
CaIr0.96 Sn0.04 O3
/ SrTiO3(001)
(µΩcm)
80K
120K
160K
200K
-5
5K
10K
20K
40K
80K
-10
[ryx(B, down) - ryx(-B, up)] / 2
-40
-10
I || [100]STO
B || [001]STO
FC(9T)
2K
5K
10K
20K
40K
10
yx
yx
(µΩcm)
I || [100]STO
B || [001]STO
FC(9T)
-20
[ryx(B, down) - ryx(-B, up)] / 2
-20
-10
10
-5
B (T)
200
CaIr0.9 Sn0.1 O3
/ SrTiO3(001)
40
-20
-40
80K
120K
160K
200K
-100
-5
I || [100]STO
B || [001]STO
FC(9T)
40K
80K
120K
160K
200K
-200 [ryx(B, down) - ryx(-B, up)] / 2
[ryx(B, down) - ryx(-B, up)] / 2
-80
-10
20 nm thick
2K
5K
10K
20K
40K
10
CaIr0.8 Sn0.2 O3
/ SrTiO3(001)
100
yx
(µΩcm)
I || [100]STO
B || [001]STO
FC(9T)
20
(d) x = 0.03.
20 nm thick
60
B (T)
(c) x = 0.03.
80
(µΩcm)
10
20
CaIr0.97 Sn0.03 O3
/ SrTiO3(001)
20
yx
(b) x = 0.02.
40
-60
B (T)
10
-10
-5
10
B (T)
B (T)
(f) x = 0.2.
(e) x = 0.1.
Figure B.1: Hall resistivity ρyx (Bz ) of CaIr1−x Snx O3 thin films. The samples
for x = 0.1 and 0.2 are 20 nm-thick, since Hall measurements on 10 nm-thick
samples with high resistivity were difficult.
75
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