# Sr2IrO4/Sr3Ir2O7 superlattice for a model 2D quantum Heisenberg
antiferromagnet

Hoon Kim  These authors contributed equally to this work.  Department of
Physics, Pohang University of Science and Technology, Pohang 790-784, Republic
of Korea  Center for Artificial Low Dimensional Electronic Systems, Institute
for Basic Science (IBS), 77 Cheongam-Ro, Pohang 37673, South Korea  Joel
Bertinshaw11footnotemark: 1 These authors contributed equally to this work.
Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569
Stuttgart, Germany  J. Porras  Max Planck Institute for Solid State Research,
Heisenbergstraße 1, D-70569 Stuttgart, Germany  B. Keimer  Max Planck
Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart,
Germany  Jungho Kim  Advanced Photon Source, Argonne National Laboratory 9700
Cass Ave, Lemont, IL 60439, USA  J.-W. Kim  Advanced Photon Source, Argonne
National Laboratory 9700 Cass Ave, Lemont, IL 60439, USA  Jimin Kim
Department of Physics, Pohang University of Science and Technology, Pohang
790-784, Republic of Korea  Center for Artificial Low Dimensional Electronic
Systems, Institute for Basic Science (IBS), 77 Cheongam-Ro, Pohang 37673,
South Korea  Jonghwan Kim  Center for Artificial Low Dimensional Electronic
Systems, Institute for Basic Science (IBS), 77 Cheongam-Ro, Pohang 37673,
South Korea  Department of Materials Science and Engineering, Pohang
University of Science and Technology, Pohang 37673, South Korea  Gahee Noh
Gi-Yeop Kim  Department of Materials Science and Engineering, Pohang
University of Science and Technology, Pohang 37673, South Korea  Si-Young Choi
Department of Materials Science and Engineering, Pohang University of Science
and Technology, Pohang 37673, South Korea  B. J. Kim  To whom correspondence
should be addressed.
<EMAIL_ADDRESS>Department of Physics, Pohang University of Science and
Technology, Pohang 790-784, Republic of Korea  Center for Artificial Low
Dimensional Electronic Systems, Institute for Basic Science (IBS), 77
Cheongam-Ro, Pohang 37673, South Korea

###### Abstract

Spin-orbit entangled pseudospins hold promise for a wide array of exotic
magnetism ranging from a Heisenberg antiferromagnet to a Kitaev spin liquid
depending on the lattice and bonding geometry, but many of the host materials
suffer from lattice distortions and deviate from idealized models in part due
to inherent strong pseudospin-lattice coupling. Here, we report on the
synthesis of a magnetic superlattice comprising the single ($n$=1) and the
double ($n$=2) layer members of the Ruddlesden-Popper series iridates
Srn+1IrnO3n+1 alternating along the $c$-axis, and provide a comprehensive
study of its lattice and magnetic structures using scanning transmission
electron microscopy, resonant elastic and inelastic x-ray scattering, third
harmonic generation measurements and Raman spectroscopy. The superlattice is
free of the structural distortions reported for the parent phases and has a
higher point group symmetry, while preserving the magnetic orders and
pseudospin dynamics inherited from the parent phases, featuring two magnetic
transitions with two symmetry-distinct orders. We infer weaker pseudospin-
lattice coupling from the analysis of Raman spectra and attribute it to
frustrated magnetic-elastic couplings. Thus, the superlattice expresses a near
ideal network of effective spin-one-half moments on a square lattice.

††preprint: APS/123-QED

##  I Introduction

The physics of $S$=1/2 antiferromagnet (AF) on a two-dimensional (2D) square
lattice has a long history of research as it is widely believed to hold the
key for the mechanism of high temperature superconductivity in copper oxide
compounds [1, 2, 3, 4, 5]. However, it is rarely realized outside of the Cu-
based compounds, and as a result its generic features are difficult to isolate
from material specifics. Ruddlesden-Popper (RP) series iridates Srn+1IrnO3n+1,
have recently emerged as a new material platform to study the same physics
with spin-orbit entangled $J_{\textrm{eff}}$=1/2 pseudospins replacing the
$S$=1/2 moments in the cuprates [6, 7, 8, 9, 10]. Indeed, the single layer
Sr2IrO4 has reproduced much of the cuprate phenomenology: a pseudogapped metal
[11, 12, 13], and a nodal metal with a $d$-wave symmetric gap indicative of
possible unconventional superconductivity [14, 15] emerge upon electron doping
from the parent phase that is approximately a Heisenberg AF [16, 17]. Further,
experiments indicate existence of various symmetry-breaking orders: polarized
neutron diffraction [18] detects time-reversal symmetry breaking above the
Néel temperature (TN), magnetic torque [19] and second harmonic generation
[20, 21] measurements indicate loss of C4 rotation symmetry, and resonant
x-ray diffraction [22] observes splitting of a magnetic Bragg peak suggesting
formation of a nearly commensurate density wave.

However, iridates are different from the cuprates in several aspects, and to
what extent they are relevant to the essential physics is an open important
issue. First, the dominant orbital character of the pseudospins leading to
strong pseudospin-lattice coupling (PLC) [23, 24, 25], which accounts largely
for the spin-wave gap, questions the validity of spin-only models. Second,
structural distortions of kinds not found in cuprates [26, 27, 28] add
complexity to theory models by allowing additional interactions. For example,
the staggered tetragonal distortion of IrO6 octahedra in Sr2IrO4, breaking the
vertical glide planes and thus lowering the space group from $I$41/$acd$ to
$I$41/$a$ [27, 26], leads to additional pseudospin exchange interactions,
which provide a mechanism for locking of pseudospin canting angles and the
octahedral rotation [29]. In the bilayer compound Sr3Ir2O7, the monoclinic
distortion, lowering the space group from orthorhombic $Bbca$ to monoclinic
$C$2/$c$ [28] results in bending of otherwise straight Ir-O-Ir $c$-axis bonds.
This in turn leads to canting of the AF moments aligned along the $c$-axis,
manifesting as small but clearly measurable net in-plane ferromagnetic moments
[30, 31]. Such distortions lead to deviation from the ideal cubic-symmetric
$J_{\textrm{eff}}$=1/2 states on rectilinear superexchange pathways, which are
assumed in theory models that predict, for example, realization of a Kitaev
spin liquid in a honeycomb lattice [8, 32].

Figure 1:  (color online). Stacking pattern of the superlattice as imaged by
STEM. (a) Wide field-of-view STEM image along [100] projection. The
alternation between single-layers (blue) and double-layers (orange) is well
maintained over the entire field of view. (b) Magnified HAADF-STEM image with
single-layer (blue) and double-layer (orange) indicated. (c) A structural
model for the superlattice. The single-layer and double-layer are shifted by a
half unit cell on the SrO planes. IrO6 octahedra are rotated about the
$c$-axis as in the parent compounds. (d) [110]- and (e) [100]-projected HAADF
(left)- and ABF (right)-STEM images overlaid with the atom positions (Sr,
grey; Ir, blue, orange; O, red) from the model.

Here, we report on the synthesis of a Sr2IrO4/Sr3Ir2O7 superlattice, and
provide a comprehensive study of its lattice and magnetic structures. The
lattice structure is investigated by scanning transmission electron microscopy
(STEM), resonant x-ray diffraction (RXD), and rotational anisotropy third
harmonic generation measurements (RA-THG), and the magnetic structure by
magnetometry, RXD, resonant inelastic x-ray scattering (RIXS), and Raman
scattering. The superlattice is free of structural distortions reported for
the parent phases while leaving their magnetic structures intact. The
superlattice features two magnetic transitions with two different orders:
canted $ab$-plane AF and $c$-axis collinear AF inherited from Sr2IrO4 and
Sr3Ir2O7, respectively. Their contrasting pseudospin dynamics, of Heisenberg
and Ising types, also remain unchanged within our experimental resolutions.
However, $ab$-plane magnetic anisotropy of the Heisenberg pseudospins is
significantly reduced indicating weaker PLC, possibly due to the Ising
pseudospins aligned along the $c$-axis resisting the orthorhombic distortions.
Our result shows that two distinct types of quasi-2D magnetism can be
compounded in a superlattice to realize a pseudospin system closer to an ideal
model.

##  II Lattice Structure

The superlattice has the nominal chemical composition Sr5Ir3O11 and can be
regarded as a $n$=1.5 member of the RP series. Although this phase is not
quite thermodynamically stable, it forms transiently during a flux growth
before either $n$=1 or $n$=2 phase eventually stabilizes depending on the
starting composition of Sr2CO3 and IrO2 molten in SrCl2 flux and dwelling
temperature. Thermal quenching at high temperature leads to intergrowth of
both phases, and a highly ordered superlattice can be found by a careful
control of the heating sequence. The resulting “crystals” have typically a few
microns thickness, thicker than layer-by-layer grown thin films but thinner
than typical bulk crystals. As the conventional structure refinement is
limited by the small sample volume, we rely on STEM and RXD to verify the
superlattice formation.

Figure 1(a) shows a wide field-of-view STEM image along [100] projection
showing the stacking of single (SL) and double-layer (DL) units alternating
over $>$ 40 unit cells. The stacking sequence is indicated in Fig. 1(b) and
the unit cell is depicted in Fig. 1(c), which is modeled from the known
structures of Sr2IrO4 (Ref. 33) and Sr3Ir2O7 (Ref. 34). Figures 1(d) and 1(e)
show representative high-angle annular dark field (HAADF) and annular bright
field (ABF) images along [110] projection and [100] projection, respectively.
The images are overlaid with the atomic positions based on the unit cell in
Fig. 1(c). In the [100] projection, the staggered rotation of IrO6 octahedra
about the $c$-axis as in the parent compounds is seen as diffuse rods (see
also Figs. S1 and S2). Overall, our data is in good agreement with the model.

Figure 2:  (color online). RXD on the superlattice at the Ir $L_{3}$-edge.
Sharp (a) (0 0 L) and (b) (0 2 L) charge reflections are centered at integer-L
values (dashed lines), indicating the superlattice is well ordered across the
bulk of the sample. Minor impurity peaks that match Sr2IrO4 and Sr3Ir2O7 are
marked by cyan and orange sticks, respectively. Miller indices are in the
orthorhombic notation; i.e., reciprocal lattice vectors corresponding to the
unit cell shown in Fig. 1(c).

The superlattice formation is confirmed to represent the bulk of the sample
via RXD conducted at the Ir $L_{3}$-edge. Figures 2(a) and 2(b) plot scans
along (0 0 L) and (0 2 L), respectively, which show reflections centered at
integer-L values with $\sim$ 0.01 Å widths. Impurity peaks of intensities of
the order of $\lesssim$ 1 % of the main peaks are observed, which match the
$c$-axis lattice parameters of either Sr2IrO4 or Sr3Ir2O7. The sharp
reflections and negligible impurity peaks indicate that the superlattice
structure remains well correlated at a macroscopic level. Whereas the in-plane
lattice parameters ($\approx$ 5.502 Å) match those of the parent systems, the
$c$-axis is unique with a length of 16.93 Å. According to the study by Harlow
et al. [35], however, diffraction patterns from a randomly-stacked intergrowth
of $n$=1 and $n$=2 phases can misleadingly appear similar to those of an
ordered phase. Such possibility is ruled out in our sample by selectively
measuring the periodicity of DL, by exploiting the fact that only DLs are
magnetically ordered in the temperature range between T= 220 K and 280 K (to
be discussed in section III).

Figure 3:  (color online). RA-THG patterns of the superlattice (open circles)
taken under (a) $PP$, (b) $PS$, (c) $SP$, (d) $SS$ geometries. Incident 1200
nm light was used at room temperature. The third harmonic 400 nm light was
collected as a function of azimuth-angle while the scattering plane rotates
about $c$-axis [36, 37]. The THG signals are normalized by the $PP$ trace,
overlaid with the best fits to bulk electric dipole induced THG tensor of
4/$mmm$ point group (navy lines).

Next, we further refine the structure using RA-THG, a nonlinear optical
process highly sensitive to the bulk crystal symmetry through nonlinear
susceptibility tensors [36, 37, 38]. This technique has been used for Sr2IrO4
and Sr3Ir2O7 to detect subtle structure distortions [27, 28, 21]. Figure 3
shows the azimuth-angle dependence of the third harmonic signals as the
scattering plane is rotated about the $c$-axis, for the four different
polarization configurations of the incident and reflected light, which can be
either parallel ($P$) or perpendicular ($S$) to the scattering plane. The
patterns are symmetric with respect to mirror reflections $a$$\rightarrow$$-a$
and $b$$\rightarrow$$-b$, and four-fold rotations about the $c$-axis. The
combination of both symmetries leads to eight-fold symmetric patterns for the
$PS$ and $SP$. To confirm, the patterns are overlaid with the best fit to
electric-dipole induced THG tensor for 4/$mmm$ (navy), whose expression is
given in Appendix A. We find an excellent agreement and conclude that the
superlattice has a higher point group symmetry than Sr2IrO4 (Ref. 27) and
Sr3Ir2O7 (Ref. 28), in both of which the patterns manifestly lack the mirror
symmetries.

##  III Magnetic structure

Figure 4:  (color online). Magnetometry of the superlattice. (a) The
superlattice magnetic order consistent with our data. (b) Field-cooled M-T
curves of the superlattice (navy), Sr2IrO4 (cyan) and Sr3Ir2O7 (orange). (c)
M-H hysteresis at 5 K comparing the superlattice (navy) and the bulk Sr2IrO4
(cyan). For a direct comparison, Sr2IrO4 curves are multiplied by the mass
proportion ($\approx$ 0.36) of SL in the superlattice. (d) M-T curves measured
with fields applied along [100] and [110].  Figure 5:  (color online).
Magnetic RXD study on the superlattice. (a) Magnetic (1 0 L) reflections
appear at every integer L values, contributed by signals from both SL and DL.
(b) (1 0 L) scans measured at every 5 K upon heating from 200 K to 245 K. (1 0
21) reflection dominated by SL disappears around T = 220 K. (c) At 250 K, the
intensity modulation along (1 0 L) coincides with DL structure factor squared
(dotted line), indicating that the magnetic intensities are dominated by DL.
(d) Temperature dependence of (1 0 8) and (1 0 10) reveal two magnetic
transitions at $T_{N}^{A}$ = 220 K and $T_{N}^{B}$ = 280 K. (e) Polarization
analysis to separate AF signals from in-plane (blue) and out-of-plane (orange)
moments.

Having established the lattice structure of the superlattice, we now turn to
its magnetic structure. In short, the magnetic structure remains almost
unchanged from the parent systems: SL has $ab$-plane canted AF structure while
DL has $c$-axis collinear AF structure, as shown in Fig. 4(a). The net
ferromagnetic response to the dc field with the saturation moment close to
one-third of that of Sr2IrO4 [Figs. 4(b) and 4(c)] suggests that the SL (which
makes up one-third of the superlattice in terms of the number of Ir ions) has
in-plane canted AF structure, while DL has $c$-axis collinear AF structure. We
note that the AF ordering in Sr3Ir2O7 is visible as a small jump in the
magnetization due to its slight monoclinicity $\beta$ $\sim$ 90.05 ∘ (and
thereby canting of the moments [28, 30]), but no such anomaly indicative of DL
magnetic ordering is seen in our tetragonal superlattice [Fig. 4(b)]. Unlike
in Sr2IrO4, we observe a ferromagnetic hysteresis loop in the M-H curve shown
in Fig. 4(c), which implies ferromagnetic staking of SL net moments. Based on
our M-H and M-T curves [Figs. 4(c) and 4(d)] measured for fields along [100]
and [110] directions, we are not able to identify the magnetic easy axis in
the $ab$-plane, which in Sr2IrO4 is clearly along the $a$-axis [24, 23]. This
signifies reduced magnetic anisotropy, which will be discussed in more detail
later on.

Figure 6:  (color online). Magnetic excitations in the superlattice. (a) RIXS
map measured at T =10 K along high symmetry directions indicate that the SL
and DL modes follow the dispersions of the parent systems (plotted with
markers). (b) Spectra at select $\bf{q}$ points. The fitted peaks (solid
lines) are compared with those of the parent systems (markers). (c) The
superlattice spectrum at the zone corner ($\pi$,0) (navy line) is well
reproduced by a linear sum of Sr2IrO4 and Sr3Ir2O7 spectra (black line). (d)
The two-magnon Raman spectrum (navy dots), measured in the $B_{\textrm{2g}}$
channel at T = 15 K, is also well approximated by summing the Sr2IrO4 and
Sr3Ir2O7 spectral intensities (black line).

We confirm the magnetic structure shown in Fig. 4(a) using RXD. As in the case
of Sr2IrO4 and Sr3Ir2O7, magnetic reflections are found along (1 0 L) [Fig.
5(a)], but at every integer L, which has contributions from both SL and DL.
However, they can be separated by exploiting the DL structure factor. The
ratio of Ir-O-Ir bond length along the $c$-axis to $c$ lattice parameter
returns oscillation period of $\sim$ 4.15. For example, the DL contribution
nearly vanishes for (1 0 8) and (1 0 21). Indeed, L scans shown in Fig. 5(b)
shows that (1 0 21) peak disappears around T = 220 K as temperature increases
while (1 0 22) peak is present up to T = 250 K. At this temperature, the
intensity modulation well agrees with the DL structure factor squared [Fig.
5(c)], implying that the peaks are due to reflections from DL only. This is
unambiguous evidence for coherent superlattice formation over the probing
depth of x-ray (290 nm $\sim$ 3.1 $\mu$m as calculated in Ref. 39). The SL
transition temperature is measured to be $T_{N}^{A}$ = 220 K from the
temperature dependence of (1 0 8) peak shown in Fig. 5(d). At (1 0 10), two
transitions are seen, the higher temperature one at $T_{N}^{B}$ = 280 K being
the transition in DL.

Additional measurements were conducted using polarization analysis in order to
separate the $ab$-plane and $c$-axis components of the antiferromagnetic
moments. By studying the magnetic (0 5 2) reflection in a horizontal
scattering geometry [Fig. 5(e)], the $\pi$-$\sigma^{\prime}$ channel mostly
detects in-plane moments, whereas $\pi$-$\pi^{\prime}$ is sensitive to out-of-
plane moments. The temperature dependence of the integrated intensities in the
two channels, shown in Fig. 5(e), reveals that the out-of-plane (in-plane)
magnetic signal arises below $T_{N}^{B}$ = 280 K ($T_{N}^{A}$ = 220 K),
thereby located at DL (SL), consistent with the magnetic structure in Fig.
4(a).

##  IV Pseudospin dynamics

Having established the static magnetic structure, we now turn to the
pseudospin dynamics. Figure 6(a) plots the pseudospin excitation spectrum
along high symmetry directions. Select $\mathbf{q}$-points are plotted in Fig.
6(b). The spectra are fitted with two peaks and their energy positions are
compared with the spin-wave dispersions for the parent systems. Overall, the
spectra are well described as having two peaks corresponding to spin waves in
SL and DL. It is known that Sr2IrO4 is almost gapless at the magnetic zone
center reflecting the quasi-continuous symmetry in the $ab$-plane [16],
whereas Sr3Ir2O7 has an exceptionally large gap of $\approx$ 90 meV (Ref. 40).
Except in the immediate vicinity of the magnetic zone center, we find a good
agreement with the parent systems. In particular, the spectra at the zone
corner ($\pi$, 0) is well reproduced by a linear sum of the spectra of Sr2IrO4
and Sr3Ir2O7 at the same momenta, as shown in Fig. 6(c). Further, the two-
magnon spectrum measured by Raman scattering [Fig. 6(d)], which is dominated
by zone-boundary modes, is in perfect agreement with a linear sum of those in
Sr2IrO4 and Sr3Ir2O7. Together, these data indicate that the nearest-neighbor
spin exchange couplings remain unaltered with respect to the parent systems.

Figure 7:  (color online). Pseudospin-lattice coupling estimated by Raman
spectroscopy. (a) The magnetic mode at the zone center is observed in
$B_{\textrm{2g}}$ scattering geometry (superlattice, navy; Sr2IrO4, blue
gray). (b) The temperature dependent component of the spin-wave gap
$\Delta(T)$ extracted from Raman spectra in (a). The trend of the superlattice
and Sr2IrO4 share the same functional form $A\sqrt{1-T/T_{N}}+B$, where $A$ is
the offset in the log-log plot and proportional to the strength of PLC.
Temperature dependence of $A_{\textrm{1g}}$ phonons in (c) Sr3Ir2O7 and (d)
the superlattice. (e) Integrated intensity of the lower energy
$A_{\textrm{1g}}$ phonon. The spin-dependent component scales with the ordered
moment squared $M_{AF}^{2}$, and dashed lines are fits to functional form of
$1-(T/T_{N})$, whose slopes are proportional to the PLC strength $\Lambda$.
All Raman spectra are corrected for laser heating and Bose factors.

It is perhaps not surprising that there is no significant change in the
pseudospin dynamics across the majority of the Brillouin zone for both SL and
DL, considering that these are quasi-2D systems and only the stacking sequence
is altered. However, it is rather unusual that the two magnetic subsystems
behave almost independently of each other. In particular, magnetic ordering in
DL occurs across SL that remains paramagnetic down to $T_{N}^{A}$. That no
other static order exists in SL above $T_{N}^{A}$ is confirmed from its almost
identical RIXS spectra measured across $T_{N}^{A}$ (Fig. S4). Our
representation analysis (Appendix B) shows that the SL and the DL magnetic
orders belong to different irreducible representations, which guarantees that
they are not coupled in the linear order (this, however, does not rule out
interactions between SL and DL). Further, we note that both $T_{N}^{A}$ and
$T_{N}^{B}$ are reduced only by few degrees from their bulk counterparts,
which confirms that interlayer couplings play a minor role in the critical
phenomena [8, 41, 42].

While the magnetic properties of the superlattice mostly inherit from the
parent Sr2IrO4 and Sr3Ir2O7, some differences are also found. Unlike in the
case of Sr2IrO4, the in-plane magnetic anistropy of SL is hardly visible in
the magnetometry data [Fig. 4(c)]. In Sr2IrO4, the magnetic anisotropy is
known to arise mostly from PLC [23, 24] stabilizing the magnetic ordering
along the $a$\- or $b$-axis. The PLC dominates over the nearest-neighbor
pseudospin exchange anisotropies favoring alignment along the bond directions
(i.e. along [110]), and also accounts for a dominant part of the in-plane
magnon gap [24]. To compare the strength of PLC, we analyze the temperature
dependence of Raman spectra in $B_{\textrm{2g}}$ symmetry channel, which
measures the magnon gap at the zone center [see Fig. 7(a)]. It is seen in Fig.
7(b) that the magnon gap of both Sr2IrO4 and the superlattice follow the same
mean-field-like functional form of $A\sqrt{1-T/T_{N}}+B$, where the
temperature-independent constant $B$ arises from anisotropic magnetic
interactions, and $A$ measures the strength of PLC that scales with the size
of the ordered moment [23, 24, 25]. From the intercept at T = 0 in the log-log
plot shown in Fig. 7(b), we find that the PLC is drastically reduced by a
factor of two. The reduced PLC in SL can be understood in terms of the
structural rigidity provided by DL resisting orthorhombic distortions, which
would be energetically unfavorable for the $c$-axis collinear AF structure.

An indication of suppressed PLC can also be found from a phonon mode strongly
coupled to the AF order in DL. In Sr3Ir2O7, a recent ultrafast optical
spectroscopy study has shown that strong PLC manifests as an abrupt large
enhancement across $T_{N}$ of the amplitude of the coherent oscillation of the
impulsive 4.4 THz ($\approx$ 18 meV) $A_{\textrm{1g}}$ phonon mode [25]. The
intensity follows the phenomenological relation $\sqrt{I(T)}\propto
Z-(\Lambda/4\mu_{B}^{2})M_{AF}^{2}$, where $\Lambda$ and $Z$ are the PLC
strength and temperature-independent spectral weight, respectively [43]. The
strength of PLC in Sr3Ir2O7 is estimated to be two orders of magnitude
stronger than in cubic perovskite manganites with strong spin-lattice
couplings [44]. Since the oscillation amplitude is linearly dependent on Raman
tensor $\partial\alpha/\partial Q$ [45], where $\alpha$ is the polarizability
and $Q$ is the normal coordinate of the phonon mode, the enhancement should be
also visible in Raman spectra. Indeed, we observe a strong enhancement upon
cooling of the 18 meV $A_{\textrm{1g}}$ mode intensity as shown in Fig. 7(c).
However, the corresponding mode in the superlattice at $\approx$ 15 meV shows
only a modest increase comparable to that of the 23 meV mode [Fig. 7(e)].
Taken as a whole, the absence of discernible anisotropy in the magnetization
data, the reduced magnon gap, and the insensitivty of the $A_{\textrm{1g}}$
mode to the magnetic order all consistently point to significant reduction of
PLC in the superlattice.

##  V Summary

Recent advances in the control and understanding of 2D materials has recently
expanded into the research of magnetism in the extreme quantum 2D limit and in
artificial heterostructures. In this work, we have demonstrated a successful
growth of a Sr2IrO4/Sr3Ir2O7 magnetic superlattice, whose constituent bulk
phases exhibit novel quantum magnetism in the limit of strong spin-orbit
coupling. While intergrowth of different phases in a RP series is frequently
found, a natural formation of an ordered superlattice is extremely rare. The
superlattice has a lattice symmetry higher than those of the bulk phases and
realize an undistorted square lattice geometry. Thus, the superlattice offers
a unique opportunity to study the pseudospin physics in an ideal setting.

The superlattice preserves the bulk magnetic orders and interleaves $ab$-plane
canted AF and $c$-axis collinear AF alternately stacked along the $c$-axis.
The two mutually orthogonal orders, however, behave independently of each
order reflecting weak interlayer couplings expected for quasi-2D systems. In
particular, there is a temperature range where only one magnetic subsystem
develops an order across the other that remains paramagnetic. Further, the
pseudsospin dynamics remains unchanged from the parent systems for the most
part of the Brillouin zone.

Instead, the incompatible nature of the magnetic orders manifests as a strong
suppression of the PLC, which is expected to be generally strong for iridates.
The reduced PLC in SL is inferred from the smaller zone-center magnon gap,
which in Sr2IrO4 is largely accounted for by the PLC through a pseudo-Jahn-
Teller effect that results in an orthorhombic distortion as the $ab$-plane
magnetic order breaks the tetragonal symmetry of the lattice. This effect,
however, is counteracted in the superlattice by DL. The magnetic order in DL
is collinear along the straight $c$-axis bond, which in Sr3Ir2O7 is bent due
to a slight monoclinicity.

The origin of the distortions in the parent compounds and their absence in the
superlattice is a subject of future research. To the best of our knowledge,
the breaking of glide symmetries as seen in Sr2IrO4, attributed to staggered
tetragonal distortions, is not found in any other transition-metal compounds
of the RP type, which suggests that the distortion is not due to an
instability of the lattice, but rather its interactions with pseudospins whose
magnetic moment size strongly depends on lattice distortions. Similarly, it
remains to be understood if PLC plays any role in stablizing the monoclinic
structure in Sr3Ir2O7. At any rate, many iridates in bulk form exhibit lattice
distortions of some sort and deviate from idealized models, and in this regard
the superlattice stands out as a realization of pseudospin one-half physics on
an undistorted square lattice.

The persistent magnetic orders in the superlattice also allows investigation
of their evolution upon carrier doping. It is known that Sr3Ir2O7 is on the
verge of a metal-insulator transition, and therefore it may well be that DL
turns into a Fermi liquid metal while SL remains a correlated fluid, a
situation akin to the case of electron-doped Sr2IrO4 via surface alkali metal
dosing, where Fermi arcs and a $d$-wave gap are observed, which possibly
involve screening effects from the surface metallic layer. Our results
presented here provide a solid foundation for these future investigations.

##  VI Methods

STEM measurements were conducted using JEMARM200F, JEOL at 200 kV with 5th-
order probe-corrector (ASCOR, CEOS GmbH, Germany). The specimens were prepared
by dual-beam focused ion beam (FIB) with Ga ion beams of 1 $\sim$ 5 kV
(Nanolab G3 CX, FEI), and further milled by Ar ion beams of 100 meV (PIPS II,
Gatan) to minimize the surface damage. RXD and RIXS measurements were carried
out at Beamline 6-ID-B and Beamline 27-ID, respectively, at the Advanced
Photon Source, Argonne National Laboratory. For RA-THG measurements, we
adapted the scheme reported in [37] by replacing the phase mask by a pair of
wedge prisms to accommodate a wider wavelength range of incident light (from
800 nm to 1200 nm). The incident 1200 nm light was provided by an optical
parametric amplifier (Orpheus-F, Light Conversion) powered by a femtosecond
laser of 100 kHz repetition rate (Pharos, Light Conversion). Raman
spectroscopy is measured with 633 nm He-Ne laser, which beam of 0.8 mW is
focused on $\sim$2 $\mu$m.

## Acknowledgement

This project is supported by IBS-R014-A2 and National Research Foundation
(NRF) of Korea through the SRC (no. 2018R1A5A6075964). We acknowledge
financial support by the European Research Council under Advanced Grant No.
669550 (Com4Com). The use of the Advanced Photon Source at the Argonne
National Laboratory was supported by the U. S. DOE under Contract No. DE-
AC02-06CH11357. We acknowledge DESY (Hamburg, Germany), a member of the
Helmholtz Association HGF, for the provision of experimental facilities. J. B.
was supported by the Alexander von Humboldt Foundation. G. Noh, G.-Y. Kim, and
S.-Y. Choi acknowledge the support of the Global Frontier Hybrid Interface
Materials by the NRF (Grant No. 2013M3A6B1078872).

## APPENDIX A: Third Harmonic Generation Tensor

We obtain the general form of the bulk electric dipole induced THG tensor for
the 4/$mmm$ point group by starting from the most general form of a fourth-
rank Cartesian tensor and requiring it to be invariant under all of the
symmetry operations contained in the group as:

$\chi^{ED}_{ijkl}=\begin{pmatrix}\begin{pmatrix}xxxx&0&0\\\ 0&xxyy&0\\\
0&0&xxzz\end{pmatrix}&\begin{pmatrix}0&xxyy&0\\\ xxyy&0&0\\\
0&0&0\end{pmatrix}&\begin{pmatrix}0&0&xxzz\\\ 0&0&0\\\ xxzz&0&\end{pmatrix}\\\
\begin{pmatrix}0&xxyy&0\\\ xxyy&0&0\\\
0&0&0\end{pmatrix}&\begin{pmatrix}xxyy&0&0\\\ 0&xxxx&0\\\
0&0&xxzz\end{pmatrix}&\begin{pmatrix}0&0&0\\\ 0&0&xxzz\\\
0&xxzz&0\end{pmatrix}\\\ \begin{pmatrix}0&0&zxxz\\\ 0&0&0\\\
zxxz&0&0\end{pmatrix}&\begin{pmatrix}0&0&0\\\ 0&0&zxxz\\\
0&zxxz&0\end{pmatrix}&\begin{pmatrix}zxxz&0&0\\\ 0&zxxz&0\\\
0&0&zzzz\end{pmatrix}\par\end{pmatrix}\;,$ (1)

where $jkl$($i$) stands for incident(scattered) light polarizations. In our
experiment, the light is incident on the sample surface normal to the $c$-axis
with the incidence angle $\theta$ and azimuth angle $\psi$, which is defined
to be zero when the scattering plane contains the $a$ and $c$ axes). Then, the
polarization vectors are given by

$\displaystyle\vec{\epsilon}_{s}\,$
$\displaystyle=\,(\sin\psi,\,-\cos\psi,\,0)\;,$
$\displaystyle\vec{\epsilon}_{in,p}\,$
$\displaystyle=\,(-\cos\theta\cos\psi,\,-\cos\theta\sin\psi,\,\sin\theta)\;,$
(A2) $\displaystyle\vec{\epsilon}_{out,p}\,$
$\displaystyle=\,(\cos\theta\cos\psi,\,\cos\theta\sin\psi,\,\sin\theta)\;,$

Multiplying the tensor with the polarization vectors, the expressions for the
THG intensity simplify as

$\displaystyle I^{SS}(3\omega)\,\sim\,$ $\displaystyle|A+B\cos(4\psi)|^{2}\;,$
$\displaystyle I^{PS}(3\omega)\,\sim\,$ $\displaystyle|B\sin(4\psi)|^{2}\;,$
(A3) $\displaystyle I^{SP}(3\omega)\,\sim\,$
$\displaystyle|B\sin(4\psi)|^{2}\;,$ $\displaystyle I^{PP}(3\omega)\,\sim\,$
$\displaystyle|A^{\prime}+B\cos(4\psi)|^{2}\;,$

where $A$, $A^{\prime}$ and $B$ are adjustable parameters. The formulae are
consistent with the 4/$mmm$ point group symmetry, invariant under both mirror
reflections ($\psi$ $\rightarrow$ $\pi-\psi$ and $\psi$ $\rightarrow$ $-\psi$)
and C4 rotation about the $c$-axis ($\psi$ $\rightarrow$ $\pi/2+\psi$). The
full expressions and those for lower symmetry point groups are given in the
supplemental materials.

|  |  |  |  |  |  |
---|---|---|---|---|---|---|---
Irrep. | Single layer |  | Double layer
|  a1 |  a2 |  |  b1 |  b2 |  b3 |  b4
|  |  |  |  |  |  |
$\Gamma_{1}$ |  (m1, m2, 0) |  (-m1, m2, 0) |  |  (m3, m4, 0) |  (m5, m6, 0) |  (-m3, m4, 0) |  (-m5, m6, 0)
|  (-m2, m1, 0) |  (-m2, -m1, 0) |  |  (-m6, -m5, 0) |  (-m4, -m3, 0) |  (-m6, m5, 0) |  (-m4, m3, 0)
$\Gamma_{2}$ |  |  |  |  (0, 0, m1) |  (0, 0, -m1) |  (0, 0, m1) |  (0, 0, -m1)
$\Gamma_{3}$ |  |  |  |  (0, 0, m1) |  (0, 0, m1) |  (0, 0, -m1) |  (0, 0, -m1)
$\Gamma_{4}$ |  (0, 0, m1) |  (0, 0, m1) |  |  (0, 0, m2) |  (0, 0, m2) |  (0, 0, m2) |  (0, 0, m2)
$\Gamma_{5}$ |  (0, 0, m1) |  (0, 0, -m1) |  |  (0, 0, -m2) |  (0, 0, m2) |  (0, 0, m2) |  (0, 0, -m2)
Table 1: Irreducible representations and basis vectors for the magnetic
structures allowed in the superlattice. mi (i$=1,\cdots,6$) are independent
parameters for the magnetic moments. Iridium ions are located at a1:(0,0,0),
a2:(1/2,1/2,0), b1:(0,1/2,$\delta$), b2:(0,1/2,1-$\delta$),
b3:(1/2,0,$\delta$), b4:(1/2,0,1-$\delta$) in the unit cell Fig. 1(c), where
$\delta$ = 0.3791. The magnetic structure in Fig. 4(a) comprises canted
$ab$-plane AF of $\Gamma_{1}$ and $c$-axis collinear AF of $\Gamma_{5}$.

## APPENDIX B: Representation Analysis of the magnetic structure

We present a representation analysis based on the lattice structure shown in
Fig. 1(c), assuming $\mathbf{q}$ = 0 propagation vector based on the fact that
all observed magnetic reflections have integer Miller indices. Its space group
is $P\bar{4}b$2, which lacks inversion symmetry and thus its point group
($\bar{4}m2$) is of lower symmetry than 4/$mmm$. RA-THG is, however,
insensitive to the inversion symmetry and has the same tensor structure for
the two point groups. The inversion symmetry is broken by the way in which
octahdera are rotated in DL in the current model. An inversion symmetric
structure model can be made by doubling the unit cell in such a way that the
octahedral rotation is opposite on two neighboring DLs. Thus, the
determination of the presence of inversion symmetry requires full structure
refinement including the octahedral rotation on each layers, which is beyond
the scope of this work. However, our result that the magnetic orders in SL and
DL belong to different irreducible representations (IR) is not affected by
these details.

In the superlattice, iridium ions in SL and DL are not symmetry related and
thus their magnetic structures are analyzed separately. The result of the
analysis is shown in Table 1. In both SL and DL, the $ab$-plane and $c$-axis
components belong to different irreducible representations. This can easily be
seen from the transformation property under the two-fold rotation about
$c$-axis; the $ab$-plane moments are flipped, whereas the $c$-axis moments
remain invariant. As long as the $ab$-plane and $c$-axis components are not
mixed by any of the symmetry operations contained in the space group, their
different characters for the two-fold rotation guarantee that they belong to
different IRs. A more detailed version of the analysis is presented in the
supplemental material.

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