Magnetic order, disorder, and excitations under pressure in the Mott insulator Sr
2
IrO
4
Xiang Li,
1, 2
S.E. Cooper,
2
A. Krishnadas,
2
A. de la Torre,
1, 3
R.S. Perry,
4, 5
F.
Baumberger,
3
D.M. Silevitch,
1
D. Hsieh,
1
T.F. Rosenbaum,
1,
∗
and Yejun Feng
1, 2,
∗
1
Division of Physics, Mathematics, and Astronomy,
California Institute of Technology, Pasadena California 91125, USA
2
Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904-0495, Japan
3
Department of Quantum Matter Physics, University of Geneva, 1211 Geneva 4, Switzerland
4
London Centre for Nanotechnology and Department of Physics and Astronomy,
University College London, London WC1E 6BT, UK
5
ISIS Facility, Rutherford Appleton Laboratory, Didcot OX11 0QX, UK
(Dated: October 25, 2021)
Protected by the interplay of on-site Coulomb interactions and spin-orbit coupling, Sr
2
IrO
4
at
high pressure is a rare example of a Mott insulator with a paramagnetic ground state. Here,
using optical Raman scattering, we measure both the phonon and magnon evolution in Sr
2
IrO
4
under pressure, and identify three different magnetically-ordered phases, culminating in a spin-
disordered state beyond 18 GPa. A strong first-order structural phase transition drives the magnetic
evolution at
∼
10 GPa with reduced structural anisotropy in the IrO
6
cages, leading to increasingly
isotropic exchange interactions between the Heisenberg spins and a spin-flip transition to
c
-axis-
aligned antiferromagnetic order. In the disordered phase of Heisenberg
J
eff
= 1
/
2 pseudospins, the
spin excitations are quasi-elastic and continuous to 10 meV, potentially hosting a gapless quantum
spin liquid in Sr
2
IrO
4
.
Mott’s treatment of the metal-insulator transition [1]
is a central pillar in the understanding of correlated-
electron systems.
In 3
d
transition-metal compounds,
electron correlations are governed by the on-site Coulomb
potential
U
, in relationship with other inter-atomic vari-
ables such as the hopping integral, super-exchange inter-
actions, and crystal fields. The intra-atomic spin-orbit
coupling
λ
is weak and can be treated in most cases as a
perturbation [1, 2]. In 4
d
and 5
d
transition-metal com-
pounds, the strong
λ
opens an extra dimension in param-
eter space. The interaction between
U
and
λ
can lead to
new states across insulating, magnetic, and topological
phases [3].
Sr
2
IrO
4
exhibits the characteristics of 5
d
spin-orbit-
coupling assisted “Mottness” [1, 3–6]. The insulating
state with
J
eff
= 1
/
2 pseudospins arises from a Coulomb
U
splitting the half-filled upper
t
2
g
band, which is created
by the combined effect of crystal field and spin-orbit cou-
pling [3, 4, 6]. The magnetic moments of the Ir
4+
ions are
well protected from many distortions of the local octahe-
dral IrO
6
cages (Fig. 1a), such as a tetragonal stretch in
Sr
2
IrO
4
[7], trigonal distortions in both Na
2
IrO
3
[8] and
A
2
Ir
2
O
7
(
A
=Gd, Sm, Eu, Nd, Pr) [9], and a triclinic dis-
tortion of the local
x
−
y
−
z
coordinates in Sr
3
CuIrO
6
[10]. Similarly, the measured staggered moment of Ir
4+
is consistent across systems built on the IrO
6
unit, rang-
ing between 0
.
12
−
0
.
37
μ
B
/
Ir [7, 8, 11–13] in the systems
above, smaller than expected for a
J
eff
= 1
/
2 state [7, 8].
At ambient pressure, Sr
2
IrO
4
is antiferromagnetic be-
low
T
N
= 240 K. Within each two-dimensional plane of
IrO
6
cages, magnetic moments arrange non-collinearly to
form a (1
,
1
,
0) wave vector; they also collectively tilt to
form a small ferromagnetic component along either the
a
-
or
b
-axis in the square lattice [7]. An additional wave vec-
tor of (0
,
0
,
1) is formed by stacking the moments in each
plane along the
c
-axis in a “
−
+ +
−
” pattern [4], leading
to an overall (1
,
1
,
1) wave vector [7]. To understand the
underlying physics of the strongly-correlated electronic
state, Sr
2
IrO
4
has been examined under external tun-
ing parameters such as chemical doping, pressure, and
varying IrO
6
plane stacking configurations in Sr
3
Ir
2
O
7
[14–19]. Both Sr
3
Ir
2
O
7
[14] and Mn or Ru doped Sr
2
IrO
4
[15, 16] are antiferromagnets with the Ir moments aligned
parallel to the
c
-axis, and insulators even in the param-
agnetic phase [14–16]. Under pressure, the insulating
phase in Sr
2
IrO
4
and Sr
3
Ir
2
O
7
persists to at least 185
and 104 GPa, respectively [17, 18]. By contrast, the an-
tiferromagnetic order in Sr
2
IrO
4
is likely suppressed at
about 20 GPa [19]. The nature and the number of unique
magnetic phases over this pressure range, and a full de-
scription of the transitions between them, have not been
explored definitively.
Both the insulating phase and an individual magnetic
Ir
4+
state in the IrO
6
cage are protected by the intra-
atomic
U
and
λ
respectively, and are robust under pres-
sure. By contrast, the antiferromagnetism is not pro-
tected and its specific forms are dependent on the de-
tailed balance between various exchange interactions at
the inter-atomic level. Here we employ high-pressure,
optical Raman scattering [20] to probe simultaneously
the evolution of the lattice and spin degrees of free-
dom, and their excitations, in Sr
2
IrO
4
, revealing four
unique magnetic phases from ambient pressure to be-
yond 20 GPa (Fig.1), all connected through first-order
phase transitions. At 10 GPa, a change of lattice symme-
try from tetragonal to orthorhombic significantly reduces
arXiv:2110.11588v1 [cond-mat.str-el] 22 Oct 2021
2
30
20
10
0
Pressure (GPa)
AFM-111
AFM-mix
AFM-c
Disordered
c
̄
(
ab
)
c
a
̄
(
cb
)
a
T=4.8 ± 0.3 K
c
̄
(
ab
)
c
a
̄
(
cb
)
a
Ir
(a)
(b)
(c)
(d)
Sr
2
IrO
4
FIG. 1. (a) Schematics of Sr
2
IrO
4
lattice structure, empha-
sizing both Ir
4+
ions (red) and octahedral IrO
6
cages (grey).
(b, c) Schematics of two Raman scattering geometries (laser
wavevectors
k
i
,
k
o
, and polarizations
P
,
P
′
) relative to single
crystal lattice coordinates
a
,
b
,
c
inside the high-pressure di-
amond anvil cell, and photographs of real assemblies. (d) A
summary of magnetic evolution, including schematics of four
different spin arrangements under pressure.
the anisotropy in the IrO
6
cage and exchange anisotropy,
as confirmed by magnetic Raman scattering. The in-
creasingly Heisenberg-type spins flip to align antiferro-
magnetically along the
c
-axis. In the high-pressure spin-
disordered phase, we measure a broad spin excitation
spectrum down to at least 9 cm
−
1
in the low temper-
ature limit. A high-pressure paramagnetic ground state
of
J
eff
= 1
/
2 Heisenberg pseudospins in the presence of
a Mott gap serve as necessary conditions for a quantum
spin liquid, and our bounding of spin excitations to en-
ergies below 1.1 meV constrains the nature of the para-
magnetic state with regards to the potential quantum
order.
To fully access the phonon and magnon modes, our Ra-
man instrument was built to measure inelastic energies
down to 9 cm
−
1
at 4
.
8 K and above 20 GPa in two differ-
ent sample configurations [20]. Phonon Raman spectra
are measured in the ̄
c
(
CU
)
c
and ̄
a
(
CU
)
a
configurations,
with ̄
c/
̄
a
and
c/a
indicating incident and scattered laser
directions in a backscattering geometry to the sample co-
ordinate and parallel to the sample surface normal (Fig.
1).
C
and
U
represent circularly polarized (for incident)
and unpolarized (for detected) photons, respectively. For
magnetic Raman scattering (Fig. 2), the polarizations
of the incident and scattered light are kept orthogonal,
in ̄
c
(
ab
)
c
and ̄
a
(
cb
)
a
, enhancing the magnon cross sec-
tion relative to the inelastic charge background. We fre-
quently checked the (
CU
) configuration under pressure
and noticed no alteration of the observed magnon modes.
The ambient pressure Raman phonon spectra in both
configurations (Fig. 3a) reveal four
A
1
g
, one
B
1
g
, and
two
B
2
g
modes (189, 278, 337, 395, 495, 562, and 692
cm
−
1
) that are consistent with Ref. [21]. We attribute
two others (240 and 718 cm
−
1
) to
E
g
modes [21, 22]
where a polarization component along the
c
-axis is in-
cluded (Fig. 3a). Both the ̄
c
(
ab
)
c
and the ̄
a
(
cb
)
a
scat-
tering configurations identify a single magnon mode at
19-20 cm
−
1
at ambient pressure (Fig. 2), with otherwise
featureless spectra between 9 cm
−
1
and the
A
1
g
mode at
189 cm
−
1
.
From 0 to 24 GPa, we observe distinctive spectroscopic
signatures of four magnetic ground states (Fig. 2), all
connected through first-order phase transitions with large
coexistence regions. The ambient pressure order persists
to
∼
3 GPa, indicated by a single magnon at
∼
20 cm
−
1
(Figs. 2a-2d).
Between 3 to 10
+
GPa, variations in the magnon spec-
tra emerge, with distinctions between the ̄
c
(
ab
)
c
and
̄
a
(
cb
)
a
configurations and spatial variation across the
sample surface. The ̄
c
(
ab
)
c
magnon spectra typically ex-
hibit two peaks at 10-14 cm
−
1
and 18-20 cm
−
1
, respec-
tively (Fig. 2e), with varying intensity ratios at differ-
ent sample surface spots, indicating intrinsically differ-
ent volumes. Previous Raman measurements of Sr
2
IrO
4
in the ̄
c
(
ab
)
c
configuration with a 0.5 T magnetic field
in the
a
-
b
plane demonstrate a single magnon peak at
10-12 cm
−
1
[23], indicative of a
c
-axis stacking pattern
of “+ + ++” [4]. While the 20 cm
−
1
magnon repre-
sents the “
−
+ +
−
” stacking pattern along the
c
-axis,
our observation points to a coexistence of the “
−
+ +
−
”
and “+ + ++” phases. Furthermore, magnon spectra
in the ̄
a
(
cb
)
a
configuration demonstrate both the spa-
tial inhomogeneity with different profiles across the sam-
ple surface and collective spectral weight covering the
range between 20 and 80 cm
−
1
(Fig. 2f). While magnon
spectra are sensitive signatures of underlying antiferro-
magnetic order, the large variety, with an overall broad
and continuous distribution of magnon energies, indicates
that this AFM-mix phase features many types of
c
-axis
stacking patterns such as “
−
+
−
+”, “
−
+ +
−
”, and
“++++” [5], with spatially varying domain composition.
The sharp peak profiles of Raman scattering, even at the
upper limit of 16.1 GPa [24], signify that these stackings
are thermodynamic phases with finite correlation lengths
along the
c
-axis. Recent resonant x-ray diffraction mea-
surements under pressure [19] suggest that the Ir spins
remain confined to the
a
-
b
plane and order antiferromag-
netically within each IrO
6
layer. The layers experience
a crossover from “
−
+ +
−
” to “+ + ++” stacking as
pressure increases. Our results instead suggest a hetero-
geneous phase coexistence of many distinct, but energet-
ically close stacking configurations exist for 3
−
10
+
GPa.
Our magnetic Raman scattering clarifies the ambiguity
in Ref. [19] with regard to the extent of both the phase
region and the distinctive types of antiferromagnetic or-
der present.
When the pressure reaches above 10 GPa, the magnon
3
4000
0
1000
0
4000
0
1.0 mW
0.1 mW
2.0 mW
1.0 mW
0.1 mW
1000
0
100
50
0
-50
2.0 mW
1.0 mW
0.1 mW
0.03 mW
250
0
60
30
0
100
50
0
-50
2.0 mW
1.0 mW
0.1 mW
6000
0
c
̄
(
ab
)
c
a
̄
(
cb
)
a
c
̄
(
ab
)
c
c
̄
(
ab
)
c
c
̄
(
ab
)
c
a
̄
(
cb
)
a
a
̄
(
cb
)
a
Frequency (cm
-1
)
2.9 GPa
1.0 mW
1.8 GPa
0.1 mW
7.9 GPa
1.0 mW
6.3 GPa
0.1 mW
10.3 GPa
18.0 GPa
23.4 GPa
AFM-111
AFM-mix
AFM-c
Disordered
(a)
(b)
0 GPa
1.0 mW
0 GPa
0.1 mW
c
̄
(
ab
)
c
a
̄
(
cb
)
a
Counts
Counts
Counts
Counts
19.5 GPa
c
̄
(
ab
)
c
Counts
Frequency (cm
-1
)
(c)
(e)
(g)
(i)
(d)
(f)
(h)
(j)
Sr
2
IrO
4
FIG. 2. Magnetic Raman spectra, measured in the ̄
c
(
ab
)
c
and
̄
a
(
cb
)
a
configurations, are shown for (a-d) the AFM-111 phase
below 3 GPa, (e, f) the mixed
c
-axis stacking AFM between
3-10 GPa, (g, h) spins aligned parallel to the
c
-axis between
10-20 GPa, and (i, j) the disordered spin phase above 18.5
GPa. The measured Raman spectra inside the (-9, 9) cm
−
1
region are dominated by the laser line and the notch filters.
All spectra are normalized to a total incident laser exposure
of 0.9 J (
e.g.
0.1 mW over 150 mins). Spectra are presented
with measurements either (a-f) at several different spots, or
(g-j) at one spot but with different laser powers. The sample
temperature is kept at 4
.
8
±
0
.
3 K, but the local temperature
within the illuminated 5
μm
focus-spot-size surface region is
estimated to be
∼
8, 17, and 25 K for 0.1, 1 and 2 mW laser
powers, respectively, based on ratios of Stokes and anti-Stokes
line intensities. (Inset of i) The difference of QES Raman
spectra between 0.1 and 2 mW power settings (dots) is fit to
a Lorentzian form.
spectra in Sr
2
IrO
4
start to disappear in strongly first-
order fashion from the Raman sensitive region above 9
cm
−
1
for both the ̄
c
(
ab
)
c
and ̄
a
(
cb
)
a
configurations (Figs.
2g-2h). Despite the absence of low-wavenumber features
in this pressure range, the magnetic moments remain or-
dered in Sr
2
IrO
4
. This is supported by the temperature-
independent Raman spectra from 8 to 25 K, set by differ-
ent incident laser powers of 0.1 to 2.0 mW to locally heat
the scattering volume (Figs. 2g-2h). The measured Ra-
man spectra are identical when normalized by the total
flux of incident photons, in sharp contrast to the temper-
ature dependence of spectra in the disordered phase (see
below).
The featureless low-wavenumber Raman spectra (Figs.
800
700
600
500
400
300
200
6000
0
120
60
0
-60
4000
0
-60
-30
0
30
60
40000
0
500
400
6000
0
500
400
c
̄
(
ab
)
c
a
̄
(
cb
)
a
c
̄
(CU
)
c
a
̄
(CU
)
a
1.0 mW
0.9 mW
0.1 mW
0.6 mW
Frequency (cm
-1
)
a
̄
(CU
)
a
c
̄
(CU
)
c
0 GPa
(c)
x 3
A
1g
A
1g
A
1g
A
1g
E
g
B
2g
B
2g
B
1g
E
g
2.9
7.9
10.3
14.2
16.5
19.5
22.3
3.3
6.3
9.5
11.9
13.9
16.1
18.0
18.9
20.3
P (GPa)
P (GPa)
(b)
Counts/10 min
Counts/150 min
Counts/10 min
Counts/5 min
Intensity (a.u.)
(a)
Sr
2
IrO
4
FIG. 3. (a) Phonon Raman spectra in ̄
c
(
CU
)
c
and ̄
a
(
CU
)
a
configurations at ambient pressure and 4.8 K, with modes
marked with arrows and the type. (b, c) Correlated pressure
evolution of magnon and phonon behavior.
2g-2h) appear simultaneously with changes in the Ra-
man lattice modes, mainly a split of the
B
2
g
mode at
∼
395 cm
−
1
to a double-peak profile with a significantly-
reduced intensity across the pressure phase boundary
(Figs. 3b-3c). This strong correlation is observed both
for a single spot on the sample surface at different pres-
sures (Figs. 3b-3c) and in several different spots across
the sample surface at the same pressure [24]. The peak
splitting and intensity collapsing behavior of this
B
2
g
mode was also observed at 300 K and 42 GPa in Refs.
[18, 25], and correlated with a reduction to two-fold sym-
metry within the
a
-
b
plane in an orthorhombic structure
[18]. Here, the tetragonal-orthorhombic structural phase
boundary moves from
∼
42 GPa at 300 K to
∼
10 GPa at
5 K.
The new set of phonon and magnon Raman spectra
suggests a new type of spin order above 10 GPa. Ref.
[19] has stated an absence of (1, 0, odd) magnetic reflec-
tions to rule out a spin-flip transition to a
c
-axis collinear
antiferromagnetic state. However, both raw data and in-
tegrated intensities in Figs. 1e and 1g of Ref. [19] demon-
strate a significantly-reduced, but still finite amount of
(1, 0, odd) and (1, 0, even) reflections between 10 and
18 GPa. Ref. [19] attributed it to a volumetric sup-
pression of the low-pressure antiferromagnetic “
−
+ +
−
”
4
and “+ + ++” orders, but left the magnetic state in the
majority volume unexplained. We argue that the strong
reduction in magnetic diffraction intensities is indicative
of the bulk volume experiencing a spin flip transition.
Previously, a difference of over two orders of magnitude
was reported between resonant x-ray magnetic diffraction
intensities of Sr
2
IrO
4
and Sr
3
Ir
2
O
7
at ambient pressure
[14], which was attributed to a reduction of the struc-
ture factor between staggered moments aligning either
within the
a
-
b
plane or the
c
-axis. The same argument
can be applied to the observed
∼
20
×
intensity reduction
in Sr
2
IrO
4
at
∼
10 GPa [19]. Ref. [19] does not include
an x-ray polarization analysis, which is technically feasi-
ble under pressure [9, 26], to definitively verify a spin-flip
transition [16]. The existence of comparable intensities of
the (1, 0, odd) and (1, 0, even) reflections between 10-18
GPa in Ref. [19] is similar to the diffraction patterns of
c
-axis-aligned antiferromagnet Sr
3
Ir
2
O
7
at ambient pres-
sure [14], suggesting that the AFM-c phase have multi-
ple stacking patterns [14–16], analogous to the AFM-mix
phase (Fig. 1d).
Microscopically, the spin-flip process in Sr
2
IrO
4
is re-
lated to the IrO
6
cage distortion. At ambient pressure,
the Ir-O bonds in Sr
2
IrO
4
are 3.7% longer along the
c
-
axis than those within the
a
-
b
plane [7]. Under pressure,
Sr
2
IrO
4
has an anisotropic compressibility between the
a
-
b
plane and the
c
-axis [18]. While
c
is less compress-
ible than
a
and
b
both below and above the orthorhombic
structural transition, at the transition (
∼
42 GPa and 300
K) it collapses by 9.0%, whereas
a
expands by
∼
6% and
b
stays constant [18, 25]. This results in a substantial
reduction in the
c/a
and
c/b
ratios and hence a reduced
Ir-O bond length anisotropy. In Sr
3
Ir
2
O
7
, the Ir-O bond
length anisotropy is only 2.3% [11], small enough that
the single-magnon mode is not observed in Raman scat-
tering for the
c
-axis aligned spins. The 19 cm
−
1
one-
magnon peak also disappears at ambient pressure in a
Sr
2
IrO
4
crystal grown in a magnetic field [27]. Study
of its antiferromagnetic order could provide a potential
comparison, along with optical Raman studies of the
c
-
axis spin-order in Mn- and Ru-doped Sr
2
IrO
4
[15, 16].
Above 18.5 GPa, a disordered spin phase appears,
characterized by a continuous Raman excitation spec-
trum (Figs. 2i-2j) from the lower boundary of instrumen-
tal sensitivity at 9 cm
−
1
to as high as 90 cm
−
1
. This in-
elastic excitation is commonly described as quasi-elastic
scattering (QES), and is facilitated by increasing temper-
ature. With clear spatial inhomogeneity across the sam-
ple surface, QES only exists in the high-pressure phase
where the antiferromagnetic order in Sr
2
IrO
4
is fully sup-
pressed. Using incident laser power to adjust the local
sample temperature and the QES intensity, the spectral
difference of QES between two temperatures is fit to a
Lorentzian form (Fig. 2i inset), indicative of fluctua-
tions [28–30]. The half-width-at-half-maximum of QES
remains large (
∼
15 cm
−
1
) and temperature independent.
QES at this energy scale has been observed for magnetic
excitations in FePS
3
[31], SrCu
2
(BO
3
)
2
[29], and a vari-
ety of quantum spin liquid candidates [30], and at ther-
mal structural phase transition in KH
2
PO
4
[32]. QES
in Sr
2
IrO
4
exists only on the high-pressure side of the
phase transition, and persists throughout the measured
pressure range from 18.6 to 23.4 GPa (Figs. 2i-2j). Fur-
thermore, the sample temperature of 25 K with 2 mW
laser heating is still much lower than the Debye temper-
ature. All these suggest that the QES is not driven by
mechanisms specific to a phase transition and softened
phonon modes [28], but by magnetic fluctuations in the
spin-disordered phase.
Although the lattice structure and phonon Raman
modes are different between Sr
2
IrO
4
and La
2
CuO
4
, the
Cu and Ir sublattices are similar, so their magnon
spectra are expected to be determined by the same
Hamiltonian with different parameter values.
The
spin Hamiltonian is often expressed as [23, 33–35]:
H
=
J
ij
∑
〈
ij
〉
[
~
S
i
·
~
S
j
−
α
z
S
z
i
S
z
j
+
α
DM
·
(
~
S
i
×
~
S
j
]
+
Jα
⊥
∑
〈
ik
〉
~
S
i
·
~
S
k
.
The first summation describes in-
teractions between spins
〈
ij
〉
within a two-dimensional
plane, where the dominant isotropic Heisenberg ex-
change
J
is modified by anisotropic Ising spin exchange
and Dzyaloshinskii-Moriya (DM) interactions (
α
z
J
and
α
DM
J
, respectively). The last term sums over isotropic
Heisenberg interactions between spin pairs
〈
ik
〉
on neigh-
boring layers. We neglect additional anisotropic interac-
tions in the Hamiltonian, such as anisotropic interlayer,
dipolar, and Jahn-Teller spin-lattice types.
At ambient pressure, inelastic neutron scattering iden-
tified in La
2
CuO
4
two magnon gaps of 1-2 and 3-5 meV
at the zone center and an overall energy scale
J
∼
150
meV [34, 36]. The magnon gaps were attributed to a DM
interaction
α
DM
J
and an anisotropic exchange interac-
tion
α
z
J
, respectively. Optical Raman measurements re-
veal a single magnon at 17-20 cm
−
1
in both La
2
CuO
4
and Sr
2
IrO
4
at low temperature, zero field, and ambient
pressure [21, 23, 35]. While this mode was identified with
the DM anisotropy in La
2
CuO
4
[35, 36], the large differ-
ence in
λ
between Ir and Cu (0.4-0.6 and
∼
0.01 eV [37])
prevents the 20 cm
−
1
magnon in Sr
2
IrO
4
from being at-
tributed to DM interactions, but instead the anisotropic
exchange
α
z
J
. With the magnon band gap at the zone
center
J
((2 +
α
z
)
α
z
)
1
/
2
[33, 36], a gap size of 20 cm
−
1
would lead to
α
z
J
∼
0
.
03 meV in Sr
2
IrO
4
at ambient
pressure, similar to that in La
2
CuO
4
[36].
With
T
N
= 240 K and
J
∼
60 meV at ambient pres-
sure [37], and the absence of QES in ordered phases un-
der pressure, Sr
2
IrO
4
demonstrates a low level of spin
frustration. Below 10 GPa, the exchange anisotropy
α
z
is expected to increase as the
c/a
ratio increases with
pressure until the orthorhombic structural transition [18].
This explains the observed magnon energies reaching as
high as 80 cm
−
1
(Fig. 2f). However, hydrostatic pressure
5
generally reduces the anisotropy in lattice compressibility
[38]. In the AFM-c state, the reduced IrO
6
cage distor-
tion result in a more isotropic local environment and the
Ir
4+
ions approach the full rotational degrees of freedom
of Heisenberg spins. The reduced anisotropy
α
z
dimin-
ishes the energy of the zone-center magnon mode, possi-
bly to below the energy sensitivity of Raman scattering.
Raman scattering’s sensitivity to inelastic energies of
1.1 meV is comparable to the energy sensitivity of in-
elastic neutron scattering measurements [39, 40]. While
magnetic exchange interactions and gapped, discrete dis-
persion relationships at energies less than 1 meV are well
documented [40], the continuous spectral weight above
9 cm
−
1
in Figs. 2i-2j and the Lorentzian form suggest
that the QES in Sr
2
IrO
4
extends below 9 cm
−
1
and the
observed spin excitations could be gapless in zero mag-
netic field. This reflects the reduced exchange anisotropy
entering the ordered AFM-c phase continues to higher
pressure. A single IrO
6
layer in Sr
2
IrO
4
could be mapped
onto a model of Heisenberg spins on a two-dimensional
square lattice, leading to a quantum spin liquid with
SU(2) gauge structure and a gapped excitation spectrum
[19], and the broad pressure range of observed QES re-
sponse can support the necessary stability of a quantum
spin liquid. Nevertheless, optical Raman techniques only
verify inelastic energy dispersion at
q
≈
0. While our
high-pressure Raman scattering provides a strong upper
bound on the gap size and could indicate a gapless sce-
nario, dispositive experimental evidence for a quantum
spin liquid awaits additional characterization. For that,
neutron or x-ray experiments measuring the complete in-
elastic spectrum over the entire Brillouin zone are neces-
sary.
Acknowledgments: We thank G. Stenning and D. Nye
for help with the instruments in the Materials Charac-
terisation Laboratory at the ISIS Neutron and Muon
Source. Y.F. acknowledges support from the Okinawa
Institute of Science and Technology Graduate Univer-
sity, with subsidy funding from the Cabinet Office, Gov-
ernment of Japan. X.L., D.M.S., and T.F.R. acknowl-
edge support from AFOSR Grant No. FA9550-20-1-0263.
D.H. acknowledges support from DOE Grant No. DE-
SC0010533. F.B. was supported by the Swiss National
Science Foundation. A.d.l.T. acknowledges support from
the Swiss National Science Foundation through an Early
Postdoc Mobility Fellowship (P2GEP2
165044).
∗
Correspondence and requests for materials should be
addressed to T.F.R. and Y.F. tfr@caltech.edu and
yejun@oist.jp
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