# LOKII project: Advances in high-pressure laser floating zone growth

Steven J. Gomez Alvarado<EMAIL_ADDRESS>Materials Department,
University of California, Santa Barbara, CA 93106-5050, USA  Eli Zoghlin
Materials Department, University of California, Santa Barbara, CA 93106-5050,
USA  William H. Miller III Department of Physics and Astronomy, Johns Hopkins
University, Baltimore, Maryland 21218, USA  Azzedin Jackson  Linus Kautzsch
Materials Department, University of California, Santa Barbara, CA 93106-5050,
USA  Jayden Plumb  Materials Department, University of California, Santa
Barbara, CA 93106-5050, USA  Department of Mechanical Engineering, University
of California, Santa Barbara, CA 93106-5050, USA  Michael Aling  Materials
Department, University of California, Santa Barbara, CA 93106-5050, USA
Department of Mechanical Engineering, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Andrea N. Capa Salinas  Ganesh Pokharel  Yiming Pang
Reina M. Gomez  Materials Department, University of California, Santa Barbara,
CA 93106-5050, USA  Samantha Daly  Department of Mechanical Engineering,
University of California, Santa Barbara, CA 93106-5050, USA  Stephen D. Wilson
<EMAIL_ADDRESS>Materials Department, University of California, Santa
Barbara, CA 93106-5050, USA

###### Abstract

The optical floating zone crystal growth technique is a well-established
method for obtaining large, high-purity single crystals. While the floating
zone method has been constantly evolving for over six decades, the development
of high-pressure (up to 1000 bar) growth systems has only recently been
realized via the combination of laser-based heating sources with an all-metal
chamber. While our inaugural high-pressure laser floating zone furnace design
demonstrated the successful growth of new volatile and metastable phases, the
furnace design faces several limitations with imaging quality, heating profile
control, and chamber cooling power. Here, we present a second-generation
design of the high-pressure laser floating zone furnace, "LOKII", and
demonstrate that this redesign facilitates new advances in crystal growth by
highlighting several exemplar materials: $\alpha$-Fe2O3, $\beta$-Ga2O3, and
La2CuO4+δ. Notably, for La2CuO4+δ, we demonstrate the feasibility and long-
term stability of traveling solvent floating zone growth under a record
pressure of 700 bar.

##  I Introduction

For over 60 years, the optical floating zone crystal growth method [1] has
played a critical role in the development of pristine single crystals for the
study of novel electronic, optical, and magnetic phenomena. Despite being a
well-established technique, floating zone growth remains an ever-developing
frontier among active crystal growth methods.[2] Among recent advances in
optical floating zone (OFZ) technology, the application of elevated gas
pressures during growth has been particularly effective in expanding the phase
space of compounds which can be grown via the floating zone method.[3, 4]
Since the inception of the high-pressure laser floating zone (HP-LFZ) furnace
[5], which allows for the application of pressures up to 1000 bar using an
all-metal growth chamber, the HP-LFZ has proven effective in suppressing
material volatility and modifying chemical potential during growth.[6, 7, 8]
Our inaugural design of the HP-LFZ furnace has presented challenges with
imaging quality, sample heating, and chamber cooling power — issues that are
amplified at the highest operating pressures. Here, we present a second-
generation of the HP-LFZ furnace based on a redesign of the chamber geometry
which allows for in-plane viewing during growth and improved cooling of the
chamber. These design modifications are embodied in a modified furnace named
Laser Optical Kristallmacher II (LOKII). We detail the changes in this furnace
design and demonstrate that these improvements facilitate the exploration of
new regimes of OFZ crystal growth using several materials as examples.

##  II Instrument description

###  II.1 Chamber design

Figure 1: (a) Rendering of the second-generation chamber design. (b) Rendering
of the sight glass housings with a cut view highlighting the O-ring and
retaining ring which create a seal about the sapphire window. (c) Cutaways of
the chamber rendering revealing additional water cooling lines for improved
cooling power and enlarged window bores for enhanced optical access.

The new chamber design (Fig. 1) features several key differences from the
inaugural design of the HP-LFZ. Firstly, the original 45∘ out-of-plane sight
glasses used for imaging and pyrometry were removed. Viewing of the zone is
accomplished by making use of semi-transparent, laser-reflective optics that
allow for imaging and pyrometry directly down the line of sight of the lasers
(Fig. 2). This in-plane viewing geometry dramatically improves imaging quality
for volatile growths at the highest pressures and temperatures, where the
rising turbulent flow of gas inside the chamber would inhibit visual
monitoring of the growth in the out-of-plane viewing geometry. With the
removal of the out-of-plane bores, the in-plane bores now feature an increased
diameter of 9 mm allowing for a wider field of view for imaging.

Secondly, this chamber features a custom sight glass design which is composed
of a window housing made of UNS N07718 (Inconel 718) and an anti-reflection
(AR) coated sapphire sight glass (Guild Optical Associates, Inc.). The
pressure seal is achieved by a retaining ring made of CuBe alloy UNS C17200
which holds the sapphire window against a Viton O-ring (90A Duro FKM, Marco
Rubber). This window design is capable of withstanding the highest operating
pressures, though the O-ring is susceptible to softening and extrusion upon
overheating of the chamber (above 100 ∘C), which causes a failure of the
pressure seal.

To remedy this issue, we have included additional cooling water lines in the
new chamber, paired with a 1000 W water-to-water chiller (LX1 Series,
Haskris). The increased cooling power is especially important at higher
pressures, where increased fluid density enhances the heat transfer away from
the sample. The removable heat and chemical shield has also been redesigned
(Fig. 2(c)), featuring a single cylindrical quartz window which provides a
wide field of view for imaging and transmission of laser light to the sample.
Previously made of aluminum, the shield is now also made of the CuBe alloy UNS
C17200 and is capable of resisting chemical attack even at the highest
operating temperatures and O2 pressures.

Figure 2: (a) Rendering of the full HP-LFZ apparatus with all components
excluding the external frame. (b) A photograph of the HP-LFZ apparatus for
comparison. (c) Rendering of the second-generation heat and chemical shield. A
cylindrical window between the CuBe shield pieces allows for laser
transmission and imaging. (d) A cut view of the in-plane viewing optics array
with key components highlighted. Figure 3: (a) Images from a growth of Al2O3
under $P=70$ bar from the pyrometer (left) and camera (right), viewed through
the out-of-plane sight glasses in the old chamber design (Adapted from Ref.
5). (b) Corresponding images of a growth of Al2O3 repeated in the new chamber
design, viewed through in-plane sight glasses. A systematic difference in the
measured temperature is due to filtering effects caused by a laser line mirror
which sits in the line of sight of the pyrometer.

###  II.2 Laser Heating Source

In our inaugural furnace design, the HP-LFZ relies on seven diode lasers, each
capable of providing 100 W of infrared laser light at a wavelength of 820 nm.
After attempting growths of a wide array of materials, 100 W per laser (700 W
total) was found to be insufficient to melt highly refractory and thermally
conducting compounds, particularly for materials with poor optical absorption
at 820 nm. In addition, the design requirement of coupling numerous diode
outputs into a collective fiber bundle creates a larger optical source with a
correspondingly larger axial divergence. The resulting inability to tightly
collimate the beam created a lower bound on the height of the incident laser
spot at the sample position of 2.1 mm in our previous design, limiting control
over the sharpness of the heating profile.[5] Finally, when growing under the
highest pressures with significant material volatility, the increased
turbulence causes fluctuations in the density of the fluid which, in turn,
cause fluctuations in the index of refraction. The gradient of the index of
refraction results in a redirection and broadening of the incident laser
light, which decreases the amount of power transferred to the sample.

To circumvent these limitations, we constructed a second furnace (LOKII) using
seven fiber lasers that are each capable of emitting 200 W of laser light at a
wavelength of 1070 nm. Beyond the enhanced power output, these lasers also
feature a negligible divergence of the beam after collimation, resulting in an
unmodified spot size of 5 mm diameter at the sample position. Using a
conventional cylindrical focusing lens, the height of this spot can be focused
down to a line, enabling enhanced control over the heating profile.
Additionally, with a reduced incident spot size (i.e., increased power
density), higher melting points can be accessed at lower laser powers.
Together with the doubling of the maximum power output, these improvements
expand the available range of accessible melting temperatures, especially
pertinent for high-melting compounds such as refractory oxides, nitrides, and
borides. We find that the issue of spot broadening and redirection via
refraction during growths of volatile materials can be significantly
diminished by narrowing the spot size below $\approx$1.5 mm, which we
attribute to a minimization of the overlap between the turbulent layer of gas
flow and the incident laser beam.

###  II.3 Imaging and Pyrometry

To grant the camera and pyrometer optical access via the same windows through
which the laser light enters the chamber, we employ optics which allow for in-
plane imaging of the molten zone. While five lasers remain in the plane, two
lasers on opposite sides of the chamber are reflected into the chamber by
semi-transparent, laser-reflective optics allowing for transmission of visible
light into a camera for imaging and into a pyrometer for both imaging and
temperature readings (Fig. 2(d)). An alternative design where laser light is
transmitted and the optical image is reflected was rejected, as transmission
of the laser light would have resulted in more losses than reflection of the
laser light. The 820 nm furnace utilizes a Quantalux CS2100M-USB sCMOS camera
from Thorlabs, Inc. and the 1070 nm furnace utilizes an acA1300-75gcE Color
GigE Camera from Basler, both employing an Infiniprobe MS variable
magnification lens and $2\times$ magnification lens from Infinity Photo-
Optical Company. Both furnaces employ a Fluke Endurance pyrometer, model
E1RH-F0-V-0-0.

In this scheme, shown in Fig. 2(d), the laser light first leaves the laser
fiber bundle and is focused by a collimating lens (IPG Photonics). It is then
reflected 90∘ by a mirror in a kinematic mount (Thorlabs), followed by
complementary 90∘ reflection off of a semi-transparent mirror, which allows
for transmission of visible light but reflects at the laser wavelength. This
mirror is mounted in a custom kinematic mount which minimizes the path length
extension for the laser, thus reducing differences in the incident laser spot
size between the modified and unmodified laser geometries. For the camera,
this semi-transparent mirror is a dichroic mirror (Thorlabs), which reflects
wavelengths larger than 750 nm. For the pyrometer, this semi-transparent
mirror is a laser line mirror which reflects light at a range of wavelengths
tightly centered around either 820 nm (CVI Laser Optics, LLC) or 1070 nm
(Edmund Optics), respectively for each of the two furnaces. The pyrometer
measurement relies on reading wavelengths in the infrared regime which include
these bands, thus causing the measured temperature to be systematically off by
several hundreds of degrees.

Example images of the molten zone in Fig. 3 show a comparison between the
previous out-of-plane and the new in-plane viewing geometries. At higher
pressures, the imaging is significantly improved, which we attribute to a
shallower viewing angle where there is a significantly smaller volume of
turbulent fluid between the sight glass and the molten zone.

Previously, compounds with significantly volatile components (e.g., RuO2,
RhO2, and IrO2) would deposit a thick layer of powder on the viewing windows
after just a few hours of growth, precluding visual monitoring of the zone.
Now, continuous visual monitoring of the molten zone is made easier as laser
heating prevents volatilized material from cooling down enough to deposit on
the cylindrical window in the regions where the visual monitoring is being
conducted.

##  III Crystal Growth Demonstrations

###  III.1 Tuning Phase Stability in $\alpha$-Fe2O3

Figure 4: (a) Single crystal of $\alpha$-Fe2O3 obtained from the HP-LFZ — a
shiny grey boule with no visible facets. (b) Images from the pyrometer and
camera during the growth. The poor image quality at $P=540$ bar here is due to
the volatility of the material during growth. (c) Laue diffraction pattern
obtained from the boule, consistent with reflections from the (012) plane. (d)
Powder X-ray diffraction data on a crushed portion of the crystal. All peaks
can be indexed using the rhombohedral structure of $\alpha$-Fe2O3. (e)
Temperature-dependent magnetization data collected at $H=1000$ Oe on a portion
of the same powder used for X-ray diffraction. Inset shows the impurity
feature corresponding to an estimated 0.085 mol% of Fe3O4.

As a demonstration of the ability of the LOKII design to grow pressure-
stabilized oxide phases, $\alpha$-Fe2O3 (hematite) crystals were grown. In
recent years, antiferromagnets have become of interest in spintronics due to
their inherent potential to achieve faster dynamics in data recording and
manipulation when compared to ferromagnets.[9, 10, 11] Specifically,
antiferromagnets with easy-plane anisotropy, like $\alpha$-Fe2O3, provide an
opportunity to study spin-orbit torque switching. While most of the studies of
this material have been performed on thin films, bulk single crystals of
$\alpha$-Fe2O3 are ideal due to their higher purity and well-defined
orientation (i.e., single grain nature).

The growth of $\alpha$-Fe2O3 bulk single crystals at low pressure is made
challenging by the difficulty of obtaining the correct oxidation state of
Fe3+, which results in incongruent melting. To date, most bulk single crystal
samples of $\alpha$-Fe2O3 have been synthesized at low pressure using fluxes,
including crucible-based techniques[12, 13] and the traveling solvent floating
zone method.[14] Small amounts of flux incorporation modify the magnetic
properties of $\alpha$-Fe2O3, which are known to be sensitive to impurities.
One of the key advantages of the HP-LFZ is the ability to routinely apply
large overpressures of O2 and thereby favorably modify the thermodynamics of
the recrystallization process. Growth of $\alpha$-Fe2O3 provides an excellent
example of this capability, as $\alpha$-Fe2O3 has been shown to melt
congruently only at O2 pressures above 50 bar.[15] High-pressure growth thus
enables standard floating zone growth without need for a flux.[3]

High purity $\alpha$-Fe2O3 powder (Alfa Aesar, 99.995%) was dried for
$\approx$12 hours at 600 ∘C and then packed inside cylindrical rubber balloons
(diameter $\approx$ 6 mm) to make a seed rod (length $\approx$ 25 mm) and a
feed rod (length $\approx$ 100 mm). These rods were pressed using a cold
isostatic press at 3250 bar and subsequently sintered for 24 hours under O2
flow at 1200 ∘C. The growth parameters — particularly gas pressure and laser
power — were initially optimized through several iterations using
polycrystalline seed rods. For the final growth using the optimized
parameters, a single crystal from a previous growth was used as the seed. The
growth was then conducted under 550 bar of an 80:20 Ar:O2 atmosphere in order
to stabilize congruent melting. Stable melting and recrystallization of the
feed rod onto the seed was accomplished using a total applied power of 455 W,
at which point the molten zone remained stable throughout the growth. Both
feed and seed were translated at a rate of 8.5 mm/hr and counter-rotated at
rates of 8 mm/hr and 9 mm/hr, respectively.

The resulting $\alpha$-Fe2O3 sample is shown in Fig. 4(a). Laue X-ray
diffraction (Fig. 4(c)) revealed the successful formation of a single crystal
with the growth direction approximately normal to the ($0\bar{1}\bar{2}$)
plane. Powder X-ray diffraction on a crushed portion of the single crystal
using a PANalytical Empyrean diffractometer suggests phase-pure
$\alpha$-Fe2O3, (Fig. 4(d)).

However, measurement of the magnetic properties using a Quantum Design MPMS3
SQUID magnetometer revealed the presence of a small amount of ferromagnetic
Fe3O4 (magnetite). The presence of Fe3O4 is indicated by the small feature
near 133 K in the magnetization data (Fig. 4(e)). This feature corresponds to
the Verwey transition[16], which appears in single-phase Fe3O4 at
$T_{V}\approx 125$ K. The fact that we were not able to detect any of the
Fe3O4 phase via X-ray diffraction sets an approximate upper bound of 1% by
mass in the sample, which is the estimated resolution limit of the powder
diffractometer. To better quantify the amount of Fe3O4 in the sample, the
height of the impurity peak from the magnetization versus temperature data was
scaled to Fe3O4 magnetization data from literature.[12] This analysis suggests
that the Fe3O4 content in the sample is approximately 0.085 mol%.

###  III.2 Growth of Wide Band Gap $\beta$-Ga2O3

Figure 5: (a) Single crystal of $\beta$-Ga2O3 obtained from the HP-LFZ — a
nearly transparent boule with noticeable facets. (b) Images from the pyrometer
and camera during growth at $P=70$ bar. (c) Laue diffraction pattern obtained
from the boule, consistent with reflections from the (001) plane.

As a demonstration of the ability for the relatively low frequency,
monochromatic laser light of the LOKII design to couple to and melt large band
gap insulators, growth of $\beta$-Ga2O3 was performed. $\beta$-Ga2O3 is a wide
band gap (4.8 eV) material of interest for its applications in optoelectronics
and power electronics. This compound has been grown using both conventional
[17, 18] and CO2 laser-based floating zone techniques.[19] Due to its wide
band gap, $\beta$-Ga2O3 exhibits low absorptivity in the infrared, resulting
in poor coupling to the 820 nm laser light used for this growth. This was
demonstrated by heating a seed rod using up to 100 W of 820 nm light per laser
(700 W total), which proved incapable of melting the sample. To circumvent
this issue, a rod of Al2O3 (96.0 $\%$ \- 99.8 $\%$, McMaster-Carr) was used as
the seed for the growth, to serve as an initial susceptor of the laser light,
and a rod of $\beta$-Ga2O3 was used as the feed. Starting powder of
$\beta$-Ga2O3 (99.99 $\%$, Alfa Aesar) was dried overnight at 1200 ∘C and then
pressed into 4 mm diameter rods at 3275 bar using a cold isostatic press. The
rods were then sintered at 1200 ∘C for 10 hours in air.

The Al2O3 was first melted using a total applied power of 216 W at 820 nm, and
a feed of $\beta$-Ga2O3 was joined into the melt. Subsequent translation
rapidly diluted any Al content out of the molten zone and resulted in a
colorless crystal of $\beta$-Ga2O3 (Fig. 5(a)). The growth was carried out
with a translation rate of 15 mm/hr and counter-rotation rate of 10 rpm for
both the feed and seed rods, using 70 bar of an 80:20 Ar:O2 atmosphere to
mitigate volatility.

To assess the phase purity and crystal structure, a micron-scale piece of the
resulting crystal was broken off and measured on a Kappa Apex II single-
crystal diffractometer with a fast charge-coupled device (CCD) detector and a
Mo source. The single crystal X-ray diffraction pattern was refined using the
SHELX software package.[20] The refined crystal structure consists of two and
three different crystallographic sites for Ga and O, respectively, and is
consistent with the previously reported structure of $\beta$-Ga2O3.[18, 21]

###  III.3 High-Pressure Traveling Solvent Growth of La2CuO4+δ

Figure 6: (a) Single crystal of La2CuO4+δ obtained from the first traveling
solvent floating zone carried out in the HP-LFZ — a shiny grey boule with an a
subtle facet corresponding to the (001) plane. (b) Images of the growth from
the camera (top) and pyrometer (bottom) at $P=550$ bar. (c) Laue diffraction
pattern obtained from a diced and polished cross section of the boule,
consistent with reflections from the (001) plane. (d) Temperature-dependent
magnetic susceptibility data at $H=20$ Oe. Two superconducting transitions are
marked with asterisks (*). An increase in superconducting volume fraction at
higher pressures is attributed to enhanced O2 intercalation. Inset shows
variation in the Néel transition temperature, with the transitions marked by
downward arrows.

Finally, we demonstrate the first traveling solvent floating zone growth at
the high pressures achievable in the LOKII design by performing crystal growth
of La2CuO4+δ at 700 bar. La2CuO4 is a canonical parent material to high-
temperature superconductivity upon hole doping via cation substitution in
La2-xSrxCuO4 and La2-xBaxCuO4, or via interstitial oxygen excess in La2CuO4+δ.
Superconductivity can be achieved at temperatures $T_{\mathrm{c}}\geq 40~{}$K
in La2CuO4+δ.[22] Because La2CuO4 decomposes peritectically near
$1325~{}^{\circ}$C,[23] a flux must be employed to grow crystals from a melt.
Thus, La2CuO4 is conventionally grown using the traveling solvent floating
zone technique, in which a CuO-rich flux is used to dissolve the feed rod and
precipitate out the grown crystal. Here, we achieve the first traveling
solvent floating zone growth operated at 700 bar, and demonstrate an increased
oxygen solubility in the solvent as a function of pressure.

Tuning the doping level in La2CuO4+δ using oxygen excess is typically achieved
by post-growth annealing in high-pressure O2,[24, 25, 26, 27] electrochemical
methods,[28, 29] or chemical oxidation via an oxidizing agent.[30, 31, 32, 33]
The oxygen intercalates between the CuO2 layers and can undergo ordering
phenomena in stages, much like the intercalation of chemical species between
layers of graphite.[34, 35, 36, 37, 38, 39, 40] Traveling solvent floating
zone growth of La2CuO4 requires some O2 pressure (conventionally on the order
of 1 bar) in order to stabilize the Cu2+ oxidation state,[41, 42, 43] and this
results in as-grown samples exhibiting a partial volume fraction of
superconducting phase due to intercalation of excess oxygen into the lattice.

Here we employ a standard recipe, using a flux with molar composition of 4:1
CuO:La2O3 and a feed rod containing 2% excess CuO to sustain the flux
composition during growth. To prepare both the feed rod and the flux, we began
by grinding and mixing stoichiometric amounts of La2O3 (99.99%, Alfa Aesar)
and CuO (99.9995% Thermo Scientific) powders. This mixture was then loaded
into a latex balloon and pressed into a pellet using 3275 bar in a cold
isostatic press.

The feed rod precursors underwent a three-step firing process with
intermittent grinding and pressing steps to avoid inhomogeneity. First, the
feed pellet was fired at 800 ∘C for 24 hours in air. After the first firing,
the resulting material was then reground into a fine powder before pressing
and firing again, this time at 900 ∘C for another 24 hours in air. Finally,
the pellet was reground, pressed into a rod, and sintered at 1200 ∘C for 10
hours under flowing O2. In a similar fashion, the flux pellet was first fired
at 800 ∘C for 24 hours in air, then at 800 ∘C for 24 hours in air, and lastly
at 850 ∘C for 12 hours in air.

Prior to the growth, a piece of the flux was first fused to a single crystal
seed rod in ambient atmosphere using a total melting power of $\approx$40 W,
to avoid the challenge of balancing a disc of the flux on the seed while
pressurizing the growth chamber. The growth was carried out under a total
pressure of 700 bar of 80:20 Ar:O2 mix, requiring a total power of 140 W to
melt the flux. The rods were translated at a rate of 1 mm/hr, with rotation
rates of 5 rpm and 10 rpm for the feed and seed, respectively. A stable zone
was sustained for several days, producing multi-centimeter sized boules (Fig.
6(a)). The surfaces of the crystals were shiny grey with a subtle facet
visible on two opposite sides, and a Laue diffraction pattern on a piece diced
from a boule in this orientation shows well-defined reflections corresponding
to the (001) plane of the La2CuO4 phase (Fig. 6(c)).

Magnetization measurements on crystals diced from boules grown at pressures of
550 bar and 700 bar reveal two superconducting transitions near $T_{c1}=28$ K
and $T_{c2}=16$ K (Fig. 6(d)), suggestive of a mixed state where two different
and unknown orderings of interstitial oxygen coexist in segregated regions of
the sample.[40] Compared to samples grown under 1 atm of O2 in a conventional
mirror furnace, crystals grown in the HP-LFZ exhibit a larger superconducting
volume fraction, which we attribute to higher amounts of intercalated oxygen
inherent to the growth process under higher pressures of O2. To assess the
distribution of oxygen within the boule, two pieces were measured for the 550
bar growth: one piece diced from the center of the boule and one piece diced
from the exterior. The piece taken from the exterior exhibited a significantly
higher volume fraction, suggesting a radial gradient in the doping level.
Thermogravimetric analysis (TGA) measurements were performed on a crushed
piece of the 700 bar growth in flowing N2 to estimate the amount of
intercalated oxygen ($\delta$) lost after heating as-grown La2CuO4+δ to 950
∘C. The resulting mass loss suggested an average composition $\delta=0.07$ of
the as-grown boule. These results suggest that higher O2 partial pressures
lead to a increase in the activity of oxygen in the growth process compared to
growth under conventional pressures.

##  IV Summary

A second generation design of the high-pressure laser floating zone furnace,
LOKII, is presented. This design advance uses an optics array that allows for
in-plane imaging and higher power at the growth front. Additionally, the
removal of out-of-plane sight glasses on the chamber allows for better cooling
of the chamber and window housings. The growth of several representative
oxides demonstrates the ability of a high-pressure growth environment to tune
chemical potential and mitigate material volatility. We further demonstrate
the feasibility of the traveling solvent floating zone technique at a pressure
of 700 bar and show that wide band gap materials can be grown in regimes where
initial coupling to the laser light is weak. This second-generation design is
expected to aid in realizing the high quality single crystal growth of other
volatile and metastable phases of interest in the field of quantum materials.

##  V Acknowledgments

Jude Quirinale, in memoriam.

The authors acknowledge fruitful conversations with Brenden R. Ortiz, Paul M.
Sarte, Bin Gao, Karthik Rao, Alon H. Avidor, Pedro A. Barrera, and Casandra J.
Gomez Alvarado. This work was supported via the UC Santa Barbara NSF Quantum
Foundry funded via the Q-AMASE-i program under award DMR-1906325. S.J.G.A.
acknowledges additional financial support from the National Science Foundation
Graduate Research Fellowship under Grant No. 1650114. This research also made
use of the shared facilities of the NSF Materials Research Science and
Engineering Center at UC Santa Barbara, Grant No. DMR-1720256.

##  VI Author Declarations

###  VI.1 Conflict of Interest

The author has no conflicts to disclose.

###  VI.2 Author Contributions

Steven J. Gomez Alvarado: Investigation (lead); Methodology (lead); Software
(lead); Validation (lead); Visualization (equal); Writing - original draft
(lead). Writing - review & editing (equal). Eli Zoghlin: Investigation
(equal); Methodology (equal); Project administration (equal); Supervision
(equal); Validation (equal); Writing - review & editing (equal). Azzedin
Jackson: Methodology (equal); Validation (equal). Linus Kautzsch:
Investigation (equal); Methodology (equal); Validation (equal). Jayden Plumb:
Formal analysis (equal); Investigation (equal); Methodology (equal);
Validation (equal); Visualization (equal). Michael Aling: Formal analysis
(lead); Investigation (equal); Methodology (equal); Visualization (lead).
Andrea N. Capa Salinas: Investigation (equal); Visualization (equal). Ganesh
Pokharel: Investigation (equal); Visualization (equal). Yiming Pang:
Investigation (equal); Methodology (equal); Validation (equal). Reina M.
Gomez: Investigation (equal); Methodology (equal); Validation (equal).
Samantha Daly: Supervision (equal); Writing - review & editing (equal).
Stephen D. Wilson: Conceptualization (lead); Funding acquisition (lead);
Project administration (lead); Resources (lead); Supervision (lead); Writing -
review & editing (equal).

##  VII Data Availability

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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