# Chemical tuning of a honeycomb magnet through a critical point

Austin M. Ferrenti  Department of Chemistry, The Johns Hopkins University,
Baltimore, Maryland 21218, USA  Maxime A. Siegler  Department of Chemistry,
The Johns Hopkins University, Baltimore, Maryland 21218, USA  Shreenanda Ghosh
Institute for Quantum Matter, William H. Miller III Department of Physics and
Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
Hector K. Vivanco  Department of Chemistry, The Johns Hopkins University,
Baltimore, Maryland 21218, USA  Nina Kintop  Fraunhofer Research Institution
for Materials Recycling and Resource Strategies IWKS, Aschaffenburger Straße
121, 64357 Hanau, Germany  Chris Lygouras  Institute for Quantum Matter,
William H. Miller III Department of Physics and Astronomy, The Johns Hopkins
University, Baltimore, Maryland 21218, USA  Thomas Halloran  Institute for
Quantum Matter, William H. Miller III Department of Physics and Astronomy, The
Johns Hopkins University, Baltimore, Maryland 21218, USA  Sebastian Klemenz
Fraunhofer Research Institution for Materials Recycling and Resource
Strategies IWKS, Aschaffenburger Straße 121, 64357 Hanau, Germany  Collin
Broholm  Institute for Quantum Matter, William H. Miller III Department of
Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland
21218, USA  Natalia Drichko  Institute for Quantum Matter, William H. Miller
III Department of Physics and Astronomy, The Johns Hopkins University,
Baltimore, Maryland 21218, USA  Tyrel M. McQueen  Department of Chemistry, The
Johns Hopkins University, Baltimore, Maryland 21218, USA<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

BaCo2(AsO4)2, or BCAO, has seen extensive study since its initial
identification as a proximate Kitaev quantum spin liquid (KQSL) candidate.
Although recent studies suggest its magnetic ground state is better described
by the highly anisotropic XXZ-$J_{1}$-$J_{3}$ model, the ease with which
magnetic order is suppressed with the application of a small in-plane magnetic
field indicates proximity to a spin liquid phase. Upon chemical tuning via
partial arsenic substitution with vanadium, we show an initial suppression of
long-range order in the BCAO system to _T_ $\sim$ 3.0 K, followed by the
introduction of increased spin freezing at higher substitution levels. Between
these two regions at x = 0.10, the system is shown via AC and DC
susceptibility, Raman scattering spectroscopy, and heat capacity measurements
to pass through a critical point where no phase transition is apparent, down
to _T_ = 0.40 K. At this level of substitution, the competing nearest-neighbor
$J_{1}$ and third nearest-neighbor $J_{3}$ interactions apparently become more
balanced, producing a more complex magnetic ground state, likely stabilized by
quantum fluctuations. This state shows how slight compositional change in
magnetically-frustrated systems may be leveraged to tune ground state
degeneracies and potentially realize a quantum spin liquid state.

Institute for Quantum Matter, William H. Miller III Department of Physics and
Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
Institute for Quantum Matter, William H. Miller III Department of Physics and
Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA
Department of Materials Science and Engineering, The Johns Hopkins University,
Baltimore, Maryland 21218, USA NIST Center for Neutron Research, Gaithersburg,
Maryland 20899, USA Institute for Quantum Matter, William H. Miller III
Department of Physics and Astronomy, The Johns Hopkins University, Baltimore,
Maryland 21218, USA Department of Materials Science and Engineering, The Johns
Hopkins University, Baltimore, Maryland 21218, USA

##  1 Introduction

In the development of novel materials possessing improved mechanical,
optoelectronic, and magnetic properties, small compositional changes can
radically change the behaviors exhibited. To address long-standing scientific
challenges - such as the stabilization of typically fragile, long-range spin
entanglement in a real quantum spin liquid (QSL) - subtle modifications to
promising, yet ultimately flawed candidates may be necessary.1, 2 The chemical
tuning of a magnetic system, particularly where there exists a significant
degree of spin frustration, can provide a broader understanding of the
competing exchange interactions which determine the degeneracy of the magnetic
ground state and often results in the discovery of exotic quantum phenomena.3
While direct substitution on the magnetic sublattice can yield important
information about the type and magnitude of exchange occurring in a material,
the realization of a stable spin liquid state in a magnetically frustrated
system requires a more thorough understanding of other structural features
that help mediate magnetic exchange. This is especially relevant for phases
mimicking the prototypical Kitaev spin liquid (KQSL), where S = 1/2 moments on
the vertices of a honeycomb lattice experience only highly anisotropic, Ising-
type interactions.4, 5 The bond-dependent nature of Kitaev exchange
interactions makes such systems particularly sensitive to minor structural
change.

One of the most intensely studied honeycomb spin liquid candidates,
BaCo2(AsO4)2, consists of d7, octahedrally-coordinated Co2+ ions, possessing a
pseudospin-1/2 ground state doublet.6 The honeycomb lattice in BaCo2(AsO4)2,
or BCAO, consists of edge-sharing, lightly-distorted CoO6 octahedra, which are
believed to account for the high degree of planar anisotropy observed in its
magnetic behavior at low temperatures (Figure 1a-c).7 BCAO orders
antiferromagnetically at _T_ ${}_{\text{N}}$ = 5.4 K, with dominant in-plane
ferromagnetic (FM) exchange, and has been shown to undergo two magnetic phase
transitions upon the application of a $\mu_{0}\text{H}$ = 0.26 T and
$\mu_{0}\text{H}$ = 0.53 T in-plane field, respectively.6 This suppression of
the magnetic order with the application of only a relatively weak field was
initially believed to indicate the presence of fairly weak non-Kitaev
interactions in the material, relative to similar systems, which led to its
identification as a proximate KQSL candidate. However, recent experimental
studies point to a non-Kitaev, highly anisotropic and geometrically-frustrated
ground state, better described by the XXZ-$J_{1}$-$J_{3}$ model, as opposed to
the JK$\Gamma$ model associated with the KQSL.8 The frustration in BCAO then
arises due not to Kitaev-type bond-dependent interactions, but rather due to
competition between ferromagnetic superexchange ($J_{1}$) and third nearest-
neighbor antiferromagnetic ($J_{3}$) exchange between Co2+ ions in the
honeycomb plane.

While its promise as a quantum spin liquid candidate is ultimately dampened by
the fact that it magnetically orders, the closeness of BCAO to the ideal
octahedral Co2+ geometry was initially believed to indicate that the material
itself may be chemically tuned to exhibit more ideal QSL behavior. In order to
do so without otherwise disrupting the honeycomb geometry of the cobalt layer,
two potential avenues for improvement via chemical substitution exist. The
substitution of some small percentage of either the interlayer polyanion group
(AsO4^3-) or alkaline earth atom (Ba^2+) may alter the local Co^2+
coordination environment enough to produce more perpendicular Co-O-Co bond
angles, and subsequently more perfect octahedral coordination, that would
allow for maximal Kitaev and minimal Heisenberg exchange in the honeycomb
plane. In particular, substitution of the interlayer polyanion group is
expected to more significantly influence the third neighbor exchange
interaction $J_{3}$, and thus also the degree of frustration in the
$J_{1}-J_{3}$ model.

Of the divalent, reliably non-magnetic ions, partial substitution of the
12-fold coordinate Ba^2+ would likely only be possible with either Sr^2+ or
Pb^2+, both of which would represent a roughly 13% reduction in ionic radius –
an increase in size, at least with simpler ions, would not be possible. A pure
Pb-analogue of BCAO is not known to exist, and the reported SrCo2(AsO4)2 phase
does not contain Co on a honeycomb lattice. 9 More flexibility exists for
partial As-substitution, with tetrahedrally-coordinated V^5+, P^5+, Sb^5+, and
Nb^5+ all being potentially viable. Of these, only the P-analogue has been
previously synthesized, and existing studies thereof have been significantly
hindered by the higher stability of two competing polymorphs.10 The maximum
amount of substitution without the introduction of significant structural
deformations would likely occur for V^5+, as its tetrahedral metal-oxygen bond
lengths are roughly analogous to that of As^5+, whereas Nb^5+ and Sb^5+ would
represent a significant increase, and P^5+ a significant decrease,
respectively.

Here we report the synthesis and structural and magnetic characterization of a
series of V-substituted BCAO compositions (BaCo2(AsO4)_2-2x(VO4)_2x), 0.025
$\leq$ x $\leq$ 0.70. At low substitution levels, 0.025 $\leq$ x $\leq$ 0.09,
long-range order in the system is gradually suppressed to _T_ $\sim$ 3.0 K,
before disappearing down to at least _T_ = 0.4 K in the intermediate
substitution region. At higher substitution levels, 0.15 $\leq$ x $\leq$ 0.70,
signs of spin freezing become apparent, long-range order reappears, and the
system begins to behave similar to the fully-substituted BaCo2(VO4)2 phase.
The x = 0.10 composition appears to represent a critical point between these
two regions, displaying signatures of strong spin correlations and minor
changes to the cobalt coordination environment, but not a transition to a
long-range ordered state, possibly due to enhanced quantum fluctuations in the
magnetic ground state.

##  2 Results and discussion

###  2.1 Synthesis and characterization

Polycrystalline samples of V-substituted BaCo2(AsO4)2 were produced by the
heating of well-ground mixtures of 2.9 mol BaCO3 (Strem Chemicals, 99.9%), 2.0
mol Co3O4 (NOAH Technologies, 99.5%, 325 mesh), and a combined 6.0 mol
NH4H2AsO4 (Alfa Aesar, 98%)/NH4VO3 (Beantown Chemical, ACS, 99.0%). The
mixtures were placed in an uncovered alumina crucible in air, heated to 305°C,
held for 12 hours, heated to 875°C, held for 48 hours, cooled to room
temperature, and finally heated to 925°C for 12 hours before again cooling to
room temperature. All ramp rates were set at 100°C per hour. Both the 875°C
and 925°C annealing steps, with an intermediate cooling to room temperature,
were found to be necessary to minimize impurity phase formation. In each
trial, the resulting product was found to consist largely of the expected
BaCo2(AsO4)_2-2x(VO4)_2x phase, as well as a small diamagnetic Ba3(AsO4)2
impurity. The omission of either the initial 875°C anneal or the intermediate
cooling step resulted in a higher Ba3(AsO4)2 concentration and an additional
Co3(AsO4)2 impurity. This also occurred when the stoichiometric 3.0 mol of
BaCO3 was used in each synthesis, likely due to minor hydration of the Co3O4
precursor. Independent adjustments to the Co3O4 and NH4H2AsO4 concentrations
were also attempted, but were not found to produce a purer product. As a
result, representative BaCo2(AsO4)_2-2x(VO4)_2x compositions were synthesized
with a nominal 3.3% BaCO3 deficiency.

Single crystals of each composition were produced via melting under static
vacuum. Polycrystalline samples were added to an uncovered alumina crucible,
placed in a 12mm ID, 16mm OD quartz tube, and sealed under vacuum. The tube
was then heated at 1150°C for 12 hours, with heating and cooling rates of
100°C per hour. The resulting mass of crystals was then pried from the
crucible and mechanically separated along the cleavage planes. Due to their
layered morphology, the thinnest crystals were found to be the most reliably
single-domain, however thicker crystals without noticeable signs of grain
boundaries were also commonly produced. Powder and single crystal samples of
the non-magnetic analogue of BCAO, BaMg2(AsO4)2 (BMAO) and its V-substituted
compositions (BMAO-V) were produced by the heating and subsequent melting of
0.97 mol BaCO3 (Strem Chemicals, 99.9%), 2.0 mol MgO (NOAH Technologies,
99.99%, 325 mesh), and a combined 2.0 mol NH4H2AsO4 (Alfa Aesar, 98%)/NH4VO3
(Beantown Chemical, ACS, 99.0%) under conditions identical to that described
above for the BCAO-V series.

Similar substitution trials were also attempted with partial Nb, P, and Sb
substitution for As, as well as with partial substitution of Pb and Sr for Ba.
In all cases, only very minor shifts are observed in the measured powder X-ray
diffraction patterns, owing to the lower probability of incorporation for ions
significantly larger or smaller than those in pure BCAO. Initial magnetic
characterization of several of these compositions is consistent with the
larger distortions of the host lattice expected from partial substitution with
the other species. The ordering transition is observed to occur at higher
temperatures for all samples measured and for Nb-, Pb-, and Sb-substituted
compositions a second, relatively broad transition appears at _T_ = 2.0-3.0 K.
This broad transition can likely be attributed to the freezing of spins in
samples with more heavily-distorted Co-coordination environments.

Powder X-ray diffraction (pXRD) patterns were collected on a laboratory Bruker
D8 Focus diffractometer with LynxEye detector and Cu K$\alpha$ radiation in
the 2$\theta$ range from 5-120 degrees. All shifts in reflection position were
initially determined relative to a silicon standard to ensure a reliable
benchmark across compositions before subsequent Rietveld refinements.
Refinements on pXRD data were performed using Topas 5.0 (Bruker). Calculated
vanadium substitution levels were obtained via refinement of the arsenic site
occupancy in each composition. The combined As and V occupancy on this site
was constrained to one. All other site occupancies were also constrained to
one. Structures were visualized with the Vesta 3 program.11

Single crystal X-ray diffraction (SCXRD) measurements were performed using a
SuperNova diffractometer (equipped with Atlas detector) with Mo K$\alpha$
radiation ($\lambda$ = 0.71073 Å) under the program CrysAlisPro (Versions
1.171.41.93a and 1.171.42.49, Rigaku OD, 2020-2022). The same program was used
to refine the cell dimensions and for data reduction. All reflection
intensities were measured at _T_ = 213(2) K. The structure was solved with the
program SHELXS-2018/3 and was refined on _F 2_ with SHELXL-2018/3.12
Analytical numeric absorption correction using a multifaceted crystal model (x
= 0.05, 0.075, 0.10, and 0.50 compositions) or empirical absorption correction
using spherical harmonics (x = 0.025 composition) were performed using
CrysAlisPro. The temperature of the data collection was controlled using the
Cryojet system (manufactured by Oxford Instruments). Calculated vanadium
substitution levels were obtained via free variable refinement of the arsenic
site occupancy in each composition. To account for the net decrease of 10
electrons on each vanadium-substituted arsenic site, the refined As-site
occupancy was scaled by:

$x=(33-33z)/10$ (1)

where $x$ is the estimated % V-content for each sample and $z$ is the refined
occupancy factor for As.12 This accounts for the 10-electron difference
between arsenic and vanadium, allowing for a more reliable estimate of
V-occupancy on the As-site.

Optical emission spectroscopy based on inductively coupled plasma (ICP-OES)
was used to experimentally determine the metal ratios in the samples. Crystals
were dissolved in aqua regia at 240 °C (at 1200 W) for 1 h in a turboWAVE
system from MLS-MWS. This process was repeated twice for each sample. The
resulting concentration of Ba, Co, V, and As was measured 3 times and averaged
using a PerkinElmer Optima 8300 ICP-OES spectrometer system. Additionally, the
concentrations of Al, Ca, Mg, Na, and Si were recorded.

Raman scattering spectra were measured in the backscattering geometry over the
range from 100-1100 cm-1 using a Horiba JY T64000 spectrometer equipped with
an Olympus microscope, using a laser probe with a diameter of 2 microns and a
laser power below 1 mW. The spectra were excited using the 514.5 nm line of a
Coherent Innova 70C Spectrum laser. Representative spectra were collected with
the $e_{l}$ polarization of the excitation light applied parallel to the _ab_
-plane of BCAO-V single crystals. Spectra were measured in parallel (x,x) and
cross (x,y) polarizations, where x was oriented randomly in the (a,b) plane.
No signs of laser-induced degradation of the samples were observed over the
course of each measurement. All sample spectra were calibrated with a silicon
standard to ensure a reliable comparison of frequency shifts on increasing
vanadium substitution.

Magnetization data was collected on a Quantum Design Magnetic Property
Measurement System (MPMS3). Magnetic susceptibility was approximated as
magnetization divided by the applied magnetic field ($\chi\approx M/H$). AC
magnetic susceptibility as a function of temperature ($\chi_{AC}$ vs. T) was
measured for each powder composition with no applied DC field and an AC
frequency of $f$ = 600 Hz. For the single crystal compositions, this was
measured with no applied DC fields and applied frequencies of $f$ = 300 Hz,
$f$ = 600 Hz, and $f$ =900 Hz. AC magnetic susceptibility as a function of
applied DC field ($\chi_{AC}$ vs. B) was measured for each single crystal
composition with an applied AC frequency of $f$ = 775 Hz. Assuming minimal
interactions between neighboring clusters, the frequency dependence of the
measured AC susceptibility was fit to the Arrhenius law, where
E${}_{\text{a}}$ is the activation energy for spin reorientation,
k${}_{\text{B}}$ is Boltzmann’s constant, and T${}_{\text{f}}$ is the
transition temperature observed:

$\omega=\omega_{0}\cdot exp(E_{a}/k_{B}T_{f})$ (2)

The linear fitting of a plot of 1/T${}_{\text{f}}$ vs ln($\omega$) for each
composition yields E${}_{\text{a}}$/kB as the slope and the characteristic
frequency $\omega_{\text{0}}$ as the y-intercept.

Heat-capacity data was collected on a Quantum Design Physical Property
Measurement System (PPMS) using the semi-adiabatic pulse technique with a 1%
temperature rise and over three time constants. The change in magnetic entropy
as a function of temperature, $\Delta S_{\mathrm{mag}}$, was approximated as
$\Delta S_{\mathrm{mag}}$ = $\int C_{\mathrm{p}}/T\,dT$ of the measured
$C_{\mathrm{p,mag}}$ for each composition ($C_{\mathrm{p,total,BCAO-V}}$ \-
$C_{\mathrm{p,total,BMAO-V}}$), from _T_ = 0–50 K. The entropy rise from _T_ =
0 K to 2.0 K was estimated from linear extrapolation over this range. The
measured $C_{\mathrm{p}}/T$ of pure BMAO and its 5%, 10%, 15%, and 20%
V-substituted analogues was scaled by a factor of 1.20, 1.29, 1.44, 1.38, and
1.54, respectively, to ensure convergence with and subtraction from that of
the Co-analogue by _T_ = 50 K.

###  2.2 pXRD

Initial attempts at partial As-substitution with vanadium in trigonal BCAO
[space group _R $\overline{3}$H_ (148)] resulted in a series of compositions
with clear, progressive shifts in both structural and magnetic properties. The
powder diffraction patterns measured for each composition, shown in Figure S1,
show shifts to higher 2$\theta$ for the majority of (h0l), (0kl), and (00l)
reflections, and a slight shift to lower 2$\theta$ for the singular (hk0)
reflection around 35.8 degrees. Assuming random incorporation of vanadium into
the structure, Rietveld refinement of the experimental pXRD and SCXRD data in
the _R $\overline{3}$H_ space group resulted in similarly good fits for all
compositions upon initial and secondary heating (Tables S1-S4, S5-S10).
Several compositions initially possessed a small ($\sim$3-5 wt%) Ba3(AsO4)2
impurity phase, which was typically removed via a secondary heating step above
the materials’ melting point. Reflections corresponding to this impurity phase
were also observed to shift with increasing nominal V-substitution of the
target phase, indicating that partial substitution of arsenic with vanadium
occurs for both phases present in the initial product mixture. Up to x = 0.70,
the roughly 0.02 Å increase in M-O bond lengths for tetrahedrally-coordinated
vanadium is observed to produce a gradual contraction of the unit cell along
the c-axis, as well as a gradual expansion of the a-axis, by 0.835 Å and 0.054
Å respectively (Figures 1d-e). Relative to BCAO, these relative shifts $\Delta
c/c=-3.6\%$ and $\Delta a/a=1.1\%$ correspond to a volumetric contraction of
$\Delta v/v=-1.4\%$. When substituted for the arsenate groups present in pure
BCAO, the longer V-O bond lengths in the BCAO-V compositions produce both a
compression of the interplanar region along the stacking axis and an
additional tilting of the Co octahedra within the honeycomb plane. Beyond x =
0.70, the tetragonal structure of the pure BaCo2(VO4)2 (BCVO) phase [space
group _I4 1/acd_ (142)] begins to appear, with slight shifts in the observed
reflections due to partial As-substitution for vanadium, and the trigonal BCAO
structure gradually disappears. Similar to previous reports of vanadium
substitution for phosphorus in BaCo2(PO4)2 (BCPO), the effective upper limit
of vanadium uptake in the trigonal BCAO phase appears to be around 70%.13

The true degree of vanadium substitution in each composition was both
estimated from refinement of the experimental diffraction data and confirmed
via ICP-OES analysis. Calculated V-substitution levels obtained via Rietveld
refinement of the As-site in BCAO after the first and second heating steps are
shown in Figure S6a. Vanadium occupancies on the As-site typically refine
close to nominal values for powder samples produced via initial heating of the
reaction mixture, while the secondary heating step is observed to either meet
or slightly exceed the expected occupancy. This can likely be attributed to
the incorporation of the V-substituted Ba3(AsO4)2 impurity phase from the
initial reaction mixture into the BCAO structure upon further annealing.

ICP-OES analysis of synthesized BCAO-V samples agrees well with the
V-substitution levels estimated via Rietveld powder and single crystal
structural refinement, shown in Figure S6b and summarized in Table S11. No
significant recovery of vanadium is observed from the initial powder synthesis
to the secondary crystallization step, indicating that initial V-substituted
Ba3(AsO4)2 impurity concentrations are actually generally minor. The measured
V-content in the maximally-substituted composition suggests an upper limit of
around 56.0% before the tetragonal structure becomes more prevalent. A second
sample of the x = 0.10 composition was also analyzed and was found to possess
closer to 17% V. This sample was grown by the vertical Bridgman method, where
the initial powder product was placed in a pointed alumina crucible, sealed
under vacuum in a quartz tube, melted and slowly recrystallized. Due to the
vertical temperature gradient, the slow re-solidification may have resulted in
inhomogeneous distributions of vanadium throughout the grown crystal mass, and
as a result these crystals were not used for further characterization.

As the shifts in both lattice parameters appear to be progressive over the
studied composition range and the shift observed along the a-axis is small
relative to that observed along the c-axis, it is likely that vanadium does
not substitute for arsenic randomly in the structure, but rather as discrete
domains. Attempts to generate accurate unit cells for each composition,
particularly at low substitution levels, would thus be dependent on the manner
in which these vanadium clusters are distributed throughout the structure.
This would also imply a wider distribution of distinct cobalt coordination
environments, producing a more complex magnetic ground state. Due to the
difficulty in making this determination concretely, refinements on both pXRD
and SCXRD data presented in this work were performed under the assumption of
random substitution. Regardless of the true vanadium distribution, the
progressive trends in the pXRD and SCXRD data and color changes in the grown
crystals from pink (pure BCAO) to red (lightly V-substituted) and gradually to
black (x $\geq$ 0.40), together indicate average changes in the crystal field
splitting energy of the octahedrally-coordinated Co and potentially also in
the trigonal distortion thereof.

###  2.3 Raman scattering spectroscopy

Representative Raman scattering spectra collected from BCAO-V single crystals
provide additional evidence for the gradual tuning of the Co coordination
environment upon substitution of the interlayer polyanion group (Figure 2). In
pure BCAO, the symmetry of the trigonal _R $\overline{3}$H_ structure is well-
described by the $C_{3i}$ point group. Of the symmetrically-allowed optical
modes, 18 are expected to be Raman-active (12 in the (ab) plane (6$A_{g}$ \+
6$E_{g}$)) and 10 of which have been previously observed below 900 cm-1.14 The
polarization dependence of band intensities was used to distinguish between
$A_{g}$ and $E_{g}$ modes, which were observed to be strongest in the (x,x)
and (x,y) configurations, respectively (Figure S2).14

Upon partial substitution of As with V, this polarization dependence remains
relatively consistent, with singlet $A_{g}$ modes initially predominating in
the parallel polarization (x,x) configuration, doublet $E_{g}$ modes in the
(x,y) configuration, and the overall measured intensity remaining higher for
the former. The measured frequency shifts and linewidths for each vibrational
mode as a function of substituted vanadium content are shown in Figure S3. Up
to x = 0.075, all $E_{g}$ and lower-energy $A_{g}$ modes begin to harden,
while the $A_{g}$(5) mode begins to soften, all without significant
broadening. The higher-energy $E_{g}$ modes also begin to decrease in
intensity.

At x = 0.10, the intensity of the measured spectra in both configurations
drops significantly, with that of the (x,y) polarization decreasing to less
than half of that observed in either the x = 0.075 or x = 0.15 compositions.
Interestingly, the intensity of the two highest-frequency $A_{g}$(5) and
$E_{g}$(5) modes decreases by over an order of magnitude relative to the same
samples, indicative of more considerable changes to the local bonding
environment in BCAO. While reproducible across several single crystal samples,
powder samples of this composition do not possess such a drop in magnitude, as
shown in Figure S4. This effect likely then arises as a consequence of a
distinctive clustering order for the x = 0.10 phase that manifests only across
larger domains. Beyond x = 0.10, the majority of singlet modes begin to soften
and the majority of the bands begin to broaden more significantly. The higher-
energy $E_{g}$ modes are not observed to shift in frequency, but rather
decrease in intensity and are entirely absent by the x = 0.20 composition. At
and above this level of substitution, the intensity ratio of the remaining
$A_{g}$ and $E_{g}$ modes is no longer dependent on the experimental
configuration and the spectra differ only in magnitude. An additional broad
feature also appears at $\sim$875 cm-1 at higher substitution levels and is
most prominent for the x = 0.20 composition. This likely indicates a more
significantly disordered bonding environment that introduces greater spin
freezing in this region.

Upon chemical substitution, the majority of systems display significant
broadening of Raman active modes, indicative of random displacement of the
substituted atom and subsequently higher disorder throughout the material.15,
16 While slight broadening of several modes is observed upon partial
V-substitution of BCAO, the bands remain comparatively sharp, indicating that
vanadium does not purely substitute randomly and further supporting that it
may do so in a periodic manner.

Although not explicitly assigned in previous reports, the highest frequency of
these likely correspond to breathing modes of the two distinct oxygen sites
present in the structure.17 The frequencies at which these modes appear agree
well with those previously attributed to honeycomb lattice materials
containing edge-sharing Co-octahedra.18, 16 As increasing vanadium
incorporation is accompanied by a larger contraction of the unit cell along
the stacking axis than expansion within the honeycomb plane, the oxygen
vibrations occurring between cobalt layers would be expected to be more
significantly impacted by greater substitution. The most impacted, highest-
energy oxygen modes [$A_{g}$(5) and $E_{g}$(5)] are thus attributed to the
apical oxygen of each arsenate/vanadate group not bound within the honeycomb
plane, labeled O2 in Figure 1a. The lower frequency oxygen modes [$A_{g}$(4)
and $E_{g}$(4)], then correspond to the oxygens directly bound to Co atoms,
labeled O1 in Figure 1a. In the absence of broader structural change, these
modes would be less significantly impacted by substitution outside of the
honeycomb planes.

The anomalous frequency and linewidth trends observed for vibrational modes in
the x = 0.10 composition, combined with the sharp decrease in measured
intensity, provide evidence for a critical point at which signs of a more
symmetric bonding environment emerge, despite the retention of the trigonal _R
$\overline{3}$H_ structure suggested by the diffraction data. Whereas the
gradual shifts observed in the calculated lattice parameters for each
composition provide evidence for the amount of vanadium substituting into the
BCAO structure, this critical point illustrates that the way in which that
vanadium is incorporated is not consistent throughout the series. This
composition clearly delineates the BCAO-V series between regions of order and
disorder, driven by increased steric pressure about the honeycomb plane.

###  2.4 Magnetic characterization

Temperature-dependent DC magnetic susceptibility measurements of V-substituted
BCAO powder compositions, the ordering transition temperatures of which are
shown in red in Figure 3, suggest a gradual tuning of the magnetic ground
state of the system with increasing vanadium content. In pure BCAO, long-range
antiferromagnetic (AFM) order is suppressed above _T_ = 5.4 K. From 0.025
$\leq$ x $\leq$ 0.09, the observed transition to a long-range ordered state
decreases in temperature to _T_ $\sim$ 3.0 K, less than half that of the
parent material. From 0.10 $\leq$ x $\leq$ 0.25, no transition is observed,
but rather the susceptibility rounds off and stagnates, down to at least _T_ =
0.4 K. Above x = 0.25, the transition reappears and gradually increases in
temperature to exceed that of either pure BCAO or BCVO, before again
decreasing to match that observed in the fully-substituted end-member with the
dominance of the tetragonal-type phase.

To better understand how the magnetic ground state of the system evolves with
increasing vanadium content, particularly for the low (x = 0.025-0.20)
V-substituted samples, temperature-dependent DC magnetic susceptibility
measurements were also performed on single crystals of these compositions.
With the field applied within the honeycomb plane ($\mu_{0}\text{H}\perp$ c,
Figure S7), the long-range ordering transition declines to _T_ = 4.06 K in the
x = 0.075 sample, slightly higher than that observed in the powder
measurements. At and above x = 0.10, the susceptibility instead plateaus below
_T_ = 3.0 K, indicating that long-range order is suppressed in these
compositions. These higher-substituted samples also exhibit a bifurcation
between the zero-field-cooled (ZFC) and field-cooled (FC) susceptibility
measurements below _T_ = 2.0 K, indicating some degree of spin freezing. The
ZFC susceptibility for the x = 0.15 composition also trends negative below
$T_{\text{f}}$, a feature typically attributed to materials containing
multiple, highly anisotropic magnetic sublattices.19 As Co^2+ is the only
magnetic cation present in the BCAO-V system, this composition must possess a
higher proportion of discrete cobalt clusters which produce a net negative
magnetization at low temperatures.

Curie-Weiss analysis at high temperatures (_T_ = 150 K – 300 K) for
($\mu_{0}\text{H}\perp$ c) yields a Curie-Weiss temperature
$\theta_{\text{CW}}$ $\approx$ 37(1) K for all compositions and an effective
magnetic moment $p_{\text{eff}}$ $\approx$ 5.5(2) $\mu_{B}$ (Table 1, Figure
S9), which lies between the effective moments 3.87 $\mu_{B}$ and 6.54
$\mu_{B}$ calculated for the ${}^{4}F_{9/2}$ term of the Co2+ $3d^{7}$ ion in
the spin only versus the full spin-orbital limits, respectively. The
relatively stable positive Curie-Weiss temperature indicates the preservation
of dominant FM coupling between adjacent Co^2+ ions. Yet $\theta_{\text{CW}}$
is $\approx$20% larger for the x = 0.10 and x = 0.15 samples, suggesting a net
enhancement of ferromagnetism with V substitution. The effective moment
$p_{\text{eff}}$ for these compositions is also slightly lower than for either
the other compositions or the parent BCAO, indicating additional minor
quenching of the Co^2+ orbital angular momentum due to an increase in orbital
symmetry. Although the substitution of the apical polyanion groups would not
be expected to greatly impact the in-plane magnetic exchange pathways, these
results, as well as the slight expansion of the _a_ lattice parameter with
greater vanadium-content, likely indicate minor modification of the Co-O-Co
bond angle, the AFM $J_{3}$ exchange that involves the AsO4 versus VO4
polyanion, and the degree of distortion of the cobalt octahedra.

When the field is instead applied along the stacking axis
($\mu_{0}\text{H}\parallel$ c), more significant changes are observed in the
measured DC magnetic susceptibility and calculated Curie-Weiss parameters
(Figure S8). As in the in-plane measurements, increasing vanadium substitution
results in a suppression of the long-range ordering transition to _T_ = 4.06 K
by x = 0.075, beyond which the susceptibility plateaus below _T_ = 3.0 K.
Curie-Weiss analysis of the high-temperature susceptibility results in
negative $\theta_{\text{CW}}$ of variable magnitude, as well as more
significantly reduced effective magnetic moments, relative to pure BCAO (Table
S12, Figure S9). All derived $\theta_{\text{CW}}$ for compositions in this
range are smaller than that of the parent phase. The $\theta_{\text{CW}}$ for
both the x = 0.025 and x = 0.20 crystals, _T_ = -67.8 K and _T_ = -62.8 K
respectively, represent local minima in the series. Changes in superexchange
pathways as well as in the spin-orbital crystal field levels could both be
significant factors. With increasing substitution, the effective moment
$p_{\text{eff}}$ is more variable, however generally trends downward. This may
arise due to the variable number of distinct cobalt coordination environments
created as progressively more vanadium is incorporated into the structure. A
wider distribution of coordination environments would possess more variability
in the average degree of orbital quenching amongst Co^2+ ions in each
honeycomb layer and potentially a lower net effective moment as a result.

A clearer comparison between the observed trends in relative magnetic
interaction strength for spin components within and perpendicular to the
honeycomb plane can be drawn from the Curie-Weiss-normalized temperature-
dependent magnetic susceptibility of each composition, where _C_
/[($\chi-\chi_{0}$) $|\theta|$] =  _T_ /$|\theta|$ \+ 1 for dominant AFM
interactions, and _C_ /[($\chi-\chi_{0}$) $|\theta|$] =  _T_ /$|\theta|$ \- 1
for dominant FM interactions (Figure 4). For all compositions, spin components
parallel to _c_ exhibit AFM deviations from Curie-Weiss behavior above the
respective $T_{\text{N}}$, below which FM deviations are observed. These low-
temperature deviations are attributed to the development of net AFM planar
spin correlations, and decrease in magnitude with increasing vanadium
substitution. When the field is applied within the honeycomb plane
($\mu_{0}H\perp c$), FM deviations from Curie-Weiss behavior dominate for
temperatures above _T_ $\approx$ 150 K. Below this temperature, AFM
correlations become more prevalent. The full suppression of the AFM ordering
transition for the x = 0.10 composition is apparent in the absence of a
thermal anomaly in both $\chi_{\parallel c}$ and $\chi_{\perp c}$.

A convenient measure of the magnetic anisotropy and its dependence on doping
and temperature lies in the susceptibility ratio,
$\chi_{\perp}c/\chi_{\parallel}c$, which varies significantly as a function of
V-substitution (Figure S9c). In pure BCAO,
$\chi_{\perp}c/\chi_{\parallel}c\approx$ 62, a value which drops considerably
to 9 by x = 0.025, before slowly increasing as a function of further
substitution. At x = 0.10, there is an additional slight decrease in the
observed anisotropy. The trends in the magnetization measured along each of
the principal axes are however not directly correlated. The magnetization
gradually decreases when measured along the stacking axis with increasing
V-content, while in-plane measurements are relatively consistent, with two
sharper declines at x = 0.025 and x = 0.10. As no substitution occurs within
the honeycomb lattice, but rather adjacent to it, little variation would be
expected in the strength of the $J_{1}$ superexchange interactions between
neighboring cobalt atoms in the _ab_ plane, though its spin-space anisotropy
could change. With substitution of a minimal amount of vanadium into the
structure and the corresponding contraction of the unit cell along the _c_
axis, Co2+ ions within the honeycomb layer are pushed closer to and then
further from perfect octahedral coordination. Further incorporation into and
distortion of the parent structure progressively tunes the competing
$J_{1}$/$J_{3}$ exchange interactions, with the x = 0.10 composition
representing a critical point at which long-range order is suppressed with the
introduction of minimal glassiness to the system.

One feature commonly observed among magnetic cobaltates is the presence of
metamagnetic transitions in field-dependent magnetization measurements, which
are associated with the strong anisotropy of the Co2+ Kramers doublet ground
state.20, 21, 22 In pure BCAO, this manifests as a pair of low-field
metamagnetic phase transitions ($\mu_{0}\text{H}_{c1}$ = 0.26 T and
$\mu_{0}\text{H}_{c2}$ = 0.52 T) which together produce the dumbbell-shaped
hysteresis observed at _T_ = 1.8 K.6 Field-dependent magnetization
measurements performed on representative BCAO-V powder compositions, shown in
Figure 5 as the derivative of magnetization with respect to the applied field
strength, display a clear reduction in both the magnitude and applied field
strength at which the Co^2+ metamagnetic transitions appear. Upon any amount
of V-substitution, the dumbbell-shaped hysteresis observed in pure BCAO at _T_
= =2.0 K is no longer present, with the two metamagnetic transitions gradually
merging into one and broadening. At and above x = 0.25, minor remanence
reemerges and the system begins to behave more like the fully-substituted BCVO
phase. The suppression of metamagnetism in this system is indicative of a
gradual shift toward more perfect octahedral coordination and an increase in
orbital symmetry of the Co2+ cations. The disorder associated with
V-substitution may also play a role, as it can impede phase transitions
between the long wave length modulated spin structures associated with the
metamagnetic transitions in pure BCAO.

Measurements performed on lower V-content BCAO-V single crystal compositions
provide additional insight into the evolution of the observed transitions with
increasing substitution. In-plane ($\mu_{0}\text{H}\perp$ c) magnetization
measurements (Figure 6) show no sign of hysteresis in any composition at
either _T_ = 2.0 K or _T_ = 5.0 K, with all saturating by $\mu_{0}\text{H}$ =
$\pm$ 1 T. At _T_ = 0.4 K, only a weak remanence is present from x =
0.10-0.20, which can likely be attributed to the weak FM coupling between
neighboring Co2+ ions within the honeycomb plane. The two sharp transitions
observed in pure BCAO are significantly broadened in all substituted
compositions and gradually merge by the x = 0.10 sample, leaving only a single
smoothed curve. This indicates some alteration of the average cobalt
coordination environment in the substituted structure upon increasing
V-content and subsequently also to the ground state degeneracy of the system.
Alternatively, the $J_{1}/J_{3}$ ratio may be passing through a critical value
driven by V-substitution. Out-of-plane ($\mu_{0}\text{H}\parallel$ c)
magnetization measurements show only a linear field-dependence and no
significant hysteresis at both _T_ = 2.0 K and _T_ = 5.0 K, as in the parent
material (Figure S10).

The evolution of the cobalt metamagnetic transitions in V-substituted BCAO is
also observed in the in-plane, field-dependent AC magnetic susceptibility
data, shown in Figure S11. At x = 0.025, two transitions are visible at
$\mu_{0}$H = 0.25 T and $\mu_{0}$H = 0.43 T, with the former being
significantly weaker. Upon further substitution, the higher-field transition
gradually shifts to meet and merge with that occurring at lower field. The
magnitude of the combined transition then continuously decreases with
increasing V-content. In contrast to the DC magnetization data, the AC
susceptibility of the x = 0.10 sample decreases to less than half the
magnitude of the other compositions, another indication of a more complex
interplay between competing exchange interactions at low temperatures.

This discrepancy between the DC and AC response of several compositions is
also apparent in temperature-dependent AC magnetic susceptibility measurements
of BCAO-V powder samples (Figure S12). As in the DC susceptibility,
substitution of vanadium for arsenic in BCAO results in a gradual shift in the
observed transition temperature, down to _T_ = 3.6 K in the x = 0.075
composition, albeit with more significant broadening. However, at x = 0.10, a
narrower transition appears at _T_ = 2.9 K, lower in temperature than any
other member of the series. Above this level of V-substitution, the AC
transition begins to weaken, broaden, and shift higher in temperature. When
performed on single crystals of the less-substituted compositions, a similar
trend appears, however the susceptibility of the x = 0.10 sample is again
observed to be considerably lower than that of the other compositions (Figure
7). Both the temperature minimum at which the x = 0.10 transition occurs and
its sharpness relative to those of the x = 0.075 and x = 0.15 samples provide
additional evidence for a critical point in this compositional regime.

Notable differences between the magnetic response of a material via AC and DC
characterization techniques typically indicate spin glass-like behavior, and
subsequently varied spin relaxation rates in a material.23 In order to better
understand the evolution of the magnetic ground state of the BCAO-V system,
the temperature dependence of the AC magnetic susceptibility was also measured
as a function of applied AC frequency for the lower-substituted single crystal
compositions (Figure 7, zoomed view in Figure S13). From x = 0.025-0.075,
there is no observed frequency dependence to the magnetic response from $f$ =
300-900 Hz, whereas each of the x = 0.10, x = 0.15, and x = 0.20 compositions
display minimal shifts over the same range. Plotting of this frequency
dependence as 1/T vs. ln($\omega$) yields a linear trend for each of the three
higher V-content samples and indicates the presence of some degree of spin
freezing (Figure S14, Table S13). For the x = 0.15 and x = 0.20 compositions,
linear fitting yields an Arrhenius-type activation energy between
E${}_{\text{a}}$/kB = 50-60 K and a characteristic frequency on the order of
$\omega_{0}$ = 1011 Hz, representative of standard spin glass behavior.24 For
the x = 0.10 sample however, an activation energy of E${}_{\text{a}}$/kB = 85
K and a characteristic frequency on the order of $\omega_{0}$ = 1016 Hz are
observed, suggesting some amount of spin freezing more akin to cluster glass
systems.25, 26 The magnetic ground state of the BCAO-V system is then likely
best understood as a gradual suppression of long-range order down to x = 0.10,
followed by the introduction of glassiness after its disappearance, as has
been commonly reported for phases possessing significant degrees of magnetic
frustration and substitution-induced disorder.27 With respect to the
interaction strength between magnetic Co2+ ions in the BCAO-V structure, the x
= 0.10 composition then represents a critical point at which strong spin
correlations persist down to low temperatures without the onset of long-range
order. The bifurcation of FC/ZFC magnetization data for _T_ $\sim$ 1.48 K
(Figure S7(d)) indicates some degree of spin freezing at the critical point,
as is generally expected in the presence of disorder. In the analogous
BaCo2(PO4)_2-x(VO4)_x system, similar behavior was attributed to the presence
of a spin-liquid-like state stabilized by strong quantum fluctuations.13

Further evidence for a spin-glass-like ground state in this composition space
is observed in the heat capacity of representative BCAO-V polycrystalline
samples, shown in Figure 8. With increasing V-content, the transition
attributed to the onset of long-range order in pure BCAO again significantly
broadens and declines in both magnitude and temperature, down to _T_ $\sim$
4.0 K from x = 0.075-0.20. In the absence of an applied field, all substituted
compositions possess singular broad humps, higher in temperature than the
transitions observed in both DC and AC susceptibility. Beyond this level of
substitution, the transition shifts higher in temperature, in agreement with
that observed in the AC susceptibility measurements and indicative of the
reemergence of long-range order in the system.

Additional hints to the glassy nature of the magnetic ground state in the
intermediate substitution regime can be observed in the field-dependent heat
capacity of single-crystalline BCAO-V compositions. When the field is applied
within the honeycomb plane ($\mu_{0}\text{H}\perp$ c), all compositions
display a linear trend of further broadening and suppression of the transition
to higher temperature, with the application of as small as a $\mu_{0}\text{H}$
= 0.5 T field being sufficient to partially suppress the magnetic entropy
(Figure S15). This provides an additional indication of spin freezing in the
magnetic ground state and is consistent with the observed stability of the in-
plane FM correlations upon V-substitution. Conversely, application of the
field along the stacking axis yields a more varied response, with
progressively larger fields being required for any suppression of the feature
to occur (Figure 9). In the x = 0.10 sample, a $\mu_{0}\text{H}$ = 2.5 T field
is sufficient to suppress the transition by about $\Delta T$ = 3.9 K, whereas
for the x = 0.15 sample this produces a shift of only $\Delta T$ = 1.7 K and
for the x = 0.20 sample this decreases to $\Delta T$ = 1.1 K. However when the
applied field is increased to $\mu_{0}\text{H}$ = 5.0 T, the anomaly present
for all three compositions is suppressed to a comparable degree. This suggests
a finite barrier to spin reorientation which increases from the x = 0.10 to
the x = 0.20 composition, supporting the presence of two distinct ground state
phases - the latter behaving as a conventional spin glass and the former as a
more complex intermediate between the regions of order and pure glassiness
bounding the critical point.

Estimates of the magnetic contribution to the measured heat capacity were
attempted via subtraction of the non-magnetic analogue of each V-substituted
composition. Although BaMg2(AsO4)2 and its V-substituted derivatives could be
easily synthesized, both direct subtraction and rational scaling of the Mg-
analogues from the measured heat capacity of the cobalt phases ultimately did
not suggest full recovery of the expected magnetic entropy by _T_ = 50 K.
Subsequent measurement of the Raman scattering spectrum of BaMg2(AsO4)2,
compared to that of BCAO in Figure S5, revealed that the substitution of the
much smaller Mg atom for Co produces variable, non-uniform shifts in the
frequencies of the respective vibrational modes. While the two phases share
the same structure, the frequencies of phonon modes in pure and substituted
BCAO then differ too significantly for reliable approximation via subtraction
of the Mg-analogue. However, an estimate of the recovered magnetic entropy for
each composition was obtained by scaling of the BMAO-V phase, such that the
measured $C_{\mathrm{p}}/T$ converged with that of the Co-analogue by _T_ = 50
K (Figure S16). Integration of this estimated contribution over the same
temperature range yields an entropy rise greater than the predicted $\Delta
S_{\mathrm{mag}}$ = 1/2Rln2 for an ideal Kitaev system and less than the
$\Delta S_{\mathrm{mag}}$ = Rln2 expected for a typical S = 1/2
magnet.do2017majorana Modeling of the evolution of the BCAO phonon spectrum as
a function of V-substitution will ultimately be necessary to determine the
true magnetic entropy rise in this temperature regime.

Reports of other substituted honeycomb phases exhibiting such intermediate
spin relaxation rates have typically attributed this behavior to either the
presence of stacking faults or magnetic site defects.28 Due to the higher
stability of the high-spin configuration in most Co2+ compounds, as well as
low likelihood of further oxidation to the Co3+ oxidation state upon
V-substitution, the presence of significant magnetic site defects is unlikely.
In either case, the calculated effective magnetic moment would also be
expected to decrease more significantly than is observed. For each
composition, the substitution of clusters of arsenic atoms by vanadium would
generate distinct stacking sequences within the structure akin to more random
stacking faults, leading to more variability in the balance of $J_{1}$
superexchange and $J_{3}$ third nearest-neighbor interactions within the
honeycomb plane. At low substitution levels, this increases the overall degree
of geometric spin frustration, while at higher substitution levels this
frustration is relieved by typical spin-freezing. Between these two regions,
the stacking sequence in the x = 0.10 composition produces a near-optimal
tuning of the $J_{1}$/$J_{3}$ exchange interactions, fully suppressing the
onset of long-range order with the introduction of only minor spin freezing.

In solid solutions such as the BCAO-V system, qualitative changes in material
properties are typically well described by percolation theory, wherein
channels between impurity atoms form above some threshold impurity
concentration.29 These channels produce deviations from the expected trends
where impurity atoms enter the structure but largely do not interact with one
another. On the two-dimensional honeycomb lattice, this threshold has been
reported to be 0.7, which in the BCAO-V series is found to be the upper
substitutional limit before transformation to the tetragonal BaCo2(VO4)2
structure.30 However, magnetization and Raman scattering measurements show
that the system passes through a critical point at x = 0.10, suggesting that
standard percolation theory can’t be used to effectively describe the
evolution of magnetic properties in this system.

Several alternative models of exchange disorder via dilution or magnetic
substitution have also been proposed for systems believed to possess dominant
Kitaev exchange.31, 32 For the honeycomb iridate family of materials, these
models typically agree well with experimental reports, where substitution
tunes the magnetic ground state directly from long-range order to that of a
typical spin glass. In $\alpha$-RuCl3, substitution on the ruthenium site
initially suppresses the long-range zigzag order before passing through a
narrow region of short-range, quasistatic order and finally to the onset of
increased spin freezing.33, 34, 35 While substitution in these systems occurs
on the magnetic honeycomb lattice, vanadium incorporation into the BCAO
structure occurs only on the arsenic site bounding the honeycomb lattice and
not for the cobalt within it. As our results are not well-described by any
existing model for this type of substitution and direct honeycomb substitution
in these related systems has also been claimed to tune the magnitude of off-
diagonal exchange, the local minima observed in the x = 0.10 composition
likely arise from tuning of the $J_{1}$/$J_{3}$ exchange interactions via
exchange disorder.

##  3 Conclusion

In conclusion, we present the systematic study of the structural and magnetic
properties of honeycomb magnet BaCo2(AsO4)_2-2x(VO4)_2x as it is tuned through
a critical point via partial arsenic substitution with vanadium. At low
substitution levels (0.025 $\leq~{}\text{x}~{}\leq$ 0.09), magnetic
susceptibility measurements show a gradual suppression of long-range order in
the system, down to _T_ $\sim$ 3.0 K. At x = 0.10, long-range order
disappears, minor spin freezing is introduced, and both the magnitude of the
measured magnetic susceptibility and intensity of the measured Raman bands
decrease significantly. Above this level of substitution, more significant
spin freezing is introduced, long-range order reappears, and the system
gradually begins to behave akin to the fully-substituted BaCo2(VO4)2. With
increasing substitution of slightly-larger vanadium into the structure, the
unit cell shrinks along the c-axis and the relative strengths of $J_{1}$
superexchange and $J_{3}$ third nearest-neighbor exchange can be expected to
vary. In the x = 0.10 composition, these exchange interactions become more
balanced, producing a local minimum between the regions of long-range order
and pure glassiness observed at lower and higher substitution levels,
respectively. Likely stabilized by quantum fluctuations, this state represents
a compelling example of how magnetically-frustrated systems may be chemically
tuned to exhibit novel quantum phenomena and ultimately realize a true quantum
spin liquid state.

This work was supported by the Institute for Quantum Matter, an Energy
Frontier Research Center funded by the U.S. Department of Energy, Office of
Science, Office of Basic Energy Sciences, under Grant DE-SC0019331. The MPMS3
system used for magnetic characterization was funded by the National Science
Foundation, Division of Materials Research, Major Research Instrumentation
Program, under Award #1828490. TMM acknowledges support of the David and
Lucile Packard Foundation. Chemical analysis was funded by the Fraunhofer
Internal Programs under Grant No. 170-600006. The authors declare that they
have no competing interests. All data needed to evaluate the conclusions in
the paper are present in the paper and/or the Supplementary Materials. All
data underlying this study will be made openly available at the online
repository 10.34863/n3ds-9s54.

Figure 1: The crystal structure of BaCo2(AsO4)2 (BCAO) projected along a) the
_ab_ plane and b) the stacking axis. c) Trigonal distortion of the cobalt
octahedra within the honeycomb layer of pure BCAO. d) Dominant superexchange
$J_{1}$ and third nearest-neighbor $J_{3}$ exchange pathways within the
honeycomb plane described by the XXZ-$J_{1}$-$J_{3}$ model of geometric
frustration. Calculated shifts in the e) _a_ and f) _c_ lattice parameters as
a function of nominal V-substitution for As. Lattice parameters for each
composition were derived from Rietveld refinement of once- (black) and twice-
heated (red) pXRD data, as well as from refinement of twice-heated SCXRD data
(blue). General trend lines are shown in black. The calculated lattice
parameter shifts for the nominally x = 0.50 sample are lower than would be
anticipated from the broader trends observed, indicating that more V was lost
in the course of this synthesis.

Figure 2: Measured Raman scattering spectra of pure and V-substituted BCAO
with (x,x - black) and (x,y - red) polarized light. Ag singlet modes are
denoted by the green dashed lines, while Eg doublet modes are denoted by the
purple dashed lines. Ag singlet modes are largely only active in the (x,x)
polarization configuration, while Eg doublet modes appear in both polarization
configurations. All sample spectra were calibrated with a silicon standard to
ensure a reliable comparison of frequency shifts on increasing vanadium
substitution.

Figure 3: Phase diagram of the BaCo2(AsO4)_2-2x(VO4)_2x series of materials, derived from AC (_T_ ${}_{\text{N}}$ \- blue squares) and DC (_T_ ${}_{\text{N}}$ \- red triangles; _T_ ${}_{\text{f}}$ \- black circles) magnetic susceptibility, as well as heat capacity (_T_ ${}_{\text{C}}~{}-~{}$green diamonds) measurements of representative BCAO-V powder and in-plane ($\mu_{0}\text{H}\perp$ c) single crystal compositions. In the region from 0.025 $\leq~{}\text{x}~{}\leq$ 0.09, all measurements suggest a gradual suppression of the long-range order observed in pure BCAO without the introduction of glassiness. Above x = 0.20-0.25, the system begins to behave gradually more like the parent BaCo2(VO4)2, displaying an increase in all measured critical temperatures to above that observed in either parent material. In the intermediate range, 0.10 $\leq~{}\text{x}~{}\leq$ 0.20, the system shows no sign of a transition to a long-range ordered state in the measured DC susceptibility, while still possessing weaker magnetic transitions in both AC susceptibility and heat capacity measurements. As the system is not known to undergo any structural phase transitions in this temperature regime, this likely indicates a higher degree of magnetic frustration and ground state degeneracy for compositions in this range. Table 1: Fitting parameters obtained from Curie-Weiss analysis of BCAO-V single crystal magnetization measurements ($\mu_{0}\text{H}\perp$ c) from _T_ = 150-300 K. x | DC _T_ ${}_{\text{N}}$ | AC _T_ ${}_{\text{N}}$ |  _T_ ${}_{\text{f}}$ | $\theta_{\text{CW}}$ | $p_{\text{eff}}$ | $\chi_{0}$ |  $\chi_{\perp}$/$\chi_{\parallel}$
---|---|---|---|---|---|---|---
| (K) | (K) | (K) | (K) | ($\mu_{\text{B}}$) |  |
0 | 5.40 | 5.40 | - | 33.8 | 5.67 | - | 62
0.025 | 5.00 | 5.00 | - | 34.9(1) | 5.61(1) | -0.002 | 8
0.05 | 4.23 | 4.39 | - | 37.5(1) | 5.70(1) | -0.002 | 18
0.075 | 4.06 | 4.10 | - | 36.1(2) | 5.63(7) | -0.002 | 34
0.10 | - | 2.69 | 1.51 | 41.8(1) | 5.29(1) | 0 | 25
0.15 | - | 2.63 | 1.70 | 39.8(1) | 5.31(1) | 0 | 37
0.20 | - | 2.79 | 1.60 | 36.1(1) | 5.52(1) | -0.002 | 40
Figure 4: Normalized field-dependent magnetization of BCAO-V single crystal
compositions (0 $\leq~{}\text{x}~{}\leq$ 0.20), where _C_ /[($\chi-\chi_{0}$)
$|\theta|$] =  _T_ /$|\theta|$ \+ 1 for dominant antiferromagnetic (AFM)
interactions, and _C_ /[($\chi-\chi_{0}$) $|\theta|$] =  _T_ /$|\theta|$ \- 1
for dominant ferromagnetic (FM) interactions. Magnetization data presented in
previous works was extracted and scaled to fit the expected Curie-Weiss
behavior at higher _T_ for unsubstituted BaCo2(AsO4)2.6 When the field is
applied a) within the honeycomb plane ($\mu_{0}H\perp c$), FM deviations from
ideal behavior dominate in the c) low-_T_ regime. When the field is applied b)
along the stacking axis ($\mu_{0}H\parallel c$), all compositions exhibit AFM
deviations from ideal behavior just above their respective $T_{\text{N}}$,
below which FM deviations are observed, which are attributed to the in-plane
coupling between neighboring Co2+ ions. With increasing V-substitution, these
d) low-temperature FM deviations also decrease in magnitude. In both
orientations, increasing V-substitution is observed to result in a full
suppression of the AFM ordering transition by the x = 0.10 composition. Figure
5: Derivative of field-dependent magnetization with respect to field of
representative x = 0-0.50 BCAO-V powder samples at _T_ = 2.0 K. For each
composition, only one magnetization cycle is shown, however the behavior is
consistent whether the samples are positively or negatively magnetized to
$\pm$1 T. With increasing V-content, both the magnitude and field at which the
cobalt metamagnetic transitions occur are observed to decrease, as shown by
the black trend lines. No coercivity is observed from x = 0.025-0.20. x $\geq$
0.25 shown separately for clarity. Figure 6: In-plane, field-dependent
magnetization of representative a) x = 0.025, b) x = 0.05, c) x = 0.075, d) x
= 0.10, e) x = 0.15, f) x = 0.20 BCAO-V single crystals at _T_ = 0.4 K
(black), _T_ = 2.0 K (pink) and _T_ = 5.0 K (green). Relative to the parent
compound, no coercivity is observed for any composition at or above _T_ = 2 K,
and the cobalt metamagnetic transitions are gradually suppressed. Minor
hysteresis is observed for the latter three compositions at _T_ = 0.4 K,
likely due to the in-plane ferromagnetic exchange between neighboring Co2+
ions. All compositions display a saturated magnetic moment by around
$\mu_{0}\text{H}$ = 1 T, similar to the parent material. Figure 7: Real
component of the AC magnetic susceptibility of (left - from top to bottom) x =
0.025, x = 0.05, x = 0.075 and (right - from top to bottom) x = 0.10, x =
0.15, and x = 0.20 BCAO-V single crystal compositions as a function of
temperature from _T_ = 2.0-7.0 K and with an applied AC field of frequency $f$
= 300 Hz (black), $f$ = 600 Hz (red), and $f$ = 900 Hz (blue). From 0.025
$\leq x\leq$ 0.075, the transition temperature is observed to gradually
decrease with increasing x, but is frequency-independent. Above this level,
the magnitude of the measured susceptibility briefly decreases and an
increasing frequency dependence is observed.

Figure 8: Representative heat capacity of pure and x = 0-0.30 BCAO-V powder
samples as a function of temperature from _T_ = 2.0-10 K with no applied
field. With increasing V-content, the magnetic ordering transition declines in
both magnitude and temperature down to x = 0.20. Above this level, the
transition begins to shift back to higher temperatures (as highlighted by a
black dashed line), but remains broad and much weaker than in the parent
material. Figure 9: Representative heat capacity of (from top to bottom) x =
0.10, x = 0.15, and x = 0.20 BCAO-V single crystals as a function of
temperature in a $\mu_{0}$H = 0-9 T magnetic field applied along the stacking
axis. Increasing V-content results in a higher barrier to suppression of the
magnetic entropy in the system, as indicated by the shifting position of the
feature observed for each composition when measured in an applied field of
$\mu_{0}$H = 2.5 T (highlighted by a dashed black line).

## References

  * Savary and Balents 2017 Savary, L.; Balents, L. Disorder-induced quantum spin liquid in spin ice pyrochlores. _Phys. Rev. Lett._ 2017, _118_ , 087203
  * Furukawa et al. 2015 Furukawa, T.; Miyagawa, K.; Itou, T.; Ito, M.; Taniguchi, H.; Saito, M.; Iguchi, S.; Sasaki, T.; Kanoda, K. Quantum spin liquid emerging from antiferromagnetic order by introducing disorder. _Phys. Rev. Lett._ 2015, _115_ , 077001
  * Pasco et al. 2019 Pasco, C. M.; El Baggari, I.; Bianco, E.; Kourkoutis, L. F.; McQueen, T. M. Tunable magnetic transition to a singlet ground state in a 2D van der Waals layered trimerized Kagomé magnet. _ACS Nano_ 2019, _13_ , 9457–9463
  * Kitaev 2006 Kitaev, A. Anyons in an exactly solved model and beyond. _Ann. Phys._ 2006, _321_ , 2–111
  * Jackeli and Khaliullin 2009 Jackeli, G.; Khaliullin, G. Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models. _Phys. Rev. Lett._ 2009, _102_ , 017205
  * Zhong et al. 2020 Zhong, R.; Gao, T.; Ong, N. P.; Cava, R. J. Weak-field induced nonmagnetic state in a Co-based honeycomb. _Sci. Adv._ 2020, _6_ , eaay6953
  * Regnault et al. 2018 Regnault, L.-P.; Boullier, C.; Lorenzo, J. Polarized-neutron investigation of magnetic ordering and spin dynamics in BaCo2(AsO4)2 frustrated honeycomb-lattice magnet. _Heliyon_ 2018, _4_ , e00507
  * Halloran et al. 2022 Halloran, T.; Desrochers, F.; Zhang, E. Z.; Chen, T.; Chern, L. E.; Xu, Z.; Winn, B.; Graves-Brook, M.; Stone, M.; Kolesnikov, A. I., et al. Geometrical frustration versus Kitaev interactions in BaCo2(AsO4)2. _arXiv preprint arXiv:2205.15262_ 2022,
  * Osterloh and Müller-Buschbaum 1994 Osterloh, D.; Müller-Buschbaum, H. Zur Kenntnis von SrCo2V2O8 und SrCo2(AsO4)2/On SrCo2V2O8 and SrCo2(AsO4)2. _Z. Naturforsch. B_ 1994, _49_ , 923–926
  * David et al. 2013 David, R.; Kabbour, H.; Pautrat, A.; Mentre, O. Puzzling polymorphism of layered Ba(CoPO4)2. _Inorg. Chem._ 2013, _52_ , 8732–8737
  * Momma and Izumi 2011 Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. _J. Appl. Crystallogr._ 2011, _44_ , 1272–1276
  * Sheldrick 2015 Sheldrick, G. M. Crystal structure refinement with SHELXL. _Acta Crystallogr. C Struct. Chem._ 2015, _71_ , 3–8
  * Zhong et al. 2018 Zhong, R.; Chung, M.; Kong, T.; Nguyen, L. T.; Lei, S.; Cava, R. J. Field-induced spin-liquid-like state in a magnetic honeycomb lattice. _Phys. Rev. B_ 2018, _98_ , 220407
  * Zhang et al. 2021 Zhang, X.; Xu, Y.; Zhong, R.; Cava, R.; Drichko, N.; Armitage, N. In-and out-of-plane field induced quantum spin-liquid states in a more ideal Kitaev material: BaCo2(AsO4)2. _arXiv preprint arXiv:2106.13418_ 2021,
  * Zhang et al. 2009 Zhang, L.; Fujita, T.; Chen, F.; Feng, D.; Maekawa, S.; Chen, M. Doping and temperature dependence of Raman scattering from NdFeAsO_1-xF_x (x= 0–0.2) superconductor. _Phys. Rev. B_ 2009, _79_ , 052507
  * Peña et al. 2020 Peña, J. P.; Bouvier, P.; Isnard, O. Structural properties and Raman spectra of columbite-type NiNb_2-xV_xO6 synthesized under high pressure. _J. Solid State Chem._ 2020, _291_ , 121607
  * Gohil et al. 2010 Gohil, S.; Iyer, K. K.; Aswathi, P.; Ghosh, S.; Sampathkumaran, E. Raman study of Ca3Co2O6 single crystals. _J. Appl. Phys._ 2010, _108_ , 103517
  * Husson et al. 1977 Husson, E.; Repelin, Y.; Dao, N. Q.; Brusset, H. Normal coordinate analysis of the MNb2O6 series of columbite structure (M = Mg, Ca, Mn, Fe, Co, Ni, Cu, Zn, Cd). _J. Chem. Phys._ 1977, _67_ , 1157–1163
  * Kumar and Yusuf 2015 Kumar, A.; Yusuf, S. The phenomenon of negative magnetization and its implications. _Phys. Rep._ 2015, _556_ , 1–34
  * Boonmak et al. 2011 Boonmak, J.; Nakano, M.; Chaichit, N.; Pakawatchai, C.; Youngme, S. Spin canting and metamagnetism in 2D and 3D cobalt (II) coordination networks with alternating double end-on and double end-to-end azido bridges. _Inorg. Chem._ 2011, _50_ , 7324–7333
  * Leclercq et al. 2019 Leclercq, B.; Kabbour, H.; Damay, F.; Colin, C. V.; Pautrat, A.; Arevalo-Lopez, A. M.; Mentré, O. Metamagnetic Transitions versus Magnetocrystalline Anisotropy in Two Cobalt Arsenates with 1D Co2+ Chains. _Inorg. Chem._ 2019, _58_ , 12609–12617
  * Shizuya et al. 2007 Shizuya, M.; Isobe, M.; Takayama-Muromachi, E. Magnetic and electronic properties of misfit-layered cobalt oxide (Ca_1-$\delta$OH)xCoO2. _J. Appl. Phys._ 2007, _102_ , 023704
  * Snyder et al. 2001 Snyder, J.; Slusky, J.; Cava, R.; Schiffer, P. How ‘spin ice’ freezes. _Nature_ 2001, _413_ , 48–51
  * Binder and Young 1986 Binder, K.; Young, A. P. Spin glasses: Experimental facts, theoretical concepts, and open questions. _Rev. Mod. Phys._ 1986, _58_ , 801
  * Kumar et al. 2020 Kumar, A.; Schwarz, B.; Ehrenberg, H.; Dhaka, R. Evidence of discrete energy states and cluster-glass behavior in Sr_2-xLa_xCoNbO6. _Phys. Rev. B_ 2020, _102_ , 184414
  * Pakhira et al. 2020 Pakhira, S.; Sangeetha, N.; Smetana, V.; Mudring, A.-V.; Johnston, D. C. Ferromagnetic cluster-glass phase in Ca(Co_1-xIr_x)_2-yAs2 crystals. _Phys. Rev. B_ 2020, _102_ , 024410
  * Kovnir et al. 2011 Kovnir, K.; Garlea, V. O.; Thompson, C. M.; Zhou, H.; Reiff, W. M.; Ozarowski, A.; Shatruk, M. Spin-Glass Behavior in LaFe_xCo_2-xP2 Solid Solutions: Interplay Between Magnetic Properties and Crystal and Electronic Structures. _Inorg. Chem._ 2011, _50_ , 10274–10283
  * Wallace et al. 2015 Wallace, D. C.; Brown, C. M.; McQueen, T. M. Evolution of magnetism in the Na_3-$\delta$ (Na1-xMgx)Ir2O6 series of honeycomb iridates. _J. Solid State Chem._ 2015, _224_ , 28–35
  * Stauffer and Aharony 1992 Stauffer, D.; Aharony, A. _Introduction to percolation theory_ ; Taylor & Francis, 1992; pp 15–56
  * Scher and Zallen 1970 Scher, H.; Zallen, R. Critical density in percolation processes. _J. Chem. Phys._ 1970, _53_ , 3759–3761
  * Cai et al. 2017 Cai, W.; Yan, Z.; Liu, R.; Qin, M.; Zeng, M.; Lu, X.; Gao, X.; Liu, J. Magnetic impurity doping induced spin-glass state and short-range zigzag order in the honeycomb iridate Na2IrO3. _J. Phys. Condens. Matter_ 2017, _29_ , 405806
  * Andrade and Vojta 2014 Andrade, E. C.; Vojta, M. Magnetism in spin models for depleted honeycomb-lattice iridates: Spin-glass order towards percolation. _Phys. Rev. B_ 2014, _90_ , 205112
  * Lampen-Kelley et al. 2017 Lampen-Kelley, P.; Banerjee, A.; Aczel, A. A.; Cao, H.; Stone, M. B.; Bridges, C. A.; Yan, J.-Q.; Nagler, S. E.; Mandrus, D. Destabilization of magnetic order in a dilute Kitaev spin liquid candidate. _Phys. Rev. Lett._ 2017, _119_ , 237203
  * Do et al. 2018 Do, S.-H.; Lee, W.-J.; Lee, S.; Choi, Y.; Lee, K.-J.; Gorbunov, D.; Wosnitza, J.; Suh, B.; Choi, K.-Y. Short-range quasistatic order and critical spin correlations in $\alpha$-Ru_1-xIr_xCl_3. _Phys. Rev. B_ 2018, _98_ , 014407
  * Bastien et al. 2019 Bastien, G.; Roslova, M.; Haghighi, M.; Mehlawat, K.; Hunger, J.; Isaeva, A.; Doert, T.; Vojta, M.; Büchner, B.; Wolter, A. Spin-glass state and reversed magnetic anisotropy induced by Cr doping in the Kitaev magnet $\alpha$-RuCl3. _Phys. Rev. B_ 2019, _99_ , 214410