# Hydrostatic pressure effect on Co-based honeycomb magnet BaCo2(AsO4)2

Shuyuan Huyan,1 Juan Schmidt,1,2 Elena Gati,3 Ruidan Zhong,4 Robert J. Cava,4
Paul C. Canfield,1,2 and Sergey L. Bud’ko1,2 1Ames Laboratory, US DOE, Iowa
State University, Ames, Iowa 50011, USA  2Department of Physics and Astronomy,
Iowa State University, Ames, Iowa 50011, USA  3Max Planck Institute for
Chemical Physics of Solids, 01187 Dresden, Germany  4Department of Chemistry,
Princeton University, Princeton, NJ 08544, USA

###### Abstract

The honeycomb antiferromagnet BaCo2(AsO4)2, in which small in-plane magnetic
fields ($H1\,\approx\,$0.26 T and $H2\,\approx\,$0.52 T at $T\,=\,$1.8
K$\,<T_{N}\,\approx\,5.4$ K) induce two magnetic phase transitions, has
attracted attention as a possible candidate material for the realization of
Kitaev physics based on the 3$d$ element Co2+. Here, we report on the change
of the transition temperature $T_{N}$ and the critical fields $H1$ and $H2$ of
BaCo2(AsO4)2 with hydrostatic pressure up to $\sim$ 20 kbar, as determined
from magnetization and specific heat measurements. Within this pressure range,
a marginal increase of the magnetic ordering temperature is observed. At the
same time, the critical fields are changed significantly (up to $\sim\,$25 -35
%). Specifically, we find that $H1$ is increased with hydrostatic pressure,
i.e., the antiferromagnetic state is stabilized with hydrostatic pressure,
whereas $H2$, which was previously associated with a transition into a
proposed Kitaev spin liquid state, decreases with increasing pressure. These
results put constraints on the magnetic models that are used to describe the
low-temperature magnetic properties of BaCo2(AsO4)2.

##  I Introduction

The search for quantum spin liquids, a particularly exotic state of matter,
has seen a boost over the last 15 years by the postulation of (i) the
analytically exactly solvable Kitaev model [1] that hosts a spin-liquid ground
state, as well as (ii) the Jackeli-Khaliullin approach to design Kitaev
interactions in real materials [2]. The latter initially involved spin-orbit-
coupled $d^{5}$ ions in an octahedral environment in Mott insulators, in which
the combination of crystal field effects and spin-orbit coupling coupling
generates an effective $j_{\textrm{eff}}\,=\,$1/2 moment. These moments are
then coupled via bond-dependent ferromagnetic Ising interactions that are the
central ingredient of the Kitaev model. Following these discoveries, the
research concentrated on material realizations based on heavy, 4$d$ and 5$d$,
transition metals [3] due to their inherently large spin-orbit coupling.
Prominent examples include Na2IrO3 [4], $\alpha$-Li2IrO3 [5] and
$\alpha$-RuCl3 [6]. All the listed materials show antiferromagnetic order at
finite temperatures [7, 8], which is thought to obscure the observation of the
putative Kitaev spin liquid. The emergence of magnetic order is believed to
originate from the presence of sizable non-Kitaev interactions [9, 10], such
as nearest-neighbor and third nearest-neighbor Heisenberg couplings as well as
off-diagonal couplings. The existence of these couplings is generally
attributed to the spatial extent of the 4$d$ and 5$d$ orbitals which promotes
longer-range interactions. Nonetheless, theoretical and experimental efforts
have suggested that appropriate tuning via magnetic fields [11, 12, 13, 14,
15] or pressure [16, 17] can suppress non-Kitaev interactions opening the
possibility to potentially discover the enigmatic Kitaev quantum spin liquid
in a real material.

In order to identify materials that might be closer to realization of the
Kitaev model without further perturbation, new material design strategies are
coming into the focus. A specific one involves 3$d$ transition-metal based
compounds in the high-spin d7 configuration, such as Co2+ [18, 19, 20, 21,
22]. Here, the idea is that, despite smaller spin-orbit coupling as in the
4$d$ and 5$d$ cases, the symmetry-allowed existence of ferromagnetic
Heisenberg exchange of the $e_{g}$ electrons in the $d^{7}$ configuration
might largely compensate for the antiferromagnetic Heisenberg interaction from
the $t_{2g}$ orbitals, thus strengthening the Kitaev interaction with respect
to non-Kitaev type of interactions. In this context, honeycomb BaCo2(AsO4)2
(see Fig. 1 for the crystallographic structure) was suggested to be a
particularly interesting reference compound [24, 25, 26, 27, 28, 29]. This
material manifests an antiferromagnetic ground state at ambient pressure below
$T_{N}\,\approx\,$5.4 K. Upon small in-plane magnetic fields (note that no
discernable in-plane anisotropy was reported), two consecutive magnetic
transitions at $H1\,\approx\,$0.26 T and $H2\,\approx\,$0.52 T at $T\,=\,$1.8
K were observed, with the former corresponding to a transition into a
ferrimagnetic state and the latter potentially giving rise to a moment bearing
state that has no long-range order, but is still different from a trivial,
fully saturated metamagnetic state, that might be in this case the realization
of the Kitaev spin liquid [30, 31]. This notion is motivated by the analogy of
the temperature-field phase diagram to the one of $\alpha$-RuCl3 where in-
plane fields of $\sim 80$ kOe are needed to suppress magnetic order and where
signatures of the Kitaev spin liquid might have been revealed [32]. The much
smaller critical field of BaCo2(AsO4)2 was interpreted as an experimental
demonstration that non-Kitaev interactions are indeed weaker in this 3$d$
compound compared to the heavy transition-metal based compounds. Recently,
time-domain terahertz spectroscopy measurements [31] were argued to be
consistent with the behavior expected for the Kitaev model.

The proximity of BaCo2(AsO4)2 to a putative Kitaev spin liquid state motivates
to explore the possibility to further fine-tune its interactions. Applied
magnetic field is only one of the external parameters that can affect the
interactions. Other common experimental ”knobs” include chemical and/or
physical pressure, strain and either controlled or accidental disorder (and
their combinations). Of those, hydrostatic pressure is considered to be both
clean (not inherently inducing disorder) and not inherently symmetry breaking
parameter. Experimentally, it allows for accommodation of different
measurements, even for insulating samples. [33, 34]

In the context of pressure tuning, it should be noted that theoretical [16,
17] and experimental work [35, 36, 37, 38, 39, 40, 41] on the 4$d$ and 5$d$
Kitaev materials have already established that the geometry-sensitive exchange
couplings are very susceptible to pressure tuning. For example, it has been
pointed out that in $\alpha$-RuCl3 uniaxial pressure along the $c$ axis can
strengthen the Kitaev interactions while simultaneously weakening other
anisotropic couplings [17]. However, experimentally, structural changes at low
pressures [36, 37, 38, 39, 40], which cause a breakdown of the Heisenberg-
Kitaev picture, intervene in $\alpha$-RuCl3 as well as other Kitaev compounds
before a Kitaev spin liquid can be stabilized. In this regard, if the Co2+
compounds were less susceptible to structural distortions under pressure, then
they would not only offer the chance to fine-tune the balance between Kitaev
and non-Kitaev interactions, but would also allow to improve the understanding
of magnetoelastic coupling [42, 43] in spin-orbit-coupled magnets in general.

In this work, we study the effect of hydrostatic pressure up to $\sim\,$20
kbar on the temperature-magnetic field phase diagram of BaCo2(AsO4)2
experimentally. We find that pressure only moderately affects the ordering
temperature $T_{N}$, whereas it significantly changes the in-plane critical
fields $H1$ and $H2$. In particular, $H1$ is increased with hydrostatic
pressure, whereas $H2$ is decreased. This implies that the antiferromagnetic
state as well as the proposed Kitaev spin liquid are both stabilized at the
expense of the intermediate-field ferrimagnetic state by increasing applied
hydrostatic pressure, which therefore puts constraints on effective models
that are used to understand the magnetic behavior of BaCo2(AsO4)2.

##  II Experimental details

Single crystals of BaCo2(AsO4)2 were grown using NaCl flux and pre-reacted
BaCo2(AsO4)2 powder. Details of the growth and x-ray diffraction are described
in Ref. 30. Resulting crystals were dark pink plates of few mm across the
samples and sub-mm thickness.

Since BaCo2(AsO4)2 is an insulator, we are not able to use electrical
transport measurements under pressure. Instead, the measurements of two
thermodynamic properties, magnetization and specific heat were employed to
follow the changes in the ordering temperature and base temperature
metamagnetism under pressure.

Magnetization measurements at ambient and high pressure were performed for
$H\|ab$ in a Quantum Design Magnetic Property Measurement System, MPMS 3,
SQUID magnetometer. At ambient pressure the crystal was fixed on a quartz
sample holder with a small amount of Dow Corning high vacuum grease. High
pressure measurements up to $\sim 14$ kbar were performed in a commercial,
HMD, Be-Cu, piston-cylinder cell [44] with Daphne 7373 oil, which solidifies
at $\sim 22$ kbar at room temperature [45], as a pressure medium. The sample
was oriented by eye with $H\|ab$ in the pressure cell. Magnetization data were
taken upon increasing and decreasing pressure. No difference between the data
taken upon increasing and decreasing pressure was found. This indicates that
the orientation of the crystal did not change detectably through the pressure
cycle.

Specific heat measurements under pressure up to $\sim 21$ kbar were performed
using an AC calorimetry technique in a Quantum Design Physical Property
Measurement System (PPMS). Details of the setup used and the measurement
protocol are described in Ref. 46. The sample was oriented as $H\|ab$. For
magnetic field sweeps, a rate of 10 Oe/s was used. The measurements were
performed in a Be-Cu/Ni-Cr-Al hybrid piston-cylinder cell, similar to the one
described in Ref. 47. A 40:60 mixture of light mineral oil:n-pentane, which
solidifies at room temperature in the range of 30-40 kbar [48, 49], was used
as a pressure medium.

Given that (i) our ambient pressure measurements of $H1$ and $H2$ agreed well
with literature and (ii) that our pressure dependent values of $H1$ and $H2$
for multiple measurements on multiple samples with arbitrary in-plane
orientations of applied field also agreed well (see figure 8 below), we do not
further consider possible in-plane anisotropy.

For both measurements the pressure values were determined by measuring
superconducting transition of elemental Pb. [50]

Additionally, field dependent heat capacity at ambient pressure was measured
utilizing the relaxation technique with fitting of the whole temperature
response of the microcalorimeter, as implemented in the Heat Capacity option
of a PPMS. In these measurements the magnetic field was stabilized at all
points. To ensure the $H\|ab$ orientation, the sample was mounted on a small
L-shaped platform made of oxygen-free copper foil. The contribution of the
platform to the $C_{p}(H)$ data was negligible and had no effect on the signal
associated with the metamagnetic transitions.

##  III Results

Prior to a discussion of our pressure-dependent data sets, we first outline
our choice of criteria to infer the ordering temperature $T_{N}$ from the
temperature-dependent magnetization and specific heat data, as well as the
ones to determine the critical fields $H1$ and $H2$ from the field-dependent
data sets.

In general, the criteria for an antiferromagnetic, second order, transition
from $M(T)$ and $C_{p}(T)$ were discussed in Ref. 51. Throughout this
manuscript, for convenience, we will use the maxima in $d(MT)/dT$ and
$C_{p}(T)$ to define the values of the Néel temperature $T_{N}$.

Whereas the criteria used in temperature - dependent specific heat and
magnetic susceptibility, as well as in field - dependent magnetization
measurements are outlined in many publications and are reasonably well
established, it is less so the case for the magnetic field - dependent
specific heat measurements. To provide a consistent choice of criteria between
the different data sets, we compare in Fig. 2 the ambient pressure, field-
dependent magnetization and specific heat measured at $T=2$ K, with magnetic
field applied in the $ab$ plane, and with the measurements done both on
increase and decrease of magnetic field. The $M(H)$ data are consistent with
the literature [24, 30]. The lower metamagnetic transition, $H1$, has a clear
hysteresis. For $H1\,<H\,<H2$, the magnetization reaches $\sim
2\,\mu_{B}$/mol. The hysteresis of the second, final, metamagnetic transition
is negligible and $M(H)$ above $H2$ has a value close to 6 $\mu_{B}$/mol. The
specific heat data clearly show features associated with both metamagnetic
transitions. The lower transition is seen as a shoulder. Specific heat in the
antiferromagnetic phase has basically no field dependence. On further increase
of magnetic field through the $H1$ transition, $C_{p}$ decreases. In contrast,
a rather large peak in the $C_{p}(H)$ corresponds to the upper $H2$
transition. Whereas in magnetization the position of the peak in $dM/dH$ is
often taken as the criterion for the critical field of a metamagnetic
transition, it appears that (at least in our case) the positions of the
shoulder and the maximum in the $C_{p}(H)$ [see inset to Fig. 2(a)] could
approximate the lower and upper critical fields reasonably well. The slight
difference that is apparent for the upper transition could be either specific
for the measurements, or caused by slight misorientation of the samples with
respect to the applied field in these measurements.

Now we turn to our high-pressure results. Fig. 3 presents the temperature
dependence of magnetization of BaCo2(AsO4)2 crystal below 10 K and a field of
1 kOe under different pressures up to $\sim 14$ kbar. The magnetic ordering
temperature increases under pressure, but only slightly. The $M(T)$
measurements in 20 Oe field (not shown here), show very similar increase of
the Néel temperature as in 1 kOe. The specific heat measurements under
pressure performed up to $\sim 21$ kbar (Fig. 4) show a similar trend.

The evolution of $T_{N}$ with pressure, inferred from both measurements, are
combined in the phase diagram shown in Fig. 5. The results of both
measurements are consistent. The $T_{N}$ pressure derivative evaluated from
the combination of both measurements is $dT_{N}/dP=0.0068\pm 0.0008$ K/kbar,
so by 21 kbar the increase in $T_{N}$ is less than 3%.

The effect of pressure on the critical fields is more significant. Figures 6
and 7 present field-dependent magnetization and specific heat, respectively.
(Note that the overall change of the specific heat in magnetic field is
qualitatively similar for the ambient pressure data measured using the
relaxation technique and the AC calorimetry data under pressure. The
difference in the $H=0$ baseline could be due to details in sample mounts and
implementation of these techniques.) It is clear that under pressure the
critical field of the upper metamagnetic transition, $H2$, decreases, whereas
the field $H1$ of the lower transition increases. At the same time the lower
metamagnetic transition becomes less hysteretic and its signatures in both
measurements fade with the pressure increase. The resulting $P-H$ phase
diagrams are summarized in Fig. 8. For clarity and due to slightly different
measurement temperatures as well as the different choices of criteria in
$M(H)$ and $C_{p}(H)$ measurements (see Fig. 2), two phase diagrams are
plotted separately. Still they are telling the same story: by 15-20 kbar the
value of $H2$ decreases by $\sim 25$ %; $H1$ increases by $\sim 35$ % on
field-up and by $\sim 100$% on field-down, the hysteresis in $H1$ gradually
vanishes.

##  IV Discussion and Summary

To put the observed pressure dependencies into some context, we first review
in more details the characteristics of the ambient-pressure magnetism of
BaCo2(AsO4)2 in zero and finite magnetic field, including its magnetoelastic
effects, and derived proposed theoretical models.

BaCo2(AsO4)2 is known to show strongly anisotropic magnetic behavior, with the
in-plane susceptibiliy $\chi_{ab}$ greatly exceeding the out-of-plane
susceptibility $\chi_{c}$. [27, 28, 30] In addition, it was commonly observed
that the Curie-Weiss temperature is negative (positive) for fields applied
out-of-plane (in-plane), indicating dominant antiferromagnetic (ferromagnetic)
interactions in the respective direction. [27, 28, 30] Early elastic neutron
scattering studies[24, 28] in zero field magnetic order suggested that
BaCo2(AsO4)2 shows helimagnetic order with an incommensurate wave vector ${\bf
k}\simeq[0.27,0,-4/3]$ and a phase angle $\phi\simeq 80\pm 5^{\circ}$. Based
on early classical mean-field models, assuming Heisenberg interactions only,
it was argued that the helimagnetic order can be understood by taking at least
three exchange couplings $J_{1},J_{2}$ and $J_{3}$ into account with dominant
ferromagnetic nearest-neighbor interaction and an antiferromagnetic
interaction between more distant neighbors [24, 28, 52, 53]. Although somewhat
different values of $J_{1},J_{2},J_{3}$ are cited in the literature, e.g. 36
K, 4 K, -18 K (Ref. 24) or 38 K, 1.3 K, -10 K (Refs. 28, 53) (using the
convention of $J>0$ for ferromagnetic exchange interaction and $J<0$ for
antiferromagnetic), the general characteristic is that $J_{1}\,>\,0$ is
dominant ($J_{1}\,\gg\,J_{2}\,>\,0$) and $J_{3}\,<\,0$ with $\lvert
J_{3}/J_{1}\rvert\sim 0.25-0.5$. That the properties of BaCo2(AsO4)2 might
indeed be described by a Heisenberg $XXZ$ model with significant frustration
from third-neighbor antiferromagnetic interaction was also recently inferred
from ab initio calculations. [54] It is noteworthy that in the classical and
quantum model calculations [55] of the $J_{1}-J_{2}-J_{3}$ model, the proposed
helimagnetic order in zero field only exists in a very narrow region of
$J_{2}/J_{1}$ and $J_{3}/J_{1}$, which would imply that the ground state
should be sensitive to external perturbations, if this model would accurately
describe the properties of BaCo2(AsO4)2.

Elastic neutron measurements in finite field identified that the magnetic
structure between $H1$ and $H2$ is characterized by a ferrimagnetic component
and wavevectors ${\bf k_{1}}=[1/3,0,-4/3]$ and ${\bf k_{2}}=0$. [26, 28] This
structure can be viewed as a stacking of ferromagnetic chains parallel and
antiparallel to the field in a + + – + + – … sequence, with phases between two
adjacent layers being random. [28]. Assuming that the state above $H_{2}$ is
corresponding to the saturated state with magnetization $m_{sat}$ (an
assumption that is not consistent with the proposed Kitaev spin liquid), then
the magnetization of the intermediate field phase is expected to be
$m_{sat}$/3, in line with experimental observations. In the early papers (see
e.g. Ref. 28) it was argued that the intermediate field phase can also be
understood in terms of the $J_{1}-J_{2}-J_{3}$ model on a mean-field level.

Nonetheless, it must be said that not all aspects of the magnetism of
BaCo2(AsO4)2 could be successfully explained by the above-mentioned models.
For example, the ordering temperature is much lower than the models would
predict [24, 28] and also, the exchange couplings inferred from the ab initio
calculations are much larger than the ones found experimentally.[54] Thus, in
this regard, the pressure dependencies of $T_{N}$, $H1$ and $H2$ that we
reveal here in this work represent another key benchmark for refining and
testing of the theoretical models of the magnetic behavior of this compound.

They key result of our work of sizable changes of $H1$ and $H2$ with pressure
is consistent with the idea that there are multiple, nearly degenerate,
magnetic states present in BaCo2(AsO4)2 with energy differences that are
sensitive to small perturbations. What is remarkable is the fact that even
though $T_{N}$ does not change significantly with pressure, the relative
stability of the three phases observed in applied field do change
significantly. Some insight into the microscopic effect of pressure can
sometimes be inferred from considering the change of lattice parameters upon
crossing the magnetic transition temperature $T_{N}$ at ambient pressure.
Intriguingly, it was shown that the in-plane $a$ axis in BaCo2(AsO4)2 shows an
anomalous negative thermal expansion in zero field [53, 56], i.e., the $a$
axis increases upon entering the helimagnetic magnetic state. This is in
contrast to the behavior of the related compounds BaNi2(AsO4)2 and
BaNi2(PO4)2, where the $a$ axis decreases upon entering their respective
magnetic ground states (Note that these two compounds show different magnetic
structures at low temperatures). Taking this result at face value, this
implies that the helimagnetic ground state, that might be stabilized by a
sizable antiferromagnetic $J_{3}$ in the $J_{1}$-$J_{2}$-$J_{3}$ model, is
favoured by a larger in-plane lattice parameter. Suppressing this distortion
by the application of hydrostatic pressure is then naturally expected to
weaken $J_{3}$ compared to $J_{1}$. As a result, within this picture, one
would naively expect that hydrostatic pressure would move the system closer to
the ferromagnetic/fully-saturated state. This is in line with our experimental
observation of the decrease of $H2$ with pressure.

However, it is then remarkable that $H1$ increases with increasing pressure.
Given the narrow range of stability for helimagnetic order in the
$J_{1}-J_{2}-J_{3}$-model together with the tentative explanation of decrease
of $H2$ due to smaller $|J_{3}/J_{1}|$, this is counter intuitive at first.
However, so far, in our discussion within this specific model, we ignored the
impact of hydrostatic pressure on $J_{2}$, which is hard to estimate. The
classical models certainly suggest that a decrease of $J_{3}$ can be
compensated by a change in $J_{2}$.

Note that these tentative explanations for our observed pressure-induced
changes rely on simplified models that, e.g., omit non-Heisenberg interactions
as well as interlayer couplings and assume no changes in $g$ factors. These
ingredients are all important for a complete microscopic modeling of the
pressure behavior. For example, explaining the marginal response of $T_{N}$ to
pressure will certainly require an understanding of the three-dimensional
coupling scheme.

Clearly, the next step would be to follow the evolution of $H1$ and $H2$ to
higher pressures beyond 20 kbar. Questions of interest, which would provide
further benchmarks for microscopic modeling include, but are not limited to:
(i) do higher pressures suppress the intermediate-field ferrimagnetic state
completely?, (ii) can the zero-field helimagnetic order be suppressed by
pressure and if so, (iii) what is the magnetic structure of BaCo2(AsO4)2 then?
We believe that our results encourage the performance of these measurements in
the future. Ideally, these measurements would involve elastic and inelastic
neutron scattering, and x-ray scattering under pressure, as well as
thermodynamic and thermal transport (e.g. thermal Hall) measurements. It is
also evident that further theoretical understanding of the microscopics of
BaCo2(AsO4)2 in terms of Heisenberg vs. non-Heisenberg interactions at ambient
as well as finite pressure are needed.

###### Acknowledgements.

We acknowledge useful discussions with S.M. Winter. Work at the Ames
Laboratory was supported by the U.S. Department of Energy, Office of Science,
Basic Energy Sciences, Materials Sciences and Engineering Division. The Ames
Laboratory is operated for the U.S. Department of Energy by Iowa State
University under contract No. DE-AC02-07CH11358. JS was supported in part by
was supported in part by the Gordon and Betty Moore Foundation’s EPiQS
Initiative through Grant No. GBMF-4411. EG gratefully acknowledges financial
support from the Max Planck Society and the Deutsche Forschungsgemeinschaft
through SFB 1143 (Project ID 247310070) through project C09. Work in Princeton
(RZ and RJC) was supported by the Gordon and Betty Moore foundation Grant No
GBMF-4412. SLB would like to acknowledge Russian Colloquium on Modern Problems
of Condensed Matter Physics (http://www.cond-mat.ru/) for help in initiating
this project.

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Figure 1: (color online) A sketch of the crystal structure of BaCo2(AsO4)2.
The colors green, blue, grey, and red correspond to Ba, Co, As, and O atoms
respectively. The honeycomb arrangement of the Co atoms is highlighted. Note
that only half of the unit cell is shown along the $c$ axis. The structure was
drawn using VESTA. [23]

Figure 2: (color online) (a) Field-dependent magnetization, $M(H)$ and (b)
field-dependent specific heat, $C_{p}(H)$, of BaCo2(AsO4)2 both measured at
$T=2$ K, $H\|ab$, on increase and decrease of magnetic field. $H1$ and $H2$
mark lower and higher metamagnetic transitions respectively. Inset to (a):
$dM/dH$ and $C_{p}$ measured on increase of magnetic field, plotted together
for comparison. Inset to (b): low field part of the $C_{p}(H)$ data. All data
are taken at ambient pressure.

Figure 3: (color online) Low temperature magnetization of BaCo2(AsO4)2 ,
measured at different pressures in the applied field of 1 kOe ($H\|ab$). The
legend lists the pressure values in kbar. Asterisks points to measurements on
pressure decrease.

Figure 4: (color online) Low temperature specific heat of BaCo2(AsO4)2 ,
measured at different pressures. The legend lists the pressure values in kbar.
Asterisks points to measurements on pressure decrease.

Figure 5: (color online) Magnetic ordering temperature of BaCo2(AsO4)2 as a
function of pressure. Circles - from maxima in $d(MT)/dT$, triangles - from
maxima in $C_{p}(T)$. The error bars reflect temperature steps of the
measurements and the level of signal to noise. Error bars in the pressure
values do not exceed the size of the symbols.

Figure 6: (color online) Field-dependent, in-plane magnetization, $M(H)$,
measured on field increase, (a), and field decrease, (b), at $T=1.8$ K at
different pressures. The legend lists the pressure values in kbar. Asterisks
points to measurements on pressure decrease.The small dips in $M(H)$ at low
fields are due to the signal from elemental Pb.

Figure 7: (color online) Field-dependent specific heat, $C_{p}(H)$, measured
in two quadrants on field increase and field decrease at $T=2$ K at different
pressures. The legend lists the pressure values in kbar. Asterisks points to
measurements on pressure decrease.

Figure 8: (color online)Low temperature $P-H$ phase diagram of BaCo2(AsO4)2:
(a) from magnetization measurements; (b) from specific heat measurements. The
lower metamagnetic transition $H1$ has hysteresis: both field up and field
down points are plotted. The hysteresis of the upper transition is smaller
than the size of the symbols. Error bars in the pressure values do not exceed
the size of the symbols.