# Robust Antiferromagnetism in Y2Co3

Yunshu Shi  Department of Physics and Astronomy, University of California,
Davis, California 95616, USA  David S. Parker  Materials Science and
Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee
37831, USA  Eun Sang Choi  National High Magnetic Field Laboratory,
Tallahassee, Florida 32310, USA  Kasey P. Devlin  Department of Chemistry,
University of California, Davis, California 95616, USA  Li Yin  Materials
Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge,
Tennessee 37831, USA  Jingtai Zhao  Department of Physics and Astronomy,
University of California, Davis, California 95616, USA  School of Material
Science and Engineering, Guilin University of Electronic Technology, Guilin,
Guangxi 541004, China  Peter Klavins  Department of Physics and Astronomy,
University of California, Davis, California 95616, USA  Susan M. Kauzlarich
Department of Chemistry, University of California, Davis, California 95616,
USA  Valentin Taufour<EMAIL_ADDRESS>Department of Physics and
Astronomy, University of California, Davis, California 95616, USA

###### Abstract

We report on a solution-growth based method to synthesise single crystals of
Y2Co3 and on its structural and magnetic properties. We find that Y2Co3
crystallizes in the La2Ni3-type orthorhombic structure with space group Cmce
(No.64), with Co forming distorted Kagome lattices. Y2Co3 orders
antiferromagnetically below $T_{\textrm{N}}=252$ K. Magnetization measurements
reveal that the moments are primarily aligned along the $b$ axis with evidence
for some canting. Band-structure calculations indicate that ferromagnetic and
antiferromagnetic orders are nearly degenerate, at odds with experimental
results. Magnetization measurements under pressure up to 1 GPa reveal that the
Néel temperature decreases with the slope of $-1.69$ K/GPa. We observe a
field-induced spin-flop transition in the magnetization measurements at 1.5 K
and 21 T with magnetic field along the $b$ direction. The magnetization is not
saturated up to 35 T, indicating that the antiferromagnetic ordering in Y2Co3
is quite robust, which is surprising for such a Co-rich intermetallic.

##  I Introduction

Magnetic materials play an important role in the development of new energy and
quantum information technologies. When driven toward an instability, they can
also show novel physical properties such as unconventional superconductivity,
and challenge our theoretical understanding of quantum phenomena. Identifying
materials near magnetic instabilities remains a research frontier because of
the multitude of competing interactions, resulting in coupled magnetic,
electronic and structural effects. Materials with unconventional behavior can
sometimes be identified by looking at trends in properties that are
transgressed by just a few exceptional compounds. Here we report on the
physical properties of Y2Co3, which displays an antiferromagnetic order,
despite the large Co content of the material, and the relative stability of a
ferromagnetic ground state in electronic structure calculations. We also find
that the antiferromagnetic order is robust against an applied magnetic field
up to $35$ T. These results indicate that Y2Co3 has rather unusual magnetic
properties,which is likely related to the distorted Kagome lattice of Co.

Most of the Co-based compounds are ferromagnetic, particularly with high Co
content ($\geqslant$ 60%). Figure 1 shows the Curie and Néel temperatures as a
function of cobalt content for 1511 Co-based compounds with magnetic ordering.
We can see that there are no antiferromagnets among Co-based compounds with
cobalt content larger than 70 at.%. With Co content no less than 50 at.%,
there are only six antiferromagnets having relatively high Néel temperature (¿
100 K). These compounds contain electronegative ions (CoO, Co9S8 Hébert et al.
(2021)), or other magnetic elements (CoMn Menshikov et al. (1985)), or are
well understood with band structure calculations (Ti2Co3Si Hamm et al.
(2016)). However, this is not the case for Y2Co3 and La2Co3. As a rare-earth
and cobalt based compound without any electronegative anions, Y2Co3 doesn’t
seem like a candidate for antiferromagnetic ordering. We performed first
principle calculations to investigate the possible magnetic structures of
Y2Co3 and to explain its antiferromagnetic behavior. The spin-polarized
density functional theory (DFT) calculations reveal that a complex
antiferromagnetic state is energetically degenerate with a ferromagnetic
solution, indicating the proximity to a ferromagnetic instability. However,
our experimental results show that the antiferromagnetic ordering in Y2Co3 is
quite robust and difficult to suppress with the application of relatively high
magnetic fields. This illustrates that complex physics, not easily capturable
from first principle calculations, can occur even in the complete absence of
the 4f electrons commonly believed necessary for such behavior.

Single crystals of Y2Co3 are difficult to synthesize due to yttrium reacting
with common crucible materials, such as alumina, and the narrow growth region
Wu et al. (1991). As a result, previous studies on Y2Co3 were limited to poly-
crystalline samples and produced incomplete results regarding its crystal
structure. A cubic crystal structure was reported in 1965 Pelleg and Carlson
(1965), and an unparameterized orthorhombic crystal structure based on
polycrystal studies was reported in 1992 White (1992).

Figure 1: Curie and Néel temperatures as a function of Co content for Co-based
magnetic materials as a results of a systematic literature survey Byland et
al. (2021).

Using a solution growth method in tantalum crucibles, we were able to overcome
the difficulties in synthesis and produce high quality single crystals of
Y2Co3. This enables us to identify the crystal structure as the La2Ni3-type
which is exceptionally rare in magnetic materials: of all the rare-earth
cobalt (R-Co) intermetallic compounds, only neodymium Ray et al. (1973),
lanthanum Gignoux et al. (1985) and yttrium are known to form a stable
La2Ni3-type structure in combination with cobalt. In addition, a few other
rare earth elements (Pr, Sm, Gd,) can form such a structure, albeit with Si
substitutions Tencé et al. (2014); Mahon et al. (2018); Morozkin et al.
(2015). Among all of these La2Ni3-type R2Co3-xSix ($0\leq x<0.5$) compounds,
only La2Co3 and Y2Co3 have an antiferromagnetic ordering. Other compounds in
this family show ferrimagnetic orderings with Curie temperatures varying from
64 K (Pr) to 388 K (Gd) Mahon et al. (2018). Interesting magnetic properties
due to their complex magnetic structures were observed in this family,
including strong magnetocaloric effect (Gd2Co3-xSix) and metamagnetic
transition (Pr2Co2.8Si0.2) Mahon et al. (2018). However, the magnetic
structures of these R2Co3-xSix compounds are complicated by the presence of
two magnetic elements: rare-earth element and Co. In Y2Co3, the magnetic
moment is only provided by cobalt and simplifies the magnetic structure
determination. Thus, in addition to investigating the origin of the robust and
unexpected antiferromagnetic ordering in Y2Co3, understanding the magnetic
structure of Y2Co3 will help reveal the underlying contributions from Co in
these R2Co3-xSix systems.

##  II Methods

###  II.1 Single Crystal Growth

The single-crystalline Y2Co3 samples were prepared by solution growth method
Canfield and Fisher (2001). Based on the reported Y-Co binary phase diagram Wu
et al. (1991), a starting composition of Y55.5Co44.5 was arc-melted and sealed
in a clean tantalum crucible with a tantalum filter Jesche and Canfield
(2014). The tantalum assembly was sealed in a silica tube with partial argon
pressure. An initial temperature profile with a decantation at 820 $\celsius$
revealed that no crystals grow above that temperature. A follow-up decantation
at 760 $\celsius$ produced large amount of YCo single crystals but no Y2Co3
crystals. Based on these attempts, we concluded that the previously reported
binary phase diagram is inaccurate and adjusted our initial composition to
Y51.5Co48.5. Following the same experimental method, the sample was heated up
to 1150 $\celsius$ within 4 hours and held for 5 hours, quickly cooled down to
945 $\celsius$ and slowly cooled down to 825 $\celsius$ within 133 hours.
According to the previously reported Y-Co binary phase diagram Wu et al.
(1991), a large amount of single crystal YCo2 should also have been grown with
the starting composition and temperature profile described above. However, a
large amount of Y2Co3 single crystals with a small amount of polycrystals YCo2
were observed, further confirming that the Y2Co3 part of the compositional
binary phase diagram might be inaccurate.

Figure 2: Pictures of Y2Co3 single crystals.

###  II.2 Crystal Structure Identification

Single-crystal X-ray diffraction (XRD) data were collected from the silver
reflective crystal shard with a size of $0.147$ mm $\times 0.131$ mm $\times
0.088$ mm at $290$ K using a Bruker Apex-II Dual source Cu/Mo diffractometer
with CCD detector, Mo(K$\alpha$) radiation, and a graphite monochromator. Only
the highest-symmetry Bravais lattice suggested for the refined unit cell
parameters was selected for the collected data. The frames were integrated by
using SAINT program within APEX III version 2017.3-0. The centrosymmetric
space group Cmce (No. 64) was suggested by XPREP based on the analysis of
systematic absences and its figure of merit. The structure was determined
using direct methods, and difference Fourier synthesis was used to assign the
remaining atoms (SHELXTL version 6.14) Sheldrick (2008). Powder X-ray
diffraction (PXRD) measurements were performed by the Rigaku MiniFlex600
diffractometer.

###  II.3 Crystal Orientation

Two crystals are shown in Figure 2. For the crystal on the left, the naturally
grown largest surface is the (010) plane, whereas for the crystal on the
right, it is the (111) plane. This illustrate that the crystallographic
orientation cannot be easily identified from the morphology of the crystals.
In order to study the anisotropic magnetic behavior of Y2Co3, the orientation
of the single crystal was investigated with X-ray diffraction (Rigaku
MiniFlex600 diffractometer) on facets Jesche et al. (2016). A crystal was
polished in order to remove the thin layer of flux on the surface and to
create parallel facets. The crystal was then placed on the puck with one facet
facing upward for the XRD $2\theta$-scan. With the group of diffraction peaks,
the facets were identified. For all the bulk single-crystalline Y2Co3 samples,
only {111} and {010} plane families are naturally grown, while {001} and {100}
plane families were obtained from polishing and were confirmed with the XRD
result shown in Figure 3.

Figure 3: X-ray diffraction patterns for single crystals of Y2Co3 polished to
show flat surfaces perpendicular to the [001], [010], [100] directions.

###  II.4 Physical Property Measurements

Magnetization measurements were performed with a Magnetic Property Measurement
System (MPMS, Quantum Design) in the temperature range of 2 K to 300 K with
the applied magnetic fields up to 7 T. Magnetization as a function of
temperature was measured with an applied magnetic field of 2 T. Magnetization
vs magnetic field curves were measured at 5 K, 100 K and 300 K.

The high field DC magnetization data were obtained at Cell 8 using a vibrating
sample magnetometer (VSM) and a water-cooled Francis-Bitter magnet in
Tallahassee, FL. A single crystal (35.7 mg) sample was attached on a
polycarbonate sample holder using GE-7031 varnish for the VSM measurement. The
AC susceptibility measurement was performed using a home-made AC susceptometer
on the same sample measured with the VSM. The sample was cut to a smaller
piece (21.9 mg) and mounted inside a Kapton tubing. The AC excitation field
was fixed at 3.2 Oe and 131 Hz.

Magnetization under pressure was measured up to 1 GPa. Pressure was applied at
room temperature using a hybrid CuBe cylindrical high pressure cell
(HMD01-001-00 hydrostatic pressure cell, CC-Spr-$\Phi$ 8.5D-MC4 1.3 GPa model)
with Daphne 7373 as the pressure transmitting medium. To obtain the pressure
near room temperature ($p_{\textrm{290\,K}}$), we calibrated the pressure by
measuring the Curie temperature of gadolinium Bartholin and Bloch (1968) and
the superconducting transition temperature of lead Bireckoven and Wittig
(1988) ($p_{\textrm{7\,K}}$). For our measurements, we used a piece of lead
next to our sample. The pressure values in this article are given at $290$ K,
using the calibrated formula
($p_{\textrm{290\,K}}=0.3092+1.0933p_{\textrm{7\,K}}$).

Resistivity and heat capacity measurements were carried out with a Physical
Property Measurement System (PPMS, Quantum Design). Resistivity data was
measured using the four probe method with the current along the b axis.

###  II.5 First Principles Calculations

In order to develop a description of the apparent complex magnetic character
of Y2Co3, we have performed spin-polarized density functional theory
calculations of this material, using the linearized augmented plane-wave code
WIEN2K Blaha et al. (2001). We have used the generalized gradient
approximation Perdew et al. (1996), using the experimental structure with non-
symmetry-dictated internal coordinates relaxed within a ferromagnetic
configuration. While not the actual magnetic ground state, much recent
experience Sala et al. (2021); Pokharel et al. (2020) finds this to be a much
better approximation to actual structures than, for example, a non-spin
polarized calculation, which inevitably neglects potential magnetoelastic
effects Pokharel et al. (2020, 2018); Yan et al. (2020). For all these
calculations, an RKmax value of $8.0$ was employed, where RKmax is the product
of the smallest muffin tin radius - in this case, Co, at $2.14$ Bohr - and the
maximum plane-wave expansion wavevector. The radius for the Y sphere was $2.5$
Bohr, and spin-orbit coupling was not included for these calculations.

##  III Results and Discussion

###  III.1 Crystal Structure

Table 1: Atomic Positions, Equivalent Displacement Parameters (Ueq), and Occupancy (Occ) for Y2Co3 atom | site | x | y | z | Ueq | Occ
---|---|---|---|---|---|---
Y | 8f | 0 | 0.16304 | 0.09760 | 0.015 | 1
Co1 | 8e | 1/4 | 0.41353 | 1/4 | 0.016 | 1
Co2 | 4b | -1/4 | 0 | 0 | 0.015 | 1

Single crystal XRD analysis shows that Y2Co3 crystallizes in an orthorhombic
structure instead of previously reported cubic structure Pelleg and Carlson
(1965). The space group is Cmce (No. 64), La2Ni3-type structure, with cell
parameters a = 5.3302(11) Å, b = 9.5067(19) Å and c = 7.1127(14) Å. Table 1
gives the atomic position (x, y, z), equivalent parameters and occupancy for
Y2Co3. Table 2 shows the crystallographic data and XRD refinement parameters.
The crystal structure is isomorphic to that of La2Co3, a = 4.853 Å, b = 10.350
Å and c = 7.801 Å Gignoux et al. (1985)).

Table 2: Crystallographic data and refinement parameters for Y2Co3. Deposition Number on CSD: 2099730. Empirical formula |  Y2Co3
---|---
Formula weight |  354.61
Temperature |  290(2) K
Wavelength |  0.71073 Å
Crystal system |  Orthorhombic
Space group |  Cmce
Unit cell dimensions |  a = 5.3302(11) Å $\alpha$ = 90°
|  b = 9.5067(19) Å $\beta$= 90°
|  c = 7.1127(14) Å $\gamma$ = 90°
Volume |  360.42(13) Å3
Density (calculated) |  6.535 Mg/m3
Absorption coefficient |  45.092 mm-1
F(000) |  636
Crystal size |  0.147 x 0.131 x 0.088 mm3
Theta range |  4.287 to 27.524°.
Index ranges |  -6 $\leqslant$ h $\leqslant$ 6, -12 $\leqslant$ k $\leqslant$ 12, -9 $\leqslant$ l $\leqslant$9
Reflections collected |  2150
Independent reflections |  235 [R(int) = 0.0371]
Completeness to theta = 25.242° |  100.0 %
Absorption correction |  Semi-empirical from equivalents
Max. and min. transmission |  0.0439 and 0.0133
Refinement method |  Full-matrix least-squares on F2
Data / restraints / parameters |  235 / 0 / 16
Goodness-of-fit on F2 |  1.270
Final R indices [I¿2$\sigma$(I)] |  R1 = 0.0192, wR2 = 0.0458
Final R indices [all data] |  R1 = 0.0194, wR2 = 0.0458
Extinction coefficient |  n/a
Largest diff. peak and hole |  0.552 and -0.827 e.Å-3

Figure 4 shows an alternating layered Y and Co structure along the b axis. In
the ac plane, the Co atoms form distorted Kagome structures with corner
sharing triangles and hexagonal rings. In La2Co3, the Co atoms in each layer
form relatively regular Kagome nets, with 2.427 or 2.471 Å for the distances
between Co atoms and 119.4° or 121.2° for Co-Co-Co angles Gignoux et al.
(1985). In Y2Co3, however, the Co-Co distances are 2.3692(4) Å or 2.6651(5) Å
and the angles for Co-Co-Co are 139.40(3)° and 124.225(8)°. As a result, the
Kagome lattices in Y2Co3 are more distorted than in La2Co3. Table 3 lists the
cell parameters of the R2Co3-x{Si, Ga}x system (R=La, Pr, Nd, Sm, Gd). With
the increase of atomic number, the unit cell shrinks. The ratio a/b increases
and c/b remains approximately the same, which suggests that the hexagonal
rings in the ac plane are stretched along the a axis. The size of Y3+ is
smaller than that of Gd3+, thus the distortion is even larger.

Figure 5 shows the PXRD patterns with the Rietveld refinement. Peaks marked by
“$*$” are from the Y3Co2 impurity phase Moreau et al. (1975), corresponding to
the solidified flux on the surface of the single crystal samples.

Table 3: Unit cell parameters of the R2Co3-x{Si, Ga}x system. Compound | a (Å) | b (Å) | c (Å) | V (Å3) | a/b | c/b | Ref
---|---|---|---|---|---|---|---
La2Co3 | 4.853 | 10.350 | 7.801 | 391.83 | 0.4689 | 0.7537 | Gignoux et al. (1985)
Pr2Co2.85Si0.15 | 4.9064(3) | 10.0826(5) | 7.6451(5) | 378.2 | 0.4866 | 0.7582 | Mahon et al. (2018)
Nd2Co3 | 5.007(2) | 9.981(3) | 7.519(2) | 375.76 | 0.5016 | 0.7533 | Ray et al. (1973)
Sm2.1Co2.65Si0.25 | 5.3045(7) | 9.6625(1) | 7.2229(1) | 370.21 | 0.549 | 0.7475 | Mahon et al. (2018)
Gd2Co2.94Ga0.06 | 5.315(3) | 9.613(4) | 7.169(5) | 366.29 | 0.5529 | 0.7458 | Sichevich (1984)
Y2Co3 | 5.3302(11) | 9.5067(19) | 7.1127(14) | 360.42 | 0.5607 | 0.7481 | this work
Figure 4: View of crystal structure of Y2Co3. Figure 5: X-Ray powder patterns
(red line) and fits (grey line) of single crystal Y2Co3. The black bars
indicate the peak locations expected from the single crystal XRD refinement at
290 K. Peaks marked by * are from the impurity phase Y3Co2.

###  III.2 Magnetic Properties

Figure 6: (a) Magnetization and (b) inverse magnetic susceptibility of Y2Co3
as a function of temperature in an applied field of $2$ T along the a, b and c
axes. The high temperature magnetization from 300 K to 500 K was measured
using oven with magnetic field along the $ac$ plane.

Figure 6 shows the temperature dependence of magnetization M and inverse
susceptibility with magnetic field of $2$ T along the a, b and c directions. A
transition from antiferromagnetism to paramagnetism happens at TN = 252 K. A
strong anisotropic behavior is observed. When the magnetic field is along the
b axis, the magnetization shows the sharpest transition, indicating that the
magnetic moments primarily align along the b axis. The effective moment
$\mu_{eff}=2.513(4)$ $\mu_{B}$/Co in the $ab$ plane and Curie-Weiss
temperature $\theta_{CW}=59.5\pm 1.3$ K are obtained by fitting the curve
above $T_{N}$ with the Curie-Weiss law. The Curie-Weiss temperature is
relatively small, and the positive value confirms that there is weak
ferromagnetic interaction.

Figure 7: Normalized susceptibility as a function of temperature. Dashed lines
are the calculated curves in eqn. 1. with different values of $S$.

We compare the data below the Néel temperature following D. Johnston’s work
Johnston (2012) with the following equation:

$\frac{\chi_{||}(T)}{\chi(T_{N})}=\frac{1-f}{\tau^{\ast}-f},\tau^{\ast}(t)=\frac{(S+1)t}{3SB^{\prime}_{S}(y_{0})}$
(1)

where $\chi_{||}$ is the colinear parallel susceptibility,
$t=\frac{T}{T_{N}}$, $f=\frac{\theta_{CW}}{T_{N}}=-0.08$ is calculated from
the experiment data, $B^{\prime}_{S}(y_{0})=dB_{S}(y)/dy|_{y=y_{0}}$ is the
derivative of the Brillouin function, $y_{0}=\frac{3S\bar{\mu}_{0}}{(S+1)t}$,
S is the spin state of Co ions, and $\bar{\mu}_{0}$ is calculated from
$\bar{\mu}_{0}=B_{S}(y_{0})$. Figure 7 shows the calculated collinear
susceptibility along the axial direction compared with the experimental data.
The calculated result does not fit the experimental data well, which suggests
that the magnetic order in Y2Co3 is not a simple collinear antiferromagnetic
order along the $b$ axis. For comparison, La2Co3 also has a non-collinear
antiferromagnetic order. In La2Co3, the magnetic moment of the Co atoms on the
two sites are different: on 4a sites, the spins are along the $c$ axis, with
$\left|M_{c}\right|=0.35\pm 0.05\,\mu_{B}$. On 8e sites, the spins tilt away
from the $c$ axis towards the $a$ axis, with $\left|M_{c}\right|=0.85\pm
0.05\,\mu_{B}$ and $\left|M_{a}\right|=0.34\pm 0.05\,\mu_{B}$Gignoux et al.
(1985). Such planar spin alignment along the ac plane, however, is obviously
different from that of Y2Co3. In Y2Co3, the spin alignment seems to be more
complicated. Based on the magnetization anisotropy, Y2Co3 is likely to have a
combination of axial alignments along the b axis with some planar alignments
in the ac plane. Neutron scattering experiments are necessary to fully
determine the magnetic structure.

Figure 8: Magnetization as a function of magnetic field at $T=1.5$ K. A spin
flip transition is observed at 21 T when the magnetic field is along the $b$
direction.

Figure 8 shows the magnetization of Y2Co3 as a function of magnetic field at
$1.5$ K. The magnetization increases linearly up to 21 T, and a spin-flop
transition is observed at $\mu_{0}H_{SF}=21$ T, indicating that the anisotropy
energy is relatively weak compared to the antiferromagnetic exchange coupling
energy. The magnetization does not saturate with applied magnetic field up to
35 T. This indicates that the antiferromagnetic ordering is robust and hard to
suppress with the application of magnetic field. With the spin-flop transition
field $H_{sf}$ and the slope of the $M$ vs $H$ curve above $H_{sf}$, one can
estimate the magnetocrystalline anisotropy energy. The total energy per pair
of Co of the spin-flop state can be written as Blundell (2001):

$E_{sf}=-2M_{s}B\cos{\theta}+AM_{s}^{2}\cos{2\theta}-K\cos^{2}{\theta}$ (2)

where $B$ is the applied magnetic field along the direction where the magnetic
moments spontaneous align with, $A$ is the constant connected with the
exchange coupling, $K$ is the magnetocrystalline energy per pair of Co and
$\theta$ is the angle between the magnetic moment and the direction of the
magnetic field. The energy is minimized when
$\cos{\theta}=\frac{M_{s}B}{2AM_{s}^{2}-K}$. The saturation magnetic field
$B_{sat}$ can be obtained when $\theta=0\degree$, which yields
$M_{s}B_{sat}=2AM_{s}^{2}-K$. Substituting this back to Eq. 2, one obtains the
energy of spin-flop state as a function of magnetic field:

$E_{sf}=-\frac{(M_{s}B)^{2}}{B_{sat}M_{s}}-AM_{s}^{2}$ (3)

The spin-flop transition happens when the spin-flop energy equals the energy
of the antiferromagnetic state $-AM_{s}^{2}-K$ Blundell (2001).

$-\frac{(M_{s}B_{sf})^{2}}{B_{sat}M_{s}}-AM_{s}^{2}=-AM_{s}^{2}-K$ (4)

This yields

$K=\frac{(M_{s}B_{sf})^{2}}{B_{sat}M_{s}}=\frac{B_{sf}^{2}}{B_{sat}/M_{s}}$
(5)

In Y2Co3, the saturation magnetic moment and magnetic field are not available,
however, $B_{sat}/M_{s}$ in Eq. 5 can be calculated with the slope of the $M$
vs $H$ curve along the $b$ axis above the spin-flop transition field. Thus the
magnetic anisotropy of Y2Co3 can be estimated to be $5.73$ J/mol-Co or
$4.85\times 10^{-2}$ J/g. For comparison, Co-based antiferromagnets such as
CaCo2As2 has two successive spin-flop transitions with much lower applied
magnetic field at 3.5 T and 4.7 T due to the competition between exchange
energy, magnetocrystalline anisotropy energy, and Zeeman energy and the
magnetic anisotropy was reported as $3.76\times 10^{-2}$ J/g Cheng et al.
(2012), of the same scale as that of Y2Co3. Co10Ge3O16 with
$T_{\textrm{N}}=203$ K shows complicated metamagnetic behavior depending on
both temperature and magnetic field, and the metamagnetic transition was first
observed at a temperature of 180 K and magnetic field of 3.9 T Barton et al.
(2013), hydrogen containing compound such as Y2Co7H6 shows spin-flip
transitions with magnetic field of around 2 T Bartashevich et al. (1983). On
the other hand, the metamagnetic field can be very high, for example $80$ T in
K2CoF4 Goto et al. (1992), $29$ T in YCo3H4 Bartashevich et al. (1994) and
$14$ T in YCo3H3.4 Bartashevich et al. (1994).

Figure 9: AC susceptibility as a function of magnetic field at various
temperatures. Figure 10: Magnetic phase diagram of Y2Co3 with the field along
the $b$ axis. The boundary between the AFM2 state and the PM state is
speculated. Data from field sweep and temperature sweep are shown as red
squares and blue circles respectively.

Figure 9 exhibits the AC susceptibility of Y2Co3 as a function of magnetic
field along the $b$ direction at various temperatures from 1.5 K to 235 K. The
large peaks are corresponding to the spin-flop transition. Figure 10 shows the
magnetic phase diagram of Y2Co3. The AFM1 state is the zero-field magnetic
state where the magnetic moments primarily aligns along the $b$ direction and
the AFM2 state is corresponding to a new magnetic structure due to the field-
induced spin-flop transition.

###  III.3 High Pressure Behavior

Figure 11: The temperature dependence of the magnetization of Y2Co3 under
various pressures. The pressures are determined at low temperature using the
superconducting transition of Pb (and the values near room temperature are
estimated with the ferromagnetic transition of Gd). Figure 12: The pressure
dependence of the Néel temperature TN for Y2Co3.

To investigate the stability of the antiferromagnetic ordering in Y2Co3, we
performed magnetization measurements of Y2Co3 up to 1 GPa. As the pressure
increases, $T_{\textrm{N}}$ of Y2Co3 decreases, as is shown in Figs. 11 and
12, with $dT_{\textrm{N}}/dp=-1.65$ K/GPa. The antiferromagnetic ordering is
not suppressed under pressure up to $1$ GPa. Higher pressure with diamond
anvil cells are necessary to further study the robustness of the
antiferromagnetic order.

###  III.4 Electrical Resistivity

Figure 13: (a) Electrical resistivity and (b) temperature derivative of the
resistivity as a function of temperature for Y2Co3.

The temperature dependence of electrical resistivity along the b axis of Y2Co3
is shown in figure 13(a). A metallic behavior is observed below 300 K. At 252
K, there is a discontinuous change of slope of the resistivity, which is
determined by a step in $d\rho/dT$ (figure 13(b)). This corresponds to the
antiferromagnetic transition.

###  III.5 Heat Capacity

Figure 14(a) shows the temperature dependence of the heat capacity of single
crystalline Y2Co3. The peak at 252 K indicates the antiferromagnetic phase
transition, which is consistent with $T_{\textrm{N}}=252$ K obtained from the
magnetization and resistivity measurements. The finite jump of the heat
capacity at the Néel temperature is about 10 J K-1 mol-1, indicating a second
order phase transition in relatively good agreement with the classical mean
field theory where $\Delta C_{p}$ at the transition is given by
$\frac{3}{2}NR=37.4$ J K-1 mol-1 with $N=3$ the number of Co in the formula
unit Wipf (2012). Figure 14(b) shows the linear relationship between $C_{p}/T$
and $T^{2}$. Following the relation $C_{p}/T=\gamma+\beta T^{2}$, we obtain
$\gamma=23.0(3)$ mJ mol-1 K-2 and $\beta=0.581(3)$ mJ mol-1 K-4. The Debye
temperature $T_{\textrm{D}}=254$ K is obtained from
$T_{\textrm{D}}=(\frac{12\pi^{4}NR}{5\beta})^{\frac{1}{3}}$ Kittel et al.
(1996), where $N=5$ is the number of atoms in the chemical formula and
$R=8.314$ J mol-1 K-1 is the gas constant.

Figure 14: (a)Temperature dependence of specific heat capacity $C_{p}$ for
single crystal Y2Co3. (b) $C_{p}/T$ as a function of $T^{2}$. The black dash
line is the fitting curve using the formula $C_{p}/T=\gamma+\beta T^{2}$.

###  III.6 First Principles Calculations

Any attempt to develop a full picture of the magnetic interactions in this
material should begin with a careful look at its complex physical structure,
as in Fig. 4. While there are just two crystallographically distinct Co sites,
the zigzag nature of the Co layers, along with the complex hexagonal and
triangular coordination of these layers, as in the right panel of Fig. 4,
suggests that practitioners of first principles calculations are facing a
formidable physical system to describe. Despite this, we have been able to
make progress in its description.

The first experimental fact that first principles calculations should explain
is its experimentally apparent antiferromagnetism. As Figure 1 suggests,
compounds with 60 or more atomic percent of Cobalt are much more often
ferromagnetic than antiferromagnetic. While Nature delights in exceptions to
such simple classifications, such as the surprisingly paramagnetic CeCo3
Lamichhane et al. (2018, 2020); Pandey and Parker (2018), one would naively
expect antiferromagnetic behavior in this stoichiometry regime to be the
province of electronegative anions such as Oxygen, Sulfur or the Fluorine
group. Yttrium, by contrast, is known substantially for its mineral occurrence
with the “rare earth” family, and similar chemical properties, despite its
lack of $f$ electrons. Y2Co3 is hardly a likely candidate for complex
antiferromagnetic behavior, though the existence of such behavior in La2Co3 at
least makes this finding more plausible.

Our calculations in fact find evidence, when combined with experimental
information such as the substantial ordering temperature, for complex
antiferromagnetic behavior. In addition to the ferromagnetic configuration, we
also tried a ferrimagnetic calculation with the two distinct Co sites anti-
aligned (referred to as “FI1”), as well as still more complex configurations
in which each of the two distinct sites was broken into two separate sites and
a fully antiferromagnetic configuration was initialized (“AF1”), shown in Fig.
16. None of these calculations, however, produce a distinct magnetic state
energetically competitive with the ferromagnetic solution (for which the
fourfold and twofold Co sites had respective moments of $0.87$ and $1.42$
$\mu_{B}$). The state initialized as “FI1” ultimately converges to the
ferromagnetic solution, suggestive of itinerant magnetic character. Supporting
this assertion of itinerancy is the ultimate convergence of the
“AF1”-initialized calculation, not to an antiferromagnetic state, but to a
complex magnetic state with respective moments on the split four-fold and two-
fold sites of $0.16$, $0.16$, $-1.04$ and $1.28$ $\mu_{B}$. This state,
however, falls some $54$ meV/Co above the ferromagnetic configuration, though
this energy difference is at least roughly consistent with the ordering point
of $252$ K. The variability of the moment size relative to the ferromagnetic
solution is also suggestive of itinerant character.

Faced with this complicated situation, and the experimental finding of a
complex antiferromagnetic state in La2Co3, we chose to study antiferromagnetic
states in the full 4 formula unit cell with all 12 Co atoms considered as
independent. This cell is of P1 symmetry and calculations are correspondingly
protracted. Two specific states, among the manifold of possible states were
studied, which we term “P1” and “P1-2”. The initialization pattern of P1 is
shown in Fig. 15.

A rationale for the magnetic structure “P1” can be understood as follows. In
La2Co3, the shortest Co-Co distance is 2.43 Å, with a ferromagnetic
interaction between these two atoms. In Y2Co3, however, the Co-Co separations
are about 2.37 Å and 2.67 Å in the distorted hexagonal rings in the $ac$
plane, as is shown in figure 15(b). Assuming there is a critical separation of
$2.40(3)$ Å below which the direct interaction is antiferromagnetic, we obtain
the magnetic structure in the $ac$ plane shown in figure 15(b). Along the $b$
direction, the Co layers are separated by Y layers, and the antiferromagnetic
alignments show up due to the super exchange.

This initialization pattern is in fact retained throughout the calculation,
the moment magnitudes are identical (sign excepted) to that of the
ferromagnetic solution, and the energy is degenerate, within calculational
precision to the ferromagnetic solution. The finding of identical moment
magnitudes to the ferromagnetic solution is in fact suggestive of local, not
itinerant character, and one may thus consider a complicated dual itinerant-
local moment behavior, as has previously been observed for the parent
compounds of the iron-based superconductors Moon et al. (2010).

It is of interest to note that “P1” is not a “maximally” antiferromagnetic
state, in the sense of having as many nearest and next-nearest neighbor Co-Co
pairs anti-aligned. One may readily observe from Fig. 15 the existence of
ferromagnetically coupled chains in the a direction, which is the nearest-
neighbor Co-Co interaction. In the P1-2 state, we have set these nearest-
neighbors to be antiferromagnetically coupled. However, this relative
orientation switches in the course of the calculation, complex magnetic
orientations ensue, and the calculation failed to converge after some 250
iterations. This level of calculational difficulty is characteristic of rare-
earth compounds, yet Yttrium has no 4f electrons. Note also that the
initialized “P1” state ultimately converges to a state of orthorhombic (Pnma)
symmetry but this was found after the fact so that for clarity we retain the
original designation.

Note that while the “P1” state is energetically degenerate with the
ferromagnetic solution, there are numerous degrees of freedom allowing a
substantial manifold of non-collinear magnetic states (not studied here) by
which the system can very likely significantly lower its energy, in view of
the obvious competition of ferromagnetic and antiferromagnetic interactions
and the additional frustration associated with the triangular and hexagonal
planar coordination. We therefore argue that the existence of the relatively
low-lying antiferromagnetic P1 state is evidence for the complex magnetic
character observed experimentally.

Figure 15: (a) The magnetic structure of the P1 antiferromagnetic state. (b)
The magnetic structure in the $ac$ plane. Figure 16: The magnetic structure of
FI1, AF1, P1-2 and P1 states. (a) The initial state of the FI1 model, which
converges to a ferromagnetic state (d). (b) The initial state of AF1 and P1-2
models. AF1 state converge to a complex magnetic state (e) which is 54 meV/Co
above the ferromagnetic state. The P1-2 model was performed in a lower
symmetry, and the calculation failed to converge. (c) The initial state of the
P1 model, which converges to an antiferromagnetic structure (f) and is
energetically degenerate with the ferromagnetic configuration.

In Figure 17 we present the calculated density-of-states in the P1 state. As
expected, most of the character is Cobalt, and the general symmetry of spin-up
and spin-down DOS confirms the antiferromagnetic character of the P1 state.
From the Fermi-level density-of-states we find a specific-heat $\gamma$ of $9$
mJ/mol-K2, much less than the experimental value. This could suggest strong
electron-phonon coupling, but it remains an open theoretical question in view
of the uncertainty in the actual magnetic structure).

Figure 17: The calculated density-of-states of the P1 antiferromagnetic state.

In summary, our calculations of the magnetism in Y2Co3 find evidence for a
complex antiferromagnetic state, likely containing substantial components of
both itinerant and local-moment character, deriving from a complicated, rather
frustrated physical structure.

The antiferromagnetic inter-chain alignment (i.e. chains separated by half a b
lattice spacing) is very likely associated with the presence of the
intervening Y atom, while the antiferromagnetic alignment within the distorted
hexagonal plane (see Figure 15(b)), suggests that the effects of the Y atom
are not limited to its immediate physical location, but pervade throughout the
system, which is consistent with the finding of substantial itinerant
character in this complex system.

##  IV Conclusion

In summary, we report on a solution growth method to synthesize single
crystals of the new antiferromagnetic compound Y2Co3. Our study shows that
Y2Co3 has a La2Ni3-type orthorhombic crystal structure, with space group Cmce
(No.64). We find that Y2Co3 has a robust antiferromagnetic order below
$T_{\textrm{N}}=252$ K. Magnetization measurements show that the moments are
aligned mostly along the $b$ axis, with a complex non-collinear magnetic
structure, which is likely due to the distorted Kagome net of Co. High
magnetic field measurements show a spin-flop behavior at 21 T. The
antiferromagnetic order is not suppressed with the applied magnetic field up
to 35 T. The DFT calculations find evidence for a complex antiferromagnetic
state, likely containing substantial components of both itinerant and local-
moment character. However, the first principle calculations cannot easily
capture the relatively high Néel temperature and stability at high-field.

##  V Acknowledgment

We thank Shanti Deemyad and Audrey Grockowiak for useful discussions. V.T. and
Y.S. acknowledge support from the UC Lab Fees Research Program (LFR-20-653926)
and UC Davis Startup funds. Work at Oak Ridge National Laboratory (first
principles calculations) was supported by the U.S. Department of Energy,
Office of Science, Basic Energy Sciences, Materials Science and Engineering
Division. K.P.D. and S.M.K. acknowledge NSF DMR-1709382, -2001156 for funding.
A portion of this work was performed at the National High Magnetic Field
Laboratory, which is supported by the National Science Foundation Cooperative
Agreement No. DMR-1644779 and the State of Florida.

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Table a1: Label configurations for the remaining NFR classes for Task NFR,
binary classification case (continued to table for Table 6).

Label Abbr. |  Label Configuration |  NFR Label |  "Other" Label
---|---|---|---
|  |  |
Performance |  |  |
|  |  |
PE_A |  Original 1 |  "performance" |  "not about performance"
|  |  |
PE_B |  Expert curated |  "periodic execution or efficacy performance" |  "not about periodic execution or efficacy performance"
|  |  |
PE_C |  | Word Embedding
---
(selected from top 20 words)
| "throughput, reliability, scalability, responsiveness, efficiency,
---
workload, benchmark, latency, speed, improvement, or accuracy"
| "not about throughput, reliability, scalability, responsiveness,
---
efficiency, workload, benchmark, latency, speed, improvement,
or accuracy"
|  |  |
PE_D |  | Word Embedding
---
(selected from top 20 words)
\+ Original 2
| "throughput, reliability, scalability, responsiveness, efficiency,
---
workload, benchmark, latency, speed, improvement, or accuracy"
| "usability, security, operational, look & feel, legal, fault & tolerance,
---
maintainability, scalability, availability, or portability"
|  |  |
PE_E |  | Word Embedding
---
(selected from top 50 words)
\+ Original 2
| "throughput, reliability, scalability, responsiveness, efficiency,
---
workload, benchmark, latency, speed, improvement, accuracy,
achieve, tuning, bottleneck, better, high, optimize, effectiveness,
low, enhances, reducing, incresaed, quality, faster, or degrades"
| "usability, security, operational, look & feel, legal, fault & tolerance,
---
maintainability, scalability, availability, or portability"
|  |  |
Operational |  |  |
|  |  |
O_A |  Original 1 |  "operational" |  "not about operational"
|  |  |
O_B |  Expert curated |  "working, running, connecting, interfacing, or operative environment" |  | "not about working, running, connecting, interfacing,
---
or operative environment"
|  |  |
O_C |  | Word Embedding
---
(selected from top 20 words)
"environmental, organizational, coordination, systemic, or logistics" |  | "not about environmental, organizational, coordination,
---
systemic, or logistics"
|  |  |
O_D |  | Word Embedding
---
(selected from top 20 words)
\+ Original 2
"environmental, organizational, coordination, systemic, or logistics" |  | "usability, security, performance, look & feel, legal, fault & tolerance,
---
maintainability, scalability, availability, or portability"
|  |  |
O_E |  | Word Embedding
---
(selected from top 50 words)
\+ Original 2
| "environmental, organizational, coordination, systemic, logistics,
---
coordination, or automation"
| "usability, security, performance, look & feel, legal, fault & tolerance,
---
maintainability, scalability, availability, or portability"
|  |  |
Look & feel |  |  |
|  |  |
LF_A |  Original 1 |  "Look feel" |  "not about Look feel"
|  |  |
LF_B |  Expert curated |  "appearance, interface, look feel" |  "not about appearance, interface, look feel"
|  |  |
LF_C |  | Word Embedding
---
(selected from top 20 words)
| "graphical, gui, ui, widget, interaction, habit, prefer, comfortable,
friendly,
---
feeling, experience, or familiar"
| " not about graphical, gui, ui, widget, interaction, habit, prefer,
---
comfortable, friendly, feeling, experience, or familiar"
|  |  |
LF_D |  | Word Embedding
---
(selected from top 20 words)
\+ Original 2
| "graphical, gui, ui, widget, interaction, habit, prefer, comfortable,
friendly,
---
feeling, experience, or familiar"
| "usability, security, operational, performance, fault & tolerance,
---
legal, maintainability, scalability, availability, or portability"
|  |  |
LF_E |  | Word Embedding
---
(selected from top 50 words)
\+ Original 2
| "graphical, gui, ui, widget, interaction, habit, prefer, comfortable,
friendly,
---
feeling, experience, familiar, desire, customize, intent, disability,
or impression"
| "usability, security, operational, performance, fault & tolerance,
---
legal, maintainability, scalability, availability, or portability"
|  |  |
Legal |  |  |
|  |  |
L_A |  Original 1 |  "legal" |  "not about legal"
|  |  |
L_B |  Expert curated |  "legal, law, or rules" |  "not about legal, law, or rules"
|  |  |
L_C |  | Word Embedding
---
(selected from top 20 words)
| "liability, litigation, jurisdiction, regulation, copyright, legislation,
---
enforcement, governmental, directive, civil, right, patentability,
claim, violate, infringement, or counsel"
| "not about liability, litigation, jurisdiction, regulation, copyright,
---
legislation, enforcement, governmental, directive,civil, right,
patentability, claim, violate, infringement, or counsel"
|  |  |
L_D |  | Word Embedding
---
(selected from top 20 words)
\+ Original 2
| "liability, litigation, jurisdiction, regulation, copyright, legislation,
---
enforcement, governmental, directive,civil, right, patentability,
claim, violate, infringement, or counsel"
| "usability, security, operational, performance, look & feel,
---
fault & tolerance, maintainability, scalability, availability,
or portability"
|  |  |
L_E |  | Word Embedding
---
(selected from top 50 words)
\+ Original 2
| "liability, litigation, jurisdiction, regulation, copyright, legislation,
---
enforcement, governmental, directive,civil, right, patentability,
claim, violate, infringement, counsel, holder, dispute, illegal, judicial,
ruling, agreement, ownership, comply, authority, law, accountability,
abuse, intellectual, obligation, invention, court, ethical, concern, or
policy"
| "usability, security, operational, performance, look & feel,
---
fault & tolerance, maintainability, scalability, availability,
or portability"
|  |  |

Table a1: Continued

Label Abbr. | Label Configuration | NFR Label | "Other" Label
---|---|---|---
Fault tolerance |  |  |
FT_A | Original 1 | "fault tolerance" | "not about fault tolerance"
FT_B | Expert curated | "system recovery fault tolerance" | "not about system recovery fault tolerance"
FT_C |  | Word Embedding
---
(selected from top 20 words)
| "tolerance, failure, tolerant, byzantine, deadlock, exploiting,
---
reliability, isolation, fault, guarantee, or dependable"
| "not about tolerance, failure, tolerant, byzantine, deadlock, exploiting,
reliability,
---
isolation, fault, guarantee, dependable, countermeasure, resilience,
defensive,
corruption, weakness, malfunction, robustness, or stability"
FT_D |  | Word Embedding
---
(selected from top 20 words)
\+ Original 2
| "tolerance, failure, tolerant, byzantine, deadlock, exploiting,
---
reliability, isolation, fault, guarantee, or dependable"
| "usability, security, operational, performance, look & feel, legal,
maintainability,
---
scalability, availability, or portability"
FT_E |  | Word Embedding
---
(selected from top 50 words)
\+ Original 2
| "tolerance, failure, tolerant, byzantine, deadlock, exploiting,
---
reliability, isolation, fault, guarantee, dependable, countermeasure,
resilience, defensive, corruption, weakness, malfunction, robustness, or
stability"
| "usability, security, operational, performance, look & feel, legal,
maintainability,
---
scalability, availability, or portability"
Maintainability |  |  |
MN_A | Original 1 | "maintainability" | "not about maintainability"
MN_B | Expert curated | "maintaining, fixing, running or updating" | "not about maintaining, fixing, running or updating"
MN_C |  | Word Embedding
---
(selected from top 20 words)
"adaptability, effectiveness, agility, preventive, or dependability" | "not about adaptability, effectiveness, agility, preventive, or dependability"
MN_D |  | Word Embedding
---
(selected from top 20 words)
\+ Original 2
"adaptability, effectiveness, agility, preventive, or dependability" |  | "usability, security, operational, performance, look & feel, legal, fault & tolerance,
---
scalability, availability, or portability"
MN_E |  | Word Embedding
---
(selected from top 50 words)
\+ Original 2
| "adaptability, effectiveness, agility, preventive, dependability,
---
correcting, reuse, defect, mitigation, validated, resilience, achievable,
remedy, assessing, or maintaining"
| "usability, security, operational, performance, look & feel, legal, fault &
tolerance,
---
scalability, availability, or portability"
Scalability |  |  |
SC_A | Original 1 | "scalability" | "not about scalability"
SC_B | Expert curated | "scalable, increasable or developable" | "not about scalable, increasable or developable"
SC_C |  | Word Embedding
---
(selected from top 20 words)
"flexibility, workload, efficiency, or optimize" | "not about flexibility, workload, efficiency, or optimize"
SC_D |  | Word Embedding
---
(selected from top 20 words)
\+ Original 2
"flexibility, workload, efficiency, or optimize" |  | "usability, security, operational, performance, look & feel, legal, fault & tolerance,
---
maintainability, availability, or portability"
SC_E |  | Word Embedding
---
(selected from top 50 words)
\+ Original 2
| "flexibility, workload, efficiency, optimize, caching, improvement,
---
robust, overhead, adaptability, scalable, or increased"
| "usability, security, operational, performance, look & feel, legal, fault &
tolerance,
---
maintainability, availability, or portability"
Availability |  |  |
A_A | Original 1 | "availability" | "not about availability"
A_B | Expert curated | "avaliable or timely achievable" | "not about avaliable or timely achievable"
A_C |  | Word Embedding
---
(selected from top 20 words)
"reliability, dependability, resilience" | "not about reliability, dependability, resilience"
A_D |  | Word Embedding
---
(selected from top 20 words)
\+ Original 2
"reliability, dependability, resilience" |  | "usability, security, operational, performance, look & feel, legal, fault & tolerance,
---
maintainability, scalability, or portability"
A_E |  | Word Embedding
---
(selected from top 50 words)
\+ Original 2
| "reliability, dependability, resilience, flexibility, accountability,
---
ensur, disruption, timely, or standby"
| "usability, security, operational, performance, look & feel, legal, fault &
tolerance,
---
maintainability, scalability, or portability"

Table a2: Label configurations for all the NFR classes for the multi-class and
multi-label classification sub-tasks in Task NFR (cf. Table 7)

Label Abbr. | Label Configuration | List of Labels
---|---|---
MultiNFR_A | Original | ["usability", "security", "performance", "operational", "look & feel", "legal", "fault tolerance", "maintainability", scalability" availability"]
MultiNFR_B | Expert curated |  | ["instructive, easy, helpful, useful, learnable, explainable, affordable, intuitive, or understandable",
---
"security, authorization, or protection", "periodic execution or efficacy
performance",
"working, running, connecting, interfacing, or operative environment",
"appearance, interface, look & feel", "legal, law, or rules", "system recovery
& fault tolerance",
"maintaining, fixing, running or updating", "scalable, increasable or
developable", "avaliable or timely achievable"]
MultiNFR_C |  | Word Embedding
---
(selected from top 20 words)
| ["accessibility, aesthetic, contextual, experience, satisfaction, HCI, UX,
questionnaire, ease, or ergonomics" ,
---
"vulnerability, securing. protecting, protection, cybersecurity, assurance,
cyber, countermeasure, threat,
privacy, authentication, prevention, or confidentiality", "throughput,
reliability, scalability, responsiveness,
efficiency, workload, benchmark, latency, speed, improvement, or accuracy",
"environmental, organizational,
coordination, systemic, or logistics", "graphical, gui, ui, widget,
interaction, habit, prefer, comfortable,
friendly, feeling, experience, or familiar", "liability, litigation,
jurisdiction, regulation, copyright, legislation,
enforcement, governmental, directive,civil, right, patentability, claim,
violate, infringement, or counsel",
"tolerance, failure, tolerant, byzantine, deadlock, exploiting, reliability,
isolation, fault, guarantee, or dependable",
"adaptability, effectiveness, agility, preventive, or dependability",
"flexibility, workload, efficiency, or optimize",
"reliability, dependability, resilience"]
MultiNFR_D |  | Word Embedding
---
(selected from top 50 words)
| ["accessibility, aesthetic, contextual, experience, satisfaction, HCI, UX,
questionnaire, ease,
---
ergonomics, designer, evaluate, multimodal, practitioner, prototyping,
preference, personalization,
suitability, focus, clarity, responsiveness, judgement, feel, or helpful" ,
"vulnerability, security,
protection, cybersecurity, assurance, countermeasure, threat, privacy,
authentication, prevention,
confidentiality, trusted, intrusion, compromise, safety, insecure, defensive,
breach, proactive, tampering,
penetration, policy, phishing, vulnerable, authorization, dependability, or
certification",
"throughput, reliability, scalability, responsiveness, efficiency, workload,
benchmark, latency,
speed, improvement, accuracy, achieve, tuning, bottleneck, better, high,
optimize, effectiveness,
low, enhances, reducing, incresaed, quality, faster, or degrades",
"environmental, organizational,
coordination, systemic, logistics, coordination, or automation", "graphical,
gui, ui, widget, interaction,
habit, prefer, comfortable, friendly, feeling, experience, familiar, desire,
customize, intent, disability, or impression",
"liability, litigation, jurisdiction, regulation, copyright, legislation,
enforcement, governmental, directive,civil, right,
patentability, claim, violate, infringement, counsel, holder, dispute,
illegal, judicial, ruling, agreement, ownership,
comply, authority, law, accountability, abuse, intellectual, obligation,
invention, court, ethical, concern, or policy",
"tolerance, failure, tolerant, byzantine, deadlock, exploiting, reliability,
isolation, fault, guarantee, dependable,
countermeasure, resilience, defensive, corruption, weakness, malfunction,
robustness, or stability",
"adaptability, effectiveness, agility, preventive, dependability, correcting,
reuse, defect, mitigation, validated,
resilience, achievable, remedy, assessing, or maintaining",
"flexibility, workload, efficiency, optimize, caching, improvement, robust,
overhead, adaptability, scalable, or increased",
"reliability, dependability, resilience, flexibility, accountability, ensur,
disruption, timely, or standby"]