# Suppression of antiferromagnetic order and strong ferromagnetic spin
fluctuations in Ca(Co1-xNix)2-yAs2 single crystals

Santanu Pakhira  Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
Y. Lee  Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA  Liqin
Ke  Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA  V. Smetana
Department of Materials and Environmental Chemistry, Stockholm University,
Svante Arrhenius väg 16 C, 106 91 Stockholm, Sweden  A.-V. Mudring  Department
of Materials and Environmental Chemistry, Stockholm University, Svante
Arrhenius väg 16 C, 106 91 Stockholm, Sweden  Thomas Heitmann  The Missouri
Research Reactor and Department of Physics and Astronomy, University of
Missouri, Columbia, Missouri 65211, USA  David Vaknin  Ames Laboratory, Iowa
State University, Ames, Iowa 50011, USA  Department of Physics and Astronomy,
Iowa State University, Ames, Iowa 50011, USA  D. C. Johnston  Ames Laboratory,
Iowa State University, Ames, Iowa 50011, USA  Department of Physics and
Astronomy, Iowa State University, Ames, Iowa 50011, USA

###### Abstract

CaCo2-yAs2 is a unique itinerant system having strong magnetic frustration.
Here we report the effect of electron doping on the physical properties
resulting from Ni substitutions for Co. The single crystals of
Ca(Co1-xNix)2-yAs2 were characterized by single-crystal x-ray diffraction,
energy-dispersive x-ray spectroscopy, magnetization $M$ versus temperature
$T$, magnetic field $H$, and time $t$, and heat capacity $C_{\rm p}(H,T)$
measurements. The A-type antiferromagnetic (AFM) transition temperature
$T_{\rm N}=52$ K for $x=0$ decreases to 22 K with only 3% Ni substitution and
is completely suppressed for $x>0.11$. For $0.11\leq x\leq 0.52$ strong
ferromagnetic (FM) fluctuations develop as revealed by magnetic susceptibility
$\chi(T)=M(T)/H$ measurements. For $x=0.11$ and 0.16, competing AFM and FM
interactions result in spin-glass behavior at low $T$ as evidenced by
observations of thermomagnetic hysteresis and magnetic relaxation. Enhanced FM
fluctuations are also found for the $x=0.21$ and 0.31 crystals, where
$\chi_{c}$ increases significantly at low $T$. A large $\chi$ anisotropy in
these compositions where $\chi_{c}$ is up to a factor of two larger than
$\chi_{ab}$ suggests that the FM spin fluctuations are quasi-1D in nature.
Weak FM contributions to $M(H=0)$ were found at $T=2$ K for $x=0.11$–0.31.
Heat-capacity $C_{\rm p}(T)$ measurements revealed the presence of FM quantum
spin fluctuations for $0.11\leq x\leq 0.52$, where a logarithmic $T$
dependence of $C_{\rm p}(T)/T$ is observed at low $T$. The suppression of AFM
order by the development of strong FM fluctuations in Ca(Co1-xNix)2-yAs2
crystals suggests the presence of a FM quantum-critical point at $x\approx
0.20$. Our density-functional theory (DFT) calculations confirm that FM
fluctuations are enhanced by Ni substitutions for Co in CaCo2-yAs2. The
Sommerfeld electronic heat-capacity coefficient is enhanced for $x=0$, 0.21,
and 0.42 by about a factor of two compared to DFT calculations of the bare
density of states (DOS) at the Fermi energy, suggesting an enhancement of the
DOS from electron-phonon and/or electron-electron interactions. The crystals
with $x>0.52$ do not exhibit FM spin fluctuations or magnetic order at $T\geq
1.8$ K, which was found from the DFT calculations to result from a Stoner
transition. Superconductivity is not observed above 1.8 K for any of the
compositions. Neutron-diffraction studies of crystals with $x=0.11$ and 0.16
in the crossover regime $0.1\lesssim x\lesssim 0.2$ found no evidence of
A-type ordering above 4.8 K within experimental resolution as observed in the
parent compound with $x=0$. Furthermore, no other common magnetic structures,
such as FM, helical stacking of in-plane FM layers, or in-plane AFM structure,
were found above 4.8 K with an ordered moment greater than the uncertainty of
0.05 $\mu_{\rm B}$ per transition-metal atom.

##  I Introduction

The discovery of superconductivity in doped iron arsenides by suppressing the
long-range antiferromagnetic (AFM) order of parent compounds has opened up a
wide research field studying the complex interplay between superconductivity
(SC) and magnetism [1, 2, 3, 4, 5]. A considerable number of studies have been
carried out to understand the mechanism of the observed high-$T_{c}$
superconductivity in doped ${\rm ThCr_{2}Si_{2}}$-structure (122-type)
$A$Fe2As2 ($A$ = Ca, Sr, Ba, Eu) compounds [6, 7, 8, 9, 10, 11]. It has been
established that AFM fluctuations mediate the electron-pairing mechanism for
SC in the iron-arsenide family of compounds [6, 11, 12]. Depending on the
ratio of tetragonal lattice parameters $c/a$, a collapsed-tetragonal (cT) or
uncollapsed-tetragonal (ucT) version of the structure is formed (for a review,
see Ref. [13]).

In contrast to 122-type iron-arsenide compounds, none of the parent cobalt
arsenides exhibit superconductivity even with doping but are still found to be
rich in physics associated with itinerant magnetism of the conduction
electrons [14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. Interesting physical
properties are observed including non-Fermi-liquid behavior associated with a
quantum critical point, spin-glass behavior, and helical magnetic ordering in
electron- or hole-doped 122-type CoAs-materials [25, 26, 27, 28, 29, 30, 31,
32]. For example, metallic ${\rm SrCo_{2}As_{2}}$ is a Stoner-enhanced
paramagnet and does not exhibit any magnetic ordering down to a temperature
$T$ of 0.05 K; however, stripe-type AFM fluctuations were revealed via
inelastic neutron-scattering (INS) measurements [16, 17, 18]. Although the
wave vector associated with the stripe AFM fluctuations in ${\rm
SrCo_{2}As_{2}}$ is the same as that observed in the high-$T_{\rm c}$
$A$Fe2As2 parent compounds, the CoAs analogues do not exhibit SC, perhaps due
to the simultaneous presence of strong ferromagnetic (FM) spin fluctuations
[33]; however, the INS measurements in Ref. [17] indicate that dominant FM
fluctuations present at high $T$ cross over to AFM fluctuations at low $T$.
Electron doping of ${\rm SrCo_{2}As_{2}}$ via Ni substitution for Co results
in helical AFM order with only a 1.3% Ni substitution for Co [27, 28]. A
composition-induced non-Fermi-liquid behavior associated with a magnetic
quantum-critical point is also evidenced in Sr(Co1-xNix)2As2 crystals near
$x=0.3$ [27]. No magnetic ordering down to $T=1.8$ K is found in metallic
${\rm BaCo_{2}As_{2}}$ which, however, is in proximity to a FM quantum-
critical point associated with a flat electron band near the Fermi energy
$E_{\rm F}$ [21, 22, 23].

CaCo2-yAs2 is a unique member of the 122-type CoAs family with strong magnetic
frustration and itinerant magnetism [34]. In contrast to ${\rm
SrCo_{2}As_{2}}$ and ${\rm BaCo_{2}As_{2}}$ with ucT structures, CaCo2-yAs2
has a cT structure with a substantial concentration of vacancies on the Co
site [14, 15]. The compound undergoes A-type AFM ordering below $T_{\rm N}=52$
K, where the in-plane Co moments are aligned ferromagnetically along the $c$
axis, while adjacent layers of Co moments are stacked antiferromagnetically.
From magnetic susceptibility $\chi$ versus temperature $T$ measurements, the
dominant interactions are FM. INS measurements further reveal the presence of
quasi one-dimensional FM spin fluctuations in the FM square Co planes
associated with a flat band near $E_{\rm F}$, as also suggested by band-
structure calculations [34, 35].

Due to the presence of the strong magnetic frustration in CaCo2-yAs2, it is
expected that the ground state of the compound can be changed by tuning
$E_{\rm F}$ via chemical substitution. Hole doping has been accomplished by
substituting Fe for Co in Ca(Co1-xFex)2-yAs2 single crystals [26]. The
$\chi(T)$ and neutron-diffraction measurements on Ca(Co1-xFex)2-yAs2 single
crystals demonstrated that the Fe substitution suppresses the A-type AFM
ordering with a reduction in the ordered moment, with long-range magnetic
ordering disappearing by $x=0.12$. INS measurements on an $x=0.15$ single
crystal further show that although the same level of magnetic frustration is
present in $x=0.15$ and $x=0$, the spin fluctuations are strongly reduced for
$x=0.15$ [36]. Thus, hole doping eventually quenches the magnetic moments via
a Stoner transition [36].

In this paper, we report the growth of Ca(Co1-xNix)2-yAs2 single crystals and
studies of their crystallographic, magnetic, and thermal properties. These
materials are electron-doped instead of hole-doped as in Ca(Co1-xFex)2-yAs2.
The $\chi(T)$ and $M$ at fixed $H$ versus time $t$ measurements indicate that
the A-type AFM ordering for $x=0$ is suppressed to 10.5 K for $x=0.11$ and
does not occur above 1.8 K for $x=0.16$, and that spin-glass ordering occurs
below 5 K for these two compositions. Neutron-diffraction measurements of
these two compositions show no evidence for long-range magnetic ordering above
4.6 K within experimental resolution. The out-of-plane magnetic susceptibility
$\chi_{c}$ is strongly enhanced for $x\geq 0.16$, indicating the presence of
strong FM $c$-axis fluctuations which in turn suggests the presence of a
nearby FM quantum-critical point (QCP). We also report density-functional
theory (DFT) calculations of the competition between different magnetic
structures and fluctuations. The large anisotropy between $\chi_{ab}$ and
$\chi_{c}$ in the composition region $0.21<x<0.42$ suggests quasi-one-
dimensional FM spin fluctuations along the $c$ axis. The signature of critical
FM spin fluctuations is also evident in the heat capacity $C_{\rm p}(T)$ for
compositions $0.11\leq x\leq 0.52$, where $C_{\rm p}(T)/T$ versus $T$ exhibits
a low-$T$ upturn having a $\log T$ dependence that is suppressed in magnetic
fields applied along the $c$ axis. From the DFT calculations, we infer the
occurrence of a Stoner transition to a nonmagnetic metal at $x\approx 0.5$.
For $x=1$, metallic single-crystal ${\rm CaNi_{2}As_{2}}$ is reported to be
paramagnetic down to $T=2$ K with a small and nearly $T$-independent
paramagnetic $\chi$ [37].

The experimental details are given in Sec. II. The crystallography results are
presented in Sec. III, the magnetization $M$ versus applied magnetic field $H$
isotherms and the $\chi(T)$ data in Sec. IV, and the $C_{\rm p}(T)$ data in
Sec. V. The neutron-diffraction measurements are presented in Sec. VI and the
DFT calculations in Sec. VII. A summary of our results including an $H$-$T$
phase diagram constructed from the $\chi(T)$ and $M(H,t)$ isotherm
measurements is given in Sec. VIII.

##  II  Experimental and theoretical details

Single crystals of Ca(Co1-xNix)2-yAs2 with compositions $x$ = 0, 0.03, 0.05,
0.11, 0.16, 0.21, 0.31, 0.42, 0.52, 0.67, 0.81 and 1 were grown using a self-
flux solution-growth technique. The high-purity starting materials Ca
(99.999%), Co (99.998%), Ni (99.999%), and As (99.9999%) from Alfa Aesar were
placed in an alumina crucible with the molar ratio Ca:Co:Ni:As =
1.2:$4(1-x$):$4x$:4. The 20% extra Ca is found to produce larger crystals. The
loaded crucible was then put into a silica tube and quartz wool was placed
above the crucible to extract the molten flux during centrifugation. The
silica tube was then sealed under $\approx 1/4$ atm of Ar gas. The assembly
was heated to 650 ∘C at a rate of 50 ∘C/h and held there for 6 h to avoid
excess pressure created by As vapor. Then the ampule was heated to 1300 ∘C at
60 ∘C/h and held at that temperature for 20 h for homogenization. Finally, the
tube was cooled to 1180 ∘C at a rate of 6 ∘C/h and the single crystals were
separated from the excess flux using a centrifuge. Shiny platelike single
crystals of different sizes were obtained from the growths with the $c$ axis
perpendicular to the plate surfaces with typical dimensions $3\times 3\times
0.5$ mm3. The crystal size was found to increase with increasing Ni
concentration.

A scanning-electron microscope from JEOL equipped with an energy-dispersive
x-ray spectroscopy (EDS) attachment was used to check the phase homogeneity
and average compositions of the crystals. The EDS scans were taken at multiple
points on both sides of the crystals as well as on cleaved crystals to confirm
the homogeneity and the absence of any secondary phases.

Single-crystal x-ray diffraction (XRD) measurements were performed at room
temperature on a Bruker D8 Venture diffractometer operating at 50 kV and 1 mA
equipped with a Photon 100 CMOS detector, a flat graphite monochromator and a
Mo K$\alpha$ I$\mu$S microfocus source ($\lambda=0.71073$ Å). The raw frame
data were collected using the Bruker APEX3 software package [38], while the
frames were integrated with the Bruker SAINT program [39] using a narrow-frame
algorithm for integration of the data and were corrected for absorption
effects using the multiscan method (SADABS) [40]. The atomic thermal factors
were refined anisotropically. Initial models of the crystal structures were
first obtained with the program SHELXT-2014 [41] and refined using the program
SHELXL-2014 [42] within the APEX3 software package.

The temperature $T$\- and magnetic field $H$-dependent magnetic measurements
were carried out using a Quantum Design, Inc., magnetic-properties measurement
system (MPMS) SQUID magnetometer in the range $T=1.8$ to 300 K with $H$ up to
5.5 T (1 T $\equiv 10^{4}$ Oe). The heat capacity $C_{\rm p}(H,T)$
measurements were performed using the relaxation technique in a Quantum
Design, Inc., Physical-Properties Measurement System (PPMS) in the ranges
$T=1.8$–300 K and $H=0$–9 T.

Single-crystal neutron-diffraction experiments were performed in $H=0$ using
the TRIAX triple-axis spectrometer at the University of Missouri Research
Reactor (MURR). An incident neutron beam of energy $E_{i}=30.5$ meV
(wavelength $\lambda=1.6377$ Å) was directed at the sample using a pyrolytic
graphite (PG) monochromator. The $\lambda/2$ component present in the beam was
removed using PG filters placed before the monochromator and between the
sample and analyzer. Beam divergence was limited using collimators before the
monochromator; between the monochromator and sample; sample and analyzer; and
analyzer and detector of $60^{\prime}-60^{\prime}-40^{\prime}-40^{\prime}$,
respectively. Crystals of mass 20 mg were mounted on the cold tip of an
Advanced Research Systems closed-cycle refrigerator with a base temperature in
the 4.1 to 4.8 K range. The crystals were aligned in the $(H00)$ and $(00L)$
plane. Extended diffraction patterns along principal directions confirm the
$I4/mmm$ tetragonal symmetry with lattice constants $a=3.981(3)$ and
$c=10.07(4)$ Å at 4.8 K for the $x=0.16$ crystal and $a=3.980(3)$ and
$c=10.10(4)$ Å for the $x=0.11$ crystal.

DFT calculations were performed using a full-potential linear-augmented-plane-
wave (FP-LAPW) method, as implemented in wien2k [43]. We used the virtual-
crystal approximation (VCA) to simulate the doping effects. The generalized-
gradient approximation (GGA) of Perdew, Burke, and Ernzerhof [44] was used for
the correlation and exchange potentials. To generate the self-consistent
potential and charge, we employed $R_{\text{MT}}\cdot K_{\text{max}}=8.0$ with
Muffin-tin (MT) radii $R_{\text{MT}}=2.7$, 2.4, and 2.5 a.u. for Ca, Co, and
As, respectively. The calculations were performed with 264 $k$-points in the
irreducible Brillouin zone (BZ). They were iterated until the charge
differences between consecutive iterations was smaller than $1\times
10^{-3}\,e$ and the total energy difference less than 0.01 mRy.

We also calculated the magnetocrystalline anisotropy energy (MAE), which
originates from the spin-orbit coupling (SOC) [45]. The MAE is calculated as
$K=E_{100}{-}E_{001}$, where $E_{001}$ and $E_{100}$ are the total energies
for the magnetization oriented along the [001] and [100] directions,
respectively. Positive (negative) $K$ corresponds to easy-$c$-axis
(easy-$ab$-plane) anisotropy. The SOC is included using the second-variation
procedure [46].

The composition-dependent experimental lattice parameters listed in Table 1 in
the following section were adopted in the calculations.

##  III  Crystallography

The body-centered-tetragonal crystal structure of CaCo2-yAs2 is shown in Fig.
1 [47]. The room-temperature crystallographic data for Ca(Co1-xNix)2-yAs2
crystals obtained from single-crystal XRD measurements are listed in Table 1.
The listed compositions are the average compositions of the crystals from EDS
measurements. The single-crystal XRD refinement does not allow simultaneous
refinement of the total occupation of the transition metal site and the
fraction of Co/Ni at that site. Thus, only the total occupancies were refined
based on the Co/Ni ratio taken from the EDS data. All the compositions
including the parents CaCo2-yAs2 and ${\rm CaNi_{2}As_{2}}$ crystallize in the
cT ${\rm ThCr_{2}Si_{2}}$-type structure.

The tetragonal lattice parameters $a$ and $c$, unit-cell volume $V_{\rm
cell}$, $c/a$ ratio, and the $z$-axis As position parameter $z_{\rm As}$ are
plotted as a function of the Ni concentration $x$ in Fig. 2. The $a$ lattice
parameter increases and the $c$ lattice parameter decreases nonlinearly with
$x$. As a result the unit-cell volume is almost constant throughout the
composition range. Although all compositions form in the cT structure, the
decrease in the ratio $c/a$ with increasing $x$ may result in a significant
change in the interplanar magnetic coupling between the Co spins. The $z_{\rm
As}$ parameter initially decreases from $x=0$ to $x=0.03$, but then increases
with further increases in Ni concentration. The EDS scans taken at points on
both sides of each crystal confirm the homogenous nature of the crystals. The
average compositions estimated by EDS indicate that the vacancy concentration
on the transition-metal site decreases with increasing Ni substitution and
that the stoichiometric composition ${\rm CaNi_{2}As_{2}}$ is obtained within
the error bar for $x=1$.

Figure 1: Chemical and A-type AFM structure of CaCo2-yAs2. The ThCr2Si2-type chemical unit cell is body-centered tetragonal and the AFM unit cell is A-type with the ordered moments aligned along the $c$ axis. The crystal structure was drawn using the VESTA program [47]. Table 1:  Tetragonal lattice parameters $a$ and $c$, $c/a$ ratio, unit-cell volume $V_{\rm cell}$, and fractional $c$-axis position of the As site $z_{\rm As}$ obtained for Ca(Co1-xNix)2-yAs2 from room-temperature single-crystal XRD measurements. The listed values of $x$ are the average values obtained from EDS analyses. Compound |  $a$ (Å) |  $c$ (Å) | $c/a$ |  $V_{\rm cell}$ (Å3) | $z_{\rm As}$
---|---|---|---|---|---
CaCo1.86(2)As2 | 3.9837(4) | 10.2733(4) | 2.5788(6) | 163.04(9) | 0.3672(4)
Ca(Co0.970(3)Ni0.030(3))1.87(4)As2 | 3.9888(6) | 10.236(2) | 2.5661(2) | 162.87(6) | 0.36620(5)
Ca(Co0.95(1)Ni0.05(1))1.86(4)As2 | 3.988(2) | 10.258(7) | 2.5722(4) | 163.2(2) | 0.36643(8)
Ca(Co0.89(1)Ni0.11(1))1.87(4)As2 | 3.9927(8) | 10.234(3) | 2.5631(3) | 163.14(8) | 0.3666(1)
Ca(Co0.84(1)Ni0.16(1))1.89(6)As2 | 4.0025(6) | 10.197(2) | 2.5476(1) | 163.35(6) | 0.3666(1)
Ca(Co0.79(1)Ni0.21(1))1.86(3)As2 | 4.0069(8) | 10.178(4) | 2.5401(6) | 163.41(9) | 0.36701(9)
Ca(Co0.69(1)Ni0.31(1))1.87(3)As2 | 4.0109(1) | 10.1382(5) | 2.5276(1) | 163.10(1) | 0.36755(8)
Ca(Co0.58(1)Ni0.42(1))1.87(3)As2 | 4.0224(3) | 10.0935(1) | 2.5093(2) | 163.31(3) | 0.36788(5)
Ca(Co0.48(1)Ni0.52(1))1.87(4)As2 | 4.0274(3) | 10.058(1) | 2.4973(5) | 163.14(3) | 0.36807(4)
Ca(Co0.33(1)Ni0.67(1))1.89(4)As2 | 4.0368(3) | 10.017(1) | 2.4814(4) | 163.23(3) | 0.36857(6)
Ca(Co0.19(1)Ni0.81(1))1.94(3)As2 | 4.0464(2) | 9.976(1) | 2.4654(3) | 163.33(2) | 0.36931(7)
CaNi1.97(4)As2 | 4.0552(2) | 9.921(1) | 2.4464(4) | 163.14(2) | 0.36975(4)
Figure 2: Unit cell parameters (a) tetragonal lattice parameters $a$ and $c$,
(b) Unit cell volume $V_{\rm cell}$ and $c/a$ ratio, and (c) $c$-axis As
position parameter $z_{\rm As}$ obtained from the single-crystal XRD
measurements on Ca(Co1-xNix)2-yAs2 crystals as a function of Ni substitution
$x$. The solid lines are guides to the eye.

##  IV  Magnetic measurements

###  IV.1 Magnetic susceptibility

Figure 3: The temperature $T$ dependence of magnetic susceptibility $\chi$ of
Ca(Co1-xNix)2-yAs2 crystals with compositions $x$ in applied magnetic fields
$H$ in the $ab$ plane and along the $c$ axis as indicated. The data for
$x=0.11$ and 0.16 show a transition in $\chi_{c}(T)$ but not in $\chi_{ab}(T)$
as discussed separately in Sec. IV.2. Note the large decrease with $x$ of the
ordinate scales for $\chi$, indicating the loss of Co magnetic character for
$x\gtrsim 0.5$. The small anomalies at $\approx 50$ K in panels (j), (k), and
(l) may arise from small amounts of O2 adsorbed on the crystal surfaces [53].
Figure 4: Dependence of the Néel temperature $T_{\rm N}$ of Ca(Co1-xNix)2-yAs2
crystals on composition $x$.

The $T$-dependent magnetic susceptibilities $\chi=M/H$ for Ca(Co1-xNix)2-yAs2
crystals with $x$ = 0, 0.03, 0.05, 0.11, 0.16, 0.21, 0.31, 0.42, 0.52, 0.67,
0.81, and 1 are shown in Figs. 3(a)–3(l), respectively, for $H\parallel ab$
and $H\parallel c$ under both zero-field-cooled (ZFC) and field-cooled (FC)
conditions as noted in the respective panels. The parent compound CaCo2-yAs2
shows A-type AFM order with the ordered moments aligned along the $c$ axis
below the Néel temperature $T_{\rm N}=52$ K [15]. The $c$-axis susceptibility
$\chi_{c}$ approaches zero for $T\rightarrow 0$ and the in-plane
susceptibility $\chi_{ab}$ is almost independent of $T$ below $T_{\rm N}$,
consistent with collinear AFM order along the $c$ axis according to molecular-
field theory [48]. The $T_{\rm N}$ is determined from the $\chi_{ab}(T)$ data
using the Fisher criterion [49] where here the temperature of the peak in
$d(\chi_{ab}T)/dT$ corresponds to $T_{\rm N}$. The $T_{\rm N}$ drops from 52 K
for $x=0$ to 22 K with only 3% Ni doping and then decreases further (see Table
3 below) as shown in Fig. 4.

With increasing $x$, the values of $\chi_{ab}$ and $\chi_{c}$ both increase in
the ordered state, indicating enhancements by FM fluctuations. For 5% Ni
doping a small hysteresis between the ZFC and FC data for $\chi_{c}$ in Fig.
3(c) occurs at $T\ll T_{\rm N}$. The thermal hysteresis in $\chi_{c}(T)$
increases for $x=0.11$, where along with an AFM transition at $T_{\rm N}=10.5$
K, another anomaly is observed at $T_{\rm B}\approx 4.8$ K which is clearly
visible in the lower fields as shown in Fig. 5(a) for $H=0.05$ T. For
$x=0.16$, the signature of an AFM transition for $H=0.1$ T in Fig. 3(e) has
almost disappeared, replaced by a strong FM-like increase, although the low-
field data in $H=0.05$ T in Fig. 5(b) confirm the presence of two magnetic
transitions at $T_{\rm N}\sim 6.5$ K and $T_{\rm B}\sim 3.5$ K, where $T_{\rm
B}$ is identified below as a blocking temperature. A separate discussion of
the low-$T$ anomaly observed at $T_{\rm B}$ for $x=0.11$ and 0.16 is given in
the following section. No signature of AFM ordering of any kind is observed
for $x>0.16$.

For $x>0.16$, Fig. 3 shows that $\chi_{c}$ strongly increases and becomes much
larger than $\chi_{ab}$. At the lowest measured $T=2$ K, $\chi_{c}\approx
2\chi_{ab}$ for $x=0.21$. The ratio $\chi_{c}/\chi_{ab}$ increases further for
$x=0.31$. These observations indicate a strong enhancement of FM $c$-axis spin
fluctuations for $x=0.21$ and 0.31. The FM spin fluctuations and the
anisotropy is found to persist up to $x=0.52$. The suppression of AFM order
associated with the development of strong FM fluctuations in
Ca(Co1-xNix)2-yAs2 crystals suggests the presence of a nearby FM quantum-
critical point (QCP) close to $x=0.16$. We note that a FM QCP can be avoided
if preempted by an AFM transition [50, 51, 52].

Figure 5: Measurements of $\chi_{ab}(T)$ and $\chi_{c}(T)$ below 30 K for (a)
$x=0.11$ and (b) $x=0.16$ crystals measured in $H=0.05$ and 0.035 T,
respectively, under both ZFC and FC conditions (left ordinates) along with the
temperature derivative of the susceptibilities (right ordinates). Clear
signatures of two transitions at $T_{\rm N}$ and $T_{\rm B}$ are observed for
$x=0.11$. The time $t$ dependence of relative magnetic relaxation
$[M(t)-M(0)]/M(0)$ measured at different temperatures with $H\parallel c$ is
plotted in (c) and (d) for $x=0.11$ and 0.16, respectively. The solid black
lines for $T=2$ K ($x=0.11$) and $T=2$ and 5 K ($x=0.16$) with $H=0.01$ T are
fits of the respective relaxation data by Eq. (1).

The $\chi(T)$ data for the $x=0.67$ and 0.81 crystals in Fig. 3 are
significantly reduced in magnitude and are almost independent of $T$ with a
small anisotropy. The $\chi$ data are also almost independent of $T$ for
$x=1$, and exhibit larger anisotropy than for $x=0.67$ and 0.81. A
composition-independent anomaly is observed at $T\sim 50$ K for all three
compositions that may be associated with a small amount of O2 adsorbed on the
crystal surfaces [53].

###  IV.2  Low-temperature magnetic features for $x=$ 0.11 and 0.16

Figure 6: Temperature $T$ dependence of inverse magnetic susceptibility
$\chi^{-1}$ of Ca(Co1-xNix)2-yAs2 crystals with $x=0$–1 in panels (a)–(h) for
$H\parallel ab$ and $H\parallel c$ as indicated. The anomalies at $\approx 50$
K in (j)–(l) are likely experimental artifacts arising from AFM ordering of
small amounts of O2 condensed on the crystals. The red solid lines are fits by
the modified Curie-Weiss law in Eq. (2) over the temperature range noted in
the respective panel. The positive values of $\chi_{0}$ are responsible for
the negative curvature in the fits. The overall decrease in the magnitude and
associated weak $T$ dependence of $\chi(T)$ are responsible for the
increasingly negative unphysical values of $\theta_{\rm p\alpha}$ listed in
Table 3 for $x=0.42$–0.81.

The anomalies in $\chi(T)$ at low $T$ observed in Fig. 3 for the $x=0.11$ and
0.16 crystals were further investigated by measuring $\chi(T)$ at smaller $H$.
The respective $\chi(T)$ data measured in $H=0.05$ T and 0.035 T for $x=0.11$
and 0.16 are shown in Figs. 5(a) and 5(b), respectively, along with the
respective $T$ derivatives. For $x=0.11$, $T_{\rm N}=10.5$ K. The ZFC and FC
$\chi_{c}$ data for each composition diverge from each other below $T_{\rm
N}$, exhibiting an anomaly at a blocking temperature $T_{\rm B}=4.8$ K. The FM
fluctuations considerably increase for $x=0.16$ and it is difficult to
ascertain whether long-range AFM order occurs for this composition. Indeed,
the zero-field neutron diffraction measurements discussed below show no
evidence for long-range AFM ordering for $x=0.16$. On the other hand, the
$\chi(T)$ data for $x=0.16$ show clear evidence for a blocking temperature
$T_{\rm B}\approx 3.5$ K.

Thus in Ca(Co1-xNix)2-yAs2 crystals the AFM order is suppressed and FM
fluctuations increase significantly with increasing Ni substitution. It is
therefore likely that for the $x=0.11$ and 0.16 compositions AFM and FM
interactions compete with each other at low $T$ which gives rise to a
metastable glassy state at a temperature $T_{\rm B}$, similar to that observed
in many reentrant AFM spin-glass systems [54, 55, 56]. To further elucidate
this scenario, we measured the magnetic relaxation behavior at different
temperatures for both compositions. The crystals were zero-field-cooled from
the paramagnetic (PM) state to the measured temperature at which a magnetic
field was switched on and the time evolution of the magnetization $M(t)$ was
recorded. As seen from Figs. 5(c) and 5(d), a clear $t$ dependence of the
relative change in magnetization $M(t)$ is observed for $T\lesssim T_{\rm B}$
in the $x=0.11$ and 0.16 crystals. It is interesting to see that although the
relaxation for $T_{\rm B}<T<T_{\rm N}$ is negligible for $x=0.11$, the
relaxation is quite significant at $T=2$ and 5 K for $x=0.16$. This difference
suggests that the strong enhancement of FM fluctuations along the $c$ axis and
resultant strong competition between the FM and AFM interactions significantly
weakens AFM ordering and pushes the system towards metastability at low $T$.
This is consistent with the observation of thermomagnetic irreversibility just
below $T_{\rm N}$ for $x=0.11$. Moreover, magnetic relaxation is observed in
Figs. 5(c,d) at $T=2$ K for small $H=0.01$ T, whereas the larger $H=1$ T is
seen to prevent the metastable state from forming for both $x=0.11$ and
$x=0.16$.

Table 2:  Parameters obtained by fitting the magnetic relaxation behavior of Ca(Co1-xNix)2-yAs2 crystals with $x=0.11$ and 0.16 in Figs. 5(c) and 5(d) by the stretched-exponential function in Eq. (1) for $H=0.01$ T applied along the $c$ axis. $x$ |  $T$ (K) |  $\tau~{}(10^{3}$ s) | $\alpha$
---|---|---|---
0.11 | 2 | 2.98(8) | 0.46(1)
0.16 | 2 | 3.6(1) | 0.45(1)
| 5 | 2.27(5) | 0.44(1)

The relaxation behavior observed in Figs. 5(c,d) for $T\lesssim T_{\rm B}$ is
described well by the stretched-exponential dependence

$\displaystyle\frac{M(t)}{M(t=0)}=1-e^{-(t/\tau)^{\alpha}},$ (1)

similar to that observed in spin-glass systems [57, 58]. The fits at low
temperatures are shown as the solid black curves in Figs. 5(c,d) and the
fitted parameters $\tau$ and $\alpha$ are listed in Table 2. Although the
parameter $\alpha$ is similar for both crystals, a significantly larger $\tau$
is observed at $T=2$ K for $x=0.16$. This suggests that the competition
between AFM and FM interactions is stronger in the $x=0.16$ crystal,
consistent with the $\chi(T)$ data in Fig. 3. Physical interpretations of the
parameters $\tau$ and $\alpha$ are given in Ref. [58].

###  IV.3 Magnetic susceptibility

Table 3:  Parameters obtained from the modified Curie-Weiss fits to $\chi^{-1}(T)$ data in the respective temperature range noted in Fig. 6 for Ca(Co1-xNix)2-yAs2 crystals with $x=0$–0.81 using Eq. (2). The parameters listed are the Néel temperature $T_{\rm N}$ and blocking temperature $T_{\rm B}$, the magnetic-field direction $\alpha$, the $T$-independent contribution to the magnetic susceptibility $\chi_{0\alpha}$, the Curie constant per mol $C_{\alpha}$, the effective moment per transition metal atom $\mu{\rm{}_{eff\alpha}}$ calculated using Eq. (4), the spherical average $\mu_{\rm eff,ave}=\sqrt{(2\mu_{{\rm eff}\,ab}^{2}+\mu_{{\rm eff}\,c}^{2})/3}$, the Weiss temperature $\theta\rm_{p\alpha}$, and the spherical average $\theta_{\rm p,ave}=\frac{2}{3}\theta_{ab}+\frac{1}{3}\theta_{c}$.  Compound |  $T_{\rm N}$, $T_{\rm B}$ | Field | $\chi_{0\alpha}$ | $C_{\alpha}$ | $\mu_{\rm eff\alpha}$ | $\mu_{\rm eff,ave}$ | $\theta_{\rm p\alpha}$ | $\theta_{\rm p,ave}$
---|---|---|---|---|---|---|---|---
|  | direction $\alpha$ | $\rm{\left(10^{-4}~{}\frac{cm^{3}}{mol}\right)}$ | $\rm{\left(\frac{cm^{3}K}{mol}\right)}$ | $\rm{\left(\frac{\mu_{B}}{Co+Ni}\right)}$ | $\rm{\left(\frac{\mu_{B}}{Co+Ni}\right)}$ | (K) | (K)
CaCo1.86(2)As2 | 52, — | $H\parallel ab$ | 0.03(2) | 0.443(3) | 1.37(1) | 1.39(1) | 59.5(9) | 61(1)
|  | $H\parallel c$ | -0.2(2) | 0.480(1) | 1.43(1) |  | 64.5(3) |
Ca(Co0.97Ni0.03)1.86As2 | 22, — | $H\parallel ab$ | 5.84(5) | 0.299(1) | 1.14(1) | 1.17(1) | 44.2(3) | 44.6(5)
|  | $H\parallel c$ | 3.52(3) | 0.349(1) | 1.22(1) |  | 45.4(2) |
Ca(Co0.95Ni0.05)1.86As2 | 17, — | $H\parallel ab$ | 5.80(4) | 0.298(1) | 1.13(1) | 1.14(1) | 34.1(3) | 33.7(6)
|  | $H\parallel c$ | 4.70(4) | 0.322(1) | 1.17(1) |  | 33.1(3) |
Ca(Co0.89Ni0.11)1.87As2 | 10.5, 4.8 | $H\parallel ab$ | 3.66(3) | 0.318(1) | 1.16(1) | 1.19(1) | 26.7(2) | 26.7(4)
|  | $H\parallel c$ | 3.71(2) | 0.369(1) | 1.25(1) |  | 26.8(2) |
Ca(Co0.84Ni0.16)1.89As2 | —, 3.5 | $H\parallel ab$ | 4.06(2) | 0.285(1) | 1.09(1) | 1.12(1) | 18.4(1) | 18.7(2)
|  | $H\parallel c$ | 3.79(2) | 0.335(1) | 1.18(1) |  | 19.5(1) |
Ca(Co0.79Ni0.21)1.86As2 |  | $H\parallel ab$ | 6.67(3) | 0.268(1) | 1.07(1) | 1.09(1) | 10.9(2) | 11.4(4)
|  | $H\parallel c$ | 5.52(3) | 0.303(1) | 1.13(1) |  | 12.6(2) |
Ca(Co0.69Ni0.31)1.87As2 |  | $H\parallel ab$ | 6.98(5) | 0.214(2) | 0.95(1) | 0.98(1) | $-0.3(4)$ | $-0.2(7)$
|  | $H\parallel c$ | 6.77(4) | 0.252(1) | 1.03(1) |  | $-0.1(3)$ |
Ca(Co0.58Ni0.42)1.87As2 |  | $H\parallel ab$ | 4.36(3) | 0.188(1) | 0.89(1) | 0.92(1) | $-18.2(5)$ |
|  | $H\parallel c$ | 4.14(3) | 0.227(1) | 0.97(1) |  | $-16.4(4)$ |
Ca(Co0.48Ni0.52)1.87As2 |  | $H\parallel ab$ | 3.63(6) | 0.175(2) | 0.86(1) | 0.89(1) | $-45(2)$ |
|  | $H\parallel c$ | 3.98(8) | 0.211(3) | 0.94(1) |  | $-46(2)$ |
Ca(Co0.33Ni0.67)1.89As2 |  | $H\parallel ab$ | 3.73(3) | 0.128(1) | 0.73(1) | 0.77(1) | $-77(2)$ |
|  | $H\parallel c$ | 3.66(8) | 0.170(3) | 0.84(1) |  | $-90(3)$ |
Ca(Co0.19Ni0.81)1.94As2 |  | $H\parallel ab$ | 3.19(2) | 0.090(3) | 0.60(1) | 0.65(1) | $-203(16)$ |
|  | $H\parallel c$ | 3.90(3) | 0.140(2) | 0.75(1) |  | $-128(3)$ |
Figure 7: Magnetic parameters versus $x$ from Table 3: (a) Curie constants
$C_{ab},\ C_{c},\ C_{\rm ave}$ (left ordinate) and effective magnetic moments
$\mu_{{\rm eff}\,{ab}},\ \mu_{{\rm eff}\,c},\ \mu_{\rm eff\,ave}$ (right
ordinate), (b) Weiss temperatures $\theta_{{\rm{}_{p}}\,ab},\ \theta_{{\rm
p}\,c}$ and (c) $T$-independent contributions $\chi_{0,\,ab},\ \chi_{0,\,c}$.
The large negative values of $\theta_{\rm{}_{p}}$ for $x\geq 0.42$ are
unphysical and are only to be considered as fitting parameters. (d) Saturation
moments $\mu_{{\rm sat}\,ab}$, $\mu_{{\rm sat}\,c}$, and $\mu_{\rm sat\,ave}$
from Table 4. The data for $x=0$ were obtained from zero-field neutron
diffraction and $M$(2 K, $H=14$ T) data. The data for $x=0.11$–0.31 were
obtained from the Arrott plots in the insets of Fig. 9. Figure 8: Rhodes-
Wohlfarth plot of $p_{\rm c}/p_{\rm sat}$ vs $T_{\rm N}$ for the listed
Ca(Co1-xNix)2-yAs2 compositions. Although such plots are usually versus the FM
Curie temperature $T_{\rm C}$ on the abscissa, here FM interactions dominate
and hence the abscissa is the Néel temperature $T_{\rm N}$. Because the
crystals with $x=0.16$ and 0.21 do not show AFM ordering, proxies for the
$T_{\rm N}$ values are used as explained in the text.

The $T$ dependences of the inverse magnetic susceptibilities
$\chi_{ab}^{-1}(T)$ and $\chi_{c}^{-1}(T)$ for all the Ca(Co1-xNix)2-yAs2
crystal compositions $x=0$–1 are shown in Figs. 6(a)–6(l). We analyzed the
data in the PM regime $T>T_{\rm N}$ using the modified Curie-Weiss law for
local magnetic moments given by

$\displaystyle\chi_{\alpha}(T)=\chi_{0}+\frac{C_{\alpha}}{T-\theta_{\rm
p\alpha}}\qquad(\alpha=ab,\ c),$ (2)

where $\chi_{0}$ is an isotropic $T$-independent term, $\theta_{\rm p\alpha}$
is the Weiss temperature for field direction $\alpha$, and the Curie constant
$C_{\alpha}$ per mole of formula units (f.u.) is given by

$\displaystyle C_{\alpha}=\frac{N_{\rm A}{g_{\alpha}}^{2}S(S+1)\mu^{2}_{\rm
B}}{3k_{\rm B}}\quad(\alpha=ab,\ c),$ (3)

where $N_{\rm A}$ is Avogadro’s number, $g_{\alpha}$ is the spectroscopic
splitting factor ($g$ factor), $S$ is the spin angular-momentum quantum
number, $k_{\rm B}$ is Boltzmann’s constant, and $\mu_{\rm eff}$ is the
effective moment of a spin. The $\mu_{\rm eff}$ per (Co+Ni) transition metal
atom is obtained from $C_{\alpha}$ per mole of formula units using

$\displaystyle\mu_{\rm
eff\alpha}{\rm[\mu_{B}/(Co+Ni)]}=\sqrt{\frac{8C_{\alpha}{\rm[cm^{3}\,K/mol\,f.u.]}}{2-y}}.$
(4)

As shown in Figs. 6(a)–6(k), the $\chi_{ab}^{-1}(T)$ and $\chi_{c}^{-1}(T)$
data are well described by Eq. (2) in the $T$ range noted in the panel for
each crystal and the fitted parameters are listed in Table 3. The values of
$C_{\alpha}$, $\mu_{\rm eff\,\alpha}$, $\theta_{\rm{}_{p\alpha}}$, and
$\chi_{0\alpha}$ as a function of $x$ for the Ca(Co1-xNix)2-yAs2 crystals are
plotted in Figs. 7(a)–7(c). The $C_{\alpha}$ and $\mu_{\rm eff\alpha}$
decrease with increasing $x$. The positive $\theta_{\rm{}_{p\alpha}}$ also
decreases with increasing $x$ and becomes negative for $x\geq 0.31$. The large
negative value of $\theta_{\rm{}_{p\alpha}}$ for $x\geq 0.41$ is a result of
the overall suppression of $\chi(T)$ at the larger $x$ values and does not
have physical significance.

In a local-moment picture the isotropic Curie constant in units of ${\rm
cm^{3}\,K/mol\,spins}$ for Heisenberg spins $S$ with $g=2$ is given by

$\displaystyle C\left({\rm\frac{cm^{3}\,K}{mol\,spins}}\right)=0.5002S(S+1).$
(5)

Thus for the minimum $S=1/2$ with $g=2$ and two spins per formula unit, one
obtains $C_{\rm mol}=0.75~{}{\rm cm^{3}\,K/(mol\,f.u.})$. The Curie constants
for all the Ca(Co1-xNix)2-yAs2 crystals in Table 3 are much smaller than this
value and hence suggest an itinerant character of the magnetism in these
crystals as in undoped CaCo2-yAs2 where FM interactions dominate. For an
itinerant weak ferromagnet, the degree of itinerancy can be expressed in a
Rhodes-Wohlfarth (RW) plot [59, 60] of the ratio $p_{\rm c}/p_{\rm sat}$
versus the FM Curie temperature $T_{\rm C}$, where $p_{\rm sat}=\mu_{\rm
sat}/\mu_{\rm B}$ is the saturation moment per transition-metal atom
normalized by the Bohr magneton and [27]

$\displaystyle p_{\rm c}=\sqrt{1+p_{\rm eff}^{2}}-1\qquad(g=2).$ (6)

For Heisenberg local-moment spins with $g=2$ the value of $p_{\rm c}/p_{\rm
sat}$ is equal to unity, whereas a larger value of $p_{\rm c}/p_{\rm sat}$
signifies itinerant magnetic character. Figure 8 shows an RW plot of $p_{\rm
c}/p_{\rm sat}$ versus $T_{\rm N}$ for four of our Ca(Co1-xNix)2-yAs2
crystals, where the $p_{\rm c}$ values are listed in Table 3. The value of
$p_{\rm sat}$ is estimated by plotting $M^{2}$ versus $H/M$ at $T\ll T_{\rm
C}$ (i.e., $\ll T_{\rm N}$ here) known as an Arrott plot [61, 62] and
extrapolating the high-field data to $H/M=0$ [63] as shown in the insets in
Fig. 9 below. For CaCo2-yAs2 $(x=0)$ the saturation (ordered) moment is taken
to be that obtained from zero-field neutron diffraction measurements [26]. We
have seen that AFM ordering does not occur for $x\geq 0.16$. Therefore proxies
for the values of $T_{\rm N}$ for $x=0.16$ and 0.21 in the RW plot are taken
as the temperatures where the curvature of $\chi_{c}(T)$ in Figs. 3(e) and
3(f) respectively change sign from positive to negative on cooling. As seen
from Fig. 8, $p_{\rm c}/p_{\rm sat}>1$ for all measured Ca(Co1-xNix)2-yAs2
compositions and also $p_{\rm c}/p_{\rm sat}$ increases with increasing $x$.
This behavior suggests that the Ca(Co1-xNix)2-yAs2 crystals are essentially
weak itinerant ferromagnets as expected from the dominance of FM interactions
in these materials as also previously inferred for the Sr(Co1-xNix)2As2 system
[27].

###  IV.4 Magnetization versus applied magnetic field isotherms

Figure 9: Four-quadrant magnetic hysteresis measurements at $T=2$ K of
Ca(Co1-xNix)2-yAs2 crystals with $x=0$ to 1 as indicated, measured for
$H\parallel ab$ ($M_{ab}$) and $H\parallel c$ ($M_{c}$). Insets (d)–(g):
Arrott plots of $M^{2}$ vs $H/M$ for both $H\parallel ab$ and $H\parallel c$.
The linear highest-field linear $M^{2}(H/M)$ data in each panel are
extrapolated to $H=0$ to obtain the value of $M(H=0,T=0)$ and then the
saturation (ordered) moment per transition-metal atom $\mu_{\rm
sat}=M(H=0,T=0)/(2-y)$. Figure 10: (a) Expanded plots of the magnetization $M$
vs applied magnetic field $H\parallel c$ for Ca(Co1-xNix)2-yAs2 crystals with
x = 0, 0.03, 0.05, and 0.11 from Figs. 9(a)–9(d), respectively. (b) Derivative
$dM/dH$ of the $M(H)$ data in (a). Note that the peak height for $x=0$ is
divided by 3.

In order to investigate the magnetic-field evolution of the magnetic ground
state, magnetization versus applied magnetic field $M(H)$ hysteresis
measurements were carried out for each of our crystal compositions. Before
each measurement the superconducting magnet was quenched to reduce the applied
field to zero. Figures 9(a)–9(l) show $M(H)$ four-quadrant hysteresis data
with $H\parallel ab$ and $H\parallel c$ measured at $T=2$ K for each of the
Ca(Co1-xNix)2-yAs2 crystals.

As reported earlier [15, 64, 65], the undoped $x=0$ composition shows a clear
spin-flop (SF) transition in the $M_{c}(H)$ data at $H_{\rm SF}=3.6$ T,
consistent with the known collinear $c$-axis AFM ordering [26], whereas
$M_{ab}(H)$ shows a smooth behavior. Figure 10(a) shows expanded plots of the
$M_{c}(H)$ data in Fig. 9 for $x=0$, 0.03, 0.05, and 0.11. The latter three
compositions show spin-flop transitions. The derivatives $dM/dH$ versus $H$
for these three compositions are plotted in Fig. 10(b) from which we obtain
the respective spin-flop fields $H_{\rm SF}$ listed in Table 4.

Table 4:  Spin-flop transition field $H_{\rm SF}$, coercive field $H_{\rm CF}$, remanent magnetization $M_{\rm rem}$, FM ordered moment $\mu_{\rm FM}$, and $p_{\rm sat}$ values of the Ca(Co1-xNix)2-yAs2 crystals with $x=0$–0.31. The values of $p_{\rm sat}\equiv\mu_{\rm sat}/\mu_{\rm B}$ in units of $\mu_{\rm B}$ per transition metal (TM) atom were obtained from the $M^{2}$ vs $H/M$ isotherms in the insets of Figs. 9(d)–9(g). The $p_{\rm sat}$ values for $x=0$ were obtained from $M$(2 K,$H=14$ T) data [22] and $H=0$, $T=4$ K neutron-diffraction data [26] and the values for $x>0$ from Arrott plots. The $H_{\rm CF}$, $M_{\rm rem}$ and $\mu_{\rm FM}$ values associated with FM ordering were obtained from the data in Fig. 11.  $x$ | $H$ | $H_{\rm SF}$ | $H_{\rm CF}$ | $M_{\rm rem}$ | $\mu_{\rm FM}$ | $p_{\rm sat}$
---|---|---|---|---|---|---
| direction | (T) | (Oe) | ($\mu_{\rm B}$/f.u.) | ($\mu_{\rm B}$/f.u.) | ($\mu_{\rm B}$/TM)
0 | $H=0$ |  |  |  |  | 0.43(5) [26]
| $H\parallel ab$ |  |  |  |  | 0.27 [22]
| $H\parallel c$ | 3.60(1) |  |  |  | 0.29 [22]
0.03 | $H\parallel ab$ |  |  |  |  |
| $H\parallel c$ | 2.2(1) |  |  |  |
0.05 | $H\parallel ab$ |  |  |  |  |
| $H\parallel c$ | 1.5(1) |  |  |  |
0.11 | $H\parallel ab$ |  |  $\sim$ 0 | 0 |  $\sim$ 0 | 0.176(2)
| $H\parallel c$ |  | 150(5) | 0.0032 | 0.01 |
0.16 | $H\parallel ab$ |  | 20(5) | 0.0025 | 0.043 | 0.144(2)
| $H\parallel c$ |  | 160(5) | 0.0139 | 0.03 |
0.21 | $H\parallel ab$ |  |  $\sim$ 0 | 0.0020 | 0.034 | 0.127(2)
| $H\parallel c$ |  | 25(5) | 0.0163 | 0.11 |
0.31 | $H\parallel ab$ |  |  $\sim$ 0 | 0 | 0.009 | 0.094(2)
| $H\parallel c$ |  |  $\sim$ 0 | 0.0103 | 0.067 |
Figure 11: Expanded low-field plots at $T=2$ K of the $M(H)$ hysteresis loops
of Ca(Co1-xNix)2-yAs2 crystals with $x$ = 0.11, 0.16, 0.21, and 0.31 for (a)
$H\parallel ab$ and (b) $H\parallel c$.

No magnetic hysteresis is observed in Fig. 9 in either $M_{ab}(H)$ or
$M_{c}(H)$ for $x=0$, 0.03, 0.05 or $x\geq 0.41$. However hysteresis in the
$M_{c}(H)$ isotherms at low fields was detected at $T=2$ K for the crystals
with $0.11\leq x\leq 0.31$, as shown in Figs. 11(a) and 11(b) for $H\parallel
ab$ and $H\parallel c$, respectively. These data indicate the occurrence of
weak ferromagnetism and the parameters associated with it are the coercive
field $H_{\rm CM}$, remanent magnetization $M_{\rm rem}$ and FM moment
$\mu_{\rm FM}$ listed in Table 4. The observation of small $H_{\rm CF}$ values
for $x=0.11$ and 0.16 and even smaller values for $x=0.21$ and 0.31 is
consistent with the notion that the suppression of AFM ordering is mediated by
strong FM fluctuations. The quasi-1D $c$-axis FM fluctuations discussed
earlier are also reflected in the $M(H)$ behavior, where only the $M_{c}(H)$
data are hysteretic to some extent, whereas hysteresis is much smaller in the
$M_{ab}(H)$ data.

We obtained estimates of the saturation moments for $x=0.11$, 0.16, 0.31, and
0.41 from extrapolations to $H=0$ of Arrott plots of $M^{2}$ versus $H/M$
shown in the respective insets of Fig. 9. The results are listed in Table 4
and plotted in Fig. 7(d) together with the low-$T$ ordered-moment for $x=0$
obtained from zero-field neutron-diffraction [26] and $M(H=14~{}$T, $T=2$ K)
[15] measurements.

##  V  Heat capacity

Figure 12: Temperature dependence of zero-field heat capacity $C_{\rm p}(T)$ of Ca(Co1-xNix)2-yAs2 crystals with $x=0$–1 along with fits by the Debye model using Eq. (11). The humps in $C_{\rm p}(T)$ at $T\approx 290$ K are experimental artifacts. Insets: $C_{\rm p}(T)/T$ vs $T^{2}$ along with fits by Eq. (8). The fitting temperature range is 2–10 K for $x=0$, 0.03, 0.05, 0.67, 0.81, and 1, whereas for all other compositions the range is $T_{\rm min}\leq T\leq 10$ K, with $T_{\rm min}$ being the temperature where minima in $C_{\rm p}(T)/T$ vs $T^{2}$ is observed and below which the low-$T$ upturn occurs that is associated with FM fluctuations. The fits below $T_{\rm min}$ are the extrapolations of the fits to 2 K using Eq. (8). Table 5:  The fitting parameters obtained from the analysis of heat capacity data. Listed are the crystal composition, doping charge $q$ with respect to ${\rm CaCo_{2}As_{2}}$ from Eq. (7) (hole-doping values are negative), Sommerfeld coefficient $\gamma$ obtained using Eq. (8) for $x=0$, 0.03, 0.05, 0.67, 0.81, and 1 and using Eq. (9) for $x=0.11$, 0.16, 0.21, 0.31, 0.41, and 0.52; lattice heat-capacity coefficients $\beta$ and $\delta$ obtained from low-$T$ fits of the Cp/$T$ versus $T^{2}$ data; spin-fluctuation coefficient $\kappa$, spin fluctuation temperature $T_{\rm sf}$, and density of states at the Fermi energy ${\cal D}(E_{\rm F})$ derived from $\gamma$ using Eq. (10). Compound | doping $q$ | $\gamma$ | $\beta$ | $\delta$ | $\kappa$ | $T_{\rm{sf}}$ | ${\cal D}(E_{\rm F})$
---|---|---|---|---|---|---|---
|  | (mJ/mol K2) | (mJ/mol K4) | ($\mu$J/mol K6) | (mJ/mol K2) | (K) | [states/(eV f.u.)]
CaCo1.86(2)As2 | $-0.98$ | 29.6(1) | 0.391(1) | $\approx 0$ |  |  | 12.54(5)
Ca(Co0.97Ni0.03)1.86As2 | $-0.92$ | 47.59(8) | 0.126(4) | 0.52(4) |  |  | 20.17(3)
Ca(Co0.95Ni0.05)1.86As2 | $-0.89$ | 57.98(1) | 0.131(3) | 1.21(3) |  |  | 24.57(1)
Ca(Co0.89Ni0.11)1.87As2 | $-0.70$ | 53.5(7) | 0.21(1) | 0.44(7) | $-16.9(5)$ | 10.4(8) | 22.6(3)
Ca(Co0.84Ni0.16)1.89As2 | $-0.47$ | 59(1) | 0.14(4) | 0.8(2) | $-15(1)$ | 10.21(3) | 25.0(4)
Ca(Co0.79Ni0.21)1.86As2 | $-0.59$ | 55(1) | 0.14(3) | 1.3(1) | $-24(2)$ | 8.14(2) | 23.3(4)
Ca(Co0.69Ni0.31)1.87As2 | $-0.33$ | 52(1) | 0.24(3) | 0.6(1) | $-49.2(7)$ | 7(1) | 22.0(4)
Ca(Co0.58Ni0.42)1.87As2 | $-0.12$ | 40(1) | 0.35(1) | 0.37(6) | $-21.6(4)$ | 4.80(6) | 16.9(4)
Ca(Co0.48Ni0.52)1.87As2 | $0.06$ | 32.9(4) | 0.22(1) | 0.90(5) | $-9.8(4)$ | 4(1) | 13.9(2)
Ca(Co0.33Ni0.67)1.89As2 | $0.50$ | 29.62(4) | 0.10(3) | 1.67(2) |  |  | 12.55(2)
Ca(Co0.19Ni0.81)1.94As2 | $1.15$ | 18.77(6) | 0.15(3) | 1.51(3) |  |  | 7.95(3)
CaNi1.97As2 | $1.76$ | 9.3(1) | 0.15(6) | 1.7(6) |  |  | 3.94(4)
Figure 13: $C_{\rm p}/T$ vs $T$ data of Ca(Co1-xNix)2-yAs2 crystals with $x$ =
0.11 (a), 0.16 (b), 0.21 (c), 0.31 (d), 0.42 (e), and 0.52 (f), measured at
different magnetic fields applied along the $c$ axis. The zero-field data are
fitted in the temperature range 2–12 K by Eq. (9) as shown by the black solid
lines. The low-$T$ upturns are associated with FM quantum spin fluctuations
that are suppressed with increasing magnetic field. Figure 14: Sommerfeld
coefficients $\gamma$ from Table 5 of Ca(Co1-xNix)2-yAs2 crystals with $x=0$,
0.03, 0.05, 0.67, 0.81, and 1 from low-$T$ heat capacity fits using Eq. (8)
and for $x=0.11$, 0.16, 0.21, 0.31, 0.41, and 0.52 using Eq. (9) (filled red
circles). The Debye temperatures $\Theta_{\rm D}$ for all compositions from
Table 6 were determined by fitting the $C_{\rm p}(T)$ data by Eq. (11) in the
$T$ range 50–300 K (filled blue squares). The lines are guides to the eye.

The zero-field heat capacities $C_{\rm p}(T)$ for all the Ca(Co1-xNix)2-yAs2
crystal compositions are shown in Figs. 12(a)–12(l) in the $T$ range 2–300 K.
No detectable feature is observed at $T_{\rm N}$ for any of the respective
compositions, evidently due to the small magnetic entropy change in these
itinerant magnets at $T_{\rm N}$. The $C_{\rm p}(T)$ value at our high-$T$
limit of 300 K is close to the classical Dulong-Petit high-$T$ limit $C_{\rm
p}=3nR=124.7$ J/mol K where $R$ is the molar gas constant and here $n\approx
5$ is the number of atoms per formula unit. As seen from the figures for all
compositions except $x=0$, a hump-like feature appears in the $C_{\rm p}(T)$
at $T\sim 290$ K that is due to melting of the Apiezon N grease used to make
thermal contact between the sample and platform of the sample puck. This
spurious feature can be avoided by using Apiezon H grease for the high-$T$
measurements as shown for the crystal with $x=0$.

Due to the nonstoichiometry of the Ca(Co1-xNix)2-yAs2 crystals, the charge
doping with respect to stoichiometric ${\rm CaCo_{2}As_{2}}$ is not equal to
the value of $x$. Instead, noting that Co2+ and Ni2+ respectively have
$3d^{7}$ and $3d^{8}$ electron configurations, the doping charge per formula
unit $q$ in units of the elementary charge is given by

$\displaystyle q=[7(1-x)+8x](2-y)-14,$ (7)

where a negative value of $q$ corresponds to hole doping and a positive value
to electron doping. The doping levels per formula unit are given for each of
the crystal compositions in the second column of Table 5.

The insets of Figs. 12(a)–12(l) show $C_{\rm p}(T)/T$ vs $T^{2}$ for all the
Ca(Co1-xNix)2-yAs2 crystal compositions. The low-$T$ data in the range 2–10 K
for $x=0$, 0.03, 0.05, 0.67, 0.81, and 1 were fitted by the expression

$\displaystyle C_{\rm p}(T)=\gamma T+\beta T^{3}+\delta T^{5},$ (8)

where $\gamma$ is the Sommerfeld electronic heat-capacity coefficient
associated with the conduction carriers and the last two terms describe the
low-$T$ lattice heat-capacity contribution. The fitted parameters are listed
in Table 5. As shown in Fig. 12, the $C_{\rm p}(T)$ vs $T^{2}$ data for the
$x=0.11$, 0.16, 0.21, 0.31, 0.42, and 0.52 crystals exhibit an upturn below a
temperature $T_{\rm min}(x)$ below which the $C_{\rm p}(T)$ vs $T^{2}$ data
are not described by Eq. (8).

As discussed earlier, the AFM interactions are gradually suppressed with
increasing Ni substitution in the Ca(Co1-xNix)2-yAs2 crystals. For the
$x=0.11$ and 0.16 crystals the strengths of the AFM and FM interactions are
comparable so that the materials settle into a metastable state below their
respective $T_{\rm N}$. The FM spin fluctuations dominate the AFM fluctuations
with a further increase in the Ni concentration as inferred from a strong
signature of FM spin fluctuations observed in the susceptibility data for
$x=0.21$ and 0.31 giving rise to a low-$T$ upturn in the $C_{\rm p}/T$ vs
$T^{2}$ data as shown in the insets of Fig. 12 and further discussed below.

To elucidate and confirm the presence of FM spin fluctuations in the $x=0.11$,
0.16, 0.21, 0.31, 0.41, and 0.52 crystals, we measured $C_{\rm p}/T$ versus
$T$ for magnetic fields applied along the $c$ axis and the corresponding plots
are shown in Figs. 13(a)–13(f). One may argue that such upturns may also be
associated with the high-$T$ tail of a Schottky anomaly; however, in this case
an upturn is expected to increase with increasing magnetic field which
conflicts with the observed data. In particular, the upturns in the $C_{\rm
p}(T)$ data are gradually suppressed with increasing magnetic field.

In a magnetic system with FM quantum fluctuations a $C/T\sim\ln T$
contribution is observed [27, 30, 66, 67, 68, 69, 70, 71]. We found that the
zero-field $C_{\rm p}(T)$ at low $T$ of the $x=0.11$, 0.16, 0.21, 0.31, 0.41,
and 0.52 crystals can also be well described by

$\displaystyle\frac{C_{\rm p}(T)}{T}=\gamma+\beta T^{2}+\delta
T^{4}+\kappa{\rm ln}(T/T_{\rm sf}),$ (9)

where in addition to the Sommerfeld coefficient $\gamma$ and lattice
coefficients $\beta$ and $\delta$, $\kappa$ is the spin fluctuation
coefficient and $T_{\rm sf}$ is the spin-fluctuation temperature. The fitted
parameters are listed in Table 5. The FM spin fluctuations are observed over a
wide composition range in Ca(Co1-xNix)2-yAs2 in contrast to the ranges
observed in isostructural Sr(Co1-xNix)2As2 [27] and Ca(Co1-xIrx)2-yAs2 [30]
crystals where the spin fluctuations were limited to narrow composition
ranges.

The Sommerfeld coefficient $\gamma$ in Table 5 increases by nearly a factor of
two with only 3–5% Ni substitutions, indicating a corresponding rapid increase
in the electronic density of state at the Fermi energy ${\cal D}(E_{\rm F})$.
The enhanced $\gamma$ values are observed for the compositions with strong FM
fluctuations. As the strength of these fluctuations gradually decreases for
the larger $x$ values, $\gamma$ correspondingly decreases as shown in Fig. 14.
The ${\cal D}(E_{\rm F})$ values are determined from the $\gamma$ values using
the relation

$\displaystyle{\cal D}_{\gamma}(E_{\rm
F})\rm{\left(\frac{states}{eV\,f.u.}\right)=\frac{1}{2.357}\
\gamma\left(\frac{mJ}{mol\,K^{2}}\right)},$ (10)

and are listed in Table 5. Here, ${\cal D}_{\gamma}(E_{\rm F})$ is the density
of states at $E_{\rm F}$ determined from $C_{\rm p}(T)$ measurements and
includes the factor of two Zeeman degeneracy of the conduction carriers.

The $C_{\rm p}(T)$ data in the temperature range 50–300 K are analyzed
according to

$\displaystyle C_{\rm p}(T)$ $\displaystyle=$ $\displaystyle\gamma_{\rm
D}T+nC_{\rm V\,Debye}(T),$ (11) $\displaystyle C_{\rm V\,Debye}(T)$
$\displaystyle=$ $\displaystyle 9R\left(\frac{T}{\Theta_{\rm
D}}\right)^{3}\int_{0}^{\Theta_{\rm D}/T}\frac{x^{4}e^{x}}{(e^{x}-1)^{2}}dx,$

where $\gamma_{\rm D}$ is the Sommerfeld coefficient which we use as a
variable in this fit, $n$ is the number of atoms per formula unit, $C_{\rm
V\,Debye}$ is the Debye lattice heat capacity per mole of atoms at constant
volume, and $\Theta_{\rm D}$ is the Debye temperature. The high-$T$ data
associated with the phonon contribution are well described by the Debye model
as shown by the black solid lines in Figs. 12(a)–12(l). The fitted parameters
are listed in Table 6. From the Table, $\gamma_{\rm D}$ significantly differs
from $\gamma$ in Table 5 except for $x=0$ and $x=1$.

Table 6:  Sommerfeld electronic heat-capacity coefficient $\gamma_{\rm D}$ and Debye temperature $\Theta_{\rm D}$ determined by fitting the $C_{\rm p}(T)$ data for Ca(Co1-xNix)2-yAs2 crystals in the temperature range 50–300 K by Eqs. (11).  $x$ | $\gamma_{\rm D}\left(\rm{mJ/mol\,K^{2}}\right)$ |  $\Theta_{\rm D}$ (K)
---|---|---
0 | 29.4(3) | 357(4)
0.03 | 28(1) | 347(1)
0.05 | 22(1) | 340(2)
0.11 | 22(1) | 336(2)
0.16 | 16(1) | 334(2)
0.21 | 11(1) | 332(2)
0.31 | 17(1) | 327(2)
0.42 | 13(1) | 327(1)
0.52 | 12(1) | 325(1)
0.67 | 15(1) | 316(2)
0.81 | 13(1) | 319(2)
1 | 8(1) | 309(2)

##  VI  Neutron Diffraction

Figure 15:  (a) Neutron-diffraction scan along $(20L)$ reciprocal-lattice
units (r.l.u.) from a single crystal with $x=0.16$ at $T=4.8$ K and at 20 K
showing the nuclear (202) and (204) reflections with no indication of new
emerging peaks at the (201) or (203) positions which would be indicative of
the A-type AFM ordering observed for the parent compound CaCo1.86As2. (b) The
difference in intensity between the scans at $T=4.8$ K and 20 K.

Guided by the magnetic structure of the A-type antiferromagnetism exhibited by
the parent compound CaCo1.86As2, we conducted a thorough search for new
emerging magnetic Bragg reflections along the $(20L)$ r.l.u. (reciprocal-
lattice unit) direction [14]. In particular, for A-type antiferromagnetism it
is expected to observe (201) and (203) magnetic reflections. Figure 15(a)
shows scans along $(20L)$ for an $x=0.16$ crystal at base temperature and at
20 K, i.e., above the anomaly found in $\chi_{ab}$ [Fig. 3(a)]. As shown by
the difference between these two scans in Fig. 15(b), no obvious peaks are
observed over the whole $L$ range thus excluding A-type ordering. In fact,
much longer time counting longitudinal and transverse scans at the (201)
position exclude an A-type phase at $T=4.8$ K assuming that the average
ordered moment is not larger than our resolution of $\sim 0.05\,\mu_{\rm B}$
per transition-metal atom.

Additional scans along $(00L)$, $(10L)$, and $(\frac{1}{2}0L)$ at $T=4.8$ and
20 K (not shown) do not show evidence of new emerging Bragg reflections that
may indicate magnetic ordering that is different from A-type AFM ordering. For
instance, the absence of magnetic reflections along $(00L)$ eliminates the
helical structure recently discovered in the related Sr(Co1-xNix)2-yAs2 system
in which adjacent FM layers (moments aligned in the plane) are rotated at a
finite angle as they stack along the $c$ axis [29]. We note that examination
of nuclear Bragg reflections do not show increased intensity as the
temperature is lowered from 20 K to base temperature thus excluding FM
ordering of the whole system assuming that the ordered moment is not larger
than $\sim 0.1\,\mu_{\rm B}$.

Similar experiments for the $x=0.11$ crystal with scans along
$(20L),\,(00L),\,(H00),$ and $(10L)$ at base temperature and at 20 K were
conducted (not shown) and also did not yield evidence of any of the various
scenarios that were excluded above within our resolution for the $x=0.16$
crystal.

##  VII  Theory

###  VII.1 Band-filling dependence of magnetic phases and their competition

Figure 16: The effects of electron doping $x$ on the magnetic energies of
various magnetic states in the cT-phase CaCo2As2. The energy of the A-type AFM
phase is chosen as the reference zero. The energies of nonmagnetic, stripe-
AFM, and FM states are plotted. The results are calculated using the
experimental lattice parameters listed in Table 1.

Figure 16 shows the energies of four magnetic configurations, including
ferromagnetic, A-type, stripe-AFM, and nonmagnetic states in Ca(Co1-xNix)2As2.
For stoichiometric CaCo2As2, FM and A-type AFM configurations have much lower
energy than the stripe-AFM ordering, indicating FM intralayer moment alignment
is favored over the stripe-AFM intralayer alignment, as observed. The energy
difference between the stripe-AFM phase and FM phase is much larger in cT-
phase CaCo2As2 than in T-phase SrCo2As2 [72], mainly due to the different
$c/a$-ratios in the T and cT phases. As a result, stripe ordering or
fluctuations are unlikely to occur in CaCo2As2-related compounds.

The energy difference between the FM and A-type AFM configurations is much
smaller, suggesting that interlayer coupling is much weaker than intralayer
coupling. Interestingly, the stoichiometric CaCo2As2 FM state with $x=0$ even
has a lower energy than the A-type AFM state found in CaCo1.86As2 from
experiments. This suggests that the intrinsic vacancies and the induced local
structural relaxation present in experimental samples may play a significant
role in stabilizing the AFM interlayer coupling.

Compared to SrCo2As2, CaCo2-yAs2 shows a more stable magnetic ordering and the
FM fluctuations exist in a much broader doping range in the Ni-doped
compounds. This is likely due to the lack of intralayer FM-AFM competition and
the easy-axis anisotropy in CaCo2As2. The much higher stripe-phase energy
excludes stripe ordering or fluctuations in CaCo2As2, while both interlayer
and intralayer FM-AFM competition coexist in SrCo2As2. Moreover, unlike
SrCo2As2, CaCo2As2 has an easy-axis magnetocrystalline anisotropy, which is
essential to stabilize the long-range magnetic ordering in 2D systems or
layered bulk systems with very weak interlayer couplings, according to the
Mermin-Wagner theorem [73].

The calculated magnetocrystalline anisotropy energy in stoichiometric CaCo2As2
is $\Delta E=41~{}\mu$eV/Co with the easy direction along the $c$ axis,
consistent with the easy $c$-axis anisotropy found in experiments on ${\rm
CaCo_{1.86}As_{2}}$ [22]. For comparison, using the experimental value of the
$c$-axis spin-flop field $H_{\rm SF}=3.5$ T and the ordered moment
$\mu=0.28~{}\mu_{\rm B}$/Co [22], we obtain $\Delta E=\frac{1}{2}\mu H_{\rm
SF}=28~{}\mu$eV/Co. The difference between the two values may be associated
with the Co vacancies in ${\rm CaCo_{1.86}As_{2}}$ which were not accounted
for in the theoretical calculation. In addition, magnetic-dipole interactions
[74] between the Co spins in the simple-tetragonal Co structure give a small
XY anisotropy $\Delta E\approx-1.5\,\mu$eV/Co assuming Co point-dipole local
moments.

###  VII.2 Density of States

Figure 17: The effects of electron doping on the density of states (DOS)
versus energy $E$ relative to the Fermi energy $E_{\rm F}$ of
Ca(Co1-xNi${}_{x})_{2}$As2 for compositions $x=0$, 0.21, and 0.42. The DOS is
expressed per formula unit, taking into account the twofold Zeeman degeneracy
of the electron. The DOS($E_{\rm F})$ is seen to peak near zero doping and to
decrease upon electron doping.

The influence of electron doping on the nonmagnetic density of electron states
(DOS) is plotted versus energy $E$ relative to the Fermi energy $E_{\rm F}$ in
Fig. 17. The DOS in undoped CaCo2As2 peaks near $E_{\rm F}$ as previously
reported [75]. From Fig. 17, a large amount of electron doping decreases
DOS($E_{\text{F}}$) and suppresses the on-site magnetic moment according to a
Stoner-like mechanism within a rigid-band picture, as also found previously
for hole doping [75]. Indeed, with electron doping, as shown in Fig. 16 the
on-site magnetic moment of $3d$ atoms in Ca(Co1-xNix)2As2 vanishes at the
Stoner transition composition $x\approx 0.5$, which agrees well with the
experimental fact that no spin fluctuations and magnetic ordering were
observed with $x>0.52$. Interestingly, calculations also found that a smaller
amount of electron doping promotes the FM interlayer coupling against the AFM
one, consistent with the above experiments showing that electron doping
suppresses the AFM interlayer coupling and induces strong FM fluctuations.

Table 7:  Calculated total density of states at the Fermi energy ${\cal D}(E_{\rm F})$ of Ca(Co1-xNi${}_{x})_{2}$As2 per formula unit for both spin directions for compositions $x=0$, 0.21, and 0.42. Also listed are two similar electron-doping values $q$ and corresponding ${\cal D}(E_{\rm F})$ inferred for Ca(Co1-xNix)2-yAs2 from Table 5. $x$ | $q_{\rm calc}$ | ${\cal D}(E_{\rm F})_{\rm calc}$ | $q_{\rm obs}$ | ${\cal D}(E_{\rm F})_{\rm obs}$
---|---|---|---|---
| (e/f.u.) | (states/eV f.u.) | (e/f.u.) | (states/eV f.u.)
0 | 0 | 7.846 | 0.06 | 13.9(2)
0.21 | 0.42 | 6.754 | 0.50 | 12.55(2)
0.42 | 0.84 | 4.809 | 1.15 | 7.95(3)

The values of the calculated densities of states at the Fermi energy ${\cal
D}(E_{\rm F})$ from Fig. 17 are listed for $x=0$, 0.21, and 0.42 in Table 7.
Three measured values for approximately the same electron-doping levels from
Table 5 are listed for comparison. The observed values are roughly a factor of
two larger than the bare calculated values, suggesting significant
enhancements from electron-phonon and/or electron-electron interactions.

##  VIII  Summary

Figure 18: Magnetic phase diagram in the $T$-$x$ plane of the
Ca(Co1-xNix)2-yAs2 system obtained from $\chi(T)$ and $M(H)$-isotherm
measurements. Here AFM, SG, and PM stand for antiferromagnetic, spin-glass,
and paramagnetic states, respectively. The suppression of AFM order by the
development of strong FM fluctuations in Ca(Co1-xNix)2-yAs2 crystals suggest
the presence of a nearby FM QCP at $x\approx 0.2$. Note the break in the
abscissa scale between $x=0.34$ and $x=0.9$.

The magnetic phase diagram in the $T$-$x$ plane of the Ca(Co1-xNix)2-yAs2
system based on the $\chi(T)$, $M(H)$ isotherm and $M(t)$ isotherm and
isofield measurements is shown in Fig. 18. The A-type AFM ordering observed at
$T_{\rm N}=52$ K in the highly-frustrated itinerant parent compound CaCo2-yAs2
is gradually suppressed with Ni substitution and vanishes for $x>0.11$. Ni
substitution strongly enhances the FM spin fluctuations in this system and as
a result $T_{\rm N}$ rapidly drops to 22 K with only a 3% Ni substitution
along with a strong enhancement of the Sommerfeld electronic heat-capacity
coefficient.

The FM fluctuations increase further in the $x=0.11$ and 0.16 crystals and
compete with the AFM ordering in these systems until the formation of a
low-$T$ spin-glass state below a blocking temperature $T_{\rm B}\sim 5$ K.
With a further increase in Ni concentration quasi-one-dimensional $c$-axis FM
spin fluctuations dominate in the $x=0.21$ and 0.31 crystals where $\chi_{c}$
becomes much larger than $\chi_{ab}$ in the low-$T$ region. Small static FM
moments at $T=2$ K were observed for $x=0.11$, 0.16, 0.21, and 0.31 from
magnetization versus field isotherms, with a maximum value of 0.12 $\mu_{\rm
B}$/f.u. for $x=0.16$.

DFT calculations confirm that FM fluctuations are enhanced by Ni substitutions
for Co in CaCo2-yAs2. The FM spin fluctuations are observed over a wide
composition range from $x=0.11$ to $x=0.52$ at which a Stoner transition to a
nonmagnetic state occurs as previously observed in the hole-doped
Ca(Co1-xFe${}_{x})_{2-y}$As2 system [75].

The results suggest the presence of a FM quantum-critical point at $x\approx
0.20$, which is unusual in such materials. However, a FM QCP can be avoided if
preempted by an AFM transition [50, 51, 52]. If FM critical fluctuations
persist to low temperatures, a novel ground state such as $p$-wave
superconductivity is conceivable [76, 77, 78, 79] with an onset below our
low-$T$ measurement limit of 1.8 K.

###### Acknowledgements.

This research was supported by the U.S. Department of Energy, Office of Basic
Energy Sciences, Division of Materials Sciences and Engineering. Ames
Laboratory is operated for the U.S. Department of Energy by Iowa State
University under Contract No. DE-AC02-07CH11358.

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