# Ce3-xMgxCo9: transformation of a Pauli paramagnet into a strong permanent
magnet

Tej N. Lamichhane  Ames Laboratory, U.S. DOE, Ames, Iowa 50011, USA
Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011,
USA  Valentin Taufour  Ames Laboratory, U.S. DOE, Ames, Iowa 50011, USA
Department of Physics, University of California Davis, Davis, California
95616, USA  Andriy Palasyuk  Ames Laboratory, U.S. DOE, Ames, Iowa 50011, USA
Qisheng Lin  Ames Laboratory, U.S. DOE, Ames, Iowa 50011, USA  Sergey L.
Bud’ko  Ames Laboratory, U.S. DOE, Ames, Iowa 50011, USA  Department of
Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA  Paul C.
Canfield  Ames Laboratory, U.S. DOE, Ames, Iowa 50011, USA  Department of
Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

###### Abstract

We report on the synthesis of single crystalline and polycrystalline samples
of Ce3-xMgxCo9 solid solution ($0\leq x\lesssim 1.4$) and characterization of
their structural and magnetic properties. The crystal structure remains
rhombohedral in the whole composition range and Mg partially replaces Ce in
the 6c site of the CeCo3 structure. Ferromagnetism is induced by Mg
substitutions starting as low as $x=0.18$ and reaching a Curie temperature as
high as $450$ K for $x=1.35$. Measurements on single crystals with $x=1.34$
and $T_{\textrm{C}}=440$ K indicate an axial magnetic anisotropy with the
anisotropy field of $6$ T and a magnetization of $6$ $\mu_{B}/$f.u. at $300$
K. Coercicity is observed in the polycrystalline samples consistent with the
observed axial magnetic anisotropy. Our discovery of ferromagnetism with large
axial magnetic anisotropy induced by substituting a rare-earth element by Mg
is a very promising result in the search of inexpensive permanent-magnet
materials and suggests other non-magnetic phases, similar to CeCo3, may also
conceal nearby ferromagnetic phases.

##  I Introduction

Current rare-earth-based commercial magnets contain local moment bearing rare-
earth elements, mainly Nd, Sm and Dy whose availability is, according to the
United States Department of Energy, important to the clean energy economy and
also have an associated supply risk. Alternative to finding a long sought rare
earth free, high flux permanent magnet, attempts to find Ce-based permanent
magnets or substituting Ce for more critical rare-earth elements could be a
pragmatic strategy to address the criticality problem since Ce is a relatively
more abundant rare earth Haxel  _et al._ (2002) with easier extraction
chemistry. Ce is relatively easy to separate from the other rare earths since
it can easily be oxidised to CeO2 via roasting from which it can be
precipitated out in acidic solutions Patnaik (2003); Xie  _et al._ (2014). Ce
can be, in theory as well as experiment, a substitute for critical rare-earths
without much compromise in magnetic properties Pathak  _et al._ (2015).
Because of the volatile price of critical rare-earths, Ce is drawing attention
for developing gap-magnets which will populate the gap in energy product (in
the range of 10-20 MGOe) in between low flux (Alnico, ferrites) and commercial
rare-earth based magnets such as SmCo5 and Nd2Fe14B. Additionally, the study
of new Ce based compounds often can reveal interesting physics; Ce exhibits
diverse electronic and magnetic properties like local moment bearing Ce3+ ion,
nonmagnetic Ce4+ ion, mixed valency, intermediate valence and itinerant
magnetism.

Ce3-xMgxCo9 alloys are substitution derivatives of CeCo3 in which Mg partially
replace Ce in the 6c position. The hydrogenation properties of the compound
Ce2MgCo9 ($x=1$) and Nd3-xMgxCo9 alloys ($x\leq 1.5$) have been recently
investigated Denys  _et al._ (2012); Shtender  _et al._ (2017). In addition,
it was shown that the substitution of Nd by Mg increases the Curie temperature
from $381$ K for NdCo3 Bartashevich  _et al._ (1993) to $633$ K for Nd2MgCo9
Shtender  _et al._ (2017).

In this work we present structural and magnetic properties of both single
crystalline and polycrystalline Ce3-xMgxCo9 for $0\leq x\lesssim 1.4$. The
anisotropic magnetic properties are studied for a single crystal of
Ce1.662(4)Mg1.338(4)Co9 (Hereafter we round off the single crystalline
composition to 3-significant digits as Ce1.66Mg1.34Co9.). We find a remarkable
transformation of a Pauli-paramagnet CeCo3 (Ce3Co9) into the potential
permanent magnet Ce3-xMgxCo9 which develops $2.2$ MJ/m3 of uniaxial anisotropy
energy at $2$ K for the Ce1.66Mg1.34Co9.

Figure 1: Co-rich portion of the Co-Mg-Ce ternary phase diagram showing the
Ce3-xMgxCo9 solid solution line and 1:2 type impurity phases. Ce9Mg24Co9 is
the optimised initial melt composition for the solution growth of single
crystalline Ce1.66Mg1.34Co9. (See text for details.)

##  II Experimental Methods

To establish the existence range of the solid solution Ce3-xMgxCo9, we
prepared polycrystals with various nominal compositions of $0\leq x\leq 2.00$
(see TABLE 3 below). Ce metal from the Ames Laboratory Material Preparation
Center (purity $>$ 99.99%), Co chunks ($99.95\%$, Alfa Aesar), and Mg
($99.95\%$,Gallium Source, LLC) were packed in a 3-capped Ta crucible Canfield
and Fisher (2001) under an Ar atmosphere. The Ta crucible was then sealed into
an amorphous silica ampoule. The ampoule was heated to
$900\leavevmode\nobreak\ {{}^{\circ}}\mathrm{C}$ over $3$ hours and held there
for $3$ hours. This step allows the reaction of Ce and Mg at low temperature
and avoids the excessive boiling of Mg inside the Ta crucible. The ampoule was
then heated to $1200\leavevmode\nobreak\ {{}^{\circ}}\mathrm{C}$ over $3$
hours and held there for 10 hours. At this point, the ampoule was spun in a
centrifuge and all the molten growth material was decanted and quenched in
catch side of the Ta-tube. This step confirmed that the mixture was forming a
homogeneous melt at $1200\leavevmode\nobreak\ {{}^{\circ}}\mathrm{C}$. The
ampoule was put back into a furnace then annealed at $900\leavevmode\nobreak\
{{}^{\circ}}\mathrm{C}$ for $24$ hours. Mg free CeCo3 was also synthesized by
arcmelting the stoichiometric composition and annealing at
$900\leavevmode\nobreak\ {{}^{\circ}}\mathrm{C}$ for 1 week.

Single crystals of Ce3-xMgxCo9 were grown using a solution growth technique.
An initial composition of Ce9Mg24Co67 (see FIG. 1) was packed in a 3-capped Ta
crucible Canfield and Fisher (2001) and heated to $1200\leavevmode\nobreak\
{{}^{\circ}}\mathrm{C}$ similar to the polycrystals. The ampoule was then
cooled down to $1100\leavevmode\nobreak\ {{}^{\circ}}\mathrm{C}$ over $75$
hours after which crystals were separated from the flux by using a centrifuge.
Similarly, CeCo3 single crystals were prepared by cooling a Ce30Co70 melt from
$1200^{\circ}$ to $1100\leavevmode\nobreak\ {{}^{\circ}}\mathrm{C}$ in 1 hour
and then to $1050\leavevmode\nobreak\ {{}^{\circ}}\mathrm{C}$ over 75
hoursOkamoto (1990).

Elemental analysis of the samples was performed using Energy Dispersive
Spectroscopy(EDS). Polycrystalline samples were embedded in epoxy resin and
finely polished. The polished samples were examined with EDS on 6-10 spots and
a statistical average composition is reported. Thin plate-like single
crystalline samples, see FIG. 2(a), were mounted on a conducting carbon tape.
Self-flux grown MgCo2 and CeCo2 single crystals were used as absorption
standards for the Ce-Co-Mg alloy composition analyses. Powder X-ray
diffraction data were collected at room temperature on a Rigaku MiniFlex II
diffractometer with Cu K$\alpha$ radiation. Data were collected with a $3$
seconds dwell time for each interval of $0.01^{\circ}$ within a 2$\theta$
range of $10-100^{\circ}$. Lattice parameters were refined by the Rietveld
analysis method using GSAS Larson and Von Dreele (2004) and EXPGUI Toby
(2001).

Single crystal X-ray diffraction was carried out on a Bruker Smart APEX II
diffractometer with graphite-monochromatized Mo-Kα radiation ($0.71073$ Å).
Reflections were gathered at room temperature by taking four sets of $360$
frames with $0.5^{\circ}$ scans in $\omega$, with an exposure time of $10$ s.
The crystal-to-detector distance was maintained $60$ mm. The reflections were
collected over the range of $3^{\circ}$ to $62^{\circ}$ in $2\theta$.

Electrical resistivity was measured on single crystals using the 4-probe
technique with a Linear Research, Inc. ac resistance bridge (LR700, f = 17
Hz). A Quantum Design (QD) Magnetic Property Measurement System (MPMS) was
used for the temperature control. Samples were sliced into thin rectangular
bars (approximately 0.9 mm x 0.45 mm x 0.04 mm) and platinum wires were
attached to the samples with Dupont 4929N silver paint. The contact
resistances were less than 2 $\Omega$.

Magnetization was measured using a QD-VersaLab Vibrating Sample Magnetometer
(VSM). The standard option was used in the temperature range $50$-$400$ K and
the oven option in the range $300$-$1000$ K. Loctite 435 and Zircar cement
were used to attach the samples in the standard and oven options,
respectively. Field dependent magnetization isotherms were also measured down
to $2$ K in a MPMS. The details of sample mounting and experimental
determination of demagnetization factor along the easy axis are discussed in
references Lamichhane  _et al._ , 2016a and Lamichhane  _et al._ , 2016b.

##  III Composition and structural properties

###  III.0.1 Single crystal: Characterization and structure

Figure 2: (a) Single crystals of Ce1.66Mg1.34Co9. (b) Backscattered Laue photograph of Ce1.66Mg1.34Co9 with X-ray beam perpendicular to plate. (c) Monochromatic X-ray diffraction from the surface of single crystal using Bragg-Brentano geometry. (d) Powder XRD for Ce1.66Mg1.34Co9 where I(Obs), I(Cal) and I(Bkg) are experimental, Rietveld refined and instrumental background data respectively. The lower section of the graph shows the Bragg’s peaks positions with olive vertical lines and the differential X-ray diffractrogram I(Obs-Cal).  Table 1: Crystallographic data and refinement parameters for Ce1.662(4)Mg1.338(4)Co9. Empirical formula | Ce1.662(4)Mg1.338(4)Co9
---|---
Formula weight | 796.32
Crystal system, space group | trigonal, R-3m h
Unit cell dimensions |  $a=4.9260(7)$ Å
|  $c=24.019(5)$ Å
Volume |  $504.75(18)$ Å3
Z, Calculated density |  $3$, $7.859$ g/cm3
Absorption coefficient |  $32.577$ mm-1
Reflections collected | 2000 [R${}_{(\textit{int})}$ = 0.0408]
Data / restraints / parameters | 224 / 0 / 18
Goodness-of-fit on $|F|^{2}$ | 1.149
Final $R$ indices [$I>4\sigma(I)$] |  $R1=0.0204$, $wR2=0.0450$
$R$ indices (all data) |  $R1=0.0226$, $wR2=0.0455$
Largest diff. peak and hole | 1.917 and -1.477 e.Å-3
Table 2: Atomic coordinates and equivalent isotropic displacement parameters ($\AA^{2}\times 10^{-3}$) for Ce1.66Mg1.34Co9. U${}_{(\textit{eq})}$ is defined as one third of the trace of the orthogonalized U${}_{\textit{ij}}$ tensor. atom |  Wyckoff site |  Occ |  x |  y |  z |  U${}_{\textit{eq}}$
---|---|---|---|---|---|---
Ce(1) |  3a |  1 |  0 |  0 |  0 |  14(1)
Ce(2) |  6c |  0.338
(4) |  0 |  0 |  0.1414(1) |  12(1)
Mg(2) |  6c |  0.662
(4) |  0 |  0 |  0.1414(1) |  12(1)
Co(1) |  3b |  1 |  0 |  0 |  $\frac{1}{2}$ |  11(1)
Co(2) |  6c |  1 |  0 |  0 |  0.3339(1) |  17(1)
Co(3) |  18h |  1 |  0.5014(1) |  0.4986(1) |  0.0840(1) |  11(1)
Figure 3: The crystal structure for Ce3-xMgxCo9 showing the stacking sequence
of CaCu5 type plane (A) and MgCu2 type plane (B) visualized along [010]
direction.

A picture of as grown Ce1.66Mg1.34Co9 single crystals, a Laue backscattered
photograph and single crystal surface diffracted monochromatic XRD data
collected via Rigaku MiniFlex II diffractrometer with Bragg-Brentano geometry
Jesche  _et al._ (2016) are presented in pannels (a), (b) and (c) of FIG. 2
respectively. Both Laue and monochromatic single crystalline XRD data
confirmed that the single crystals grow with a planar morphology with the
c-axis perpendicular to the plates.

The crystallographic data obtained from the single crystal X-ray diffraction
for Ce1.66Mg1.34Co9 grown out of Ce9Mg24Co67 initial melt are summarized in
TABLES. 1, and 2. FIG. 2(d) shows a powder X-ray diffraction pattern of the
crushed single crystals which has some noticeable mismatch in observed and
Rietveld refined intensity of {00l} families of the peaks, indicating a degree
of preferred orientation in the powder sample. As mentioned above, the
relatively small crystal size made it difficult to acquire enough powder
sample to obtain less noisy XRD data and better statistics in the Rietveld
refinement. To reduce the intensity mismatch, a preferred orientation
correction was employed in the Rietveld refinement using spherical harmonics
up to 12th order and absorption correction for plate like grains in the powder
sample. The Rietveld refined lattice parameters for powder XRD data of the
single crystal Ce1.66Mg1.34Co9 are a = $4.923(1)\leavevmode\nobreak\ \AA$ and
c = $24.026(1)\leavevmode\nobreak\ \AA$ with Rp = 0.09 which are in close
agreement (within 2-3$\sigma$) with single crystal XRD data as shown in TABLE
1. The single crystal XRD composition was Ce13.92Mg11.08Co75
(Ce1.662(4)Mg1.338(4)Co9). Although we did not make quantitative compositional
analysis measurement on the single crystalline sample with EDS (The crystals
were too thin to readily polish and small droplets of Mg rich flux was on
their surfaces.) we could detect the minor presence of Ta, (up to 1 at.%) most
likely caused by slight dissolution of the inner wall surfaces of Ta reaction
container and diffusion of Ta atoms into the reaction liquid during the long
term dwelling process at the maximum temperature of $1200^{\circ}$ C as well
as at ramping down to $1100^{\circ}$ C over 75 hours. However, an attempt to
solve the crystal structure along with inclusion of Ta in any Wyckoff sites or
interstitial sites was unsuccessful. We believe that Ta is distributed in our
crystals in the form of nano-sized precipitates rather than incorporated into
interstices of the crystals structure.

The crystal structure of Ce3-xMgxCo9 is rhombohedral and belongs to the PuNi3
type structureDenys  _et al._ (2012). Similar to the R3-xMgxNi9 series, the
Co-containing structure is an intergrowth of CaCu5-type (A) and MgCu2-type (B)
building blocks with a repeating sequence of ABA’B’A”B”A as shown in FIG. 3.
Here A’, B’ and A”, B” are introduced to show the relative translation of the
growth layers with respect to c-axis during stacking. There are two
independent sites for Ce atoms in this structure: one 3a site is located at
the center of a face-shared anti-hexagonal prism defined by 18 Co atoms; the
other 6c site is surrounded by 12 Co atoms defining a truncated tetrahedron
plus four capping atoms at longer distances. As expected from the polyhedra
volume, the statistically distributed Ce/Mg mixtures prefer to occupy the
Wyckoff 6c site with its smaller volume.

###  III.0.2 Polycrystalline samples: Composition and lattice parameters

Table 3: The comparison of the loaded compositions with the EDS determined
composition. A nominal presence of Ta (up to 1 at.%) was found in the
homogeneous Ce3-xMgxCo9 samples. Some of the higher-Mg samples showed traces
of a TaCo3 impurity phase and low-Mg content samples showed a TaCo2 phase.
Loaded composition
(Nominal) |  EDS composition |  Rietveld Refinement % of majority phase:
Ce3-xMgxCo9
---|---|---
CeCo3
(arcmelted and annealed at $900^{\circ}$C for 7 days) |  CeCo3 \+ CeCo2 |  $\geq 88\%$
Ce2.75Mg0.25Co9 |  Ce2.82Mg0.18Co9 \+ Ce0.86Mg0.14Co2 \+ TaCo2 |  $\geq 67\%$
Ce2.50Mg0.5Co9 |  Ce2.66Mg0.34Co9 \+ Ce0.77Mg0.23Co2 |  $\geq 76\%$
Ce2.25Mg0.75Co9 |  Ce2.40Mg0.60Co9 \+ Ce0.80Mg0.20Co2 |  $\geq 80\%$
Ce2Mg1.0Co9 |  Ce2.18Mg0.82Co9 |  $\approx$ single phase
Ce1.67Mg1.33Co9 |  Ce1.89Mg1.11Co9 |  $\approx$ single phase
Ce1.5Mg1.5Co9 |  Ce1.77Mg1.23Co9 |  $\approx$ single phase
Ce1.33Mg1.67Co9 |  Ce1.65Mg1.35Co9 |  $\approx$ single phase
CeMg2Co9 |  Ce1.42Mg1.58Co9 \+ MgCo2 \+ Co |  $\geq 50\%$
Figure 4: SEM images of mixed phase and predominantly single phase Ce3-xMgxCo9
samples (a) Nominal Ce2.25Mg0.75Co9 which gave a mixture of Ce2.40Mg0.60Co9
(majority phase) and Ce0.80Mg0.20Co2 (minority phase demonstrated as faint
small white spots along the diagonal of the black box in the panel (a)) and
large white stripes of TaCo3 impurity phase (b) Predominantly single phase
Ce1.89Mg1.11Co9 along with some traces of TaCo3 impurity. The black parallel
grooves in the image represent the cracks in the polished sample. Figure 5: A
typical example of multiphase polycrystalline XRD pattern for nominal
Ce2.75Mg0.25Co9 sample. The enlarged peak on the left top of the graph shows
the broadening of the highest intensity peak of Ce3-xMgxCo9 around $2\theta$
value of $42^{\circ}$ due to presence of Mg doped CeCo2 diffraction peak.
I(Obs), I(Cal) and I(Bkg) are experimental, Rietveld refined and instrumental
background data respectively. The lower section of the graph shows the Bragg’s
peaks positions with different coloured vertical lines for phases shown in the
graph and the differential X-ray diffractrogram I(Obs-Cal). Figure 6: Powder
XRD pattern for nominal Ce2.50Mg0.50Co9 sample. TaCo2 phase is almost not
detectable for XRD however an unidentified XRD peak is observed around
2$\theta$ value of $25^{\circ}$. I(Obs), I(Cal) and I(Bkg) are experimental,
Rietveld refined and instrumental background data respectively. The lower
section of the graph shows the Bragg’s peaks positions with different coloured
vertical lines for phases shown in the graph and the differential X-ray
diffractrogram I(Obs-Cal) Figure 7: A typical example of predominantly single
phase polycrystalline XRD pattern for EDS characterized Ce1.89Mg1.11Co9
sample. I(Obs), I(Cal) and I(Bkg) are experimental, Rietveld refined and
instrumental background data respectively. The lower section of the graph
shows the Bragg’s peaks positions with olive vertical lines and the
differential X-ray diffractrogram I(Obs-Cal) Figure 8: Variation of lattice
parameters (a,c) and unit cell volume (v) of polycrystalline with Mg content
inferred from EDS. Cubic Ce1-xMgxCo2 types impurity phases were obtained for
$x\leq 0.6$ and predominant single phase Ce3-xMgxCo9 is obtained for
$0.6<x\leq 1.4$. The lattice parameters for single crystalline Ce1.66Mg1.34Co9
are presented with corresponding color stars. The uncertainty in the refined
lattice parameters is less than 0.01% of the reported lattice parameters and
too small to clearly show as an error bar in the diagram.

The nominal and EDS composition of the polycrystalline samples are presented
in TABLE 3 along with the Rietveld refined percentage of the majority phase in
the sample. The SEM images for mixed and predominantly single phase
Ce3-xMgxCo9 samples are presented in FIG. 4. Panel (a) in FIG. 4 shows the
mixed phase sample that forms out of a nominal composition Ce2.25Mg0.75Co9 and
the panel (b) shows the predominantly single phase sample with EDS composition
Ce1.89Mg1.11Co9. In addition TABLE 3 summarizes phase analysis based on powder
XRD data.

The crystallographic information file obtained from single crystal XRD was
used to perform Rietveld refinement of the powder XRD data of polycrystal
samples listed in TABLE 3. Rietveld refined XRD patterns for a multiple phase
polycrystalline samples (Nominal Ce2.75Mg0.25Co9 with $R_{p}$ = 0.09 and
Ce2.50Mg0.50Co9 with $R_{p}$ = 0.10) and single phase polycrystalline
Ce1.89Mg1.11Co9 (EDS composition) with $R_{p}$ = 0.08 are presented in FIG. 5,
6 and 7 respectively. The melt-annealed nominal Ce2.75Mg0.25Co9 sample
contains $\sim 67\%$ of Ce2.82Mg0.18Co9 phase, $\sim 23\%$ of Ce0.86Mg0.14Co2
and $\sim 10\%$ of TaCo2 inferred from Rietveld refinement. The TaCo2 phase is
not observed in the nominal Ce2.50Mg0.5Co9 and higher content of Mg as shown
in FIG. 6 and 7. An unidentified XRD peak was observed in nominal
Ce2.50Mg0.50Co9 sample as shown in FIG. 6 however TaCo2 phase was almost
reduced to zero in comparison to nominal composition Ce2.75Mg0.25Co9 as shown
in FIG. 5. But traces of TaCo3 phase was observed in predominantly single
phases Ce3-xMgxCo9 samples. These results combined with the fact that even
pure (Mg = 0) CeCo3 remains mixed phase after 7 days of annealing, suggest
that Mg be assisting the annealing of polycrystalline Ce3-xMgxCo9 samples.

For nominal $x=2$ and higher, Ce3-xMgxCo9 can no longer be considered a clear
majority phase with the presence of the significant amount of CoMg2 and Co.
Looking at the composition of the Ce3-xMgxCo9 alloys from EDS, it seems that
$x\approx 1.4$ is the maximum solid solubility. In the Nd3-xMgxCo9 alloys, the
structure changes from the trigonal structure for $x\leq 1.5$ to a tetragonal
structure at $x=2$ (YIn2Ni9-type) Shtender  _et al._ (2017). The solubility
range of Mg in CeCo3 is therefore similar but we do not observe a phase
corresponding with the YIn2Ni9-type structure for $x\geq 2$. Instead, a three
phase region of MgCo2, Ce3-xMgxCo9 and Co is observed (see TABLE 3). The
compositional range of our Ce3-xMgxCo9 samples is summarized in FIG. 1.

The variation of the polycrystalline lattice parameters and unit cell volume
as a function of the Mg content in the Ce3-xMgxCo9 phase as determined from
EDS is shown in FIG. 8. As expected, the substitution of Ce by Mg results in
the reduction of the unit cell volume, similar to the case of Nd3-xMgxCo9
alloys Shtender  _et al._ (2017). Neither the a or c-lattice parameter follows
a linear relation with Mg content x. The variation in a lattice parameter
shows the slight positive deviation and c lattice parameter shows the slight
negative deviation starting in the middle of the single phase region. The
negative deviation of lattice parameter c might indicate that the covalent
bonding is increased along that direction. It should be noted that the lattice
parameters (a, c, v) and composition inferred from the single crystal X-rays
(shown as corresponding color $\star$s ) agree very well with what we inferred
from EDS measurements on the polycrystalline samples.

##  IV Magnetic Properties

Previously reported data do not agree about the magnetic properties of the
parent compound, CeCo3. Lemaire reported CeCo3 as a ferromagnetic material
with Curie temperature $78$ K Lemair (1966). Buschow identified it as a Pauli-
paramagnetic phase however he left a room for further investigation mentioning
CeCo3 could be ferromagnetic below $10$ KBuschow (1980). To clarify this
issue, we measured the temperature dependent magnetization and electric
resistivity of our single crystalline samples down to $2$ K as shown in FIG.
9. The magnetization data shows no signature of a phase transition and is only
weakly temperature dependent and is consistent with a Pauli-paramagnet and an
impurity tail below $20$ K. Assuming Curie tail is because of Ce3+ magnetic
ions in the single crystalline CeCo3 sample, magnetic susceptibility was
fitted to Curie-Weiss law up to $150$ K as:

$\chi(T)=\chi_{0}+\frac{C}{T-\theta}$

where $\chi_{0}$ is high temperature asymptotic susceptibility, C is Curie
constant and $\theta$ is Curie-Weiss temperature. The concentration of Ce3+
ions was estimated to be $\sim 20$% ( with $\theta$ = $3.8$ K) using the spin
only moment of $2.54\mu_{B}$ per Ce3+ ion. The electrical resistivity does not
show any signature of a loss of spin disorder scattering that would be
anticipated for a magnetic phase transition.

Figure 9: Temperature dependent susceptibility (H = 0.1 T $\perp$ [001] ) and
electrical resistivity (excitation current $\perp$ to [001]) of CeCo3 single
crystal. The picture in the inset shows the resistivity bar for four probe
measurement. The sample was 60 micrometer thick. Figure 10: Temperature
dependent magnetization of single crystalline (x = 0 and 1.34) polycrystalline
Ce3-xMgxCo9 measured under a magnetic field of $0.1$ T. The arrow pointed Mg
content (x) for each M(T) graph are inferred from EDS analysis. The olive
coloured straight lines above and below the point of inflection of M(T) data
for for x = 1.11 and x = 1.23 shows the scheme for inferring the Curie
temperature. Thus obtained Curie temperatures and Mg content phase diagram is
presented in the inset. The black $\star$ represents the Curie temperature
inferred from the tangents intersection scheme for single crystalline
Ce1.66Mg1.34Co9 sample on the M(T) data measured along the hard axis of the
plate.

The temperature dependence of the magnetization data of the single phase
Ce3-xMgxCo9 polycrystalline samples are shown in FIG. 10. A rapid increase of
the magnetization upon cooling below the Curie temperature is observed for x =
0.82 - 1.35 indicating the appearance of ferromagnetism with Mg substitution.

The Curie temperature $T_{\textrm{C}}$ is estimated as the cross-point of
linear extrapolations of two tangents to magnetization curve around the point
of inflection as indicated on the curve $x=1.11$ and x = 1.23 in FIG. 10. The
variation of $T_{\textrm{C}}$ with Mg substitution is shown in the inset. The
Curie temperature increases with Mg concentration and reaches as high as $450$
K for $x=1.35$.

The substitution of Mg for Ce changes a Pauli-paramagnet (CeCo3) into a
ferromagnet that has TC increase with Mg content. The most likely reason for
this is associated with valency and band filling. In CeCo3, the Ce is
essentially non-moment bearing; this implies a Ce4+ valency. As Mg2+ is added,
there will be a clear change in band filling that most likely leads to Stoner-
type magnetism associated with the Co 3-d bands. Further work, both
computational and experimental will be needed to better appreciate the origin
of the observed ferromagnetism.

Figure 11: Magnetic hysteresis loop of various annealed polycrystalline
Ce3-xMgxCo9 samples at $50$ K. The values of Mg content are from EDS analysis.
The inset shows the variation of the observed coercivity fields of the samples
as a function of Mg content.

Figure 11 shows the magnetic hysteresis curves of various polycrystals along
with observed coercivity fields at $50$ K (inset). The coercivity field
increases with Mg content, becomes maximum ($\sim 0.35$ T) for x = 0.82 and
then decreases. The observation of coercivity is consistent with the axial
nature of the magnetic anisotropy as will be detailed below. The abruptly
increased coercivity for  x = 0.82 and spontaneous magnetization for  x = 1.11
magnesium containing phases were reproduced in multiple samples. It should be
noted that differing saturation values for differing x are most likely due to
non-random distribution of grains in these as-cast samples. In addition, the
non-saturating behaviour of the x = 1.35 sample indicates either the presence
of the preferred orientations of the grains with their hard axis along the
applied field or presence of some anisotropic magnetic impurity in the sample.
The former argument can be easily visualized in M(T) data as x = 1.35
polycrystalline sample and single crystalline Ce1.66Mg1.34Co9 M(T) data along
the hard axis are almost identical in nature as shown in FIG. 10. The fact
that as-cast samples show coercivity is promising for the development of
permanent magnets out of this system.

Figure 12: Anisotropic temperature dependent magnetization for Ce1.66Mg1.34Co9
at various applied fields and directions. Dashed lines are for H = 0.1 T an
solid lines are for H = 1.0 T. Individual data points (red squares) are
spontaneous magnetization, MS inferred from M(H) isotherms. The inset shows
the zero field cooled (ZFC) and field cooled (FC) magnetization data along the
easy axis of magnetization to temperature above the sample decomposition
point.

Our single crystal sample can provide further insight into this system’s
promise as a permanent magnet material. FIG. 12 shows the temperature
dependence of the magnetization parallel and perpendicular to the c-axis of
the single crystal of Ce1.66Mg1.34Co9 up to $550$ K. The c-axis is the easy
axis of magnetization and the saturation magnetization at low temperature is
$8$ $\mu_{B}$/f.u. The spontaneous magnetization data points for
Ce1.66Mg1.34Co9, represented with red squares, are obtained by the Y-intercept
of linear fitting of the high field M(H) data ($>$1.5 T) in the first
quadrant. No hysteresis was observed in the M(H) loops. The absence of
hysteresis in M(H) isotherms measured in single crystals is due to absence of
grain boundaries, defects and impurity atoms capable of pinning of the
ferromagnetic domains. When measurements were performed up to $1000$ K, we
noticed a non-reproducibility of the results as shown in the inset of FIG. 12.
Thermo-gravimetric analysis (not shown here) showed evidence for a
decomposition of the samples, this degradation was not observed when limiting
the measurements to a maximum temperature of $550$ K.

Figure 13: Arrott plot for a Ce1.66Mg1.34Co9 single crystal within the
temperature range of $432$ K to $452$ K at a step of 2 K between adjacent
curves. The Curie temperature is determined to be $440$ K.

An Arrott plot with several isotherms near the Curie temperature is shown in
FIG. 13. The internal magnetic field $H_{int}$ was determined using the
relation $H_{int}=H_{app}-N*M$, where $H_{app}$ is the applied field, $N$ is
the demagnetization factor which is experimentally determined along the easy
axis ($N_{c}=0.78$) Lamichhane  _et al._ (2016a, b) and $M$ is the
magnetization. The Arrott curves are not linear indicating Ce1.66Mg1.34Co9
does not follow the mean field theory. The Curie temperature of
Ce1.66Mg1.34Co9 is $440$ K since Arrott curve corresponding to $440$ K passes
through the origin. This is comparable with the values of TC obtained from
polycrystals of similar composition (see inset of FIG. 10).

Figure 14: Anisotropic field dependent magnetization of Ce1.66Mg1.34Co9 at
$50$ K (H${}_{a}\approx$10$\leavevmode\nobreak\ T)$ and $300$ K
(H${}_{a}\approx 6$ T). Figure 15: Sucksmith-Thompson plot for Ce1.66Mg1.34Co9
to obtain anisotropy constants K1 and K2. The field dependent magnetization
data were measured up to $7$ T along the hard axis of magnetization. The
dotted straight lines are the linear fit to $\frac{\mu_{0}H}{M}$ at high field
magnetization data to obtain the intercepts and slopes of the isotherms. The
inset shows the Sucksmith-Thompson plots for VSM data measured along hard axis
( $\textit{H}\perp[001]$) up to $3$ T field. K1 and K2 obtained by VSM data
were matched to MPMS data at $300$ K.

The magnetocrystalline anisotropy field was determined to be $\sim 10$ T (T =
2 K) and $\sim 6$ T (T = 300 K) for a Ce1.66Mg1.34Co9 single crystalline
sample, as shown in FIG. 14. The anisotropy field was determined by the linear
extrapolation of the observed moment along the plane up to the saturation
moment.

Figure 16: Temperature dependent anisotropy energy constants for
Ce1.66Mg1.34Co9. The anisotropy constants were determined from the Sucksmith-
Thompson plot. The K1 and K2 values up to $300$ K were measured using MPMS and
higher temperature data are measured using VSM.

The anisotropy energy was quantified by using the Sucksmith-Thompson plot for
field dependent magnetization data along the plane as shown in FIG. 15. In the
Sucksmith-Thompson plot, the ratio of magnetizing field with hard axis
magnetization data is related to the anisotropy constants $K_{1}$ and $K_{2}$,
saturation magnetization $M_{s}$ and hard axis magnetization ($M_{\perp}$) as
shown in equation (1)(Sucksmith and Thompson, 1954; Taufour  _et al._ , 2015).

$\displaystyle\frac{\mu_{0}H}{M_{\perp}}=\frac{2K_{1}}{M_{s}^{2}}+\frac{4K_{2}}{M_{s}^{4}}M_{\perp}^{2}$
(1)

The intercept of the Sucksmith-Thompson plot gives the anisotropy constant
$K_{1}$ and slope gives the anisotropy constant $K_{2}$. FIG. 16 shows the
temperature variation of the measured anisotropy constants. There was a slight
mismatch ($<2\%$) in the anisotropies data above and below the $300$ K
obtained from VSM and MPMS data. The VSM data were scaled to MPMS data at
$300$ K since slope of Sucksmith-Thompson plot are better determined with
higher applied field. Here the total anisotropy energy of Ce1.66Mg1.34Co9 is
determined to be $2.2$ MJ/m3. Such high anisotropy energy density makes the
Ce1.66Mg1.34Co9 as a potential candidate for permanent magnet applications.

##  V Conclusions

We investigated the effect of Mg substitution into the Ce3Co9 (e.g. CeCo3)
binary phase where Mg partially replaces the Ce atom on the 6c
crystallographic site giving rise to the Ce3-xMgxCo9 solid solution for $0\leq
x\lesssim 1.4$. The substituted Mg induces ferromagnetism; the Curie
temperature of the solid solution increases with higher content of Mg and
becomes maximum ($450$ K) for Mg content x = 1.35. The magnetic anisotropy was
determined for a self-flux grown Ce1.66Mg1.34Co9 single crystal. The uniaxial-
anisotropy field was determined to be $\sim 10$ T at $2$ K and $\sim 6$ T at
$300$ K. The anisotropy energy density was determined to be $2.2$ MJ/m3 at $2$
K. With these observed magnetic properties, Ce3-xMgxCo9 solution shows a
potential to be used as a permanent magnet.

##  VI Acknowledgements

We would like to thank Dr. T. Kong for useful discussions. Dr. Warren
Straszheim is acknowledged for doing SEM on various samples. This research was
supported by the Critical Materials Institute, an Energy Innovation Hub funded
by the U.S. Department of Energy, Office of Energy Efficiency and Renewable
Energy, Advanced Manufacturing Office. Q.L. is supported by the office of
Basic Energy Sciences, Materials Sciences Division, U.S. DOE. This work was
performed at the Ames Laboratory, operated for DOE by Iowa State University
under Contract No. DE-AC02-07CH11358.

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