# La4Co4X (X = Pb, Bi, Sb): a demonstration of antagonistic pairs as a route
to quasi-low dimensional ternary compounds

Tyler J. Slade1∗, Nao Furukawa1,2, Matthew Dygert1,3, Siham Mohamed,1,4
Atreyee Das1,2,
Weiyi Xia1,2, Cai-Zhuang Wang1,2, Sergey L. Bud’ko1,2, Paul C. Canfield1,2∗

###### Abstract

We outline how pairs of strongly immiscible elements, referred to here as
antagonistic pairs, can be used to synthesize ternary compounds with low or
quasi-reduced dimensional motifs intrinsically built into their crystal
structures. By identifying third elements that are mutually compatible with a
given antagonistic pair, ternary compounds can be formed in which the third
element segregates the immiscible atoms into spatially separated
substructures. Quasi-low dimensional structural units, such as sheets, chains,
or clusters are a natural consequence of the immiscible atoms seeking to avoid
close contact in the solid-state. As proof of principle, we present the
discovery, crystal growth, and basic physical properties of La4Co4X (X = Pb,
Bi, Sb), a new family of intermetallic compounds based on the antagonistic
pairs Co-Pb and Co-Bi. La4Co4X adopts a new orthorhombic crystal structure
(space group Pbam) containing quasi-2D Co slabs and La-X polyhedra that stack
in an alternating manner along the a-axis. Consistent with our proposal, the
La atoms separate the Co and X substructures, ensuring there are no direct
contacts between the members of the immiscible (antagonistic) pair. Within the
Co slabs, the atoms occupy the vertices of corner sharing tetrahedra and
triangles, and this bonding motif produces flat electronic bands near the
Fermi level that favor magnetism. The Co is moment bearing in each La4Co4X
compound studied, and we show that whereas La4Co4Pb behaves as a three
dimensional antiferromagnet with T${}_{\text{N}}$ = 220 K, La4Co4Bi and
La4Co4Sb have behavior consistent with low dimensional magnetic coupling and
ordering, with T${}_{\text{N}}$ = 153 K and 143 K respectively. In addition to
the Pb, Bi, and Sb based La4Co4X compounds, we also were likely able to
produce an analogous La4Co4Sn in polycrystalline form, although we were unable
to isolate single crystals. We anticipate that identifying and using mutually
compatible third elements together with an antagonistic pair represents a
novel and generalizable design principle for discovering new materials and new
structure types containing low-dimensional substructures.

1Ames National Laboratory, US DOE, Iowa State University, Ames, Iowa 50011,
USA

2Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011,
USA

3Department of Physics and Astronomy, University of Missouri, Columbia,
Missouri 65211, USA

4Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA

##  1 Introduction

A foundational aspiration of solid state chemistry is to develop general
design principles for producing materials with targeted structural motifs and
physical properties. Here, we demonstrate how strongly immiscible pairs of
elements can be leveraged to synthesize ternary compounds with reduced or
quasi-reduced dimensional motifs such as 2D sheets, 1D chains, or 0D clusters
intrinsically built into their crystal structures. To introduce the basic
idea, consider the two binary phase diagrams for Co-Pb and Co-Bi displayed in
Figures 1a and 1b. The diagrams show that Co is extraordinarily immiscible
with Pb and Bi at temperatures up to at least 1400°C, and extrapolating to
higher temperatures, remain immiscible as liquids even at thousands of
degrees. We use the term “antagonistic pairs” to refer to such pairs of
elements with similarly extreme levels of immiscibility,[1] of which other
examples include, but are not limited to, Ba-Fe and La-Cr.

Figure 1: (a) Binary phase diagram for Co and Pb (ASM Diagram
$\\#$900732,[2]). (b) Binary phase diagram for Co and Bi (ASM Diagram
$\\#$900429,[3]). The diagrams demonstrate the extreme immiscibility of Co
with Pb and Bi Figure 2: Crystal structures of the previously reported ternary
compounds containing La, Co, and Pb. (a) La5CoPb3, La6Co13Pb, and (c)
La12Co6Pb. (d) shows the local coordination environment of the Pb atoms in
La12Co6Pb (pannel (c)), emphasizing the complete encapsulation of Pb by La
with no Pb-Co contacts.

The heart of this work is the question: for any given immiscible pair of
elements, what third element can be introduced to produce stable ternary
compounds? Remarkably, a survey of crystallographic databases reveals that for
many ternary compounds that contain an antagonistic pair, the strong
immiscibility of the antagonistic elements often remains preserved in the
crystal structure, with the third element separating the immiscible elements
into distinct, quasi low dimensional substructures.[1] As an example, the pair
Co-Pb forms ternary compounds with most rare earth elements, and Figure 2
illustrate the crystal structures for La5CoPb3, La6Co13Pb, and La12Co6Pb,
which span the known structure types found in the broader R-Co-Pb (R = rare
earth atom) phase space.[4, 5, 6] The crystal structures each clearly reflect
the immiscibility of the Co and Pb atoms. La5CoPb3 contains quasi-1D chains of
Co atoms that extend down the c-axis and are separated from the Pb by sheaths
of La. The structure of La6Co13Pb can be envisioned as 2D slabs of Co and
sheets of Pb that stack along the c-axis and are separated by layers of La
atoms. Finally, in La12Co6Pb, single, “zero-dimensional,” Pb atoms are fully
encapsulated by La such that there are no nearest neighbor Pb-Co contacts.

The key insight from Figure 2 is that in each structure, the addition of the
mutually compatible third element, La, to the immiscibile pair, Co-Pb,
produces ternary compounds in which the La atoms segregate the Co and the Pb,
giving materials in which at least one of the atoms occupies a quasi-reduced
dimensional substructure like the 1-D Co chains in La5CoPb3, 2-D Co slabs in
La6Co13Pb, or 0-D Pb atoms in La12Co6Pb. Other examples based on different
antagonistic pairs, such as LaCrGe3 and the AEFe2As2 (AE = alkali earth)
superconductors, display similar structural segregation and quasi-low
dimensional motifs in their crystal structures (the immiscible pairs are in
bold). Importantly, in systems containing magnetic, or potentially moment
bearing atoms, such as 3d transition metals, the reduced dimensionality may
lead to enhanced fluctuations and emergent, correlated phases with exotic
physical properties such as the unconventional superconductivity in the iron-
arsenides[7, 8] or fragile, itinerant, magnetism in LaCeGe3.[9, 10, 11]

We propose here that searching for ternary compounds based upon a strongly
immiscible pair of elements constitutes a very general design principle for
identifying and discovering novel materials with low dimensional structural
motifs favorable for exhibiting emergent quantum properties. As a proof of
principle, we outline the discovery of a new family of ternary compounds
La4Co4X (X = Pb, Bi, Sb) that are based on the antagonistic pairs Co-Pb and
Co-Bi. The La4Co4X adopt a new structure type with an orthorhombic Pbam
arrangement. Like the compounds discussed above, the La4Co4X structure
reflects the strong Co-X immisicibility, and consists of staggered, quasi-2D
slabs of Co separated by layers of La-encapsulated X atoms. The Co slabs can
be visualized as chains of corner sharing tetrahedra that run down the c-axis
and are linked along the b-direction by corner sharing triangles. The Co is
moment bearing in each compound, with La4Co4Pb showing behavior typical of a
three dimensional antiferromagnet with T${}_{\text{N}}$ = 220 K, whereas
La4Co4Bi and La4Co4Sb have temperature dependent magnetization characteristic
of low dimensional coupling and ordering, with T${}_{\text{N}}$ = 153 K and
143 K respectively. This work demonstrates that the extreme immiscibility of
antagonistic element pairs can be overcome and exploited using a mututally
compatible third element to produce new quantum materials and new structure
types with built-in quasi-reduced dimensionality.

##  2 Experimental Details

###  2.1 Crystal Growth

Table 1: Single crystal data and structural refinement information for La4Co4X
(X = Pb, Bi, Sb).

Chemical formula | La4Co4Pb | La4Co4Bi | La4Co4Sb
---|---|---|---
Formula weight (g/mol) | 998.55 | 1000.34 | 913.11
Temperature | 295.3(7) | 294.7(3) | 295.32(10)
Wavelength (Å, Ag K$\alpha$) | 0.56087 | 0.56087 | 0.56087
Crystal system | orthorhombic | orthorhombic | orthorhombic
Space group |  Pbam (# 55) |  Pbam (# 55) |  Pbam (# 55)
Unit cell dimensions |  a = 21.9909(3) Å, $\alpha$ = 90° |  a = 22.1952(10) Å, $\alpha$ = 90° |  a = 22.0031(4) Å, $\alpha$ = 90°
b = 8.28370(10) Å, $\beta$ = 90° |  b = 8.3236(3) Å, $\beta$ = 90° |  b = 8.2780(2) Å, $\beta$ = 90°
c = 4.74940(10) Å, $\gamma$ = 90° |  c = 4.7224(2) Å, $\gamma$ = 90° |  c = 4.71320(10) Å, $\gamma$ = 90°
Volume (cm3) | 865.18(2) | 872.43(6) | 858.47(3)
Z | 4 | 4 | 4
Calculated density (g/cm3) | 7.666 | 7.616 | 7.065
Absorption coefficient (mm-1) | 24.366 | 24.868 | 15.721
Absorption Correction | Face indexed | multi-scan | Face indexed
F(000) | 1672 | 1676 | 1548
Crystal size (mm) | 0.26 x 0.19 x 0.08 | 0.2 x 0.17 x 0.13 | 0.16 x 0.13 x 0.1
theta range for data collection | 2.4020-24.6820 | 2.4-28.9270 | 2.423-29.2900
Index ranges (min/max, h, k, l) | [-32/30, -11/11, -6/6] | [-35/34, -13/13, -7/8] | [-36/35, -13/13, -8,7]
Reflections collected | 19831 | 30382 | 34091
Independent reflections | 1454 ($R_{\text{int}}$ = 0.0708) | 2411 ($R_{\text{int}}$ = 0.0625) | 2366 ($R_{\text{int}}$ = 0.0528)
Completeness | 99.9 | 99.8 | 99.8
Refinement method | Full-matrix least-squares on F2 | Full-matrix least-squares on F2 | Full-matrix least-squares on F2
Data / restrains / parameters | 2146 / 0 / 55 | 2411 / 0 / 55 | 2366 / 0 / 55
GOF | 1.286 | 1.232 | 1.253
Final R indices [I $>$ 2$\sigma$(I)] |  $R_{\text{obs}}$ = 0.0272, $wR_{\text{obs}}$ = 0.0652 |  $R_{\text{obs}}$ = 0.0233, $wR_{\text{obs}}$ = 0.0429 |  $R_{\text{obs}}$ = 0.0198, $wR_{\text{obs}}$ = 0.0385
R indices [all data] |  $R_{\text{all}}$ = 0.0279, $wR_{\text{all}}$ = 0.0655 |  $R_{\text{all}}$ = 0.0263, $wR_{\text{all}}$ = 0.0434 |  $R_{\text{all}}$ = 0.0221, $wR_{\text{all}}$ = 0.0390
Extinction coefficient | 0.00413(19) | 0.00122(6) | 0.00433(12)
Largest diff. peak and hole (e-/Å3) | 2.907 and -3.117 | 1.834 and -1.683 | 1.266 and -1.484
CSD Number | 2333895 | 2333982 | 2333786

Whereas Co is strongly immiscible with Pb and Bi, all three elements, Co, Pb,
and Bi, mix readily with La.[12] The Co-La binary phase diagram shows a
relatively deep eutectic near $\approx$ 70 $\%$ La, and compositions near the
eutectic point allow for access to single phase liquid at temperatures below
750°C for $\approx$ 45-85 $\%$ La,[12] and therefore are attractive solvents
from which to grow La-Co-X ternary compounds.

We grew the La4Co4X single crystals by adding small quantities of X = Pb, Bi,
Sb to Co-La based melts as follows. Elemental La (Ames Laboratory, 99.9+ $\%$)
Co pieces (American Elements, 99.99 $\%$), and Pb (Alfa Aesar, 99.99 $\%$), Bi
(Alfa Aesar, 99.99 $\%$), or Sb (Alfa Aesar, 99.99 $\%$) were weighed in molar
ratios of La45Co45Pb10, La51Co46Bi3, and La43Co53Sb4 and placed in a Ta
crucible set with home made Ta caps and filter.[13, 14] The Ta crucibles were
sealed under an Ar atmosphere using an arc melter, and then the crucibles were
flame sealed under vacuum in fused silica ampoules. The ampoules were heated
in a box furnace to 1150°C. After dwelling at 1150°C for 10 h, the furnace was
cooled to 775°C over 100-200 h after which the samples were removed from the
furnace and the excess flux was decanted in a centrifuge with metal cups and
rotors.[1] After cooling to room temperature, the tubes were opened to reveal
a mixture of plate-like crystals and smaller, thin blade-like rods for samples
containing Pb and Sb, whereas the Bi containing samples only yielded the
blades. The inset to Figure 4a shows typical example of the blade-like
crystals. We emphasize that the above compositions were those used to grow the
specific crystals whose data is presented in the following sections. Other,
similar, ratios of La, Co, and X were also used in an attempt to increase the
crystal size and/or phase purity. These other attempts generally produced
qualitatively similar mixtures of plates and blades.

EDS and powder x-ray diffraction indicated the larger plates to be the known
ternary La6Co13X (X = Pb or Sb)[5] and the blade-like rods to be a new ternary
compound with the chemical formula La4Co4X (X = Pb, Bi, or Sb). The crystals
were found to be oxygen and/or moisture sensitive, and the bright, metallic
luster of the as-grown samples darkened even after several minutes of air
exposure. Therefore, the samples were stored in a nitrogen glovebox until
needed for characterization. We also attempted to grow a X = Sn member.
Although we were unable to isolate suitable crystals for further
characterization, our polycrystalline samples had clear evidence of a La4Co4Sn
phase. More details on our attempts to grow La4Co4Sn are outlined in the
supporting information.

###  2.2 Elemental analysis

The composition of the blade-like samples was determined by Energy Dispersive
Spectroscopy (EDS) quantitative chemical analysis using a ThermoFisher (FEI)
Teneo Lovac FE-scanning electron microscope (SEM). The data was analyzed using
an Oxford Instruments Aztec System with X-Max-80 detector, attached to the
Teneo. The measurements were conducted with an acceleration voltage of 20 kV,
current of 1.6 nA, working distance of 10 mm, and a take off angle of 35°. We
analyzed three separate crystals from each batch, respectively corresponding
to Pb, Bi, and Sb containing samples, and the composition of each crystal was
measured at 4-8 different spots, revealing good homogeneity in each case. The
standards used for reference are internal to the Oxford software. The EDS data
for each sample is summarized in Tables S1-S3 in the supporting information.

###  2.3 X-ray diffraction

Single crystal X-ray diffraction was performed using a Rigaku XtaLab Synergy-S
diffractometer with Ag radiation (0.56087 Å ) operating at 65 kV and 0.67 mA.
The samples were held in a nylon loop with vacuum grease, and the data was
collected at room temperature. The total number of runs and images was based
on the strategy calculation from the program CrysAlisPro (Rigaku OD, 2023).
The data integration and reduction were also performed using CrysAlisPro, and
a numerical absorption correction was applied based on Gaussian integration
over a face-indexed crystal. For La4Co4Bi, the crystal was irregularly shaped
and we were unable to index the faces, so we employed an empirical multi-scan
absorption correction using spherical harmonics, implemented in the SCALE3
ABSPACK scaling algorithm. The structures were solved by intrinsic phasing
using the SHELXT software package and were refined with SHELXL. The
crystallographic data and refinement results are given Tables 1, and the
atomic positions and thermal displacement parameters are listed in Tables
S4-S9 in the supporting information.

Powder X-ray diffraction patterns were obtained using a Rigaku Miniflex-II
instrument operating with Cu-K$\alpha$ radiation with $\lambda$ = 1.5406 Å
(K$\alpha$1) and 1.5443 Å (K$\alpha$2) at 30 kV and 15 mA. The samples were
prepared by grinding a representative number of crystals (5-10) to a fine
powder. The powder patterns were refined using the Rietveld method with GSAS-
II software.[15] To address air sensitivity, we also measured the powders on a
Rigaku Miniflex-I instrument (same Cu-radiation and wavelength) contained in a
nitrogen filled glovebox. The patterns are shown in Figures S1 and S2 in the
supplemental information and were not found to be significantly different when
comparing measurements conducted in air or nitrogen environments.

###  2.4 Physical property measurements

Figure 3: Crystal structure of La4Co4X (X = Pb, Bi, Sb). (a) Unit cell of
La4Co4X viewed down the c-axis. (b) Extended view of the structure in the same
orientation as (a) emphasizing the alternating stacks of Co-slabs and La-X
polyhedral layers along the a-direction. (c) Unit cell viewed down the b-axis.
(d) Extended view of the orientation in (c) showing the face-sharing
connectivity of the La-X polyhedra along the b-direction and the quasi-
layered, distinct Co- and La9X-based structrual units. (e) Isolated
coordination environment of X surrounded by La to form tri-capped trigonal
prisms. (f) Corner sharing tetrahedra and triangle sub-units that make up the
Co slabs. (g) Connectivity of the two structural sub-units shown in (f) into
extended Co-slabs that span the bc-plane.

Temperature dependent resistance measurements were performed between 4-300 K
in a closed-cycle cryostat (Janis SHI-950). The AC resistance was measured
using LakeShore AC resistance bridges (models 370 and 372), with a frequency
of 17 Hz and a 3 mA excitation current. The temperature was measured by a
calibrated Cernox 1030 sensor connected to a LakeShore 336 controller. As the
crystals naturally grew with a blade-like morphology, we measured the
resistances along the long-axis of the blade, which was determined with a Laue
camera to be the c-crystallographic axis. To prepare the samples, the surfaces
of the crystals were lightly polished, and contacts were made by spot welding
25 $\mu$m thick annealed Pt wire onto the (100) faces of the crystals in
standard four point geometry. After spot welding, a small amount of silver
epoxy was painted onto the contacts to ensure good mechanical strength, and
typical contact resistances were $\approx$ 1 $\Omega$.

Magnetization measurements were performed in a Quantum Design Magnetic
Property Measurement System (MPMS-classic) SQUID magnetometer operating in the
DC measurement mode. The measurements were performed with the field applied
along the a, b, and c crystallographic directions, and the samples were
oriented with a Laue camera. For La4Co4Pb and La4Co4Bi, the samples were
mounted between two straws for measurements in the H $\parallel$ b and H
$\parallel$ c orientations. To measure with H $\parallel$ a (perpendicular to
the thinnest direction of the blade-like crystals), the samples were glued to
a Kel-F disc, which was then placed inside of a straw. Prior to measuring, the
blank disc was first measured at the same temperatures and fields to use as a
background subtraction. For La4Co4Sb, the sample was mounted to the disc to
measure all orientations.

###  2.5 Electronic structure calculations

Density functional theory (DFT) was used to calculate the electronic structure
of La4Co4X with X = Pb, Bi, and Sb. The DFT calculations were performed by
using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional within
the framework of GGA[16] as implemented in the Vienna Ab initio Simulation
Package (VASP).[17, 18] A plane-wave cutoff energy was set to 520 eV, the
experimental lattice parameters were used, and the positions of atoms were
fully optimized with the force tolerance of 0.01 eV/ÅṪhe accuracy of the
electron self-consistent field is set to 10-4 eV, and the Brillouin zone is
sampled using a set of gamma-centered uniform 2 $\times$ 8 $\times$ 16 grids
with tetrahedron method for the density of states calculations.

##  3 Results and Discussion

Figure 4: (a) Temperature dependent resistivity (left axis, in red) and its
derivative d$\rho$/dT (right axis, in blue), (b) Anisotropic temperature
dependent magnetization (M/H), and (c) polycrystalline average of M/H (left
axis, orange) and d[(Mavg/H)T]/dT (right axis, light blue) of the
magnetization data in (b). (a)-(c) show the data for La4Co4Pb, (d-f) the data
for La4Co4Bi, and (g-i) the data for La4Co4Sb. The inset in (a) shows a
picture of typical La4Co4Pb crystals on a mm grid. Figure 5: Field dependent
magnetization isotherms measured at T = 2 K for (a) La4Co4Pb, (b) La4Co4Bi,
and (c) La4Co4Sb. Figure 6: DFT calculated electronic band structures for (a)
La4Co4Pb, (b) La4Co4Bi, and (c) La4Co4Sb. (d-f) show the calculated density of
states for the corresponding band structures in (a-c).

The La4Co4X (X = Pb, Bi, or Sb) compounds adopt a new orthorhombic structure
type with space group Pbam. The crystal structure is illustrated in Figure 3,
and information regarding the structural refinements is given in Table 1. The
atomic positions and thermal displacement parameters are summarized in Tables
S4-S9 in the supporting information. As shown in Figures 3a and 3b, La4Co4X
adopts a quasi-layered structure featuring striking segregation of the
immiscible Co and X atoms into two distinct structural sub-units, Co slabs and
slabs formed from La9X polyhedra. The Co and La-X slabs each span the bc-plane
and stack in an alternating manner along the a-axis. Within the La-X slabs,
the X atoms are nine-fold coordinated at the center of tricapped trigonal
prisms (see Figure 3e), and the polyhedra have face-sharing connectivity that
extends linearly down the c axis and is staggered along the b-direction, as
emphasized in Figures 3c and 3d.

Figure 3f shows that the Co atoms sit at the vertices of two structural sub-
units within the greater Co-slabs: pairs of corner sharing tetrahedra and
corner sharing triangles. The tetrahedra extend in chains down the c-axis and
are linked in the b-direction by the corner sharing triangles to give the
network shown in Figure 3g. An alternative way to view the Co-slabs is as a
corrugated Kagome lattice that is bent in a zig-zag fashion along the b-axis
with additional Co atoms (Co3, see atomic positions listed in Tables S4, S6,
and S8 supporting information) sitting above and below the corrugated kagome
layers.

The existence of stable ternary compounds containing the pairs Co-Pb and Co-Bi
demonstrates that the extreme immiscibility of Co with Pb and Bi may be
overcome by using a third element that is mutually compatible with the
antagonistic elements. In this case, Co and Pb/Bi are all soluble in excess La
at temperatures above 800° C.[12] Within the La4Co4X crystal structure, the La
clearly acts to spatially segregate the Co and X, as the complete
encapsulation of X into the La9X polyhedra ensures the X atoms are chemically
isolated from the Co slabs. As the La4Co4X family are new materials that adopt
a new structure type, this work serves as a proof-of-principle that highly
immiscible pairs of atoms can be leveraged to form new materials with quasi-
reduced dimensional motifs intrinsically built into their crystal structures,
which we suggest naturally form as immiscible atoms continue to avoid close
contact in the solid-state.

In La4Co4X, the most interesting structural motifs are the quasi-2D slabs of
Co the span the bc-plane. As described above, these slabs are composed of
corner sharing tetrahedra that form chains along the c-axis and that are
linked by pairs of corner sharing triangles along the b-direction. Such
networks of corner sharing tetrahdra or triangles form the basis of pyrochlore
and Kagome lattices, both of which are currently attracting immense interest
as potential platforms for studying many-body topological physics.[19, 21, 22,
23, 24, 25, 26, 26, 27, 20] In simplified models for metals with pyrochlore
and Kagome lattices, frustrated hopping from adjacent sites leads to quenching
of the electron kinetic energy and electronic localization. This produces flat
electronic bands in momentum space and increases the relative strength of the
Coulomb interaction between electrons, potentially providing a driver for
correlated states including itinerant magnetism,[28] charge density waves,[28,
29, 30, 31] and unconventional superconductivity.[32, 33, 34, 35, 36]

To determine if the La4Co4X family shows interesting physical properties, we
measured the temperature and field dependence of the resistivity and
magnetization of each. The data is presented in Figure 4. The top row, Figures
4a, 4d, and 4g show the resistivity ($\rho$, left axis, in red) and its
derivative d$\rho$/dT (right axis, in blue) of each La4Co4X compound. The
La4Co4X materials all show metallic behavior where the resistivity decreases
with cooling between 4-300 K. The residual resistivity ratios, $\rho$(300
K)/$\rho$(4 K), are reasonably high, spanning 10-25, indicating good crystal
quality. At high temperatures, the resistivity of each material has a modest
slope, but each shows a kink on cooling that suggests a loss of spin disorder
scattering as the samples enter a magnetically ordered state. The peaks in the
resistance derivatives were used to assign the transition temperatures of TN =
219 K for La4Co4Pb, 153 K for La4Co4Bi, and 145 K for La4Co4Sb,[37] and we
find that the d$\rho$/dT peak is substantially stronger in La4Co4Pb than
either La4Co4Bi or La4Co4Sb. We will return to this point when discussing the
magnetic data.

Figures 4b, 4e, and 4h display the anisotropic temperature dependent
magnetization, shown as M/H. The magnetic data confirm that Co is moment
bearing and orders in each La4Co4X compound. Like in the resistivity data, the
transition is most apparent (sharpest) in La4Co4Pb. As shown in Figure 4b, the
H $\parallel$ b and H $\parallel$ c magnetization of La4Co4Pb first increases
on cooling and reaches a peak near 220 K, characteristic of antiferromagnetic
order in which the moments are aligned along the b-axis. Above the transition,
M/H increases in a Curie-Weiss like manner, with substantial anisotropy
between different orientations. Curie-Weiss fits, shown in Figure S6 in the
supporting information, to the the M/H data suggest an effective moment of
$\mu_{\text{eff}}$ = 3.5(1) $\mu_{\text{B}}$/Co and Weiss temperatures
$\theta$ = 166(3) K, which is slightly smaller than, but in reasonable
agreement with the 3.87 $\mu_{\text{B}}$ expected for Co2+ moments.

In the Bi and Sb containing compounds, Figures 4e and 4h show that M/H first
increases with cooling but with a non Curie-Weiss like, essentially linear,
temperature dependence. Likewise, instead of a sharp peak like that observed
in La4Co4Pb, the magnetization of La4Co4Bi and La4Co4Sb reaches a very broad
maximum centered respectively at 195 K and 170 K in each material. Below the
maximum, M/H decreases rapidly when H $\parallel$ b, but only subtly in the H
$\parallel$ a and H $\parallel$ c orientations before settling into a
relatively weak, slightly positive temperature dependence. The fact that the
M/H is smallest for the H $\parallel$ b orientation in each sample suggests
that the ordered moments may be aligned primarily along the b-axis within the
antifferomagnetic state. We also note that the small downturn in M/H observed
for La4Co4Sb is an artifact from subtracting the disc (see experimental
details), and is likely apparent owing to the small, $\approx$ 0.5 mg, sample
mass and resulting weak signal.

To estimate the Neel temperatures from the magnetic data, we calculated the
polycrystalline average of the anisotropic data (shown in Figures 4c, 4f, and
4i, left axis in orange), where M${}_{\text{avg}}$/H = 1/3(M${}_{\text{a}}$ \+
M${}_{\text{b}}$ \+ M${}_{\text{c}}$)/H. The Neel temperatures were then
determined using the derivatives d[(M${}_{\text{avg}}$/H)T]/dT,[38] which are
presented in Figures 4c, 4f, and 4i (right axis, in light blue). The inferred
T${}_{\text{N}}$ agree well with the transition temperatures determined from
the resistivity derivatives, with TN = 220 K, 155 K, and 146 for respective X
= Pb, Bi and Sb samples. Like in the d$\rho$/dT data, the
d[(M${}_{\text{avg}}$/H)T]/dT behaves differently at TN for La4Co4Pb, in which
d[(M${}_{\text{avg}}$/H)T]/dT has a sharp step/discontinuity corresponding to
the maximum in M/H. Instead of a discontinuity, the
d[(M${}_{\text{avg}}$/H)T]/dT curves for La4Co4Bi and La4Co4Sb have peaks at
the respective temperatures that M${}_{\text{avg}}$/H reaches its greatest
decreasing slope, approximately 20 K below the respective broad M/H maxima.

Figure 5 shows the field dependent magnetization collected at a base
temperature of 2 K for each compound. Corresponding data collected at 300 K is
shown in Figure S5 in the supporting information and is consistent with
paramagnetic behavior of the bulk, La4Co4X. At 2 K, the low-field
magnetization is smallest for all samples when the field is applied along the
b-axis. In the H $\parallel$ a and H $\parallel$ c orientations, the
magnetization isotherms for each material have a near linear field dependence
up to at least 70 kOe, and the samples all show metamagnetic transitions when
H $\parallel$ b. Like the M/H data, the isotherms shown in Figure 5 again
demonstrate that La4Co4Pb behaves qualitatively different than X = Bi and Sb
samples, with a much sharper feature in the M(H) isotherm. In La4Co4Pb, the
b-axis magnetization is extremely flat, and essentially independent of field
up to 35 kOe, upon which it undergoes a step-like transition to a high-field
state in which the magnetization is again nearly independent of field, with a
saturated value of 0.53 $\mu_{\text{B}}$/Co. In La4Co4Bi and La4Co4Sb, the H
$\parallel$ b isotherms also show a field induced transition beginning near
55-60 kOe that is incomplete at our maximum field of 70 kOe. However, the
transition in the X = Bi and Sb compounds appears substantially broadened
compared to that observed in La4Co4Pb. Finally, we note that for La4Co4Sb, the
small upturn in each isotherm below 5 kOe indicates this sample contains a
small quantity of a ferromagnetic impurity (likely La6Co13Sb with TC = 490
K[5]), and a similar feature is observed in data collected at 300 K for this
sample (see Figure S5 supporting information).

Taken together, La4Co4Pb exhibits distinct magnetic behavior from that of
La4Co4Bi and La4Co4Sb. The magnetization of La4Co4Pb, with Curie-Weiss like
M/H in the high temperature paramagnetic regime and a well defined maximum at
the Neel temperature, is typical of an intermetallic antiferromagnet with
three dimensional coupling and ordering. La4Co4Bi and La4Co4Sb differ on both
accounts, showing a broad maximum in M/H instead of a sharp peak and non
Curie-Weiss like temperature dependence in the paramagnetic regime.
Furthermore, at the temperatures and fields applied here, the overall
magnitude of M for X = Bi and Sb members is substantially smaller than that
measured for La4Co4Pb. All of these characteristics are similar to the
behavior of low dimensional systems, such as chains or sheets of coupled
spins.[39, 40]

More generally, the La4Co4X family contains at least three new Co-based
intermetallic compounds in which the Co is moment bearing. Compared to the
rare-earth atoms, which provide robust magnetism associated with their well-
localized 4f orbitals, transition metals are considerably less likely to
possess a magnetic moment in intermetallic compounds. Instead, the stronger
hybridization between d-orbitals (compared to 4f) and the s\- and/or p-like
conduction electrons often leads to electronic delocalization and Pauli-
paramagnetic behavior. In further contrast to the local moment physics found
in rare-earth based materials, the magnetism of metals containing 3d elements
is often itinerant. In these cases, the on-sight Coulomb interaction and
density of states at the Fermi level (E${}_{\text{F}}$) must be sufficient to
spin-slit the bands near E${}_{\text{F}}$, leading to a net magnetic moment
associated with the delocalized conduction electrons.[41, 42]

In La4Co4X it is possible that the bonding within the quasi-2D Co network,
consisting of chains of corner sharing tetradedra linked by corner sharing
triangles, produces flat electronic bands near the Fermi level that favor
itinerant magnetism, similar to what is observed in some metals with an ideal
kagome or pyrochlore sublattice.[25, 43, 28, 27, 20] To explore this
possibility, we calculated the nonmagnetic electronic band structure and
density of states (DOS) of each La4Co4X material, which are shown in Figure 6.
The calculations reveal each compound has relatively flat electronic bands
very close to the Fermi level. Figures 6d-6f show that the flat bands near
E${}_{\text{F}}$ are derived from Co atoms. Whereas the calculations suggest
all three La4Co4X compounds have an enhanced DOS near E${}_{\text{F}}$, both
the band structures and DOS features are different between La4Co4Pb and
La4Co4Pn (Pn = Bi, Sb). The band structures of the two pnictogen containing
compounds are very similar, and feature a very narrow spike in the density of
states at E${}_{\text{F}}$. The bands of La4Co4Pb qualitatively differ, and
the local maxima in the density of states is broader. These differences likely
reflect the greater chemical similarity between La4Co4Bi and La4Co4Sb compared
to La4Co4Pb, and are at least consistent with the experimental transport and
magnentic data, in which behavior of La4Co4Pb is distinct. Finally, we
emphasize that whereas our calculations indeed show flat, Co-based, bands in
each La4Co4X material, at present, we are unable to distinguish between the
cases of trivial narrow bands, coming from poor orbital overlap or topological
flat bands arising from destructive, out of phase hopping within the Co slabs.
We will pursue this distinction in future work, with an eye towards
understanding the conditions under which frustrated lattices which deviate
from the perfect kagome or pyrochlore arrangement may still produce
topological flat bands. In either case, the narrow bands and local maxima in
the density of states near E${}_{\text{F}}$ are both consistent with the
expectations for an intermetallic magnet based on 3d elements.

Overall, our measurements show that La4Co4X is a new family of Co based
itinerant magnets in which quasi-2D slabs of Co produce magnetic behavior that
is likely sensitive to the band filling. It will be worthwhile to pursue
deliberate substitution work, i.e. La4Co4Pb1-xBix to carefully study how the
magnetism changes as a function of the electron count. Furthermore, we intend
to also search for isostructural analogues containing moment bearing rare
earth atoms to study the more complex magnetic phases likely accessible in
such systems.

##  4 Summary and Conclusions

We highlighted how immiscibility can be exploited to target ternary compounds
with low dimensional substructures, such as sheets, chains, or clusters
intrinsically built into their crystal structures. As a demonstration, we
present the discovery of a new family of intermetallic compounds, La4Co4X (X =
Pb, Bi, Sb), that are based on the immiscible pairs Co-Pb and Co-Bi. La4Co4X
adopts a new orthorhombic structure with space group Pbam. The La atoms divide
the crystal structure into spatially separated Co and X sub-units, where the
Co atoms form quasi-2D slabs that span the bc-plane and stack along the
a-axis, where they alternate with slabs of face sharing La9X polyhedra. Co is
moment bearing in each material, and La4Co4Pb behaves as a three dimensional
antiferromagnet with TN = 220 K, whereas La4Co4Bi and La4Co4Sb both show
behavior more consistent with low dimensional magnetic coupling and order
marked by a broad maximum in the magnetization above their respective
transitions at 153 K and 143 K. We also have been able to tentatively identify
isostructural La4Co4Sn in polycrystalline form but have not yet isolated
single phase samples. This work opens the door to a generalizable strategy of
exploiting strongly immiscible pairs to target materials with low dimensional
structural motifs. By further studying the chemistry dictating what third
elements can be introduced to any given antagonistic pair to produce stable
ternary compounds, we believe this concept represents a new design principle
for the discovery of new materials and new structure types favorable for
exhibiting emergent quantum behavior.

##  5 Acknowledgements

Work at Ames National Laboratory was supported by the U.S. Department of
Energy, Office of Science, Basic Energy Sciences, Materials Sciences and
Engineering Division. Ames National Laboratory is operated for the U.S.
Department of Energy by Iowa State University under Contract No. DE-
AC02-07CH11358. All electron microscopy and related work were performed using
instruments in the Sensitive Instrument Facility at Ames National Laboratory.
M.D. was supported by the U.S. Department of Energy, Office of Science, Office
of Workforce Development for Teachers and Scientists (WDTS) under the Science
Undergraduate Laboratory Internships (SULI) program. We especially thank Prof.
Kirill Kovnir for valuable advice and discussions regarding the structure
solutions and refinements.

*corresponding authors’ email<EMAIL_ADDRESS><EMAIL_ADDRESS>
Conflicts of Interest

The authors have no conflicts of interest to declare.

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