|  Combinatorial synthesis of cation-disordered manganese tin nitride MnSnN2
thin films with magnetic and semiconducting properties
---|---
|  Christopher L. Rom,a,b Rebecca W. Smaha,a Celeste L. Melamed,a,c Rekha R.
Schnepf,a,c Karen N. Heinselman,a John S. Mangum,a Sang-Jun Lee,d Stephan
Lany,a Laura T. Schelhas,a,d Ann L. Greenaway,a James R. Neilson,b,e Sage R.
Bauers,a Jennifer S. Andrew,∗a,f Adele C. Tambolia,c
|  Magnetic semiconductors may soon improve the energy efficiency of
computers, but materials exhibiting these dual properties remain
underexplored. Here, we report the computational prediction and realization of
a new magnetic and semiconducting material, MnSnN2, via combinatorial
sputtering of thin films. Grazing incidence wide angle X-ray scattering and
laboratory X-ray diffraction studies show a wide composition tolerance for
this wurtzite-like MnSnN2, ranging from $20\%<$ Mn/(Mn+Sn) $<65$% with cation
disorder across this composition space. Magnetic susceptibility measurements
reveal a low-temperature transition ($T^{\mathrm{*}}\approx 10$ K) for MnSnN2
and strong antiferromagnetic correlations, although the ordering below this
transition may be complex. This finding contrasts with bulk MnSiN2 and MnGeN2,
which exhibited antiferromagnetic ordering above 400 K in previous studies.
Spectroscopic ellipsometry identifies an optical absorption onset of 1 eV for
the experimentally-synthesized phase exhibiting cation disorder, consistent
with the computationally-predicted 1.2 eV bandgap for the cation-ordered
structure. Electronic conductivity measurements confirm the semiconducting
nature of this new phase by showing increasing conductivity with increasing
temperature. This work adds to the set of known semiconductors that are
paramagnetic at room temperature and will help guide future work targeted at
controlling the structure and properties of semiconducting materials that
exhibit magnetic behavior.

##

††footnotetext: a National Renewable Energy Laboratory, Golden, Colorado
80401, United States††footnotetext: b Department of Chemistry, Colorado State
University, Fort Collins, CO, 80523-1872, United States††footnotetext: c
Physics Department, Colorado School of Mines, Golden, Colorado 80401, United
States††footnotetext: d Stanford Synchrotron Radiation Lightsource, SLAC
National Accelerator Laboratory, Menlo Park, California 94025, United
States††footnotetext: e School of Advanced Materials Discovery, Colorado State
University, Fort Collins, CO, 80523-1872, United States††footnotetext: f
Department of Materials Science and Engineering, University of Florida,
Gainesville, Florida 32611, United States††footnotetext: ∗ Email:
<EMAIL_ADDRESS>† Electronic Supplementary Information
(ESI) available

##  1 Introduction

Ternary nitrides are an emerging class of semiconducting materials.1 In
particular, II-IV-N2 compounds offer a highly tunable platform that are
structurally compatible with well-developed III-N technologies (e.g., GaN).2,
3 In the past few years, many new compounds were discovered in this phase
space as thin films (e.g., MgTiN2, ZnMoN2, ZnZrN2),4, 5, 6 bulk solids (e.g.,
CaSnN2, CaTiN2),7, 8 or both (e.g., MgSnN2, MgZrN2).9, 10, 11, 12 These
particular compounds—with Mg^2+, Ca^2+, and Zn^2+ as the divalent cation—have
been investigated for their semiconducting properties. However, using
transition metals with unpaired electrons—like Mn^2+—as the divalent cation
may add technologically useful magnetic properties.

For example, magnetic semiconductors are of interest for applications in
spintronic devices.13 By using both charge and spin, spintronics may enable
more energy efficient computing than traditional electronics, which rely on
charge alone. While these devices have largely relied on ferromagnetic
materials to record information in spins, ferromagnetic devices face the
drawback of memory erasure if accidentally exposed to strong magnetic
fields.14 A breakthrough came in 2016, when Wadley, et al. reported the use of
an antiferromagnetic material (CuMnAs) to read and write information based on
the direction of the anti-aligned spins.15 Basing spintronic devices on
antiferromagnetic materials comes with the benefit of rapid switching and
robust storage, and is a promising direction for increasing the efficiency of
computer processing.16

II-IV-N2 semiconductors with Mn^2+ offer an underexplored platform for these
antiferromagnetic spintronics. Bulk methods have been used to synthesize
MnSiN2 and MnGeN2, and these phases are known to be antiferromagnetic (AFM)
semiconductors with Néel temperatures of $T_{N}=490$ K and 448 K,
respectively.17, 18 These materials take on a wurtzite-derived structure, with
cations and anions in tetrahedral coordination environments. They are
structurally analogous to GaN, suggesting the possibility of AFM spintronic
integration into III-N based device stacks. In this vein, Liu, et al. reported
epitaxial growth of MnGeN2 films by molecular-beam epitaxy and identified
magnetic properties that varied with composition and substrate.19 However,
much remains to be learned about the fundamental chemistry and physics of
these materials.

We note that the tin-containing analogue, MnSnN2, has not yet been reported.
Thus, the discovery of MnSnN2 presents an opportunity to deepen our
understanding of ternary II-IV-N2 nitrides in general as well as the physics
underlying this Mn$M$N2 ($M$ = Si, Ge, Sn) wurtzite family in particular. With
the powerful tool of combinatorial sputtering, we can answer questions like:
How much off-stoichiometry can MnSnN2 accommodate? How does the cation ratio
affect the unit cell? How does cation disorder affect magnetism? To begin
answering these questions, we report on our prediction, synthesis, and
characterization of thin films of MnSnN2, a new paramagnetic semiconductor.

##  2 Methods

###  2.1 Computational methods

First-principles density functional theory (DFT) calculations were performed
using the Vienna Ab initio Simulation Package (VASP).20, 21 Electronic
structure and band gap calculations were performed using the GW approximation
22 as described previously.23 Calculations were spin polarized to account for
the expected magnetic moment of Mn. Computational results and details are
available in the NREL Materials Database (https://materials.nrel.gov/), with
ID 287033 (GW) and 287034 (DFT).

###  2.2 Synthesis

The Mn-Sn-N phase space was explored using combinatorial radiofrequency (RF)
cosputtering methods. Libraries were deposited using an AJA International ATC
2200-V sputtering chamber. The chamber base pressure was between 2 and
$5\times 10^{-8}$ Torr prior to depositions. During depositions, the pressure
was maintained at $12\pm 1$ mTorr with 15 sccm N2 and 5 sccm Ar. The N2 was
activated by passing the gas through an electron-cyclotron resonance plasma
source set at 150 W.

To create compositional gradients within each 2" x 2" sample library, metals
were cosputtered from 3" diameter Mn and Sn targets aimed towards the
substrate (Kurt J. Lesker; 99.95% and 99.998%, respectively). The substrate
was held stationary during deposition, and the relative position of the
sputtering targets (180 ° relative to one another in the plane of the
substrate) resulted in 1-dimensional gradients in composition across the
substrate. Prior to each deposition, the targets were presputtered for 30 min
with the shutters closed. Subsequently, the shutters were opened and
deposition was conducted for 120 min. The sample platens were heated with lamp
heaters during the depositions, with substrate temperature denoted here as
$T_{\text{dep}}$. This temperature was calibrated without sputtering, and
therefore provides a lower bound for the sample temperature, as the impact of
sputtered elements raises the substrate temperature. Depositions were
conducted between $T_{\text{dep}}=25$ ℃ nominally (ambient conditions) and 275
℃. Cation composition was tuned by varying magnetron power, with Mn held at
108 W and Sn at either 36 W or 48 W. Most substrates were p-type Si wafers
with native surface oxide, although select samples were grown on Eagle Corning
XG glass (EXG, optically transparent and electronically insulating) and p-type
Si with 100 nm of thermal oxide (electronically insulating) for certain
property measurements as denoted in the text.

###  2.3 Characterization

Each 2" $\times$ 2" sample library was mapped as a $4\times 11$ grid following
the standard combinatorial mapping workflow at the National Renewable Energy
Laboratory (NREL).24 Experimental data used by this study have been analyzed
using the COMBIgor software package24 and are publicly available in the high-
throughput experimental materials database at https://htem.nrel.gov.25.

High-throughput X-ray diffraction (XRD) mapping was conducted using a Bruker
D8 Discover (Cu K$\alpha$ radiation) equipped with an area detector. High
resolution synchrotron grazing incidence wide angle X-ray scattering (GIWAXS)
measurements were conducted on select samples at beamline 11-3 of the Stanford
Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory with
$\lambda=0.9744$ Å, a 3° incident angle, and spot size of 50 microns vertical
$\times$ 150 microns horizontal. GIWAXS images were integrated with GSAS-II.26
LeBail refinements were used to extract lattice parameters for MnSnN2 in the
$P6_{3}mc$ space group, performed with TOPAS Academic v6.27. Peak broadening
was modeled via the Thompson-Cox-Hastings pseudo-Voigt “TCHZ” peak type as
implemented in TOPAS. Reference patterns were generated using VESTA for visual
comparisons.28 As the MnSnN2 phase has not been previously reported, we
modeled the structure as follows: starting from the wurtzite AlN structure,29
we replaced Al^3+ with a 1:1 mixture of Mn^2+ and Sn^4+ and shifted the unit
cell parameters to match the LeBail refinement for the near-stoichiometric
MnSnN2 pattern (51% Mn/(Mn+Sn)). Those refined cell parameters are $a=3.441$ Å
and $c=5.562$ Å (Table S1).

Compositional analysis was performed with X-ray fluorescence (XRF) and
Rutherford Back-Scattering (RBS) methods. Metal ratios were mapped using a
Fischer XDV-SDD XRF with a Rh source and a 3 mm diameter spot size. The
measurements were performed at ambient pressure with an exposure time of 60 s
for each measurement. Nitrogen and oxygen ratios for select samples were
quantified with RBS. RBS was run in a 168° backscattering configuration using
a model 3S-MR10 RBS system from National Electrostatics Corporation with a 2
MeV He+ beam energy. Samples were measured for a total integrated charge of
160 uC. RBS spectra were modeled with the RUMP software package.30 Agreement
on metal ratios between XRF and RBS are shown in Figure S8. A representative
RBS spectrum and fit are shown in Figure S9.

Film thicknesses were measured using a Dektak profilometer and were
approximately 200 to 300 nm following 2 h growth times. Cross-sectional
scanning electron microscopy (SEM) was conducted for select samples on a
Hitachi S-4800 SEM operating at 3 keV accelerating voltage and 8 mm working
distance to corroborate film thickness measurements and identify film
morphology.

DC magnetic susceptibility was measured in a Quantum Design Magnetic
Properties Measurement System (MPMS3) via vibrating sample magnetometry. The
films were measured from 2 K to 300 K under applied fields from -7 to +7 T,
with the applied field parallel to the plane of the film. The measured samples
were 5 mm $\times$ 5 mm squares from a sample library deposited at
$T_{\text{dep}}=225$ ℃ on a substrate of 100 nm of SiO2 on pSi(100). Each
square was characterized by XRF and synchrotron GIWAXS to ensure magnetic
properties were accurately correlated with composition and structure. To
isolate the signal of the films, a bare substrate (100 nm of SiO2 on pSi(100))
was also measured and subtracted (Figure S11 and S12). Additional analysis
details are in the Electronic Supplementary Information.

Room temperature conductivity was measured using a custom built collinear
four-point probe instrument by sweeping current between the outer two pins
while measuring voltage between the inner pins (1 mm between each pin).
Conventional geometric corrections were applied to convert the measured
resistance into sheet resistance and then conductivity.31 Error bars are
propagated from sheet resistance error (from I-V curve fits) and an estimated
5% relative error in profilometry thickness measurements.

Temperature-dependent electrical conductivity was measured using a Lake Shore
Cryotronics Model 8425. A 5 mm $\times$ 5 mm square was scribed out of a
library deposited on EXG at approximately 200 ℃. Although the deposition
temperature on EXG was not calibrated, XRD patterns appeared similar to those
deposited on at a calibrated $T_{\text{dep}}=225$ ℃ on silicon (i.e., XRD
showed only MnSnN2 with no signs of Sn or Mn3N2 decomposition products).
Indium contacts were pressed into the square near the corners of the film, and
temperature-dependent sheet resistance was measured from 104 K to 298 K.
Conductivity was calculated using the profilometry-measured thickness of 260
nm.

Spectroscopic ellipsometry was performed on a single row of a select sample
library (11 points per row) using a J.A. Woollam Co. M-2000 variable angle
ellipsometer. CompleteEASE software (version 6.56) was used to do the
modeling. The data were modeled by fitting the imaginary part of the
dielectric function with a combination of one Tauc-Lorentz, one Gaussian, and
one Drude oscillator.

##  3 Results and Discussion

###  3.1 Computational findings

Figure 1: A) A psuedobinary phase diagram of the space from Sn3N4 to Mn3N2 at
$T=0$ K. The solid blue trace shows the hull under activated nitrogen
conditions ($\mu_{\mathrm{N}}=+1$ eV/atom), as occurs in plasma synthesis.32,
33 Cation-ordered MnSnN2 is more stable than a linear combination of these two
binary nitrides. B) Total density of states calculated for cation-ordered
MnSnN2 in the $Pna2_{1}$ space group. The calculated band gap ($E_{g}$) is
1.22 eV, shown in grey. N-p and Mn-d states comprise the valence band, while
the conduction band consists of Sn-s and N-p states.

To investigate the stability of a possible MnSnN2 phase, we performed density
functional theory (DFT) calculations. We hypothesized that this phase would
form in the wurtzite-derived structure and therefore constructed a cation-
ordered MnSnN2 structure in the orthorhombic space group $Pna2_{1}$. DFT
calculations suggest that this cation-ordered orthorhombic MnSnN2 is slightly
metastable (+0.038 eV/atom above the hull, Figure 1A). Therefore, a
traditional bulk synthetic approach of reacting Mn and Sn under 1 atm of N2
would likely fail. However, sputtering in an activated nitrogen atmosphere
(i.e., a N2 plasma) stabilizes metastable phases (e.g., Cu3N and Sn3N4) by
increasing the chemical potential of nitrogen up to +1 eV/atom.32, 34 Figure
1A shows that while MnSnN2 is metastable with respect to Sn+N2 and Mn3N2, the
phase is stable with respect to Sn3N4 and Mn3N2. Therefore, the nitrogen
plasma environment that rendered Sn3N4 synthetically accessible should also
stabilize MnSnN2.

Our calculations also suggest that MnSnN2 should exhibit semiconducting
properties and antiferromagnetic behavior. The calculated bandgap is 1.22 eV
(Figure 1B), with a density of states (DOS) effective hole mass of
$m_{h}^{*}=5.9m_{0}$. The band effective mass is $m_{e}^{*}=0.22m_{0}$. The
low electron mass is remarkable for a transition metal compound (Mott
insulator), but not uncommon for Mn^2+.35, 36 The local magnetic moment is
calculated as $\mu_{\mathrm{eff}}=4.3\leavevmode\nobreak\ \mu_{\mathrm{B}}$
per Mn. This $\mu_{\mathrm{eff}}$ is less than the spin-only value expected
for high-spin Mn^2+ ($S=\frac{5}{2}$;
$\mu_{\mathrm{eff}}=5.9\leavevmode\nobreak\ \mu_{\mathrm{B}}$), indicating
that some spin density resides on the nitride. The four Mn atoms per cell
exhibit antiferromagnetic order in the ground state, resulting in a net moment
of 0 $\mu_{\mathrm{B}}$ per cell.

###  3.2 Synthesis and structure of MnSnN2 thin films

Figure 2: A) The unit cell of MnSnN2 in the experimentally observed cation-
disordered hexagonal structure ($P6_{3}mc$), and the B) computationally
predicted ordered orthorhombic structure ($Pna2_{1}$). C) Synchrotron GIWAXS
data of samples with Mn/(Mn+Sn) = 50% deposited at various temperatures
($T_{\mathrm{dep}}$) are shown in the bottom box, with reference patterns
shown in the top box. The optimal deposition temperature for single phase
crystalline MnSnN2 ($P6_{3}mc$) is $T_{\mathrm{dep}}=225$ ℃. The ordered
MnSnN2 ($Pna2_{1}$) phase is not observed.

####  3.2.1 Stability and cation disorder

We synthesized MnSnN2 films using combinatorial cosputtering and assessed the
crystallinity using X-ray diffraction techniques (synchrotron GIWAXS and
laboratory XRD). Synchrotron GIWAXS of stoichiometric films shows that MnSnN2
crystallizes in a phase-pure cation-disordered wurtzite structure at
$T_{\mathrm{dep}}=225$ ℃ (Figure 3.2A,C). The absence of supercell reflections
(peaks near $Q=1.5$ Å-1) of the $Pna2_{1}$ space group indicate that long-
range ordering of cations in MnSnN2 does not occur in these samples (Figure
3.2B,C). Above $T_{\mathrm{dep}}=225$ ℃, Sn and Mn3N2 are also observed in the
diffraction patterns, while below 225 ℃, the material is poorly crystalline.
These trends are true across the compositional gradient (Figure S1). This
relatively low decomposition temperature ($T_{\mathrm{dep}}\sim 250$ ℃)
suggests that MnSnN2 is less stable than related ternary nitrides like MgSnN2
(stable up to 500 ℃ in the same deposition chamber)9 and ZnSnN2 (stable up to
340 ℃).37 Annealing experiments under flowing N2 suggest that, once deposited,
MnSnN2 films are stable up to $T_{\mathrm{anneal}}=300$ ℃, but decomposition
is still observed by $T_{\mathrm{anneal}}=400$ ℃ (Figure S6).

We conducted these annealing experiments in an attempt to induce cation
ordering,38 but saw no evidence of cation order below the decomposition
temperature of $T_{\mathrm{anneal}}=400$ ℃ (Figure S6). By the methods applied
here, long-range cation ordering of MnSnN2 appears inaccessible. In contrast,
the bulk synthesis methods employed for MnSiN2 and MnGeN2 yielded cation-
ordered phases (space group $Pna2_{1}$).17, 18 The prior report on thin films
of MnGeN2 did not assess cation ordering via diffraction.19

The lack of long-range cation ordering exhibited by MnSnN2 is common in
sputtered films. MgSnN2 and ZnSnN2 thin films are both cation disordered,9, 37
and ZnGeN2 forms as a cation-disordered thin film but crystallizes in the
ordered $Pna2_{1}$ structure when synthesized by bulk ammonolysis.39, 40 The
high effective temperature of the sputtering synthesis technique, along with
the entropic benefit of disorder, can stabilize a disordered structure by
approximately 0.1 eV/atom relative to the DFT-predicted ordered structures.6
II-Sn-N2 phases in particular have a tendency for disorder because Sn^4+ is
closer in ionic radius (0.55 Å) to the divalent cations—Mn^2+ (0.66 Å), Mg
(0.57 Å), and Zn (0.60 Å)—than the other main group elements—Ge^4+ (0.39 Å)
and Si^4+ (0.26 Å).9, 41, 42 This size similarity leads to cation disorder
even in bulk MgSnN2.10 While short-range ordering is possible even with the
absence of a supercell reflection and may impact properties,38, 43, 44 such
analysis is beyond the scope of this study.

####  3.2.2 Compositional and structural trends

Figure 3: A) Synchrotron GIWAXS data of select samples from a combinatorial
library row deposited at $T_{\text{dep}}=225$ ℃ shows that reflections can be
indexed to the $P6_{3}mc$ space group, indicative of a cation-disordered
wurtzite structure. B) Magnified $Q$ range of the diffraction patterns,
showing the shift in the (002) reflection with changing Mn/(Mn+Sn). C) The c
axis contracts relative to the a axis with increasing Mn content, which causes
the $c/a$ ratio to decrease. The vertical dotted line indicates the
composition of stoichiometric MnSnN2 and the horizontal dashed line indicates
the ideal c/a ratio of the wurtzite structure ($\sqrt{8}/3$). Fits to the data
are shown in Figure S1.

Despite this low thermal stability, the wurtzite structure of MnSnN2
accommodates a wide range of cation off-stoichiometry ($18\%<$ Mn/(Mn+Sn)
$<65\%$) when deposited at the optimal temperature of $T_{\text{dep}}=225$ ℃.
Within the composition range of Mn/(Mn+Sn) = 38% to 65%, all reflections in
the GIWAXS patterns can be indexed to $P6_{3}mc$ symmetry (Figure 3.2.2). In
laboratory XRD, we observe MnSnN2 down to Mn/(Mn+Sn) = 18% (the Mn-poor limit
of the library, Figure S7). However, this may not be the true lower
compositional limit of this phase. In contrast, we have determined that the
upper limit of Mn content in MnSnN2 by diffraction is Mn/(Mn+Sn) $\approx
65\%$. At high Mn content ($>65$%), the lattice parameters of MnSnN2 plateau
and the uncertainty in the refinement grows (Figures 3.2.2C and S3). Broad
peaks that index to Mn3N2 also appear, indicative of a two-phase region. The
only other known Mn-Sn-N ternary compound is the antiperovskite Mn3SnN
(Mn/(Mn+Sn) = 75%),45, 46 which is more Mn-rich than our depositions and does
not appear in our diffraction patterns.

This wide range of off-stoichiometry can make naming ternary nitrides
difficult, as noted by Woods-Robinson, et al.6 A precise formula would be
MnxSn1-xN1-yOy, where $x$ is the cation fraction of Mn/(Mn+Sn) and $y$ is the
amount of oxygen substitution for nitrogen (estimated to be $y\approx 0.2$ by
RBS, Figure S8B). The oxygen likely originates from oxide contamination of the
Mn sputter target, and either charge balances with Mn^2+ via (MnSnN2)1-x(MnO)x
or with Mn^3+ via Mn1+xSn1-xN2-xOx. For simplicity, we use “MnSnN2” to refer
to the cation-disordered wurtzite-like phase across the whole composition
range and specify a cation fraction as a percentage of Mn/(Mn+Sn) where
relevant (i.e., stoichiometric MnSnN2 has Mn/(Mn+Sn) = 50%).

Figure 4: Cross-sectional SEM micrograph showing columnar grains typical of
sputtered films. This representative image shows a 50% Mn/(Mn+Sn) film
deposited on a silicon substrate with 100 nm of SiO2. The scale bar is 300 nm.

The c/a ratio of MnSnN2 varies with composition, but deviates only slightly
from the ideal wurtzite value of 1.633 (Figure 3.2.2C). For stoichiometric
MnSnN2, c/a = $5.562$ Å / $3.441$ Å $=1.616$, which—although smaller than the
ideal wurtzite—is larger than MgSnN2 (1.598).9 The change in c/a is driven
primarily by a change in the c lattice parameter while the a lattice parameter
remains largely unchanged (Figure S3A), suggesting that the tetrahedra may be
distorting along the c axis. That shift may be caused by metal vacancies, a
change in electron count of the metals, oxygen incorporation (observed by RBS,
Figure S8B), or some combination thereof as the system shifts to maintain
charge neutrality across this compositional range. However, since atomic
positions cannot be resolved from the synchrotron GIWAXS data sets, we cannot
more precisely identify the cause of this distortion.

To probe the microstructure of the film, we turn to electron microscopy and
diffraction analysis. SEM shows columnar grain morphology that is typical for
sputtered films (Figure 4). Diffraction images display some signs of texturing
(Figure S1). The (002) reflection appears towards the edges of the integration
window, suggesting the {002} planes are oriented normal to the plane of the
substrate. In contrast, the (100) reflection appears strongly in the center
axis of the frame, 90 ° relative to the (002) reflection, and diminishes in
intensity towards the edge of the integration window, suggesting preferential
growth along the [100] direction (Figure 3.2.2B). This finding stands in
contrast to typical wurtzite films, which tend to grow with (002) preferential
orientation.47, 37

###  3.3 Magnetic properties

Given the presence of tetrahedrally coordinated Mn^2+ (expected:
$S=\frac{5}{2}$ and $\mu_{\mathrm{eff}}=$5.9 $\mu_{\mathrm{B}}$) cations in
stoichiometric MnSnN2, as well as the possible presence of Mn^3+ (expected:
$S=2$ and $\mu_{\mathrm{eff}}=$4.9 $\mu_{\mathrm{B}}$) in Mn-rich
compositions, DC magnetic susceptibility was employed to investigate the
magnetic response of several thin films with a range of compositions 42%
$\leq$ Mn/(Mn+Sn) $\leq$ 56%. We cannot independently determine the film mass,
so susceptibility ($\chi$) was calculated from the raw moment data using the
same estimated mass (0.04 mg) for each sample. Uncertainty in film thickness,
composition, and porosity may introduce substantial error in the calculated
mass of the films, and by extension, the absolute value of $\chi$. In
addition, each measured sample contains a compositional gradient of
approximately 4% Mn/(Mn+Sn). Despite these caveats, errors from sample to
sample are likely systematic, allowing us to identify trends in magnetism
related to composition. Additional details and discussion are in the
Electronic Supplementary Information (Section 3).

Figure 5: A) Zero-field-cooled (ZFC) DC magnetic susceptibility ($\chi$) as a
function of temperature measured in an applied field of $\mu_{0}H=5$ T, show a
peak in $\chi$ at $T^{\mathrm{*}}\approx 10$ K across a range of Mn contents.
The inset shows $\chi^{-1}$ as a function of temperature with a diamagnetic
correction $\chi_{0}=-5.5\times 10^{-3}$ emu Oe-1 mol-1 for 51% Mn/(Mn+Sn).
The dashed trace shows the Curie-Weiss fit from 150 K to 300 K. B) Extracted
transition temperatures ($T^{\mathrm{*}}$, left axis) and Weiss temperatures
($\Theta_{CW}$, right axis) as a function of increasing Mn content. C) ZFC and
field-cooled (FC) DC magnetic susceptibility measurements at lower applied
field of $\mu_{0}H=0.1$ T show bifurcation below the transition temperature.

As shown in Figure 5A, zero-field-cooled (ZFC) temperature-dependent
susceptibility measurements performed at high applied field exhibit peaks near
$10$ K, indicating a magnetic transition ($T^{\mathrm{*}}$). The
$T^{\mathrm{*}}$, extracted as the temperature where $\chi$ reaches a maximum,
increases slightly with increasing Mn content, from $T^{\mathrm{*}}\approx 6$
K at 42% Mn to $T^{\mathrm{*}}\approx 12$ K at 56% Mn (Figure 5B). Curie-Weiss
fits in the paramagnetic region 150–300 K (see inset of Figure 5A and Figure
S13) show large, negative Weiss temperatures ($\Theta_{CW}$, Figure 5B),
consistent with overall antiferromagnetic (AFM) correlations. However, the
uncertainties in background subtraction and in the calculation of $\chi$
inhibit meaningful extraction of Curie constants and effective moments from
these fits (see Electronic Supplementary Information Section 3). The magnitude
of $\chi$ decreases with increasing Mn fraction, which would be consistent
with Mn^3+ replacing Mn^2+. However, we are not able to detect a significant
amount of Mn^3+ in XANES measurements (Figure S10). This apparent shift in
$\chi$ may therefore be an artifact of the uncertainty in film mass.
Measurements in lower applied field ($\mu_{0}H=0.1$ T; Figure 5C) show clear
bifurcation in ZFC and field-cooled (FC) susceptibility below the transition
temperature, which is consistent with either long-range AFM order or a spin-
glass ground state.

Figure 6: Background-subtracted isothermal magnetization measurements of near-
stoichiometric MnSnN2 at $T=2$ K (solid circles) and $T=40$ K (open circles).
The inset details the small net ferromagnetic moment at $T=2$ K and the
absence of such net moment at $T=40$ K.

The magnetic moment measured as a function of applied field at $T=2$ K (below
the transition at $T^{\mathrm{*}}\approx 10$ K) is consistent with AFM
correlations, shown for Mn/(Mn+Sn) = 51% in Figure 6 and for the remaining
samples in Figure S3.2. In the $T=2$ K data of all samples measured, there is
small but observable hysteresis with a minute net moment at zero field (inset
of Figure 6). This net moment may originate from spin canting, uncompensated
moments from defects, the Dzyaloshinsky-Moriya interaction, or slow magnetic
relaxation of a spin glass state. Similar net moments were observed in thin
films of MnGeN2 and were attributed to cation site disorder.19 Above
$T^{\mathrm{*}}$, (e.g., at $T=40$ K), the linear behavior is consistent with
paramagnetism. The traces do not plateau at high fields, indicating that the
magnetic moment is not saturated at $\mu_{0}H=\pm 7$ T.

Overall, the susceptibility measurements and Curie-Weiss fit results point to
clear, strong AFM correlations in MnSnN2 with a transition at approximately
$T^{\mathrm{*}}\approx 10$ K. This transition shifts as a function of
Mn/(Mn+Sn). We are unable to determine whether the ground state below this
transition temperature is long-range AFM order or spin glass.48 If the ground
state is an ordered AFM, it would likely be complex, especially given the
cation disorder and compositional gradients in these samples. The small net
moment observed at $T<T^{\mathrm{*}}$ may imply the presence of spin canting,
Dzyaloshinsky-Moriya interactions, or uncompensated residual spins, as
mentioned above, and the ZFC-FC splitting suggests a relaxation process.
However, the Mn content in these samples (41–56%) is well above the
percolation threshold (20% for this hexagonal close packed metal
sublattice),49 so the AFM correlations likely extend throughout the
crystalline domains. To probe the possibility of spin glass behavior, we
performed AC susceptibility measurements, but the signal was below the
instrumental sensitivity limit.

The low-temperature magnetic transition ($T^{\mathrm{*}}\approx 10$ K) of the
cation-disordered MnSnN2 thin films examined here contrasts starkly with the
high-temperature AFM ordering of cation-ordered MnGeN2 ($T_{N}=448$ K) and
MnSiN2 ($T_{N}=490$ K) synthesized as bulk single crystals.18, 17 To explain
these differences, we posit that cation ordering is an important factor in
determining the energy scale of magnetic order in this family of wurtzite
ternary nitrides. That influence may be exerted via magnetic frustration, if
the ground state is AFM order: the tetrahedrally-based lattice of Mn^2+,
together with the large ratio of the Weiss temperatures
($\Theta_{CW}\approx-200$ K) and the low transition temperatures
($T^{\mathrm{*}}\approx 10$ K) of these films, suggest the presence of a high
degree of magnetic frustration.48, 50 This is not unexpected, as triangular-
based lattices are one of the most common hosts of geometric frustration, and
frustration also often arises from cation disorder.51, 52 In addition,
frustration was observed even in the cation-ordered MnSiN2.17 Should bulk
powders or single crystals of MnSnN2 be synthesized, comparing their magnetic
properties and defect chemistry with the thin film behavior observed here
would be illuminating.

###  3.4 Optoelectronic properties

Figure 7: A) Room temperature conductivity measurements performed in a
collinear four-point probe configuration show that conductivity initially
decreases slightly with increasing Mn content, then increases rapidly above
60% Mn/(Mn+Sn). B) Conductivity increases as a function of temperature,
confirming the semiconducting nature of MnSnN2 films. The anomaly in slope
near 250 K is an instrumental artifact. C) Optical ellipsometry measurements
indicate a gradual absorption onset, with minima in the absorption
coefficients near 1 eV.

Room temperature conductivity measurements show that the MnSnN2 films exhibit
conductivity on the order of 20 S/cm (Figure 7A). Conductivity decreases
slightly as Mn content increases from 38% to 60% Mn/(Mn+Sn) but then increases
as a metallic secondary phase (Mn3N2) grows in. This increase in conductivity
for Mn/(Mn+Sn) $\geq 60$% suggests that the true single-phase region may have
a lower Mn limit ($\sim$60% maximum) than detected by GIWAXS ($\sim$65%
maximum). For the Mn/(Mn+Sn) $<60$% region, conductivity is likely tuned by
carrier concentration. Prior work on ZnSnN2 demonstrated that a similar trend
(decreasing conductivity with increasing Zn) was correlated with a decrease in
carrier concentration (while mobility was unaffected).37 In both cases (MnSnN2
and ZnSnN2), the conductivity reaches a minimum in the Sn-poor region (i.e.,
Zn or Mn $\approx$60%), as the excess Zn or Mn compensate for oxygen
substitution on nitrogen sites. At Mn/(Mn+Sn) = 60%, the charge-balanced
chemical formula is Mn_0.6Sn_0.4N_0.8O_0.2 (assuming Mn^2+ and Sn^4+),
consistent with the oxygen content identified by RBS (Figure S8B).

Temperature-dependent conductivity measurements performed in Van der Pauw
geometry on films grown on insulating EXG glass show that the conductivity
increases with increasing temperature, confirming semiconducting behavior in
MnSnN2 (Figure 7B). Increasing conductivity with increasing temperature
suggests that mobile carriers are thermally activated (i.e., a bandgap is
present in the material). However, the conductivity is only weakly dependent
on temperature, with the conductivity at 298 K only 30% greater than the
conductivity at 104 K.

Ellipsometry measurements and modeling show that MnSnN2 has a gradual
absorption onset near 1 eV (Figure 7C). Overall, the absorptivity increases
slightly with increasing Mn content, although the absorption onset stays
relatively constant. This absorption onset may be attributable to a bandgap,
as the bandgap for this material is expected to be lower than the
experimentally reported bandgaps in cation-ordered MnSiN2 (3.5 eV) and MnGeN2
(2.5 eV).53 The DFT-calculated bandgap for cation-ordered MnSnN2 is 1.22 eV
(Figure 1B), and the cation-disorder of the material synthesized here tends to
lower the bandgap relative to cation-ordered analogues.38 However, Mn^2+ d-d
transitions are also known to occur in this energy region,17 and
unfortunately, this technique cannot distinguish between single-ion electronic
transitions and bandgap excitations. We also attempted UV-vis measurements of
films deposited on transparent substrates to verify the optical absorption
onset, but the onset was below the limit of the instrument (Figure S4).
Regardless, the optoelectronic and magnetic behavior of this new compound
present opportunities for further study.

##  4 Conclusions

We have synthesized thin films of a new ternary nitride material, MnSnN2,
using combinatorial co-sputtering. The material crystallizes in a cation-
disordered wurtzite-like structure common for II-IV-N2 semiconductors with
lattice parameters $a=3.441$ Å and $c=5.562$ Å for the stoichiometric
material. MnSnN2 exhibits semiconducting properties, including a bandgap near
1 eV—the lowest bandgap yet observed in the MnMN2 wurtzite family.53 We
observe a magnetic transition in cation-disordered MnSnN2 at low temperature
($T^{\mathrm{*}}\approx$10 K) consistent with AFM correlations, which
contrasts dramatically with the high AFM ordering temperatures of cation-
ordered MnGeN2 and MnSiN2 ($T_{N}=448$ K and 490 K, respectively).17, 18 These
discoveries suggest that future work could use composition and cation disorder
in the Mn-$M$-N2 ($M$ = Si, Ge, Sn) system to tune both semiconducting and
magnetic properties.

## Author Contributions

J.S.A. and A.C.T. conceived of the project. J.S.A. and C.L.R. conducted
depositions, XRF, and XRD measurements. C.L.R. and R.W.S conducted magnetism
and electronic conductivity measurements. R.R.S. and C.L.M. conducted
ellipsometry measurements. L.T.S. and C.L.R. conducted synchrotron GIWAXS
measurements. K.N.H. conducted RBS analysis. J.S.M. conducted microscopy.
S.-J.L. conducted XAS measurements. S.L. conducted DFT calculations. C.L.M.
and A.L.G. aided in synthesis and maintenance of the deposition chamber.
C.L.R. and R.W.S. wrote the majority of the manuscript with guidance from
S.R.B., J.R.N., A.C.T., and J.S.A as well as feedback from all other authors.

## Conflicts of interest

There are no conflicts of interest to declare

## Acknowledgements

This work was authored in part by the National Renewable Energy Laboratory
(NREL), operated by Alliance for Sustainable Energy, LLC, for the U.S.
Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Primary
funding was provided by the U.S. Department of Energy, Office of Science,
Basic Energy Sciences, Materials Sciences and Engineering Division. C.L.R.
acknowledges support from the DOE Science Graduate Research Program (SCGSR).
R.W.S. acknowledges support from the Director’s Fellowship within NREL’s
Laboratory Directed Research and Development program. Use of the Stanford
Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is
supported by the U.S. Department of Energy, Office of Science, Office of Basic
Energy Sciences under Contract No. DE-AC02-76SF00515. We thank the Analytical
Resources Core at Colorado State University for instrument access and
training. We thank Charles Titus and Andriy Zakutayev for helpful
conversations. The views expressed in the article do not necessarily represent
the views of the DOE or the U.S. Government.

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## †ELECTRONIC SUPPLEMENTARY INFORMATION

###### Contents

  1. 1 Introduction
  2. 2 Methods
    1. 2.1 Computational methods
    2. 2.2 Synthesis
    3. 2.3 Characterization
  3. 3 Results and Discussion
    1. 3.1 Computational findings
    2. 3.2 Synthesis and structure of MnSnN2 thin films
      1. 3.2.1 Stability and cation disorder
      2. 3.2.2 Compositional and structural trends
    3. 3.3 Magnetic properties
    4. 3.4 Optoelectronic properties
  4. 4 Conclusions
  5. S1 Structural characterization
  6. S2 Compositional characterization
    1. S2.1 RBS
    2. S2.2 XANES
  7. S3 Magnetic properties
    1. S3.1 Background subtraction and data analysis
    2. S3.2 Additional data
  8. S4 Optoelectronic measurements

##  S1 Structural characterization

Synchrotron grazing incidence wide angle X-ray scattering (GIWAXS) reveals the
polycrystalline nature of the films deposited on silicon with a 100 nm surface
layer of SiO2 (Figure S1). Hot pixels were manually masked when identified to
avoid spurious peaks in the integrated patterns. Broad and weak reflection
spots are visible and attributable to silicon, but these spots were not masked
owing to significant overlap with the powder rings. These spots contribute to
elevated background scattering in the integrated diffraction patterns. Full
LeBail fits for the patterns shown in Figure 3.2.2 are shown in Figure S1.
Figure S3A shows the extracted hexagonal lattice parameters and Figure S3B
show the fit residuals.

Figure S1: A representative 2-D diffraction image from a GIWAXS measurement at
SSRL beamline 11-3. Hot pixels are masked in red to avoid background
contribution to the integrated diffraction pattern. The first six reflections
of MnSnN2 are also labeled. Strong spots from the Si substrate (331) planes
are visible near the edge of the frame. Figure S2: A) Full patterns of the
GIWAXS data presented in Figure 3.2.2 of the main text. VESTA-generated
reference patterns are shown at the top. The main reflections match the
$P6_{3}mc$ space group of the cation-disordered wurtzite structure type
MnSnN2. Evidence of cation ordering is not observed in diffraction. At Mn-rich
compositions ($\geq 69$ %), broad peaks corresponding to Mn3N2 appear. LeBail
refinements were conducted on these patterns to extract lattice parameters of
the wurtzite phase MnSnN2. Black points are data, orange traces are fits, and
blue traces are difference curves. B) Focused $Q$-range of fits to the first
three wurtzite reflections, corresponding to Figure 3.2.2B of the main text.
Although the peak broadness is poorly captured owing to anisotropic
broadening, the peak positions are relatively well described by the fit.
Figure S3: A) Extracted lattice parameters $a$ (green circles) and $c$ (gold
squares) from LeBail refinements used to calculate the $c/a$ ratio in Figure
3.2.2C. Error bars are within the size of the markers. B) Residuals from the
LeBail refinements presented in Figure S1. The modeled $P6_{3}mc$ phase fits
best with the slightly Mn-rich composition. Anisotropic peak broadening
worsens the fit in the Mn-poor region. A poorly crystalline Mn3N2 secondary
phase, which was not included in the model, worsens the fit in the Mn-rich
region.

Fitting residuals were minimized for the patterns with slight excess Mn, with
worsening fits in the Mn-poor and Mn-rich regions (Figure S3B). Fit residuals
also increase in the Mn-rich region, here owing to the growth of a secondary
Mn3N2 phase that is visible as broad peaks but was not modeled. Some of this
broadening may also be due to scattering from the silicon substrate, which may
vary from sample to sample depending on the exact orientation of the
substrate. Lastly, some degree of texturing is observed (Figure S1), which
affects the relative heights of integrated peaks.

Figure S4: GIWAXS patterns were collected on select points from a variety of
libraries. Manual inspection revealed the predominance of a single phase,
MnSnN2 up to 225 ℃. However, at higher temperatures, the MnSnN2 phase begins
decomposing into Mn3N2 and Sn. The coexistence of all three suggests non-
equilibrium conditions. Figure S5: GIWAXS pattern for a sample at 68%
Mn/(Mn+Sn) and $T_{\mathrm{dep}}$ = 100 ℃ showing a rocksalt
($Fm\overline{3}m$) crystal structure ($a=4.378$ Å).

A major finding in the thin film synthesis of MgSnN2 by Greenaway et al. was a
wurtzite-to-rocksalt structural transition, and we find a small amount of
evidence that a similar phenomenon occurs in the MnSnN2 system (Figure S1). In
our studies of MnSnN2, a single synchrotron GIWAXS pattern revealed a rocksalt
type structure at Mn/(Mn+Sn) = 68%. The rocksalt appears under similar
conditions needed for rocksalt MgSnN2 (Sn poor, low $T_{\mathrm{dep}}$).
However, the refined lattice parameter for our MnSnN2 rock salt ($a=4.378$ Å)
is very similar to the rocksalt lattice parameter for MnO ($a=4.446$ Å); the
ternary is 1.5% smaller than the binary. In contrast, rocksalt MgSnN2
($a=4.483$ Å) is 6.3% larger than MgO ($a=4.217$ Å). The presence of a
rocksalt polymorph in the Mn-Sn-N system may merit further study.

Rapid thermal annealing experiments revealed that the MnSnN2 phase is stable
against decomposition up to at least $T_{\mathrm{anneal}}=300$ ℃ for 30
minutes (Figure S6). At $T_{\text{anneal}}=400$ ℃, the ternary phase begins
decomposing to Sn, Mn4N, and N2. This stability up to 300 ℃ suggests either i)
that cation-disordered MnSnN2 is more thermodynamically stable that predicted
for the cation-ordered phase (+0.038 eV/atom above the hull) or ii) that
decomposition up to 300 ℃ is kinetically slow.

Figure S6: Rapid thermal annealing experiments show that a library row
synthesized at $T_{\text{dep}}=225$ ℃ is stable up to an annealing temperature
of 300 ℃. Annealing experiments were conducted on individual rows from a
library, first heated to 100 ℃ to drive off adsorbed water, then heated to the
$T_{anneal}$ temperature for a 30 min anneal. Heating ramps for each step were
conducted in 1 minute, and cooling occurred by turning the power to the
furnace off. The sample was enclosed in flowing N2 for the duration of the
experiment.  Figure S7: A library deposited under Mn-poor conditions at
$T_{\text{dep}}=225$ ℃ show the continued presence of wurtzite peaks. A
structural change to the spinel Sn3N4 is not observed, although prior
sputtering syntheses of this binary phase revealed poor crystallinity of
binary Sn-N nitrides.33

To assess the limits of off stoichiometry in the hexagonal MnSnN2 phase, one
library was deposited with a lower power on the Mn target (54 W as opposed to
the typical 108 W), leading to a Mn-poor film (Figure S7). This Mn-poor film
still exhibited wurtzite-like reflections down to approximately 18%
Mn/(Mn+Sn), limited by the edge of the library rather than by a structural
change. This composition nominally corresponds to Mn_0.36Sn_1.64N2 (assuming a
fixed anion content). For compositions with Mn/(Mn+Sn)$<50$%, charge balancing
must occur through either Sn^2+ substitution for Mn^2+ or metal vacancies.
Although we did not explore this Mn-poor region further, this finding suggests
that Mn-poor MnSnN2 could be of interest for dilute magnetic semiconductor
studies.

##  S2 Compositional characterization

###  S2.1 RBS

RBS measurements for select samples corroborate the high-throughput XRF
measurements done for each combinatorial film (Figure S8A). Furthermore, RBS
measurements identify the presence of oxygen in the MnSnN2 films (Figure S8B).
The convolution of the N and O signals in RBS with the signal from the
substrate inhibit the quantitative relation of anion content (N+O) with cation
content (Mn+Sn) (Figure S9), but the qualitative comparison of the trends in
O/(N+O) as a function of cation content are still valid. Oxygen content
increases with increasing Mn content, consistent with the lower
electronegativity of Mn (1.55 on the Pauling scale) compared to Sn (1.96). The
width of the oxygen region of the RBS spectra is similar to the width of the
other elemental regions, suggesting that oxygen is distributed throughout the
film thickness rather than being isolated to the surface. Oxygen substitution
might help charge balance excess Mn via Mn_1+$y$Sn_1-$y$N_2-$y$O_$y$, where
$y$ is both the number of oxides substituting for nitrides and the number of
Mn^3+ ions substituting for Sn^4+. Alternatively, oxygen substitution could
occur with exclusively Mn^2+, following a formula of (MnO)x(MnSnN2)(1-x),
similar to the oxygen balancing seen in MgZrN2 thin films.54

Figure S8: A) XRF measurements of % Mn/(Mn+Sn) agree well with measurements by
RBS. The grey trace represents perfect agreement between the techniques. Blue
squares are the data. B) RBS measurements of % O/(N+O) show that the
proportion of oxygen content increases slightly with increasing Mn content.
Figure S9: Representative RBS data (black traces) of one sample and fits (red
traces) following different fitting procedures. A) Fit by freely varying a
fuzz parameter, film thickness, and relative amounts of Mn, N, O, normalized
to Sn = 1. The minimization overfits the anion content, leading to an
unreasonable ratio of (N+O)/(Mn+Sn) = 1.6 (expecting 1 for the wurtzite
structure). B) Fitting the same data by refining thickness and Mn content and
constraining N content to N = Mn+Sn (i.e., Sn = 1, Mn = 0.8, N = 1.8). While
the lack of a fuzz parameter leads to poor fitting of curvature, the
constrained anion content still produces a reasonable fit to the intensity in
the 0.5 MeV region. Quantitative assessment of low-atomic number anion content
is therefore tricky given the low signal and high background. However, these
data show a non-zero oxygen content with a substantially larger proportion of
nitrogen content.

###  S2.2 XANES

In an attempt to identify the presence of Mn^3+ and assess Mn^2+:Mn^3+ ratios,
high-resolution Mn $L_{3}$-edge X-ray absorption near-edge spectroscopy
(XANES) measurements were conducted. Measurements were carried out on thin
films at room temperature at the Stanford Synchrotron Radiation Lightsource
(SSRL), SLAC National Accelerator Laboratory, beamline 10-1. Samples were
measured under high vacuum conditions of $\sim$2.7$\times 10^{-6}$ Pa
($\sim$2$\times 10^{-8}$ Torr) with a ring current of 500 mA. The synchrotron
radiation was monochromatized using the beamline’s 600 line/mm monochromator
with entrance and exit slits of 35 $\mu$m. A transition edge sensor (TES)
spectrometer 55 was used to collect resonant inelastic x-ray scattering (RIXS)
planes with a resolution of 2 eV. The energy measured by the TES was
calibrated by periodically measuring a reference sample of graphite, BN,
Fe2O3, NiO, and CuO, which provide a stable set of emission lines. From the
RIXS planes, we extracted the $L_{\alpha}$ and $L_{\beta}$ lines, leading to
partial fluorescence yield XAS.

Figure S10:  The XANES total electron yield (A) and partial fluorescence yield
(B) of the Mn-L edge shows that all three samples used for the magnetism
measurements have similar spectral profiles. This profile matches Mn^2+
compounds in literature.56, 57 Subtle differences can be seen on the peak
shoulders of the L3 edge, but these shifts are near the noise level of the
measurement.

XANES measurements (Figure S10) show consistent spectra across the measured
composition range, so we are not able to identify a change in oxidation state.
There are subtle differences between the spectra, as highlighted in the
insets, but these differences are hard to distinguish from noise. We observe
no consistent trend with composition and no distinct features indicative of
Mn^3+. Instead, each the spectral profile is consistent with Mn^2+ spectra
seen in literature.56, 57

##  S3 Magnetic properties

###  S3.1 Background subtraction and data analysis

As noted in the main text, for each magnetic measurement performed, an
analogous blank substrate was measured with identical scan parameters,
allowing for direct, point by point background subtraction. These blanks were
5 mm $\times$ 5 mm squares of the substrate alone (100 nm SiO2 on pSi), taken
from the same wafer batch used for the deposition. Figure S11–S12 show
examples of the background subtraction for temperature- and applied field-
dependent measurements, respectively.

Figure S11: Background subtraction example for zero-field cooled temperature
sweeps measured at $\mu_{0}H=5$ T. The raw moments of the sample and a blank
substrate are shown, along with the background-subtracted data showing
magnetism from the film alone (sample $-$ blank). Figure S12: Background
subtraction example for applied field sweeps measured at $T=2$ K. The raw
moments of the sample and a blank substrate are shown, along with the
background-subtracted data showing magnetism from the film alone (sample -
blank)

Following background subtraction, the susceptibility ($\chi$) was calculated
using the background-subtracted raw moment value described above, along with a
film mass of 0.00004 g and the molar mass calculated as Mn_2$x$ Sn_2-2$x$N2
(Table S1) where $x$ is the Mn fraction of cation content (Mn/[Mn+Sn]). The %
Mn/(Mn+Sn) values were determined by XRF on the individual squares. We note
that the small mass of Mn_2xSn_2-2xN2 present during the measurements and the
several possible sources of error in the film mass calculation and background
subtraction make direct, quantitative comparisons of the magnitude of $\chi$
between samples difficult. The value of 0.00004 g for a film mass is a
reasonable approximation given the film surface area (25 mm2), thickness, and
composition.

% Mn/(Mn+Sn) | Molar Mass (g/mol) | Thickness ($\mu$m) |  $a$ (Å) |  $c$ (Å) |  $T^{\mathrm{*}}$ (K)
---|---|---|---|---|---
42 | 212 | 0.305 | 3.449 | 5.667 | 6
51 | 201 | 0.304 | 3.441 | 5.562 | 10
56 | 194 | 0.302 | 3.438 | 5.536 | 12
Table S1: Summary of composition, thickness, hexagonal lattice parameters, and
magnetic transition temperatures ($T^{\mathrm{*}}$) for the samples selected
for magnetic measurements.

###  S3.2 Additional data

Inverse susceptibility data as a function of temperature show an approximately
linear region above the $T^{\mathrm{*}}\sim$10 K transition temperatures for
each composition, provided a diamagnetic correction ($\chi_{0}$) is applied
(Figure S13). Inverse $\chi$ without a diamagnetic correction exhibits
significant non-linearity (Figure S13A). Therefore, Curie-Weiss fits were
performed on $(\chi-\chi_{0})^{-1}$ from 150–300 K, as shown in Figure S13B.
As the inverse $\chi$ plots exhibited a second linear region (50–150 K), we
also applied Curie-Weiss analysis to this lower temperature region (Figure
S13C), which resulted in a smaller magnitude $\Theta_{CW}$ and a smaller
magnitude $\chi_{0}$ than the high temperature fits (Table S2). Weiss
temperatures from both fit ranges indicate antiferromagnetic (AFM)
correlations. The change in slope may indicate a change in the energy scale of
the dominant interactions in different temperature regions, or the emergence
of competing interactions, although further investigation will be required to
elucidate these subtle differences. We note that the uncertainty in background
subtraction and film mass discussed above and in the main text inhibits
quantitative extraction of Curie constants ($C$) or effective moments
($\mu_{\text{eff}}$) from the Curie-Weiss fits.

Figure S13: A) Inverse susceptibility plotted without a diamagnetic correction factor shows significant non-linearity. Inverse susceptibility data and Curie-Weiss fits performed with a diamagnetic correction ($\chi_{0}$) between B) 150–300 K C) 50–150K. The fits are shown as solid bars. Parameters $\Theta_{CW}$ and $\chi_{0}$ are shown in Table S2. C)  Table S2: Weiss temperatures ($\Theta_{CW}$) extracted from Curie-Weiss fits performed from 50–150K and 150–300 K with the diamagnetic corrections ($\chi_{0}$) listed. % Mn/(Mn+Sn) | 50–150 K | 150–300 K
---|---|---
$\Theta_{CW}$ (K) |  $\chi_{0}$ (emu/Oe mol) |  $\Theta_{CW}$ (K) |  $\chi_{0}$ (emu/Oe mol)
42 | -47 | -0.0025 | -324 | -0.0083
51 | -63 | -0.0030 | -243 | -0.0055
56 | -79 | -0.0038 | -356 | -0.0057

Figure S3.2 shows the background-subtracted moment as a function of applied
field measured at $T=2$ K for all samples. This low-temperature behavior
(below the transition temperature) is consistent with an AFM ground state
across the composition series. The small hysteresis and net ferromagnetic
moment noted in the Mn/(Mn+Sn) = 51% sample (Figure 6 in the main text) are
also present across the measured composition range, supporting our assignment
of this moment arising from canting or defects. The samples do not exhibit a
plateau in moment, suggesting that the magnetism is not saturated at the limit
of the instrument ($\mu_{0}H=7$ T). The moment at $\mu_{0}H=7$ T decreases
with increasing Mn/(Mn+Sn) content, attributable to either the substitution of
Mn^3+ for Mn^2+ or uncertainty in the mass used for normalization. Also, the
low-field slope changes with increasing Mn/(Mn+Sn): at Mn/(Mn+Sn) = 56%, it
appears to have two components, while at Mn/(Mn+Sn) = 42% there is only one
component. This behavior may be related to uncompensated moments from Mn^3+.

Figure S14: Isothermal magnetic moment measurements at 2 K of MnSnN2 samples
show decreasing moment with increasing Mn content. Traces are offset
horizontally by $\mu_{0}H=3$ T for clarity (grey lines guide the eye to each
origin). The substrate contribution has been subtracted.

##  S4 Optoelectronic measurements

In addition to the ellipsometry measurements and modeling reported in the main
text (Figure 7C), we conducted transmission and reflection UV-vis measurements
on select substrates deposited on EXG, a transparent substrate (Figure S4).
Transmission ($T$) and reflectance ($R$) spectra were collected in the UV-Vis-
NIR spectral ranges (300–1100 nm) using a home-built thin film optical
spectroscopy system equipped with deuterium and tungsten/halogen light sources
and a Si detector array. The collected spectra were then used to calculate
absorbance using the relation Absorbance, $A=\ln{[T/(1-R)]}$. Unfortunately,
the UV-vis spectrometer did not reach a sufficiently low energy to observe the
absorption onset (1 eV, 1200 nm). However, these data support a low energy
absorption onset without the need for modeling of the spectra (as needed for
ellipsometry).

Figure S15: A) Photo of a library deposited on a 2x2" Eagle XG glass
substrate. The library was deposited at a set point of 250 ℃, which
corresponds to a substrate temperature of $<225$ ℃ as evidenced by the lack of
decomposition of the MnSnN2 phase (confirmed by XRD). The film is dark brown
in color. B) Reflectance R and C) Reflection-corrected transmittance T were
used to calculate the absorbance via Absorbance $A=\ln{\frac{T}{1-R}}$, as
implemented in Combigor.24. D) The absorbance is high across measurable range.
The colorbar shown in panel B is used for panels C and D as well.

In addition to measuring electrical conductivity of a film on EXG (Figure 7),
we also conducted temperature dependent electrical measurements on select
samples deposited on an insulating 100 nm of SiO2 on Si (Figure S4). These
measurements were consistent with our observations for the sample on EXG
(Figure 7B), showing increasing conductivity with increasing temperature.
However, these blanket films on 100 nm of SiO2 have a tendency to short across
such a narrow insulating layer if cleaved (as for these samples). To ensure we
were exclusively measuring conductivity of the film, rather than the Si
substrate, we repeated the measurement on EXG and report that in the main body
of the text.

Figure S16: Conductivity measurements on 5 mm $\times$ 5 mm squares scribed
from a library deposited at $T_{\text{dep}}=225$ ℃ on Si with 100 nm SiO2.