# Li2Sr[MnN]2: a magnetically ordered, metallic nitride

F. Hirschberger  EP VI, Center for Electronic Correlations and Magnetism,
Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany  T. J.
Ballé  EP VI, Center for Electronic Correlations and Magnetism, Institute of
Physics, University of Augsburg, D-86135 Augsburg, Germany  C. Haas  W.
Scherer  CPM, Institute of Physics, University of Augsburg, D-86135 Augsburg,
Germany  A. A. Tsirlin  EP VI, Center for Electronic Correlations and
Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg,
Germany  Yu. Prots  P. Höhn  Max-Planck-Institut für Chemische Physik fester
Stoffe, Nöthnitzer Str. 40, D-01187 Dresden, Germany  A. Jesche  EP VI, Center
for Electronic Correlations and Magnetism, Institute of Physics, University of
Augsburg, D-86135 Augsburg, Germany

###### Abstract

Li2Sr[MnN]2 single crystals were successfully grown out of Li rich flux. The
crystal structure was determined by single crystal X-ray diffraction and
revealed almost linear $-$N$-$Mn$-$N$-$Mn$-$ chains as central structural
motif. Tetragonal columns of this air and moisture sensitive nitridomanganate
were employed for electrical transport, heat capacity, and anisotropic
magnetization measurements. Both the electronic and magnetic properties are
most remarkable, in particular the linear increase of the magnetic
susceptibility with temperature that is reminiscent of underdoped cuprate and
Fe-based superconductors. Clear indications for antiferromagnetic ordering at
$T_{N}=290$ K were obtained. Metallic transport behavior is experimentally
observed in accordance with electronic band structure calculations.

##  I Introduction

Oxides are normally associated with ionic bonding and insulating electrical
transport behavior. When this intuition fails, particularly interesting
physical properties and ground states can be found. Well known examples are
ferrites above the Verwey transition [1], cuprate superconductors [2], or
delafossites [3]. In general, nitrides tend to behave similar to oxides,
however, metallic behavior is arguably even more rare.

Binary transition metal nitrides attract considerable interest due to their
valuable mechanical, electrical and magnetic properties. In contrast,
chemistry and physics of multinary nitrides have been far less thoroughly
explored [4]. Nitridometalates of $d$ metals $T$ represent an interesting
class of solid state phases, which contain nitrogen as isolated anions N3- or
feature complex anions [TxNy]z- of different dimensionalities with
coordination numbers of $T$ by N typically between two and four and oxidation
states of the transition metals being comparatively low. Whereas the bonding
within these complex anions and frameworks is essentially covalent,
nitridometalates are stabilized by predominantly ionic bonding through
counterions of electropositive metals like alkali ($A$) or alkaline-earth
($AE$) cations.

Nitridomanganates show a wide variety of structures and properties: manganese
may be coordinated tetrahedrally (Li7[MnVN4] [5]) or trigonal-planar
(Li24[MnIIIN3]3N2 [5], Ca6[MnIIIN3]N2 [6], Ca3[MnIIIN3] [7], Sr3[MnIIIN3] [8,
9], Ba3[MnIIIN3] [8, 9], Sr8[MnIII,IVN3]3 [10]) in isolated units; ethane-like
units are observed in Li6Ca2[Mn${}^{\mathrm{IV}}_{2}$N6] [11] and
Li6Sr2[Mn${}^{\mathrm{IV}}_{2}$N6] [12]. Charge ordering is observed in chains
of edge-sharing tetrahedra in Ba4[Mn${}^{\mathrm{II,IV}}_{3}$N6] [13] whereas
complex 2D structures of mixed valent manganese in both tetrahedral and
trigonal-planar coordination are observed in
Ca12[Mn${}^{\mathrm{II,III}}_{19}$N23] and
Ca133[Mn${}^{\mathrm{II,III}}_{216}$N260] [14]. Both of those semiconducting
phases order antiferromagnetically; their localized magnetism originates from
only a small fraction of the Mn atoms not involved in metal-metal bonding and
is characterized by a large orbital contribution. Anti-rutile-type (Mn2-xLix)N
[15] features 3D networks of trigonal-planar coordinated manganese. Linear
substituted chains [(Li1-xMnx)N] are observed in
Li2[(Li1-xMn${}^{\mathrm{I}}_{x}$)N] [5, 16],
Li5[(Li1-xMn${}^{\mathrm{I,II}}_{x}$)N]3 [5] and Li2Ca[(Li1-xMnx)N]2 [17].

The single crystal growth of nitrides is often challenging due to the large
dissociation energy of the N2 molecule, the reactivity of the starting
materials and enhanced vapor pressures, but the high temperature
centrifugation aided filtration (HTCAF) technique [18, 19] using Li as a flux
provides a powerful tool to produce large single crystals of a large variety
of phases even in complex systems such as nitridometalates (e. g.
Li2Sr[(Li1-xFe${}^{\mathrm{I}}_{x}$)N]2 [20], LiSr2[CoIN2] [21]) or nitride
metalides like LiSr3Ga2N [22]. Although magnetic properties were reported for
only few nitridometalates containing alkaline-earth metals, these new phases
show high magnetic anisotropy (Li2Sr[(Li1-xFe${}^{\mathrm{I}}_{x}$)N]2 [20])
and ferromagnetic (LiSr2[CoIN2] [21]) or antiferromagnetic (LiSr2[FeIN2] [23])
ordering.

Here we present a metallic nitride based on the ionic alkali-alkaline-earth-
nitrogen host Li4SrN2 substituted with Mn. Since Mn almost fully occupies one
of the two Li sites of Li4SrN2 and is absent on the other one, we refer to the
material as Li2Sr[MnN]2. The phase is isotypic to
Li2Sr[(Li1-xFe${}^{\mathrm{I}}_{x}$)N]2, but shows a significantly different
magnetic behavior [20]. Single crystals of several millimeter along a side can
be obtained from Li-rich flux. We find clear indications for magnetic ordering
close to room temperature and metallic electrical transport behavior.

Figure 1:  Crystal structure of Li2Sr[MnN]2, the unit cell is indicated by the
grey lines (space group $I\,4_{1}/a\,m\,d$). Mn is substituted in linear, two-
fold coordination between N. One set of the $-$N$-$Mn$-$N$-$Mn$-$ chains is
oriented vertical, the other one roughly perpendicular to the paper plane.

##  II Methods

Starting materials were lithium rod (Evochem, 99 %), manganese powder (Alfa
Aesar, 99.9998 %), strontium nitride (Sr2N) powder [prepared from strontium
metal (Alfa Aesar, distilled dendritic pieces, 99.95 %) and nitrogen
(Westfalengas, 99.999 %, additionally purified by molecular sieves and BTS
catalyst)] and sodium azide (NaN3) powder (Roth, 99 %) as a further nitrogen
source. Tantalum ampules were produced on-site from pre-cleaned tantalum tube
and tantalum sheet (Plansee) in an arc furnace located within a glove box.

Laue back-reflection pattern were taken with a digital Dual FDI NTX camera
manufactured by Photonic Science (tungsten anode, $U=20$ kV). The calculated
pattern as well as the picture of the crystal structure were created using
CrystalMaker and SingleCrystal. Laboratory powder X-ray diffraction data of
finely ground (gray) powder samples were collected on a Huber G670 imaging
plate Guinier camera using a curved germanium (111) monochromator and
Cu-K$\alpha$1 radiation in the range $4^{\circ}\leq 2\theta\leq 100^{\circ}$
with an increment of $0.005^{\circ}$ at 293(1) K. The powder samples were
placed between Kapton foils to avoid degradation in air. All preparations and
sample handling were performed under inert atmosphere (Ar). Phase
identification was done using the WinXPow program package[24].

The crystal structures and the compositions of several crystals obtained in
different experiments of the title compound Li2Sr[(Li1-xMnx)N]2 were refined
from single-crystal X-ray diffraction data. Data for single crystals 1,2, and
4 were collected at temperatures 400 K, 300 K, and 100 K, respectively, on a
Bruker APEX2 diffractometer with a D8 goniometer and Ag-K$\alpha$
($\lambda=0.56087$ Å) employing Helios mirror optics (Incoatec). The crystal
was kept at 100 K and 400 K using a Cryostream 700 low temperature device
(Oxford Cryosystems) during data collection. Using Olex2 [25] the structure
was solved with the ShelXS [26] structure solution program using Direct
Methods and refined with the ShelXL [27] refinement package using Least
Squares minimisation.

Data for single crystal 3 was collected at room temperature on a Rigaku AFC7
four circle diffractometer equipped with a redSaturn 724+ CCD detector
(Mo-K$\alpha$ radiation, graphite monochromator). For numerical absorption
correction, an optimized shape of the single crystal was employed [28, 29].
After data collection the structure was confirmed by direct methods, using
SHELXS [26] and subsequently refined by using the full-matrix least-squares
procedure with SHELXL [27]. Further details on the crystal structure
investigations may be obtained from the Fachinformationszentrum Karlsruhe,
76344 Eggenstein-Leopoldshafen, Germany (Fax: +49-7247-808-666; e-mail:
crysdata@fiz-karlsruhe.de), on quoting the depository numbers CSD-xxxxxx, the
names of the authors, and the journal citation.

The magnetization was measured using a 7 T Magnetic Property Measurement
System (MPMS3) manufactured by Quantum Design. The electrical transport
properties were measured as a four-probe measurement with spring loaded
contacts using a 14 T Physical Properties Measurement Systems which was also
manufactured by Quantum Design. The side of the few millimeter sized samples
on which the contacts were placed was ground off under argon atmosphere before
each run. This served to remove insulating layers from the surface of the
crystals, which are sensitive to air and moisture. Due to the limited size of
the available crystals and the measurement setup, it was not possible to
investigate the anisotropy of electrical transport. The data shown in this
work were obtained from AC electrical transport measurements at a frequency of
117 Hz and 9 Hz. The specific electric resistivity was calculated from the
measured resistance based on the sample geometry by following the procedure
described in Eder [30].

Density-functional (DFT) band-structure calculations were performed in the
FPLO code [31] using local density approximation (LDA) for the exchange-
correlation potential [32]. Correlation effects in the Mn $3d$ shell were
introduced on the mean-field DFT+$U$ level with the double-counting correction
in the atomic limit. The on-site Hund’s coupling was fixed to $J_{H}=1$ eV,
while the Coulomb repulsion parameter $U$ was varied between 1 and 10 eV to
explore the influence of correlation effects on the electronic structure.
Magnetic moments in spin-polarized calculations are estimated by the internal
routine of FPLO via projections on local atomic orbitals. Experimental
structural parameters at 300 K (data set 2b) were used in all calculations.

Figure 2:  X-ray diffraction pattern measured after grinding part of the
product obtained by Li flux growth. Both Li2Sr[MnN]2 and Li4Sr[MnN3] were
identified (Cu-K$\mathrm{\alpha}$ radiation, $\lambda=1.54056\,$Å). The inset
shows a single crystal of Li2Sr[MnN]2 on a millimeter grid. b) Laue back-
reflection pattern recorded along the $c$-axis of the Li2Sr[MnN]2 single
crystal shown above. The calculated pattern (red spots) is slightly rotated
for clarity

.

##  III Single crystal growth

Due to the air and moisture sensitivity of both the reactants (Li, NaN3, Sr2N)
and the final product Li2Sr[(Li1-xMnx)N]2 all manipulations including grinding
and weighing, as well as complete sample preparations for measurements were
carried out in an inert gas glove box (Ar, O2 and H2O$\leq 1$ ppm). Large
single crystals of Li2Sr[(Li1-xMnx)N]2 in the form of square columns with a
silverish luster were obtained by reaction of Sr2N, Mn, NaN3, and Li in molar
ratio 10 : 34 : 1 : 340 with NaN3 acting as a nitrogen source and Li as flux
and mineralizer.

The mixtures with total mass of about 0.6 g were placed into tantalum ampules
equipped with a sieve [33], sealed by arc welding under inert atmosphere of
700 mbar argon and subsequently encapsulated in a quartz tube with an internal
argon pressure of 300 mbar in order to prevent oxidation of the tantalum. The
samples were heated from room temperature to $T=1023$ K with a rate of 100
Kh-1, annealed for 2 h, subsequently cooled to 600 K with 1 Kh-1 and further
with 2 Kh-1 to 400 K. After centrifugation with 3000 min-1 employing the HTCAF
method [18, 19] to separate the single crystals from the excess flux.

Large single crystals of the title compound in form of tetragonal columns with
a silverish black lustre were obtained in addition to greenish black single
crystals of the new phase Li4Sr[MnN3] and a small amount of hexagonal reddish
black Li3N as side phases. Using a two-probe multimeter, the differently
colored phases showed remarkably different resistivities further enabling the
discrimination of the various phases. Small single crystals suitable for X-ray
diffraction were obtained either directly selected from the product or by
crushing larger specimens. One of the largest Li2Sr[MnN]2 single crystals
obtained is shown as an inset of Fig. 2(a).

The HTCAF technique using a Li-rich flux has been successfully employed for
the growth of large single crystals of Mn-substituted Li4SrN2. However, it was
not possible to obtain single phase material using this reaction route up to
now. Although no binary intermetallic phases seem to be stable under these
conditions, other nitrides and nitridometalates may form in this quinary (Li-
Sr-Mn-N-Ta) system depending on composition, temperature and reaction time.
Whereas the ratio AE/N significantly influences product formation, the amount
of Li as flux seems to play only a minor role. During short-term reactions,
excess N results in formation of highly oxidized transition metals or Li3N,
whereas after long reaction times also reactions with the crucible materials
come into play as evidenced by the formation of Li7[TaN4]. Our attempts to
synthesize strontium nitridomanganates yielded a large variety of phases such
as Li2Sr[(Li1-xMn${}^{\mathrm{I}}_{x}$)N]2, Li4Sr[MnIIIN3], or Sr3[MnIIIN3].
Whether large single crystals of other known nitridomanganates as well as
phases with Mn in other oxidation states can be grown by adjusting temperature
profile and/or the ratio of the starting materials is subject of ongoing
research. Altogether, the HTCAF method may prove a useful tool for a wide
range of applications.

Table 1:  Crystallographic data and experimental details for the single crystal structure refinements of different crystals of Li2Sr[(Li1-xMnx)N]2. sample | 1 | 2 | 3 | 4
---|---|---|---|---
T [K] | 400 | 300 | 295(2) | 100
Mn occupancy (x) | 0.954(5) | 0.946(3) | 0.931(5) | 0.949(4)
crystal system | tetragonal | tetragonal | tetragonal | tetragonal
space group |  $I\,4_{1}/a\,m\,d$ (No. 141) |  $I\,4_{1}/a\,m\,d$ (No. 141) |  $I\,4_{1}/a\,m\,d$ (No. 141) |  $I\,4_{1}/a\,m\,d$ (No. 141)
$a$ [Å] | 3.8151(3) | 3.8115(4) | 3.8126(2) | 3.8101(6)
$c$ [Å] | 28.445(2) | 28.347(3) | 28.372(3) | 28.245(5)
$V$ [Å3] | 414.02(7) | 411.82(10) | 412.41(6) | 410.03(14)
$Z$ | 4 | 4 | 4 | 4
$\rho_{\mathrm{calc}}$ [gcm-3] | 3.769 | 3.778 | 3.740 | 3.800
crystal color, habit | metallic, black, block | metallic, black, block | silverish, tetragonal column | metallic, black, block
crystal size [mm] | 0.175$\times$0.153x0.115 | 0.223$\times$0.16$\times$0.107 | 0.15$\times$0.18$\times$0.20 | 0.192$\times$0.185$\times$0.126
$\mu$ [mm-1] | 9.791 | 9.821 | 18.264 | 9.875
sin $\theta_{\rm max}/\lambda$ [1/$\lambda$] | 1.00 | 1.00 | 0.89 | 1.00
diffractometer | BRUKER APEX2 | BRUKER APEX2 | RIGAKU AFC7 | BRUKER APEX2
wavelength [Å] | 0.56087 (Ag-K$\alpha$) | 0.56087 (Ag-K$\alpha$) | 0.71069 (Mo-K$\alpha$) | 0.56087 (Ag-K$\alpha$)
monochromator | mirror optics | mirror optics | graphite | mirror optics
scan mode |  $\omega$ scans |  $\omega$ scans |  $\varphi$ scans |  $\omega$ scans
measured reflections | 13690 | 7790 | 3266 | 8813
observed reflections | 525 | 509 | 370 | 512
$[I_{\mathrm{o}}>2\sigma(I_{\mathrm{o}})]$ |  |  |  |
$R_{\mathrm{int}}$ | 0.0517 | 0.0418 | 0.0765 | 0.0508
number of parameters | 16 | 16 | 16 | 16
goodness-of-fit on $F^{2}$ | 1.345 | 1.216 | 1.161 | 1.274
wR2 | 0.0616 | 0.0554 | 0.0981 | 0.0659
R1 [$F_{\mathrm{o}}>4\sigma(F_{\mathrm{o}})$] | 0.0320 | 0.0249 | 0.0376 | 0.0300
R1 (all data) | 0.0354 | 0.0291 | 0.0507 | 0.0332
residual electron density | 1.31/-1.57 | 0.920 /-0.788 | 1.66/-2.01 | 1.520/-1.343
$[e\times 10^{-6}\,\mathrm{pm}^{-3}]$ |  |  |  |

##  IV Crystal structure

Table 2:  Atomic positions and equivalent displacement parameters [Å2] for Li2Sr[(Li1-xMnx)N]2 for crystals 1-4. The Li occupancy on the MnLi site is obtained by $1-x$(Mn), all other parameters for this site were constrained to equal values for Mn and Li. | $x$ | $y$ | $z$ | $U_{\mathrm{eq}}$ | $x(\mathrm{Mn})$
---|---|---|---|---|---
Sr1 | 1/2 | 1/4 | 1/8 | 0.01016(9) |
|  |  |  | 0.00838(7) |
|  |  |  | 0.01286(19) |
|  |  |  | 0.00420(8) |
MnLi | 0 | 3/4 | 0.05213(2) | 0.01076(13) | 0.954(5)
|  |  | 0.05210(2) | 0.00844(10) | 0.946(3)
|  |  | 0.05209(3) | 0.0118(3) | 0.931(5)
|  |  | 0.05213(2) | 0.00470(11) | 0.949(4)
N1 | 1/2 | 3/4 | 0.05444(10) | 0.0091(4) |
|  |  | 0.05452(8) | 0.0076(3) |
|  |  | 0.05455(15) | 0.0128(7) |
|  |  | 0.05450(9) | 0.0051(3) |
Li1 | 1/2 | 3/4 | -0.0225(3) | 0.0156(13) |
|  |  | -0.0226(2) | 0.0128(9) |
|  |  | -0.0224(4) | 0.0182(18) |
|  |  | -0.0223(3) | 0.0096(11) |
Table 3:  Anisotropic displacement parameters [Å2] for Li2Sr[(Li1-xMnx)N]2 for crystals 1-4. ($U_{12}=U_{13}=U_{23}=0$, Li and Mn on the MnLi site were treated identical). Atom | $U_{11}$ | $U_{22}$ | $U_{33}$
---|---|---|---
Sr1 | 0.01062(12) |  | 0.00923(15)
| 0.00836(9) |  | 0.00843(12)
| 0.0114(2) | $U_{11}$ | 0.0157(3)
| 0.00404(10) |  | 0.00451(13)
MnLi | 0.00363(18) | 0.0145(2) | 0.0142(2)
| 0.00300(13) | 0.01057(16) | 0.01174(18)
| 0.0057(3) | 0.0131(4) | 0.0165(5)
| 0.00195(17) | 0.00571(19) | 0.00643(19)
N1 | 0.0039(8) | 0.0100(10) | 0.0134(9)
| 0.0039(6) | 0.0078(7) | 0.0110(7)
| 0.0109(16) | 0.0111(16) | 0.0165(18)
| 0.0032(8) | 0.0047(9) | 0.0076(8)
Li1 | 0.021(4) | 0.012(3) | 0.014(3)
| 0.016(2) | 0.009(2) | 0.013(2)
| 0.015(4) | 0.018(4) | 0.022(4)
| 0.012(3) | 0.006(3) | 0.010(2)
Table 4:  Relevant distances (in Å) and angles in Li2Sr[(Li1-xMnx)N]2 [Å] for crystals 1-4.  |  | 1 | 2 | 3 | 4
---|---|---|---|---|---
Sr1-N1 | 4x | 2.769(2) | 2.761(2) | 2.762(3) | 2.756(2)
N1-MnLi | 2x | 1.9087(2) | 1.9070(2) | 1.9076(2) | 1.9062(3)
N1-Li1 | 2x | 2.113(4) | 2.110(3) | 2.113(5) | 2.111(3)
N1-Li1 | 1x | 2.189(8) | 2.185(6) | 2.184(11) | 2.170(7)
$\angle$N1-MnLi-N1 |  | 176.0(2) | 175.9(2) | 175.8(3) | 176.0(2)

Figure 2 shows the X-ray powder diffraction pattern measured on a ground
mixture of single crystals of Li2Sr[(Li1-xMnx)N]2 and Li4Sr[MnN3]. Lattice
parameters of $a=3.8087(3)$ Å and $c=28.334(4)$ Å obtained from the
Li2Sr[(Li1-xMnx)N]2 powder differ somewhat from single crystal data (see
below) indicating a variation of the Mn concentration within the samples. The
decrease in $a$ by 0.34 % and increase in $c$ by 4.8 % with increasing Mn
content $x$ in comparison to the parent compound Li4SrN2 ($a=3.822(2)$ Å,
$c=27.042(9)$ Å [34]) is in line with the trend reported for the isotypic iron
($x=0.32$, $a=3.79536(9)$ Å, $c=27.6492(13)$ Å [20]; $x=0.46$, $a=3.7909(2)$
Å, $c=27.719(3)$ Å [35]), cobalt ($x=0.3$, $a=3.7363(3)$ Å, $c=27.9063(24)$ Å
[23]), nickel ($x=0.1$, $a=3.823(1)$ Å, $c=27.074(5)$ Å [34]), and copper
phases ($x=0.39$, $a=3.770(1)$ Å, $c=27.386(6)$ Å [36]).

Smaller crystals were obtained from several different crushed samples and
selected for single crystal X-ray diffraction at several temperatures. The
results are summarized in Tables 1 \- 4. Li2Sr[(Li1-xMnx)N]2 crystallizes
tetragonal in space group $I\,4_{1}/a\,m\,d$ and is a substitution variant of
Li4SrN2 [34].

Predominant structural feature of Li2Sr[(Li1-xMnx)N]2 are 2D fragments of the
Li3N structure with composition Li[(Li1-xMnx)N]. These slabs are connected by
tetrahedrally coordinated Sr atoms and stacked along [001] in such a way that
each layer is rotated 90 ∘ to the previous one. Powder as well as single
crystal X-ray diffraction revealed slightly varying Mn-concentrations of
$x=0.94\pm 0.02$; the slight differences between powder and single crystal
data may also stem from slight inhomogeneities within the samples. As
indicated by the notation of the chemical formula, Li2Sr[(Li1-xMnx)N]2, the
substituted Mn atoms occupy only one of the two Li-sites: whereas there is no
evidence for substitution on the trigonal planar coordinated Li position, the
almost linearly ($\angle$N1-MnLi-N1 = 176(0.2)∘, see Table 4) coordinated
chain position [(Li1-xMnx)N] is nearly completely substituted by Mn
($x=0.94(2)$, see Table 2). Compared to a truly linear chain, the (Li1-xMnx)
atoms are deflected towards the Li[(Li1-xMnx)N] slabs. A designation as
Li2Sr[MnN]2 is also conceivable and used in this article, since on average
only every 18th manganese atom within the chains is substituted by lithium.
Laue back-reflection pattern calculated based on the obtained structure are in
excellent agreement with measurements recorded on large single crystals [Fig.
2(b)].

The structural feature of linear substituted chains [(Li1-xMnx)N] is also
observed in Li2[(Li1-xMn${}^{\mathrm{I}}_{x}$)N] [5, 6],
Li5[(Li1-xMn${}^{\mathrm{I,II}}_{x}$)N]3 [5] and Li2Ca[(Li1-xMnx)N]2 [17].
Whereas distances $d$(Li${}_{1-x}T_{x}$-N) decrease significantly with
increasing $x$ for $T$ = Fe, Co, Ni [37] and to a certain extent Cu [36], this
effect is less pronounced in nitridomangantes: $d$(Li1-xMnx-N) = 1.9076(2) Å
in Li2Sr[(Li0.07Mn0.92)N]2 , 1.911 Å in
Li5[(Li0.33Mn${}^{\mathrm{I,II}}_{0.67}$)N]3 [5], 1.914 Å in
Li2[(Li0.27Mn${}^{\mathrm{I}}_{0.73}$)N] [16] and 1.916 Å in
Li2Ca[(Li0.06Mn0.94)N]2 [17] compared to $d$(Li-N) = 1.938 Å in Li3N [38] and
1.913 Å in Li4SrN2 [34].

Considering all isotypic substitution variants, the manganese phase is a
special case, as there is almost complete substitution ($x=0.94(2)$) of the
linearly coordinated lithium position (compared to obtained substitution
levels in Li2Ca[(Li1-xFex)N]2: $x=0.3$ [35], Li2Sr[(Li1-xFex)N]2: $x=0.46$
[35], Li2Sr[(Li1-xCox)N]2: $x=0.3$ [23], Li2Sr[(Li1-xNix)N]2: $x=0.1$ [34],
Li2Sr[(Li1-xCux)N]2: $x=0.39$ [36]). It is also interesting to note that the
angle $\angle$N-$T$-N in the chain [(Li${}_{1-x}T_{x}$)N] increases ($x=0$:
174.5 ∘) [34] with increasing $x$ for all $T$ to values between $175.5-177.5$
∘. In contrast, Li2Ca[(Li1-xMnx)N]2 [17] exhibits a different structure type.

##  V Electrical transport

Figure 3:  Electrical transport properties of Li2Sr[MnN]2 obtained by using
spring loaded, four wire contacts. (a) Linear temperature-dependence and
relatively low absolute values at room temperature as key properties of
metallic systems. (b) Ohmic current-voltage characteristics. (c) Pronounced
anisotropy of the magneto-resistance at low temperatures.

Initial two-probe measurements using a standard multimeter indicated metallic
behavior and motivated more accurate resistivity measurements as a function of
temperature, excitation current, and magnetic field. Figure 3(a) shows the
temperature-dependent electrical resistivity, $\rho(T)$ for $j\perp c$
measured on two different samples. Absolute values amount to $\rho\sim
500\,\mu\Omega$cm at room temperature, a value that is larger than the one of
elemental metals (for example $140\,\mu\Omega$cm for Mn). Resistivities of
this order of magnitude are somewhat smaller or comparable to what is referred
to as ’bad metal’ [39]. A linear temperature-dependence - a key property of a
metallic material - is observed above $T\approx 200$ K. The residual
resistivity ratio of $RRR>3$ indicates an acceptable sample quality. The gaps
in $\rho(T)$ at $T<100$ K that appear for sample 1 are caused by a temporary
loss of contacts caused by thermal expansion and/or a mechanical blocking of
the springs. Storing the measurement setup in a desiccator in between the runs
helped to prevent those contact failures.

Ohmic current-voltage characteristics are found up to currents of at least 0.1
A [Fig. 3(b)]. Using larger currents increases the risk of loosing the
contacts presumably due to heating at the contact tips, which causes a local
disintegration of the sample material.

The magneto-resistance was measured for two different orientations of the
crystal: $H\perp c$ with $j\parallel H$ and $H\parallel c$ with $j\perp H$.
Figure 3(c) shows pronounced anisotropy and moderate absolute values obtained
at $T=2.5$ K: the resistivity increases for field applied perpendicular to the
$c$-axis but decreases for field applied parallel to $c$ (that is
perpendicular to the $-$N$-$Mn$-$N$-$Mn$-$ chains).

##  VI Magnetization

Figure 4:  Temperature- and field dependent magnetization of Li2Sr[MnN]2($T>2$
K). (a) Magnetic susceptibility $\chi=M/H$ exhibits low anisotropy and
temperature-dependence. The magnetization is linear in field (inset). A clear
anomaly is observed at $T_{N}=290$ K. (b) $H\parallel c$: The step-like
decrease in $\chi(T)$ at $T_{N}$ indicates antiferromangetic ordering in
accordance with the anomaly shifting to lower temperature in larger applied
fields. (c) $H\perp c$: a well-defined maximum is observed for $\mu_{0}H\leq
1$ T at $T_{N}$. For larger applied fields $\chi(T)$ shows a monotonic
increase upon cooling with a change of slope at $T_{N}$.

The magnetization was measured for two orientations: the applied field was
aligned parallel ($H\parallel c$) or perpendicular ($H\perp c$) to the
crystallographic $c$-axis. The obtained magnetic susceptibility $\chi(T)=M/H$
is plotted in Fig. 4a. Nearly isotropic behavior is found for $T>300$ K with
large absolute values and a linear increase of $\chi(T)$ with $T$. The
magnetization is linear in field for temperatures $T>2$ K as shown in the
inset. A significant increase of $\chi(T)$ for cooling below $T\sim 50$ K
indicates the presence of local magnetic moments (Curie tail).

A clear anomaly is observed around room temperature with the strongest change
of slope at $T_{N}=290$ K ($H\parallel c$). Antiferromagnetic (AFM) ordering
is inferred from the step-like decrease upon cooling and the slight shift of
the anomaly towards lower temperature for increasing applied fields [Fig.
4(b), $H\parallel c$]. For $H\perp c$, a local maximum in $\chi(T)$ at $T=288$
K is found for $\mu_{0}H\leq 1$ T. As shown in Fig. 4(c), a strong change of
this behavior is observable in larger applied fields: a thermal hysteresis
emerges and the anomaly gets broader for $\mu_{0}H=2$ T. A monotonous increase
upon cooling is found for 3 T$\leq\mu_{0}H\leq 7$ T with the strongest change
of slope close to $T_{N}$.

##  VII Specific heat and magnetization at $T<2$ K

Figure 5:  Specific heat $C(T)$ and magnetization of Li2Sr[MnN]2 for $T<2$ K.
(a) Electron and phonon contribution lead to the expected linear behavior of
$C/T$ as a function of $T^{2}$. The Sommerfeld coefficient is estimated to
$\gamma=5.7$ mJ mol${}^{-1}_{\rm Mn}$ K-2. (b) A broad maximum appears at
$T_{f}=1.2$ K. The magnetic contribution was estimated by fitting a polynomial
to the data points above and below the anomaly (dashed, orange line). The
transition is associated with a significant amount of magnetic entropy $S_{\rm
mag}$. (c) The magnetic susceptibility $\chi(T)=M/H$ shows a maximum at
$T_{f}$ in zero-field-cooled (ZFC) measurements for $H\perp c$ and $H\parallel
c$. The field-cooled (FC) curves split from the ZFC at $T_{f}$ for both
orientations. (d) Even at the lowest accessible temperature of $T=400$ mK, the
field-dependent, isothermal magnetization is only slightly curved.

Figure 5(a) shows the specific heat $C(T)$ plotted as $C(T)/T$ as a function
of $T^{2}$. A linear dependence is observed for 4 K $<T<10$ K with a slightly
enhanced Sommerfeld coefficient of $\gamma=5.7$ mJ mol${}^{-1}_{\rm Mn}$ K-2.
Towards lower temperatures, $C(T)$ increases and a comparatively broad peak is
found at $T_{f}=1.2$ K [Fig. 5(b)]. In order to estimate the corresponding
magnetic entropy, $S_{\rm mag}$, a 3rd order polynomial was fit to the data
below $T=0.6$ K and above $T=1.6$ K (dashed line). We find $S_{\rm mag}\approx
2.3$ mJ mol${}^{-1}_{\rm Mn}$ K-1.

Fig. 5(c) shows low temperature $\chi(T)=M/H$ for $H\parallel c$ and $H\perp
c$. Similar to the whole investigated temperature range, only a small
anisotropy is visible. A maximum is found in zero-field-cooled (ZFC)
measurements at $T_{f}=1.2$ in very good agreement with $C(T)$. Field-cooled
(FC) runs bifurcate from the ZFCs close to $T_{f}$.

Isothermal magnetization measurements at temperatures as low as $T=400$ mK are
presented in Fig. 5(d). There is no substantial change for increasing the
temperature above $T_{f}$ and further up to room temperature (dashed lines).
Even in the largest available fields, the magnetization amounts to less then
0.03 $\mu_{\rm B}$ per Mn significantly below the saturation moment of
$\mu_{\rm sat}=4$ $\mu_{\rm B}$ (for $S=2$). This proves the absence of (more
than 1 %) localized Mn magnetic moments that are free or only weakly coupled
for the whole temperature range investigated.

##  VIII Electronic Structure

LDA density of states (DOS) for Li2Sr[MnN]2 features N $2p$ band between $-6$
and $-2.5$ eV followed by the Mn $3d$ band that straddles the Fermi level
(Fig. 6). Only a tiny gap is observed between these bands, in contrast to low-
valent Mn oxides, where Mn and O bands are usually well separated from each
other. We choose MnO as the reference compound and compare its LDA DOS with
that of Li2Sr[MnN]2. The shift of the $2p$ band toward higher energies is
immediately visible in Fig. 6. It can be quantified by the charge-transfer
energy $\Delta$ that decreases from 4.1 eV in the oxide to 2.4 eV in the
nitride. Here, $\Delta$ is estimated as the difference between centers of
gravity of the Mn $3d$ and O/N $2p$ states.

Orbital-resolved DOS for Li2Sr[MnN]2 (Fig. 6, inset) suggests the splitting of
Mn $d$ states into crystal-field levels with
$\varepsilon_{3z^{2}-r^{2}}\simeq-0.98$ eV,
$\varepsilon_{xy}\simeq\varepsilon_{x^{2}-y^{2}}\simeq-0.32$ eV, and
$\varepsilon_{yz}\simeq\varepsilon_{xz}\simeq 0.30$ eV, where the $z$ axis is
chosen along the Mn–N bonds. This level scheme is consistent with the linear
coordination of Mn1+ and also shows that the charge-transfer energy for the
$3z^{2}-r^{2}$ orbital is reduced to 1.3 eV. This orbital then features a
notably broader dispersion because of a much stronger hybridization with the N
$2p$ states.

Figure 6:  LDA density of states for Li2Sr[MnN]2 (top panel) and MnO (bottom
panel). The inset shows orbital-resolved DOS for Mn atoms in the former
compound. The Fermi level is at zero energy.

To probe the effect of electronic correlations on the band structure, we
performed DFT+$U$ calculations for both MnO and Li2Sr[MnN]2. Experimental
antiferromagnetic structure was chosen for the former, while in the latter
case an antiferromagnetic structure with the highest symmetry was considered.
It keeps the periodicity of the crystal structure and comprises ferromagnetic
layers in the $ab$ plane coupled antiferromagnetically along the $c$ axis
($I\,4_{1}$ symmetry). Alternatively, a spin configuration with
antiferromagnetic order along the Mn–N chains was constructed in a four-fold
supercell and showed a very similar evolution of the band structure with $U$,
so we focused on a simpler antiferromagnetic structure that allowed faster and
more easily converged calculations at different values of $U$.

Figure 7:  (a-c) Evolution of the electronic structure for MnO (circles) and
Li2Sr[MnN]2 (diamonds) upon increasing the Coulomb repulsion parameter $U$ of
DFT+$U$: band gap (a), total DOS at the Fermi level (b), and magnetic moment
on Mn (c). (d-f) Orbital-resolved DOS for a single Mn atom in Li2Sr[MnN]2
calculated at $U=4$ eV (d), $U=6$ eV (e), and $U=8$ eV (f). The Fermi level is
at zero energy. The insets show total DOS in the vicinity of the Fermi level.
The corresponding states are mostly of N $2p$ origin, but their exact position
and, consequently, DOS at $E_{F}$, strong depend on the spin polarization of
Mn $d$ orbitals.

MnO behaves as a typical Mott insulator (Fig. 7). A band gap opens at $U=1.8$
eV and grows linearly, albeit with the gradually reduced slope at higher $U$,
whereas magnetic moment on Mn systematically increases due to increased
localization of the Mn $3d$ states. At high $U$ values, it even exceeds the
nominal value of 5 $\mu_{B}$ because of the enhanced polarization of the
surrounding oxygen atoms.

The evolution of Li2Sr[MnN]2 reveals several similarities. Its DOS at the
Fermi level, $N(E_{F})$, also decreases rapidly with $U$, whereas magnetic
moment increases and changes slope around $U=1.8$ eV, where $N(E_{F})$ drops
nearly to zero. The nominal magnetic moment of 4 $\mu_{B}$ is reached at $U=4$
eV, but in contrast to MnO, the gap never opens because a small fraction of N
$2p$ states always remains at the Fermi level. This residual metallicity is
due to the fact that the N $2p$ states are strongly mixed with Mn $3d$,
especially the lowest-lying $d_{3z^{2}-r^{2}}$ orbital. It is occupied by the
minority-spin electron of $3d^{6}$ Mn1+ and remains unpolarized (Fig. 7d), so
it can’t be localized and gapped by adding $U$. Only at $U>4$ eV does one
observe the tendency toward the gradual localization of $d_{3z^{2}-r^{2}}$
states through their spin polarization.

The steep increase in the magnetic moment of Mn above 4 $\mu_{B}$ at $U>4$ eV
reflects this tendency toward polarizing the $d_{3z^{2}-r^{2}}$ states, with
$N(E_{F})$ increasing as the minority-spin states associated with
$d_{3z^{2}-r^{2}}$ are shifted toward positive energies across the Fermi level
(Fig. 7e). This process is completed at $U>6$ eV, where the $d_{3z^{2}-r^{2}}$
states are fully polarized at the cost of placing minority-spin electron onto
the $d_{x^{2}-y^{2}}$ orbital. The resulting configuration features a
pseudogap with $N(E_{F})=0$ but no gap opened even at very high $U=8-10$ eV
(Fig. 7f).

From the experimental $\gamma\simeq 5$ mJ/mol K one expects $N(E_{F})\simeq
2.1$ eV-1/f.u., which may be compatible with the weakly correlated scenario at
$U\simeq 1$ eV or with the intermediate regime at $U=5-6$ eV (Fig. 7b),
especially if renormalization of the effective mass and slight doping caused
by the residual site mixing between Li and Mn are considered. Spectroscopic
experiments and/or direct measurements of the local magnetic moment would be
interesting to distinguish between these two possible regimes.

A more general outcome of our ab initio study is the peculiar behavior of Mn1+
nitride as a correlated material. Here, four $d$-orbitals show weaker
hybridization with nitrogen and thus Mott behavior reminiscent of MnO, whereas
the fifth $d$-orbital has a strong charge-transfer character that causes
residual metallicity due to N $2p$ states remaining at the Fermi level even in
the presence of strong correlations. Another unusual effect is the shift of
the minority-spin electron from the lower-lying $d_{3z^{2}-r^{2}}$ orbital
with the stronger charge-transfer character to the higher-lying
$d_{x^{2}-y^{2}}$ orbital with the weaker charge-transfer character, because
the latter orbital is easier to localize. This unconventional scenario reminds
of some earlier findings for a Ni1+ oxide in the strongly correlated limit
[40] and may be a general mechanism of inducing metallicity at intermediate
values of $U$. Overall, we find that Mn nitrides have a much stronger
proclivity to the metallic behavior than undoped Mn oxides, and one
$d$-orbital with the strong charge-transfer character is already sufficient to
trigger it.

##  IX Discussion

Absolute values and temperature-dependence of $\rho(T)$ as well as DFT
calculations indicate the presence of free charge carriers. There is, however,
no signature in $\rho(T)$ at $T_{N}$. If the proposed AFM ordering of Mn would
be caused by a spin-density-wave transition, as observed for example in the
parent compounds of Fe-based superconductors [41], a clear anomaly is expected
in $\rho(T)$. However, very similar transport behavior with no signature in
$\rho(T)$ at the AFM ordering is observed in underdoped cuprates [42] and
LaMnO3 [43]. This is interpreted as a sign for spatial separation of
conducting and magnetically ordering entities. Nevertheless, we are going to
discuss and disproof the following two hypothetical scenarios:

a) the anomaly in $\chi(T)$ is caused by AFM ordering of an impurity phase.
Given the large absolute values of $\chi(T)$, which exceed the nearly
itinerant ferromagnet Pd more than a factor of 2 [44], only a local moment
bearing material seems possible. Such a phase, however, is expected to show
Curie-Weiss behavior in the paramagnetic region above $T_{N}$, which is in
contrast to the linear increase of $\chi(T)$ with increasing temperature
observed experimentally [Fig. 4(a)]. Obtaining a linear $\chi(T)$ as result of
a superposition of two non-linear contributions (impurity Curie-Weiss and main
phase with high $\chi$) seems highly unlikely. Furthermore, the anisotropy of
$\chi(T)$ with an increase for $H\parallel c$ and a decrease for $H\perp c$
upon heating above $T_{N}$ seems incompatible with a paramagnetic local moment
scenario [Fig. 4(b,c)].

b) the metallic transport is caused by a conducting impurity phase. The low
absolute values of $\rho$ below m$\Omega$ cm require a significant cross
section of a potential current path even when highly conductive materials are
considered. Optical microscopy on pristine as well as on polished surfaces
never revealed indications for the presence of such a phase. Furthermore,
exposure to air leads to a rapid increase of the resistivity by several orders
of magnitude. We infer that also near-surface regions of Li2Sr[MnN]2 make an
important contribution to the electrical transport and do not only connect
spring loaded contacts and other metallic current paths. A lower air-
sensitivity is expected if already insulating Li2Sr[MnN]2 merely bridges
contact leads and a hypothetical conducting impurity phase.

Next, we focus on the high-temperature region ($T>300$ K) of $\chi(T)$. The
large absolute values of $\chi\approx 1.9\cdot 10^{-8}$m3mol${}^{-1}_{\rm Mn}$
are very unusual, in particular in combination with the linear increase with
temperature. The latter is normally not observed for local-moment-bearing or
ferromagnetically ordered materials. All other materials we are aware of,
however, show significantly smaller absolute values of $\chi$. A similar
linear increase of $\chi(T)$ with temperature is found in Fe-based
superconductors, though with lower absolute values at around room temperature
(RT): F-doped LaFeAsO with $\chi_{\rm RT}\approx 4\cdot 10^{-9}$ m3mol-1 [45],
BaFe2As2 with $\chi_{\rm RT}\approx 6\cdot 10^{-9}$ m3mol${}_{\rm Fe}^{-1}$
[46, 45], or SrFe2As2 [47] and CaFe2As2 [48] both with $\chi_{\rm RT}\approx
9\cdot 10^{-9}$ m3mol${}_{\rm Fe}^{-1}$. The peculiar temperature-dependence
was described by assuming a coexistance of localized and itinerant moments
[49], frustrated local-moment model [50], or spin-density-wave scenario with
strong antiferromagnetic fluctations above $T_{\rm N}$ [51]. Also (underdoped)
cuprates show similar temperature-dependencies of $\chi(T)$ with even lower
absolute values ($T>T_{\rm N}$), for example La2-xSrxCuO4 with $\chi\sim
1\cdot 10^{-9}$ m3mol-1 [52]. Note that $\chi$ of elemental Cr also increases
with temperature with a roughly five times smaller slope and one order of
magnitude lower $\chi_{\rm RT}=2.4\cdot 10^{-9}$ m3mol-1 [53] when compared to
Li2Sr[MnN]2.

Observing metallic conductivity in a nitride is not unprecedented, though with
significant differences to Li2Sr[MnN]2: Antiperovskite nitrides of $T_{3}X$N
type [54] (with $X$ = {Ga, Sn, $T$,…}) do show metallic conductivity and
magnetic ordering (for example Mn3ZnN [55, 56]). Those structures, however,
are based on transition-metal rich hosts in strong contrast to insulating,
primarily ionic Li4SrN2. More nitrogen-rich compounds for which a pronounced
metallic temperature-dependence of $\rho(T)$ was experimentally observed are
(SN)x [57], CaNiN [58], SrNiN [59], Sr2NiN2 [60], and Ca2N [61]. No
indications for magnetic ordering were found in any of those materials.

Finally, we discuss the low-temperature properties with anomalies in $\chi(T)$
and $C(T)$ at $T_{f}=1.2$ K. Magnetic ordering of $S=2$ spins ($3d^{6}$ spin
only, according to Mn1+), lead to a change in entropy by $S_{\rm mag}={\rm
R}\ln 5=13.4$ J mol${}^{-1}_{\rm Mn}$ K-1. The measured magnetic entropy of
$S_{\rm mag}\approx 2.3$ mJ mol${}^{-1}_{\rm Mn}$ K-1 amounts to only a small
fraction of that value (and this does not change considering $S=1/2$ instead
of $S=2$). Ordering of 0.02 % of Mn or a correspondingly small amount of
impurities are sufficient to cause the maximum in $C(T)$ and to account for
the measured $S_{\rm mag}$. Furthermore, the effective magnetic moment
obtained from the low-temperature Curie tail amounts to $\mu_{\rm
eff}=0.29(2)\,\mu_{\rm B}$ per Mn (for both orientations, 2 K $<T<50$ K, see
Fig. 4a). Assuming that a certain fraction of Mn, $x_{\rm loc}$, carries local
magnetic moments of $\mu_{\rm eff}\approx 4.9\,\mu_{\rm B}$, according to
$S=2$, leads to $x_{\rm loc}=0.36$ %. [Note that $x_{loc}=(0.29/4.9)^{2}$].
Again, a small fraction of Mn or other local moment bearing impurities is
sufficient to explain the observed behavior. The perfect agreement with the
fraction of isolated Mn atoms of 0.36 %, which follows from $x=0.94$, however,
seems to be accidental. Those Mn have two Li as next-nearest neighbor along
the chain and could be decoupled from the ordered states in longer
$-$N$-$Mn$-$N$-$Mn$-$ chains. Observing an $S_{\rm mag}$ that is one order of
magnitude smaller than expected for $x_{\rm loc}=0.36$ could be caused by the
large uncertainty in determining the non-magnetic background of $C(T)$ or
neglecting crystal electric field effects and exchange interactions. It could
also indicate magnetic frustration or spin-glass behavior with freezing of
local moments at $T_{f}$ [62]. Further similarities to spin-glasses are given
by the splitting of FC and ZFC curves of $\chi(T)$ and the comparatively broad
feature in $C(T)$. Investigating the anomaly at $T_{f}$ for varying $x$ could
serve as a very sensitive method to probe the Mn concentration and
stoichiometry of Li2Sr[MnN]2, provided isolated Mn do indeed cause the
anomaly. In particular, the question arises of whether or not the anomaly
disappears for $x\cong 1.00$. The assumption that the vast majority of Mn
participates in itinerant, magnetic ordering at $T_{\rm N}=290$ K and only a
small fraction of isolated magnetic moments (Mn or impurities) orders at
$T_{f}=1.2$ K is supported by the preponderance of the obtained experimental
data.

##  X Summary

Li2Sr[MnN]2 single crystals of several millimeter along a side were grown from
Li-rich flux. Clear indications for itinerant antiferromagnetic ordering at
$T_{\rm N}=290$ K are found. The magnetic susceptibility above $T_{\rm N}$
increases linearly with temperature and amounts to an exceptionally large
value of $\chi\approx 1.9\cdot 10^{-8}$m3mol${}^{-1}_{\rm Mn}$. The magnetic
ordering is not accompanied by a structural transition as shown by low
temperature single crystal X-ray diffraction. Our main results can be
understood based on structurally well-ordered but finite, linear chains of
$-$N$-$Mn$-$N$-$Mn$-$ that are essential for the observed metallic electrical
transport and magnetic properties. A small fraction of well below 1% of
isolated, local magnetic-moment-bearing Mn or a correspondingly small amount
of a magnetic impurity orders/freezes at $T_{f}=1.2$ K. The experimentally
observed metallic resistivity is corroborated by LDA+U calculations that
identified a strong mixing of N $2p$ with Mn $3d_{3z^{2}-r^{2}}$ states as the
cause of metallicity even in the presence of sizable electronic correlations.
Li2Sr[MnN]2 is a unique magnetically ordered, metallic nitride with a highly
unusual magnetic susceptibility that is reminiscent of the normal state of
(underdoped) cuprate and iron-based superconductors.

##  XI Acknowledgments

The authors thank Sascha Janster, Steffen Hückmann, Klaus Wiedenmann, and
Alexander Herrnberger for experimental assistance. German Hammerl is
acknowledged for help with the electrical transport measurements. This work
was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) - grant number JE748/1.

## References

  * Walz [2002] F. Walz, The verwey transition - a topical review, J. Phys. Cond. Matt. 14, R285 (2002).
  * Timusk and Statt [1999] T. Timusk and B. Statt, The pseudogap in high-temperature superconductors: an experimental survey, Rep. Prog. Phys. 62, 61 (1999).
  * Putzke  _et al._ [2020] C. Putzke, M. D. Bachmann, P. McGuinness, E. Zhakina, V. Sunko, M. Konczykowski, T. Oka, R. Moessner, A. Stern, M. König, S. Khim, A. P. Mackenzie, and P. J. W. Moll, h/e oscillations in interlayer transport of delafossites, Science 368, 1234 (2020).
  * Höhn and Niewa [2017] P. Höhn and R. Niewa, Nitrides of non-main group elements, in  _Handbook of Solid State Chemistry_ (Wiley Online Library, 2017) pp. 251–359.
  * Niewa  _et al._ [2001] R. Niewa, F. Wagner, W. Schnelle, O. Hochrein, and R. Kniep, Li24[MnN3]3N2 and Li5[(Li1-xMnx)N]3, two intermediates in the decomposition path of Li7[MnN4] to Li2[(Li1-xMnx)N]: An experimental and theoretical study, Inorg. Chem. 40, 5215 (2001).
  * Gregory  _et al._ [1995] D. Gregory, M. Barker, P. Edwards, and D. Siddons, Synthesis and structure of Ca6MnN5: A new nitridomanganate with planar [MnN3]6- anions, Inorg. Chem. 34, 5195 (1995).
  * Tennstedt  _et al._ [1993a] A. Tennstedt, C. Röhr, and R. Kniep, Ca3[MnN3], ein neues nitridomanganat (III): Anionen [MnIIIN3]6- mit C2v-Symmetrie/Ca3[MnN3], a new nitridomanganate (III): Anions [MnIIIN3]6- with C2v-symmetry, Z. Naturforsch. B 48, 1831 (1993a).
  * Tennstedt  _et al._ [1993b] A. Tennstedt, C. Röhr, and R. Kniep, Sr3[MnN3] und Ba3[MnN3], die ersten nitridomanganate (III): Trigonal-planare anionen [MnIIIN3]6-/Sr3[MnN3] and Ba3[MnN3], the first nitridomanganates (III): Trigonal-planar anions [MnIIIN3]6-, Z. Naturforsch. B 48, 794 (1993b).
  * Barker  _et al._ [1996] M. G. Barker, M. J. Begley, P. P. Edwards, D. H. Gregory, and S. E. Smith, Synthesis and crystal structures of the new ternary nitrides Sr3CrN3 and Ba3CrN3, J. Chem. Soc. Dalton 1, 1 (1996).
  * Bendyna  _et al._ [2008] J. K. Bendyna, P. Höhn, and R. Kniep, Crystal structure of tristrontium trinitridoferrate(III), Sr3[FeN3], Z. Kristallogr. - New Cryst. Struct. 223, 109 (2008).
  * Hochrein  _et al._ [1998] O. Hochrein, Yu. Grin, and R. Kniep, The hexanitridodimanganate (iv) Li6Ca2[Mn2N6]: Preparation, crystal structure, and chemical bonding, Angew. Chem. Int. Edit. 37, 1582 (1998).
  * Hochrein  _et al._ [2003] O. Hochrein, P. Höhn, and R. Kniep, Control of oxidation states of transition elements (Cr, Mn) in nitridometalates and the solid solution series Li6(Ca1-xSrx)2 [Mn2N6], Z. Anorg. Allg. Chem. 629, 923 (2003).
  * Ovchinnikov  _et al._ [2018a] A. Ovchinnikov, M. Bobnar, Yu. Prots, W. Schnelle, P. Höhn, and Yu. Grin, Ba4[Mn3N6], a quasi-one-dimensional mixed-valent nitridomanganate (II, IV), Crystals 8, 235 (2018a).
  * Ovchinnikov  _et al._ [2018b] A. Ovchinnikov, M. Bobnar, Yu. Prots, H. Borrmann, J. Sichelschmidt, Yu. Grin, and P. Höhn, Ca12[Mn19N23] and Ca133[Mn216N260]: Structural complexity by 2D intergrowth, Angew. Chem. 130, 11753 (2018b).
  * Niewa  _et al._ [1998] R. Niewa, F. DiSalvo, D.-K. Yang, D. Zax, H. Luo, and W. Yelon, Synthesis, crystal structure and properties of a lithium manganese nitride,(Li, Mn)2N, J. Alloys Compd. 266, 32 (1998).
  * Klatyk and Kniep [1999a] J. Klatyk and R. Kniep, Crystal structure of dilithium (nitridolithiate/manganate (I)), Li2[(Li1-xMnx)N], x = 0.73, Z. Krist. - New Cryst. Struc. 214, 445 (1999a).
  * Klatyk  _et al._ [2000] J. Klatyk, R. Niewa, and R. Kniep, Ca$\\{$Li2[MnIN]2$\\}$: Kristallchemischer brückenschlag zwischen lithium-nitrido-verbindungen und borid-carbiden des typs M[B2C2]/Ca$\\{$Li2[MnIN]2$\\}$: Link between crystal chemistry of lithium nitrido compounds and boride carbides of the type M[B2C2], Z. Naturforsch. B 55, 988 (2000).
  * Boström and Hovmöller [2001] M. Boström and S. Hovmöller, Preparation and crystal structure of the novel decagonal approximant Mn123Ga137, J. Alloys Compd. 314, 154 (2001).
  * Jesche and Canfield [2014] A. Jesche and P. C. Canfield, Single crystal growth from light, volatile and reactive materials using lithium and calcium flux, Philos. Mag. 94, 2372 (2014).
  * Höhn  _et al._ [2016] P. Höhn, T. J. Ball$\acute{\rm e}$, M. Fix, Yu. Prots, and A. Jesche, Single Crystal Growth and Anisotropic Magnetic Properties of Li2Sr[Li1-xFexN]2, Inorganics 4, 42 (2016).
  * Ballé  _et al._ [2019] T. J. Ballé, Z. Zangeneh, L. Hozoi, A. Jesche, and P. Höhn, Ferromagnetic ordering of linearly coordinated co ions in ${\mathrm{LiSr}}_{2}[{\mathrm{CoN}}_{2}]$, Phys. Rev. B 99, 094422 (2019).
  * Pathak  _et al._ [2017] M. Pathak, D. Stoiber, M. Bobnar, A. Ovchinnikov, A. Ormeci, R. Niewa, and P. Höhn, Synthesis, characterization, and chemical bonding analysis of the lithium alkaline-earth metal gallide nitrides Li2(Ca3N)2[Ga4] and Li2(Sr3N)2[Ga4], Z. Anorg. Allg. Chem. 643, 1557 (2017).
  * [23] P. Höhn et al., unpublished.
  * WinXPow [2003] WinXPow, STOE & Cie GmbH: Darmstadt, Germany (2003).
  * Dolomanov  _et al._ [2009] O. V. Dolomanov, L. J. Bourhis, R. J. Gildea, J. A. Howard, and H. Puschmann, Olex2: a complete structure solution, refinement and analysis program, J. Appl. Cryst. 42, 339 (2009).
  * Sheldrick [2008] G. M. Sheldrick, A short history of SHELX, Acta Crytsallogr. A 64, 112 (2008).
  * Sheldrick [2015] G. M. Sheldrick, Crystal structure refinement with SHELXL, Acta Crystallogr. C 71, 3 (2015).
  * X-RED [1999] S. X-RED, Data reduction program, STOE & Cie GmbH, Darmstadt (1999).
  * STOE [1999] X. STOE, Shape, crystal optimisation for numerical absorption correction, version 1.06/windows (1999).
  * Eder [1972] F. X. Eder,  _Moderne Messmethoden der Physik_ , edited by R. Rompr and E. Schmutzer, Hochschulbücher für Physik (VEB Deutscher Verlag der Wissenschaften, 1972).
  * Koepernik and Eschrig [1999] K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).
  * Perdew and Wang [1992] J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45, 13244 (1992).
  * Canfield and Fisher [2001] P. C. Canfield and I. R. Fisher, High-temperature solution growth of intermetallic single crystals and quasicrystals, J. Cryst. Growth 225, 155 (2001).
  * Cordier  _et al._ [1989] G. Cordier, A. Gudat, R. Kniep, and A. Rabenau, LiCaN and Li4SrN2, derivatives of the fluorite and lithium nitride structures, Angew. Chem. Int. Ed. 28, 1702 (1989).
  * Klatyk and Kniep [1999b] J. Klatyk and R. Kniep, Crystal structure of alkaline earth dilithium bis(nitridolithiate/ferrates(I)), Ca{Li2[(Li1-xFex)N]2}, $x=0.30$ and Sr{Li2[(Li1-xFexN)]2}, $x=0.46$, Z. Kristallogr. - New Cryst. Struct. 214, 449 (1999b).
  * Jäger and Kniep [1992] J. Jäger and R. Kniep, Nitridocuprate(I): Quaternaere Phasen in den Systemen Li-Ca/Sr-Cu-N., Z. Naturforsch. B 47, 1290 (1992).
  * Kniep and Höhn [2013] R. Kniep and P. Höhn, 2.06 - Low-Valency Nitridometalates, Reference Module in Chemistry, Molecular Sciences and Chemical Engineering, Comprehensive Inorganic Chemistry II (Second Edition), Volume 2 , 137 (2013).
  * Rabenau and Schulz [1976] A. Rabenau and H. Schulz, Re-evaluation of the lithium nitride structure, J. Less-Common Met. 50, 155 (1976).
  * Emery and Kivelson [1995] V. J. Emery and S. A. Kivelson, Superconductivity in bad metals, Phys. Rev. Lett. 74, 3253 (1995).
  * Lee and Pickett [2004] K.-W. Lee and W. E. Pickett, Infinite-layer LaNiO2: Ni1+ is not Cu2+, Phys. Rev. B 70, 165109 (2004).
  * Klauss  _et al._ [2008] H.-H. Klauss, H. Luetkens, R. Klingeler, C. Hess, F. J. Litterst, M. Kraken, M. M. Korshunov, I. Eremin, S.-L. Drechsler, R. Khasanov, A. Amato, J. Hamann-Borrero, N. Leps, A. Kondrat, G. Behr, J. Werner, and B. Büchner, Commensurate spin density wave in lafeaso: A local probe study, Phys. Rev. Lett. 101, 077005 (2008).
  * Ando  _et al._ [2001] Y. Ando, A. N. Lavrov, S. Komiya, K. Segawa, and X. F. Sun, Mobility of the doped holes and the antiferromagnetic correlations in underdoped high-${T}_{\mathrm{c}}$ cuprates, Phys. Rev. Lett. 87, 017001 (2001).
  * de Brion  _et al._ [1999] S. de Brion, F. Ciorcas, G. Chouteau, P. Lejay, P. Radaelli, and C. Chaillout, Magnetic and electric properties of ${\mathrm{La}}_{1-\delta}{\mathrm{MnO}}_{3}$, Phys. Rev. B 59, 1304 (1999).
  * Gerhardt  _et al._ [1981] W. Gerhardt, F. Razavi, J. S. Schilling, D. Hüser, and J. A. Mydosh, Pressure dependence of the magnetic susceptibility of pure Pd to 3.7 GPa from 1.3 to 300 K, Phys. Rev. B 24, 6744 (1981).
  * Klingeler  _et al._ [2010] R. Klingeler, N. Leps, I. Hellmann, A. Popa, U. Stockert, C. Hess, V. Kataev, H.-J. Grafe, F. Hammerath, G. Lang, S. Wurmehl, G. Behr, L. Harnagea, S. Singh, and B. Büchner, Local antiferromagnetic correlations in the iron pnictide superconductors LaFeAsO1-xFx and Ca(Fe1-xCox)2As2 as seen via normal-state susceptibility, Phys. Rev. B 81, 024506 (2010).
  * Wang  _et al._ [2009] X. F. Wang, T. Wu, G. Wu, H. Chen, Y. L. Xie, J. J. Ying, Y. J. Yan, R. H. Liu, and X. H. Chen, Anisotropy in the Electrical Resistivity and Susceptibility of Superconducting BaFe2As2 Single Crystals, Phys. Rev. Lett. 102, 117005 (2009).
  * Yan  _et al._ [2008] J.-Q. Yan, A. Kreyssig, S. Nandi, N. Ni, S. L. Bud’ko, A. Kracher, R. J. McQueeney, R. W. McCallum, T. A. Lograsso, A. I. Goldman, and P. C. Canfield, Structural transition and anisotropic properties of single-crystalline SrFe2As2, Phys. Rev. B 78, 024516 (2008).
  * Ronning  _et al._ [2008] F. Ronning, T. Klimczuk, E. D. Bauer, H. Volz, and J. D. Thompson, Synthesis and properties of CaFe2As2 single crystals, J. Phys. Condens. Matt. 20, 322201 (2008).
  * Kou  _et al._ [2009] S.-P. Kou, T. Li, and Z.-Y. Weng, Coexistence of itinerant electrons and local moments in iron-based superconductors, Europhys. Lett. 88, 17010 (2009).
  * Schmidt  _et al._ [2010] B. Schmidt, M. Siahatgar, and P. Thalmeier, Frustrated local-moment models for iron pnictide magnetism, Phys. Rev. B 81, 165101 (2010).
  * Zhang  _et al._ [2009] G. M. Zhang, Y. H. Su, Z. Y. Lu, Z. Y. Weng, D. H. Lee, and T. Xiang, Universal linear-temperature dependence of static magnetic susceptibility in iron pnictides, Europhys. Lett. 86, 37006 (2009).
  * Nakano  _et al._ [1994] T. Nakano, M. Oda, C. Manabe, N. Momono, Y. Miura, and M. Ido, Magnetic properties and electronic conduction of superconducting La2-xSrxCuO4, Phys. Rev. B 49, 16000 (1994).
  * McGuire and Kriessman [1952] T. R. McGuire and C. J. Kriessman, The magnetic susceptibility of chromium, Phys. Rev. 85, 452 (1952).
  * Ettmayer [1967] P. Ettmayer, Über ein mangan-quecksilber-nitrid mit perowskitstruktur, Monatshefte für Chemie 98, 1881 (1967).
  * Kim  _et al._ [2003] W. S. Kim, E. O. Chi, J. C. Kim, N. H. Hur, K. W. Lee, and Y. N. Choi, Cracks induced by magnetic ordering in the antiperovskite ${\mathrm{ZnNMn}}_{3}$, Phys. Rev. B 68, 172402 (2003).
  * Sun  _et al._ [2013] Y. Sun, Y. Guo, Y. Tsujimoto, J. Yang, B. Shen, W. Yi, Y. Matsushita, C. Wang, X. Wang, J. Li, C. I. Sathish, and K. Yamaura, Carbon-Induced Ferromagnetism in the Antiferromagnetic Metallic Host Material Mn3ZnN, Inorg. Chem. 52, 800 (2013).
  * Walatka  _et al._ [1973] V. V. Walatka, M. M. Labes, and J. H. Perlstein, Polysulfur nitride—a one-dimensional chain with a metallic ground state, Phys. Rev. Lett. 31, 1139 (1973).
  * Chern and Disalvo [1990] M. Y. Chern and F. J. Disalvo, Synthesis, structure, electric, and magnetic properties of CaNiN, J. Solid State Chem. 88, 459 (1990).
  * Yamamoto  _et al._ [1995] T. Yamamoto, S. Kikkawa, and F. Kanamaru, Preparation, Crystal Structure, and Properties of a New Double Metal Nitride, SrNiN, and of Ca1-xSrxNiN ($0\leq x\leq 0.5$) Solid Solutions, J. Solid State Chem. 115, 353 (1995).
  * Kowach  _et al._ [2000] G. R. Kowach, N. E. Brese, U. M. Bolle, C. J. Warren, and F. J. DiSalvo, An Unusual Metallic Nitride: Sr2NiN2, J. Solid State Chem. 154, 542 (2000).
  * Lee  _et al._ [2013] K. Lee, S. W. Kim, Y. Toda, S. Matsuishi, and H. Hosono, Dicalcium nitride as a two-dimensional electride with an anionic electron layer, Nature 494, 336 (2013).
  * Mydosh [1993] J. A. Mydosh,  _Spin glasses: an experimental introduction_ (Taylor & Francis, London + Washington, DC, 1993).