Magnetic-crystallographic phase diagram of the superconducting parent compound Fe_ {1+ x} Te

Abstract

Through neutron diffraction experiments, including spin-polarized measurements, we find a collinear incommensurate spin-density wave with propagation vector k= [0.4481(4) 0 1/2] at base temperature in the superconducting parent compound Fe1+xTe. This critical concentration of interstitial iron corresponds to x≈12% and leads to crystallographic phase separation at base temperature. The spin-density wave is short-range ordered with a correlation length of 22(3) Å, and as the ordering temperature is approached its propagation vector decreases linearly in the H direction and becomes long-range ordered. Upon further populating the interstitial iron site, the spin-density wave gives way to an incommensurate helical ordering with propagation vector k= [0.3855(2) 0 1/2] at base temperature. For a sample with x≈9(1)%, we also find an incommensurate spin-density wave that competes with the bicollinear commensurate ordering close to the Néel point. The shifting of spectral weight between competing magnetic orderings observed in several samples is supporting evidence for the phase separation being electronic in nature, and hence leads to crystallographic phase separation around the critical interstitial iron concentration of 12%. With results from both powder and single crystal samples, we construct a magnetic-crystallographic phase diagram of Fe1+xTe for 5%<x<17%.

Full text

Page 1

Magnetic-crystallographic phase diagram of superconducting parent compound
Fe1+xTe
E. E. Rodriguez,1C. Stock,1,2P. Zajdel,3K. L. Krycka,1C. F. Majkrzak,1P. Zavalij,4and M. A. Green1,5
1NIST Center for Neutron Research, NIST, 100 Bureau Dr., Gaithersburg, MD 20878
2Indiana University, 2401 Milo B. Sampson Lane, Bloomington, IN, 47408
3Division of Physics of Crystals, Institute of Physics, University of Silesia, Katowice, 40-007, Poland
4Department of Chemistry, University of Maryland, College Park, MD 20742
5Department of Materials Science and Engineering,
University of Maryland, College Park, MD 20742
Through neutron diffraction experiments, including spin-polarized measurements, we find a
collinear incommensurate spin-density wave with propagation vector k = (0.4481(4) 0
temperature in the superconducting parent compound Fe1+xTe. This critical concentration of inter-
stitial iron corresponds to x ≈ 12% and leads crystallographic phase separation at base temperature.
The spin-density wave is short-range ordered with a correlation length of 22(3)˚ A, and as the or-
dering temperature is approached its propagation vector decreases linearly in the H-direction and
becomes long-range ordered. Upon further populating the interstitial iron site, the spin-density wave
gives way to an incommensurate helical ordering with propagation vector k = (0.3855(2) 0
base temperature. For a sample with x ≈ 9(1)%, we also find an incommensurate spin-density wave
that competes with the bicollinear commensurate ordering close to the N´ eel point. The shifting of
spectral weight between competing magnetic orderings observed in several samples is supporting ev-
idence for the phase separation being electronic in nature, and hence leads to crystallographic phase
separation around the critical interstitial iron concentration of 12%. With results from both powder
and single crystal samples, we construct a magnetic-crystallographic phase diagram of Fe1+xTe for
5% < x < 17%.
1
2) at base
1
2) at
I.INTRODUCTION
As in the high-Tc cuprates, magnetism is implicated
in the superconducting mechanism of the new Fe-based
materials. Detailed phase diagrams of CeFeAsO1−xFx,1
and BaFe2−xCoxAs2,2have revealed the proximity of a
striped antiferromagnetic ordering to the superconduct-
ing regime. Unsurprisingly, the parent phases of these
superconductors are heavily studied to elucidate the pos-
sible role that magnetic ordering and crystal structure
have on the electronic properties. Structurally related to
the iron pnictides but without the need for the compen-
sating cationic layers, is the simple binary chalcogenide
Fe1+xSe, which was also found to be superconducting.3
While isostructural to Fe1+xSe, Fe1+xTe does not exhibit
bulk superconductivity unless there is sufficient anionic
substitution of Te2−by either S2−or Se2−.4–6The non-
stoichiometry of Fe1+xTe can be understood to arise from
extra interstitial iron cations between the layers of edge-
sharing FeTe4 tetrahedra. Here, we explore the crystal
and magnetic structures of the parent phase Fe1+xTe as
a function of interstitial iron x and temperature and eval-
uate the nature of its magnetic exchange interactions.
While anion substitution in Fe1+xTe is isovalent, it
does play a similar role to hole and electron doping in
the FeAs-based materials as it suppresses a structural dis-
tortion so that the crystal structure remains tetragonal
down to its ground state. Interestingly, several studies
on Fe1+xTe have also revealed that there exists a cor-
relation between the amount of anion substitution and
the amount of interstitial iron, with the “optimal dop-
ing” of S2−or Se2−corresponding to a complete ab-
sence of interstitial iron.7–9These two variables have been
decoupled in two studies on the removal of interstitial
iron topotactically through reaction of powder samples
with iodine vapor.10,11Indeed, the study on a series of
Fe1+xTe0.7Se0.3powders without varying the Se/Te ratio
demonstrated that the superconducting volume fraction
was increased as x was reduced to zero.11
One way the iron chalcogenides differ remarkably from
the FeAs-based superconductors is in the nature of the
antiferromagnetic ordering. In the FeAs-based systems,
the magnetic structure is described as a collinear striped
ordering, which is termed (π, π) ordering since it corre-
sponds to a wave vector connecting the Γ to M points in
the Brillouin zone. Contrastingly, in Fe1+xTe the long-
range magnetic ordering is a bicollinear structure that is
rotated by 45◦with respect to the ordering of the iron
arsenides.12This structure corresponds to a wave vector
of (π, 0), but can change to incommensurate (δπ, 0) with
greater amounts of interstitial iron.13Furthermore, the
size of the magnetic moment per Fe cation in Fe1+xTe
is ≈ 2 µB, much larger than those in analogous parent
phases, e.g. 0.36(5) µB in LaOFeAs,140.93(6) µB in
BaFe2As2,15and 0.09(4) µBin NaFeAs.12The magnetic
properties of the arsenides have led several researchers
to describe the observed ordering to be due to nesting
of the Fermi Surface and therefore largely due to itiner-
ant electron behavior.16For Fe1+xTe, experimental evi-
dence points to a localized model with magnetic suscepti-
bility measurements showing that it follows Curie-Weiss
behavior.12,17
The differences in magnetic ordering raise the possi-
bility that a local moment picture best describes the
arXiv:1105.1937v1 [cond-mat.supr-con] 10 May 2011

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?a*??
?a*??
Monoclinic,
commensurate
bicollinear
Orthorhombic,
incommensurate
helimagnetsim
Mixed-phase,
incommensurate SDW
Elliptical helix
Circular helix
Collinear SDW
Bicollinear AFM
0.30
0.35
0.40
0.45
0.50
0.55
0.04 0.060.080.1
x in Fe1+xTe
0.120.140.160.18
? (r.l.u.)
?a*??
? a*
FIG. 1: [color online] Magnetic-crystallographic phase diagram for Fe1+xTe constructed by plotting the δ of the propagation
vector k = (δ 0
2) versus concentration of interstitial iron at base temperature. The open circles are for data from samples in
this paper, triangle for data from Li et al.,12and diamonds from Bao et al.13At right, the four different magnetic orderings
in Fe1+xTe observed in our neutron diffraction studies. In the commensurate bicollinear antiferromagnetic (AFM) phase, the
moments are along the b-direction only. Upon increasing interstitial iron to 12%, the bicollinear AFM phase gives way to an
incommensurate spin-density wave (SDW) that is collinear and with moments pointed along the b-direction. Upon further
increasing x, a spin component develops along the c-direction, creating first an elliptical helix (elongated along b-direction) and
then circular helix phase. The direction of the propagation vector is shown for all.
1
magnetism in Fe1+xTe and that the chalcogenides are
fundamentally different types of superconductors from
the FeAs-based ones. Despite the discrepancies outlined
above, there are some conspicuous similarities between
the two systems within the superconducting state; for
example, the so-called spin resonance has been observed
as a gapped excitation in inelastic neutron scattering ex-
periments. The spin resonance is located at the (π, π)
position, with an energy that scales with Tc.
Ba1−xKxFe2As2 it was found to be ≈ 14 meV,18and
in Fe1+xTe0.6Se0.4observed around 7 meV.19Thus, sev-
eral studies have focused on the peculiar change of the
magnetic ordering wavevector from (π, 0) to (π, π) in
Fe1+xTe1−ySeyas a function of Se substitutution.20–22A
central question concerning iron telluride is whether the
effect from anionic substitution is either to suppress a
structural distortion, or just remove interstitial iron from
the lattice. Of course, another possibility is that both are
necessary for superconductivity. Comprehensive reviews
on iron-based superconductors and more particularly the
iron chalcogenides can be found elsewhere.23–25
In the
Here we study the parent phase Fe1+xTe for different
amounts of x to understand how chemical composition
controls the crystal structure and magnetic ordering. We
have prepared several single crystal and powder samples
and have outlined key structural and magnetic parame-
ters of the parent compound as a function of temperature
and interstitial iron. This led us to construct a phase di-
agram of Fe1+xTe at base temperature (5 K to 15 K)
for varying amounts of x (Fig. 1). The resulting phase
diagram for Fe1+xTe shows that the magnetic ordering
is richer than found previously and that the propagation
vector and crystal structure undergo an abrupt change at
a critical amount of interstitial iron, x ≈ 12%. Through-
out this paper we describe how studies with neutron pow-
der diffraction in combination with polarized neutron sin-
gle crystal diffraction has allowed us to determine the
relationship between the crystal structure and magnetic
ordering for samples of Fe1+xTe for 5% < x < 17%.
The polarized neutron studies distinguish between struc-
tures that are spin amplitude modulated (i.e. spin den-
sity wave) versus those that are spin direction modulated
(i.e. helical or cycloidal ordering), which were all found
in this system (Fig. 1). The results are divided according
to the different types of ordering observed for x < 12%,
x > 12%, and x ≈ 12%. We then discuss possible ex-
change couplings including both the interstitial iron and
in-plane iron to explain the diverse orderings observed in
Fe1+xTe.
II.EXPERIMENTS
The powder samples were prepared by combining nom-
inal amounts of iron and tellurium powders in evacuated
quartz ampoules, after grinding them in a mortar and
pestle. The powder mixtures were first heated to 450◦C
for a soak time of 12 hrs, followed by a slow ramp up to
750◦C for 12 hours, after which they were furnace cooled.
The single crystal samples were prepared by heating pre-
made powder samples up to 820◦C to 850◦C under vac-
uum, with the higher melt temperature for samples with
higher iron concentrations. In past studies of the Fe-
Te phase diagram,26–29the melting point seems to vary
upon iron concentration but the maximum is around 844
to 847◦C at standard temperature and pressure. The

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samples were kept above the melting point for 12 hours
and then slow-cooled at a rate of 6◦C/hr.
The amount of interstitial iron, as determined by
diffraction measurements,
mately 1 % to 3 % less iron than the nominal amount,
presumably due to reaction of the iron with the quartz
ampoule or from oxide contamination in the starting iron
powder, as previously reported for the preparation of su-
perconducting Fe1+xSe samples.30For the samples with
high iron concentration, this meant adding additional
iron powder to the mixture in the second reheat and crys-
tal growth process. The amount of interstitial iron that
can be accommodated in the layered β-phase has been
reported by several studies, and can range from 7.5% to
16.3%,27or a much narrower 4.2% to 8.7%.26,29Above
the maximum amount, the β-phase is shown to be in
equilibrium with iron metal. From our single X-ray and
neutron powder diffraction studies presented below, the
amount of interstitial iron in our samples vary between
4.2(4)% to 17.4(4)%.
Since these layered compounds cleave easily along the
(0 0 1) plane, small crystals were cleaved from the larger
crystals for single crystal X-ray diffraction in order to
characterize the amount of interstitial iron. The single
crystal XRD was performed with Mo Kα radiation (λ =
0.71073˚ A) and the data collected at 250 K.
The powder samples were characterized by the BT-1
diffractometer at the NIST Center for Neutron Research
(NCNR) with a wavelength of λ = 2.0785˚ A (Ge311
monochromator). Spallation source neutron diffraction
was also performed on select samples using the NPDF
powder diffractometer at the Lujan Neutron Center at
the Los Alamos National Laboratory.
Single crystal neutron diffraction experiments were
performed on several spectrometers at the NCNR. The
characterization of the propagation vector for several
crystals was performed on the BT-9 thermal triple axis
spectrometer with a λ = 2.0875˚ A (pyrolytic graphite
monochromator).Two-dimensional maps of the (H 0
L) plane of a 200 mg single crystal were also obtained
on the MACS cold-source spectrometer. In MACS, only
elastic scattering planes were scanned by fixing the fi-
nal and incident energies to 3.6 meV using the 20 double
bounce PG(002) analyzing crystals and a double focused
PG(002) monochromator.
Polarized neutron diffraction was performed on a 300
mg Fe1.09(1)Te single crystal and the same crystal used
in the MACS experiment. The measurements were per-
formed on the SPINS cold neutron spectrometer with
λ = 4.0449˚ A and a beam polarized vertically using su-
permirrors. The thin Fe/Si magnetic films within the
supermirror reflect spin +1
neutrons are transmitted, the latter of which were in-
cident on the sample. Polarization analysis of the re-
flected beam was performed with a similar Soller col-
limator and supermirror assembly described in earlier
work.31,32Tight collimation following the supermirrors
was used to absorb the +1
2neutrons, and flipper coils
corresponded to approxi-
2neutrons, so only spin −1
2
b
c
a
NSF?
SF
Q
P0
S
SDW model
Helical model
FIG. 2: [color online] The experimental setup for the neutron
spin polarized diffraction studies on single crystals of Fe1+xTe.
The neutron beam is polarized vertically as represented by the
vector P0, which is normal to the scattering vector Q, allow-
ing one to measure the spin amplitude vector S⊥ in the non-
spin flip (NSF) and spin flip (SF) channels. By aligning the
crystals to have the b-axis parallel to P0, one can distingish
between a magnetic structure with collinear arrangement as
the spin density wave (SDW) model or a non-collinear one
such as the helical model. The interstitial iron site is shown
in the crystal structures, but their moments (along with the
Te atoms) are excluded for clarity.
were placed before and after the sample.
The crystals were aligned so the scattering vector Q
was set perpendicular to the beam polarization direction
P0, and S⊥was measured. We define S⊥as the spin am-
plitude vector normal to Q. In the non-spin flip (NSF)
channels, the S⊥component parallel to the b-axis is mea-
sured, and in the spin flip (SF) channels, component par-
allel to the (H 0 L) plane is measured. This experimental
setup is illustrated in Fig. 2. Nuclear scattering also ap-
pears in the NSF channels and the (001) nuclear peak
was measured for both crystals to obtain the NSF/SF
ratio, or flipping ratio, which was found to be ≈ 20.
III.RESULTS
A. Crystallography
Below the the N´ eel point (≈ 60 K to 70 K), Fe1+xTe
is known to undergo a crystallographic phase transition
from tetragonal P4/nmm symmetry to either monoclinic
P21/m or orthorhombic Pmmn symmetry.12,13,33There-
fore, the neutron powder diffraction (NPD) studies on
13 samples were performed at 100 K and base tem-
perature (5 K to 15 K). The structural parameters for
all the samples were obtained using the GSAS Rietveld
suite of programs.34Although no new crystallographic
phases were found, there is a special iron concentration

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4
of x ≈ 12% that leads to phase separation at base tem-
perature as shown in Fig. 3a. At 100 K this phase can
be fit with a single tetragonal phase (Fig. 3b) even with
data from the high-resolution, backscattering banks of
NPDF and the high-resolution BT-1 diffractometer. The
structural parameters for this phase at base temperature
and 100 K from the NPDF data are given in Table I.
The structural parameters for the phase with a higher
amount of interstitial iron Fe1.142(1)Te are also presented
in Table I.
The neutron powder diffraction results confirm that
increasing interstitial iron changes the low-temperature
phase from monoclinic to orthorhombic symmetry. We
find that 11.9(1)% of excess iron is the percentage neces-
sary to nucleate the orthorhombic phase.
Lattice constants and relevant bond distances and an-
gles from the BT-1 and NPDF data are presented in
Fig. 4. The splitting of the a-parameter at the low tem-
perature transition is quite dramatic but remains mostly
constant throughout the monoclinic phase (Fig. 4a). In
the orthorhombic phase, the splitting between the a and
b parameters is reduced. The c-parameter, which corre-
sponds to interlayer spacing, decreases as the amount of
interstitial iron is increased (Fig. 3a,b). This trend makes
sense since the coordination of the interstitial iron to the
0
1
0
2
1
3
4
2
5
3
6
7
4
Observed
Calculated
Difference
Tetragonal
I normalized
100 K
15 K
Rwp = 2.20 %
Rwp = 3.86 %
0
1
2
3
4
4681012
Observed
Calculated
Difference
Monoclinic
Orthorhombic
I normalized
Q (Å-1)
15 K
Rwp = 3.86 %
(a)
(b)
4681012
Orthorhombic
I normalized
Q (Å-1)
FIG. 3: [color online] The observed and calculated neutron
powder diffraction patterns of Fe1.12Te from the time-of-flight
NPDF diffractometer with the difference pattern and phase
reflection marks below. In (a) the 15 K data is fit with mon-
oclinic and orthorhombic phases, and in (b) the 100 K data
is fit with a single tetragonal phase.
Te anions is square pyramidal, bonded to four Te atoms
within one layer and a fifth one in the adjacent layer.
As more of these interstitial sites are occupied, the effect
should be to draw the layers together and therefore de-
crease c. This trend was found for all the crystallographic
phases (Fig. 4b).
The small percent occupancy and disordered nature of
the interstitial iron site significantly increase the stan-
dard uncertainties of its structural parameters. Further-
TABLE I: Crystal structural parameters for Fe1.119(1)Te and
Fe1.142(1)Te powder samples obtained from the NPDF data at
15 K and 100 K.
Fe1.119(1)Te, 15 K, Rwp = 3.86%
P21/m (unique axis b)
a = 3.83378(6), b = 3.78667(8), c = 6.246427(8), β = 89.359(1)
atom Site xyz
Fe12e 0.7600(3) 0.250.0036(2)
Fe22e 0.240(2) 0.250.715(1)
Te2e 0.2552(4) 0.25 0.2844(2)
Uiso (˚ A2)
0.00206(2) 1.0
0.00206(2) 0.119(1)
0.00206(2) 1.0
Occ.
Pmmn (origin choice 2)
a = 3.83259(5), b = 3.78667(8), c = 6.24627(8)
atom Site x y
Fe12b 0.750.25
Fe22a 0.250.25
Te2a 0.250.25
z
0.0028(3)
0.726(2)
0.2821(3)
Uiso (˚ A2)
0.00206(2) 1.0
0.00206(2) 0.119(1)
0.00206(2) 1.0
Occ.
Fe1.0.119(1)Te, 100 K, Rwp = 2.20%
P4/nmm (origin choice 2)
a = 3.8119(1), c = 6.2468(2)
yz
2a 0.750.25
2c 0.25 0.25
2c 0.250.25
atom Site x
Fe1
Fe2
Te
Uiso˚ A2
0.00528(2) 1.0
0.00528(2) 0.119(1)
Occ.
0.0
0.7220(3)
0.28367(7) 0.00528(2) 1.0
Fe1.142(1)Te, 15 K, , Rwp = 3.42%
Pmmn (origin choice 2)
a = 3.81856(4), b = 3.79092(4), c = 6.24898(7)
atom Site xy
Fe12b 0.750.25
Fe2 2a 0.250.25
Te2a 0.250.25
z
0.0029(2)
0.6954(6)
0.2801(1)
Uiso (˚ A2)
0.00353(5) 1.0
0.00353(5) 0.142(1)
0.00353(5) 1.0
Occ.
Fe1.142(1)Te, 100 K, Rwp = 3.72%
P4/nmm (origin choice 2)
a = 3.81141(2), c = 6.24656(7)
yz
2a 0.750.25
2c 0.250.25
2c 0.250.25
atom Site x
Fe1
Fe2
Te
Uiso˚ A2
0.00506(2) 1.0
0.00506(2) 0.142(1)
0.00506(1) 1.0
Occ.
0.0
0.6953(6)
0.2801(1)

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6.250
6.260
6.270
Monoclinic
Orthorhombic
Tetragonal
y = 6.2554 - 0.043923x R= 0.68331
c lattice constant (Å)
3.78
3.79
3.80
3.81
3.82
3.83
3.84
Monoclinic
Orthorhombic
Tetragonal
y = 3.8152 - 0.028852x R= 0.88974
a,b lattice constant (Å)
a
b
2.56
118.0
2.61
2.67
2.72
Fe1-Fe1
Fe1-Fe2
Fe-Fe distance (Å)
117.0
117.5
0.030.060.090.120.15
Te-Fe-Te angle ( o )
x
(a)
(b)
(c)
(d)
FIG. 4: [color online] Lattice parameters and relevant bond
distances and angles as a function of interstitial iron, x, ob-
tained from the neutron analysis. (a) The a,b lattice con-
stants with the tetragonal data taken at 100K, and the rest
at base temperature (5 K to 15 K). (b) The c lattice constant,
or interplanar spacing. (c) The iron-iron bond distances with
Fe1 corresponding to the in-plane iron and Fe2 to the intersti-
tial iron at 100 K. (d) The Te–Fe1–Te tetrahedral bond angle
at 100 K.
more, the fractional coordinates are correlated to atomic
displacement parameters Uiso’s and occupancies. In the
refinements, the Uiso’s were constrained to be equal for all
the atoms. Since only one coordinate is refinable for the
interstitial iron (Fe2 in Table I) in the tetragonal phase,
the relevant bond distances and bond angles presented
in Fig. 4c,d are from the tetragonal phase. The Fe1-Fe1
distance is the nearest neighbor distance within the iron
square lattice (= a/√2) and Fe1-Fe2 is the distance from
the in-plane iron site (Fe1) to the interstitial iron site
(Fe2). The iron-iron distances are shown in Fig. 4c, and
it is remarkable that for most of the phase diagram, the
Fe1-Fe1 distance is smaller than the Fe1-Fe2 distance.
Only when excess iron reaches ≈ 14% does the Fe1-Fe2
distance become equal to that of Fe1-Fe1( Fig. 3c). No
doubt this shift in iron-iron distances causes a change
in exchange parameters that would explain the different
magnetic structures due to varying amounts of intersti-
tial iron.
Another interesting parameter to observe upon in-
creasing x in Fe1+xTe, is the Te–Fe–Te tetrahedral
bond angle.This tetrahedral angle along with pnic-
tide/chalcogenide height have been cited as important
structural parameters in the Fe-based superconductors.
Generally, the closer this angle gets to the ideal 109.5◦,
the higher the Tc.1,35As interstitial iron is increased, this
angle becomes more distorted in the monoclinic phase
until critical percentage of ≈ 12% above which the struc-
ture becomes orthorhombic (Fig. 4d). Within the mon-
oclinic phase, the a and b parameters are not changing
significantly with interestitial iron, unlike the interlayer
spacing and the Te–Fe–Te bond angles. Therefore, the
structural change from monoclinic to orthorhombic sym-
metry could be driven by the lattice lowering its energy
by retaining the Te–Fe–Te bond angle closer to ≈ 117.2◦,
a value common to both the low and high end of x in
Fe1+xTe (Fig. 4d).
B.Collinear magnetic ordering for x < 12%
The magnetic Bragg peaks observed in the BT-1 pow-
der data of Fe1.051(3)Te can be fit with the commensurate
magnetic structure known as a bicollinear antiferromag-
netic structure (Fig. 5). Although this is a straightfor-
ward collinear ordering, the method of respresentational
analysis was employed here in order to be consistent with
the analysis of the more complex, incommensurate order-
ings presented for x > 12. Representational analysis us-
ing the program BasIreps (version 4.0) from the FullProf
Rietveld suite was employed,36and the irreducible repre-
sentations with their basis vectors for vector k = (1
under P21m symmetry are presented in Table II.
The magnetic Bragg peaks were fit with representation
Γ1, which shows that the moment has a component only
in the b-direction and that the iron atoms at x,y,z and
-x,y +1
2,-z are ferromagnetically aligned. This leads to
the bicollinear ordering, which features two ferromagnet-
ically coupled stripes (Fig. 5). The average moment size
obtained from three powder samples is 1.78(3) µB/Fe for
both the in-plane and interstitial iron sites. This value is
close to the one reported by Ikkubo et al. of 1.86(2) µB37
but lower than the values of 2.54(2), 2.25(8), and 2.07(7)
µBfound by previous neutron studies.12,33,38One possi-
201
2)

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6
TABLE II: The basis functions ψ for each Fe atom in the unit
cell under the four irreducible representations for both space
groups P21m and Pmmn. The return vector ? is exp(−iπδ),
where δ is part of the propagation vector k = (δ 0
varies according to amount of interstitial iron x. The coordi-
nates for site 1 are x,y,z, and those for site 2 are -x,y +1
for P21m and x +1
1
2) and
2,-z
2,-y,-z for Pmmn.
P21/mPmmn
Irrep ψ for site 1 ψ for site 2 ψ for site 1 ψ for site 2
Γ1
(0 1 0)(0 1 0)
Γ2
(1 0 0)(-1 0 0)
(0 0 1)(0 0 -1)
Γ3
(1 0 0)(1 0 0)
(0 0 1) (0 0 1)
Γ4
(0 1 0) (0 -1 0)
(0 1 0)
(1 0 0)
(0 0 1)
(1 0 0)
(0 0 1)
(0 1 0)
(0 ? 0)
(-? 0 0)
(0 0 ?)
(? 0 0)
(0 0 -?)
(0 -? 0)
ble reason for this range in reported moment size could be
due to some studies allowing the moment to point in any
direction,12,33while the 1.78(3) µBfound in this study is
obtained when the moment is constrained to be along b.
The magnetic structure of all our powder samples with
interstitial iron less than 12% were successfully fit with
this representation.
Polarized neutron measurements on a single crystal
sample (SPINS) confirm that the collinear structure with
moments only along the b-axis is the correct model for
the commensurate phase. If scattering is be observed
only in the NSF channels, the ordering is collinear with
moments only along b (Γ1 representation). If there is
also scattering in the SF channels, then helical or other
noncollinear ordering is correct (Fig. 2). For a crystal
a
b
c
FIG. 5: [color online] The crystal structure of Fe1+xTe with
the layers consisting of edge-sharing FeTe4 tetrahedra. The
interstitial iron sites, shown as beach ball spheres, are par-
tially occupied and disordered. The magnetic lattice of the
antiferromagnetic structure commensurate with the chemical
lattice consists of bicollinear chains with moments pointing
in the b-direction. Only the moments of the Fe atoms in the
tetrahedral coordination are shown for clarity. Such ordering
corresponds to a magnetic propagation vector of k = (1
in reciprocal lattice units.
20
1
2)
with composition Fe1.09(1)Te, only scattering in the NSF
channel was observed (Fig. 6), which would be consistent
with the model of spin component only along b.
Contour maps of the NSF magnetic scattering ver-
sus temperature upon warming and cooling are shown
in Fig. 6a,b. One interesting feature not observed be-
fore appears close to the N´ eel point; an incommensu-
rate propagation vector competes with the commensu-
rate bicollinear ordering.Upon cooling and warming,
this incommensurate wave vector appears at H= 0.421(1)
and moves towards the commensurate H = 0.5 position
(Fig. 6b). It is important to note that this incommen-
surate wave vector, like the commensurate one, has no
scattering in the SF channels (Fig. 6c–e) proving that
the moment direction in this composition is collinear for
both the commensurate and incommensurate orderings.
The collinear incommensurate scattering seen close to
T (K)
60
50
40
30
20
10
60
58
56
54
52
50
48
46
T (K)
(a)
NSF,
warming
(b)
NSF,
cooling
(c) (d) (e)
H 0 ? (r.l.u.)
0.42 0.46 0.50
H 0 ? (r.l.u.)
0.42 0.46 0.50
0
200
400
600
0.42 0.45 0.48 0.51
H 0 1/2 (r.l.u.)
NSF
SF
Intensity (counts/min)
57 K
0.42 0.45 0.48 0.51
H 0 1/2 (r.l.u.)
50 K
0.42 0.45 0.48 0.51
H 0 1/2 (r.l.u.)
47 K
FIG. 6: [color online] The non-spin flip (NSF) magnetic scat-
tering of a single crystal with composition Fe1.09(1)Te as mea-
sured on the SPINS spectrometer with a vertically polarized
neutron beam. In (a) the contour map shows the scattering
versus temperature upon warming, and in (b) upon cooling.
Near the N´ eel point, an incommensurate wave vector is shown
in both maps to compete with the commensurate k = (1
ordering. In (c) through (e), cross sections of the scattering in
the NSF and spin-flip (SF) channels is shown for various tem-
peratures upon cooling. This data confirms a model where
the moment lies only in the b-direction for both the incom-
mensurate wave vector appearing close to the N´ eel point and
the commensurate wave vector that exists in the ground state
of Fe1.09(1)Te
.
20
1
2)

Page 7

7
0
0.2
0.4
0.6
0.8
1
4045 50
T (K)
5560
Inormalized
(a)
(b)
SDW cooling
SDW warming
Bicollinear warming
Bicollinear cooling
0.42
0.44
0.46
0.48
0.50
? (r.l.u.)
FIG. 7: [color online] Peak centers and integrated intensi-
ties from fits to the magnetic Bragg peaks of a single crystal
Fe1.09(1)Te measured in the spin polarized experiments on the
SPINS spectrometer. In (a) the peak centers and therefore
the δ from the propagation vector k = (δ 0
temperature upon warming and cooling. In (b) the integrated
intensities for the Fe1.09(1)Te crystal upon cooling and warm-
ing.
1
2) is shown versus
the N´ eel point has never been observed for the composi-
tion known to have a bicollinear ordering as its ground
state. The competition between the two types of order-
ing is better presented by plotting the peak centers, in-
tegrated intensities, and widths from Gaussian fits. In
Fig. 7a the peak center is plotted versus temperature
upon warming and cooling; the incommensurate vector
is shown to have a temperature dependence that is linear
while the commensurate vector has little temperature de-
pendence. In Fig. 7b, the integrated intensities for both
magnetic peaks at k = (1
normalized to the magnetic intensity of k = (1
10 K. Upon warming, the spectral weight of the commen-
surate ordering shifts to the incommensurate one before
the N´ eel point. The hysteresis in the temperature depen-
dence of the propagation vectors and integrated intensi-
ties suggests a first-order transition, which is consistent
with a structural transition above the magnetic ordering
one.
201
2) and k = (δ 01
2) are shown
201
2) at
C.Helical magnetism in x > 12%
The incommensurate magnetic ordering of a powder
sample (BT-1) with composition Fe1.143(3)Te was solved
with representational analysis since use of colored space
groups or Shubnikov groups is insufficient to solve such
structures.39,40For the crystal symmetry of Pmmn,
there are four symmetry elements under which the propa-
gation vector k = (δ 01
the four irreducible representations; their basis vectors ψ
are presented in Table II. For the incommensurate struc-
ture of Fe1.143(3)Te, the refinements using Γ1, Γ2, and Γ3
converge, but only Γ1fits the powder profile satisfacto-
rily (magnetic R factor = 33.3%). This representation is
related to that of Γ1under P21/m symmetry (Table II)
since it leads to ferromagnetic coupling between the same
atoms with the chief difference being that in Pmmn the
coupling is modulated by the phase factor πδ. The result-
ing structure from the fit to Γ1leads to a spin-amplitude
modulated structure or spin-density wave (SDW) order-
ing illustrated in Fig. 2.
The study by Bao et al., however, found that the in-
commensurate structure is a complex helical structure
with a moment contribution in all directions.
Fe1+xTe undergoes a first order transition, the mixing
of irreducible representations is allowed. All combina-
tions of the representations in Table II were tried, and
the only one leading to a lower residual than using Γ1
alone was the combination Γ1+Γ2(magnetic R-factor =
25.1%). In this helical ordering, the moment traces out
a circle on the bc-plane with the propagation direction of
the helix along a. This transverse helical structure shown
in Fig. 2 would also appear like the transverse SDW of
Γ1when projected down the ab-plane. However, the he-
lical model is a better fit to the neutron powder data
than the SDW ordering.The moment size of 1.60(2)
µB/Fe for both the in-plane and interstitial iron sites in-
dicates an approximate 10 % decrease from the moment
size found in the commensurate magnetic phase. Adding
a spin component along the a-direction led to a small mo-
ment size (< 0.2µB) with an uncertainty larger than the
actual parameter. We therefore rule out the possibility
of a spin-component along the a-direction.
The polarized neutron measurements on a crystal with
composition Fe1.124(5)Te revealed two magnetic propaga-
tion vectors in the ground state. The contour maps of the
magnetic scattering versus temperature upon warming
and cooling are presented in Fig. 8a–d. As can be seen
in the contour maps, the ordering with H = 0.3855(2)
has intensity in both the NSF and SF channels while
the one at H = 0.4481(4) only shows intensity in the
NSF channel. Cross sections at different temperatures
are presented in Fig. 8e–g, where the contribution from
the NSF and SF for both peaks is clearly shown. Ac-
cording to our experimental setup (Fig. 2), this implies
that the ordering for H = 0.3855(2) is non-collinear while
that for H = 0.4481(4) is collinear. In this section, we
focus on the incommensurate structure with H≈ 0.385
since this corresponds to the helical ordering, and return
to the other in the following section.
From the BT-1 powder data, the moment of the heli-
cal ordering was found to be constrained to the bc-plane
with equal contributions to the b and c directions. By
analyzing the SF/NSF ratio from the polarized single
crystal experiments, the contribution to each axis can
be calculated. Using the lattice parameters from NPD
2) remains unchanged, leading to
Since

Page 8

8
data of a similar composition, the cosine angle between
Q =(δ 01
51.2◦, which leads to the angle between c∗and S⊥to be
38.8◦. Therefore, if the spin amplitude in the b-direction
and the c-direction are equal, the SF/NSF ratio should
be equal to cos (38.8◦). However, the SF/NSF ratio is
less than this value (≈ 0.78) and remains constant around
0.5 within error as a function of temperature. The aver-
age value of of 0.49(7) for the SF/NSF ratio leads to a
spin amplitude maximum in the c-direction that is about
63(9)% the value in the b-direction. Evidently, in this
2) and c∗was calculated to be approximately
0.360.40.44 0.48
0
90
180
270
360
H 0 1/2 (r.l.u.)
45 K
0.36 0.40 0.45 0.50 0.55
H 0 ? (r.l.u.)
0.38 0.42 0.46
H 0 ? (r.l.u.)
60
50
40
30
20
T (K)
T (K)
T (K)
T (K)
60
55
50
45
40
35
60
50
40
30
20
60
55
50
45
40
35
(a)
NSF,
warming
(b)
NSF,
cooling
(c)
SF,
warming
(d)
SF,
cooling
(e)
(f)
(g)
0
90
180
270
360
0.36 0.40 0.44 0.48
H 0 1/2 (r.l.u.)
NSF
SF
360
Intensity (counts/min)
15 K
270
0.36 0.40 0.44 0.48
H 0 1/2 (r.l.u.)
SF
0
90
180
30 K
FIG. 8: [color online] The non-spin flip (NSF) and spin flip
(SF) magnetic scattering of a single crystal with composition
Fe1.124(5)Te as measured on the SPINS spectrometer with a
vertically polarized neutron beam. In (a) the contour map
shows the NSF scattering versus temperature upon warm-
ing, and in (b) upon cooling. In (c) the contour map shows
the SF scattering versus temperature upon warming, and in
(d) upon cooling. What both measurements reveal is that
the resolution-limited magnetic peak at H = 0.3855(2) corre-
sponds to a helical type of ordering whereas the broad mag-
netic peak at H = 0.4481(4) corresponds to a spin density
wave (SDW). In (e) through (g), cross sections of the scatter-
ing in the NSF and SF channels is shown for various temper-
atures upon warming.
composition of Fe1.125(5)Te the helical structure does not
trace out a circle in the bc-plane as found for Fe1.143(3)Te,
but instead an ellipse elongated in the b-direction.
D.Short-range spin density wave ordering in
x ≈ 12%
From the NPD data, the composition of x ≈ 12%
leads to crystallographic phase separation and to short-
range magnetic order. In Fig. 9a–c the low-angle mag-
netic peaks for several compositions shows that as ex-
cess iron is increased, the position, intensity, and shape
of the magnetic peak changes. For Fe1.051(3)Te the bi-
collinear commensurate ordering fits the two closely sep-
arated magnetic Bragg peaks close to the nuclear (001)
peak (Fig. 9a). At the other end of the phase diagram,
Fe1.143(3)Te, the magnetic peak is fit with the incom-
mensurate helical ordering discussed above (Fig. 9d) .
For compositions near x ≈ 12%, however, the magnetic
scattering does not correspond to either the commensu-
rate bicollinear structure nor the incommensurate helical
structure. Furthermore, the peaks in this composition
are significantly broadened with respect to the nuclear
peaks, indicating these are not long-range ordered mag-
netic structures. For Fe1.119(1)Te, the peaks move to an
intermediate scattering angle and appear to consist of
two magnetic phases (Fig. 9b), which is consistent with
the observation of two crystallographic phases at base
temperature. The trend continues for Fe1.126(2)Te, where
the magnetic phases are separate enough to be distin-
guishable, and the structure also consists of two crystal-
lographic phases.
While we can fit the magnetic structures of Fe1.051(3)Te
and Fe1.143(3)Te satisfactorily with the BT-1 pow-
der data, the fits to the intermediate structures of
Fe1.119(1)Te and Fe1.126(2)Te are complicated by their
multi-phase compositions.
bination of incommensurate structures (representation
Γ1) only to obtain the propagation vector of these in-
termediate phases (Fig. 9b,c).
tors k = (δ 01
2) were found to have δ = 0.490(1)
and δ = 0.461(1)for Fe1.119(1)Te and δ = 0.483(1) and
δ = 0.379(1) for Fe1.126(2)Te. The limited information
from powder diffraction data, however, make it impos-
sible to distinguish whether this short-range order mag-
netic phase corresponds to an SDW or a helical ordering.
The polarized neutron diffraction studies on a single crys-
tal sample clarifies this ambiguity.
For the crystal with composition Fe1.124(5)Te the con-
tour maps of the magnetic scattering from the SPINS
data versus temperature are presented in Fig. 8a–d. The
presence of two propagation vectors is consistent with the
powder studies showing that for x ≈ 12%, a short-range
magnetic ordering appears along with crystallographic
phase separation. The coexistence of two incommensu-
rate structures in a single sample allows us to compare
the difference between the incommensurate helical order-
Therefore, we fit a com-
The propagation vec-

Page 9

9
ing with H = 0.3855(2) and the intermediate one with H
= 0.4481(4) simultaneously. As can be seen in the con-
tour maps, the feature at H = 0.4481(4) only has intensity
in the NSF channel, and its peak width is considerably
broadened compared to that at H = 0.3855(2), which is
resolution limited (Fig. 8e–g). Therefore, we can con-
clude that the broad, slightly incommensurate magnetic
structure observed in both powder and single crystal sam-
ples corresponds to a short-range ordered SDW.
Although the two magnetic phases could be due to a
heterogenous distribution of interstitial iron, the temper-
ature behavior of the two magnetic peaks suggest oth-
erwise as the two phases interact with each other. As
the N´ eel point is approached upon warming, the prop-
agation vector of the SDW moves towards that of the
helical structure found at H = 0.4481(4) (Fig. 10)a. Fur-
thermore, the spectral weight of the short-range SDW
shifts to the helical structure upon warming as shown
in Fig. 10b, where the integrated intensities of the peaks
are plotted versus temperature. At base temperature the
short-range SDW comprises most of the spectral weight;
above 35 K, the intensity diminishes linearly for the SDW
while that of the helical structure increases. Since the to-
0
0.15
0.3
Icalc
Inorm
0
0.15
0.3
1416
2? (deg.)
18 20
Inorm
1416
2? (deg.)
1820
Fe1.051(3)Te
Fe1.116(2)Te
Fe1.126(2)Te
Fe1.143(3)Te
Observed Calculated
(a) (b)
(c) (d)
FIG. 9: [color online] The evolution of the magnetic propaga-
tion vector with interstitial iron as evidenced by the change
in the low-angle magnetic scattering from BT-1 neutron data.
All data is normalized to the (001) nuclear Bragg peak at
≈ 19.1 deg. 2θ. In (a) the monoclinic Fe1.051(3)Te has two
closely separated magnetic Bragg peaks which correspond to
the (+0.5 0 +0.5) and (-0.5 0 +0.5) satellite positions. In (b)
the broad magnetic scattering is fit with two magnetic phases,
slightly incommensurate at (0.489(1), 0, 0.5) and (0.460(1),
0, 0.5). In (c) the two well separated peaks can be fit with an
incommensurate and slightly incommensurate mangetic or-
dering. (d) Single incommensurate ordering at (0.380(2), 0,
0.5) for Fe1.143(3)Te.
tal magnetic intensity eventually declines, this produces
a maximum in the intensity of the helical magnetic or-
dering around 45 K (Fig. 10b).
At base temperature the peak of the incommensu-
rate SDW in Fe1.124(5)Te is much broader than the in-
commensurate helical structure, as was observed in the
powder diffraction patterns (Fig. 9b–d). Upon warming,
the full-width at half maximum (FWHM) decreases lin-
early above 35 K (Fig. 10c), which corresponds to the
same temperature at which the peak starts to lose in-
tensity. Eventually, the FWHM of the SDW becomes
nearly equivalent to that of the helical structure. Ap-
parently, the SDW is becoming long-range ordered with
increasing temperature as its propagation vector moves
from δ ≈ 0.45 to δ ≈ 0.40. Nevertheless, it remains an
SDW with its moments along b-direction as shown by
comparing the NSF and SF scattering (Fig. 8e–g).
In the SPINS experiment, the peaks were measured
only along (H 0
2), so that information on their profile
in the L-direction is unknown. This loss of information
means that the linear change in the intensity and width
with temperature could be due to shifts of the peak in
the L-direction and not to an actual change in the peak
shape. Therefore, we performed two-dimensional scans of
the magnetic scattering to ensure that the SDW is shift-
ing spectral weight to the helical ordering while becoming
1
0
10
0.2
0.4
0.6
0.8
1
2030
T (K)
405060
Inormalized
Helical cooling
SDW cooling
Helical warming
SDW warming
(a)
(b) (c)
0
10
0.01
0.02
0.03
0.04
2030
T (K)
4050 60
FWHM
0.38
0.40
0.42
0.44
0.46
102030 405060
? (r.l.u.)
T (K)
FIG. 10: [color online] Peak centers and integrated intensi-
ties from fits to the magnetic Bragg peaks of a single crystal
Fe1.124(5)Te measured in the spin polarized experiments on
the SPINS spectrometer. In (a) the peak centers and there-
fore the δ from the propagation vector k = (δ 0
versus temperature upon warming and cooling. In (b) the in-
tegrated intensities for the Fe1.124(5)Te crystal upon warming.
In (c) the full width at half maximum of the two competing
magnetic peaks is shown upon warming.
1
2) is shown

Page 10

10
Fe1.130(5)Te, Ef=3.6 meV, MACS

a) T=2 K

0.4
0.45
0.5
0.55
0.6


0.4
0.45
0.5
0.55
15
0.6
(0,0,L) (r.l.u.)


0.30.40.5
0.4
0.45
0.5
0.55
0.6
(H,0,0) (r.l.u.)


0.30.40.5
0.4
0.45
0.5
0.55
0.6
0.30.4
(H,0,0) (r.l.u.)
0.50.6
0
50
100
150
200
Intensity (Arb. Units)
0.4 0.50.6
0
50
100
150
200
250
(0,0,L) (r.l.u.)
2
4
6
8
10
5
10
1
2
3
4
0.1
0.15
0.2
b) T=45 K
c) T=55 K
f) 2 K, L=[0.48,0.52]
g) 2 K, H=[0.45,0.47]
d) T=70 K
FIG. 11: [color online] Contour maps of the (H 0 L) plane
of Fe1.124(5)Te taken on the MACS spectrometer. The final
and incident energies were set to 3.6 meV, to capture only
the elastic scattering of the two magnetic peaks. The change
in peak position and intensity as a function of temperature is
shown in panels (a)–(d). In (f) the peaks are integrated in L
over a range of 0.48 to 0.52, which shows that the broad short-
range magnetic scattering centered at H = 0.45 dominates
most of the scattering at base temperature. In (g) the width
of the peak, after integrating in H over 0.45 to 0.47, shows that
along the L-direction, the magnetic ordering is long-range.
The bars inside the peaks represent the instrument resolution.
long-range ordered.
The MACS spectrometer is optimized for constructing
two-dimensional maps in reciprocal space at different en-
ergy transfers. We performed measurements of the (H 0
L) plane on the same crystal from the SPINS experiment
at zero energy transfer to obtain the temperature behav-
ior of the purely static magnetic ordering. As shown in
Fig. 11a, the (H 0 L) map reveals that the incommen-
surate SDW is quite broad in H. At base temperature,
integrating over a range of L = 0.48 to 0.52, leads to the
intensities of the mangetic peaks shown in Fig. 11f, which
differ from those of the SPINS experiment (Fig. 8e). This
is due to the fact that in SPINS, the scan is only along
(H 01
2), whereas in MACS one can integrate the intensi-
ties of the magnetic peaks over a wide L-range. Clearly
the short-range SDW magnetic structure dominates the
scattering at base temperature in this composition.
As the temperature is increased up to the N´ eel point,
the intensity shifts dramatically towards the H= 0.385
peak (Fig. 11a–c).Above the ordering temperature,
the scattering has become quite diffuse with significant
broadening in L (Fig. 11d). The correlation length along
H of the short-range SDW can be found by fitting a
Lorentzian squared term to the peak shown in Fig. 11f.41
The correlation length along H was found to be 22(3)
˚ A for the SDW in Fe1.124(5)Te at base temperature. The
integrated intensity of this peak along (0 0 L) shows that
it is actually long-range ordered in this direction as the
peak width was nearly equal to the instrument resolution
(Fig. 11g).
Overall, the MACS data corroborates the SPINS data,
and both suggest that the two magnetic ordering vectors
within the same crystal (x ≈ 12%) occur due to some
electronic phase separation and not microscopic chemical
phase separation. Furthermore, this crystal was shown
by single crystal XRD to be a single phase at 250 K.
Likewise for the NPD patterns of Fe1.126(2)Te above the
structural transition, only a tetragonal phase is sufficient
to describe the structure. For the commensurate phase
Fe1.09(1)Te, the SDW makes a brief appearance only close
to the N´ eel point and is long-range. This suggests that in
order to observe the short-range SDW, electronic phase
separation has to occur, which would also lead to the ob-
served structural phase separation at base temperature.
This structural frustration leads to a freezing in of the
short-range SDW.
IV.DISCUSSION AND CONCLUSIONS
To summarize some of the key results presented above,
we have constructed a magnetic-crystallographic phase
diagram of our 13 powder and 6 single crystal samples.
The δ of the propagation vector k = (δ 01
against the interstitial iron concentration; various signif-
icant information regarding the magnetic and crystallo-
graphic structure is also included (Fig. 1). What is ap-
parent from this diagram is that the tuning of the propa-
gation vector according to interstitial iron does not vary
linearly as proposed in an earlier study.13Instead, there
is a threshold of interstitial iron required to change the
propagation vector from k = (1
At this critical concentration of ≈ 12%, crystallographic
phase separation including orthorhombic and monoclinic
symmetries occurs down to base temperature. Within
this phase an incommensurate and short-range ordered
spin-density wave (SDW) freezes in. Previously unknown
for Fe1+xTe, this SDW order appears at k = (≈ 0.45 01
at base temperature and upon warming, changes its posi-
tion in the H-direction, becomes long-range ordered, and
shifts its spectral weight to the other incommensurate or-
dering. It is also important to note that the bicollinear
commensurate phase also has an SDW that appears at
higher temperatures close to the N´ eel point and competes
with the commensurate phase.
Constant energy scans of the (H 0 L) plane of a single
crystal reveal that this SDW has a correlation length of
22(3)˚ A in the H-direction, but is long-range ordered in
2) is plotted
201
2) to k = (δ 01
2) .
2)

Page 11

11
the L-direction. As more interstitial iron is added, a spin
component in the c-direction develops so that the SDW
structure gives way to a helical structure elongated in the
b-direction (an elliptical helix). Once at x = 14.3(3)%,
the spin-components in the b and c-directions are equal,
so that the structure can be described as a circular helix
with a turn angle of πδ (≈ 69.3◦). This study shows that
the magnetic phase diagram of Fe1+xTe is much richer
than initially suspected, and all of these structures are
illustrated in Fig. 1.
We can attempt to explain the variety of observed mag-
netic structures to a first approximation within a local
moment picture. In the helical ordered state, we label
the exchange parameters between the nearest neighbor
iron cations as J1and second-nearest neighbor cations as
J2, which is split into J2aand J2bdue to the orthorhom-
bic distortion. For the interstitial iron sites, the same
interactions are relevant and are labeled J3 for nearest
neighbor interactions with the in-plane iron sublattice,
and J4for the nearest neighbor interaction among the in-
terstitial sites. Again, the orthorhombic distortion causes
J3to split into J3aand J3b. The labeling of the exchange
parameters in shown in Fig. 12. Based on the known he-
lical structure we found for Fe1.146(3), we can write an
expression relating the exchange parameters using the
classical Heisenberg formulation.
H =
?
<i,j>
Ji,jSi· Sj
(1)
E = N1S2[J1cos(α) + J2acos(2α) + J2b]
+N2S2[J3acos(α) + J4cos(2α) + J3b](2)
where α is the turn angle along the a-direction (=
πδ ≈ 69.3◦), N1is the number of nearest neighbor and
second-nearest neighbors within the in-plane iron square
lattice and N2is the number of nearest and second near-
est neighbors between the interstitial iron and other sites.
We can then find the relation between the exchange pa-
rameters that would lead to the lowest energy with re-
spect to the turn angle.
dE
dα
= −N1S2[J1sin(α) − 2J2asin(2α)]
−N2S2[J3asin(α) − 2J4sin(2α)]
0 = −(N1J1+ N2J3a)sin(α)
−4(N1J2a+ N2J4)sin(α)cos(α)
(3)
(4)
(N1J1+ N2J3a)
(N1J2a+ N2J4)= −4cosα(5)
This localized model shows that for the observed prop-
agation vector (4cosα > 1), the nearest neighbor in-
teractions become greater than the second-nearest inter-
actions. Therefore, the helical structure is a result of
frustration in J1and J3a, which becomes greater as the
number of interstitial iron sites N2become populated.
For the other extreme of the phase diagram, the com-
mensurate bicollinear phase, the monoclinic setting splits
J1 into J1a and J1b, relieving the frustration present
in the orthorhombic phase. Inelastic neutron scattering
measurements of the spin waves in a crystal of low in-
terstitial iron, found that J1aand J1bare indeed highly
anisotropic and ferromagnetic whereas J2was found to
be smaller, antiferromagnetic, and isotropic.42This im-
plies that the denominator of Eqn. (5) plays less of a
role determining the observed changes in the magnetic
ordering in Fe1+xTe.
From Eqn. (5), one can calculate what the angle and
therefore propagation vector should be for the case of the
ratio of the exchange parameters becoming equal. This
propagation vector corresponds to δ = 0.42, which is in-
cidentally equal to the propagation vector of the SDW
competing with the commensurate phase in Fe1.09(1)Te
(Fig. 6) as the N´ eel point is approached. This suggests
that as the structure is getting closer to the tetragonal
setting, the nearest and next nearest neighbor interac-
tions become approximately equal in magnitude.
From our NPD results, there are no obvious changes in
the ab plane as interstitial iron is increased. The largest
changes occur in the c parameter, which decreases as x
increases and the monoclinic angle β, which widens as x
increases. Instead of the entire crystal changing to the
orthorhombic phase, however, phase separation occurs.
This phase separation seems to be necessary to observe
SDW ordering with a short-range correlation length. We
speculate that an interplay between J1 and J3a and a
strong anisotropy in the b-direction leads to a collinear
b
a
J3b
J3a
J2b
J2a
J1
J4b
J4a
In-plane iron sublattice
Interstitial iron sublattice
Iron sublattice
FIG. 12: [color online] Labeling of the exchange parameters
for the helical ordering present in Fe1.143(5)Te. On top, the
three exchange parameters used for the in-plane iron atoms
(rendered) . Similar exchange parameters are present for the
interstitial sites, which are shown below with filled circles rep-
resenting the site at z ≈ 0.7 and the empty circles the site at
z ≈ 0.3. The exchange parameters linking the two iron sub-
lattices are shown to the right.

Page 12

12
SDW and then an elliptical helix elongated along the b-
direction, rather than a circular helical ordering.
More recent inelastic neutron scattering measurements
that probe low-energy excitations of two crystals repre-
senting opposite ends of the phase diagram shed light
on the role of interstitial iron on the magnetic fluctua-
tions in Fe1+xTe.43The dispersion curves of the magnetic
excitations have revealed that the commensurate phase
with low interstitial iron Fe1.057(7)Te has an energy gap
of 7 meV at base temperature. The other extreme of
the phase has no such energy gap, but is peaked at an
energy of around 4 meV. This suggests that in the com-
mensurate phase there exists an anisotropy gap favoring
moments aligned along b. This energy gap is incidently
of the same magnitude as the spin resonance observed
in the superconducting phases. The fact that the crystal
with stoichiometry Fe1.141(5)Te has no gap is perfectly
consistent with our diffraction studies showing a helical
ordering with moments directed towards the b- and c-
direction, i.e. the anisotropy gap is closed.
Several theoretical studies have tried to answer the
question of what microscopic mechanisms are responsi-
ble for the exchange interactions driving the observed
ordering of Fe1+xTe to be different from the rest of the
parent phases of iron-based superconductors. The dif-
ferent approaches can be broadly summarized into three
different models: the itinerant picture predicting the ob-
served ordering based of Fermi surface nesting, the local-
ized moment model, and finally the orbital-ordered and
double exchange model.
The localized model nicely captures a lot of the fea-
tures of the commensurate and helical phase as explained
above. Indeed, the first-principles electronic structure
calculations by Ma et al.
ordering by including nearest-, second nearest-, and
third nearest-neighbor interactions within the Heisenberg
model.44This J1-J2-J3model concludes that the domi-
nating exchange parameter is J2(next nearest) and that
these interactions arise primarily from superexchange
with the Te 5p orbitals acting as the mediating states.
These results are, however, inconsistent with the neutron
scattering work of Lipscombe et al., which show that J1
is not antiferromagnetic and that J2is not greater than
J1.42The study by Fang et al. also address the mag-
netism within a localized model and find that a critical
amount of interstitial iron induces incommensurate or-
dering mostly by affecting the strong coupling of lattice
and magnetic degrees of freedom in Fe1+xTe.45
In the itinerant model, Zhang et al. have performed
density functional studies to show that the interstitial
iron in Fe1+xTe acts as a strong local moment that inter-
acts with the itinerant magnetism of the in-plane iron.46
They model the interstitial iron as a Fe+site within a
supercell, so that they study an interstitial iron concen-
tration of 12.5%, and this moment is enough to drive
Fe1+xTe to have the observed bicollinear ordering as
opposed to a ferromagnetic, checkerboard antiferromag-
netic, or nonmangetic arrangement.
reproduces the bicollinear
A later electronic structure study by Han and Savrasov
calculates the same Fermi surface nesting vector (π, π) in
Fe1+xTe as in the iron arsenides. This difference between
their calculated structure and that observed is explained
as arising from the fact that Fe1+xTe is self-doped by the
electrons of the interstitial iron site.47In their calcula-
tions, this is enough to reshape the Fermi surface and lead
to the observed (π,0) nesting, which corresponds to the
bicollinear magnetic structure. Han and Savrasov have
to make some unphysical assumptions, however, such as
the interstitial iron donating all of its valence electrons
and therefore having an 8+oxidation state. We know
from the diffraction data presented in this paper that
the interstitial iron has a moment equal to that of the
in-plane iron, which implies that it also has an oxidation
state of 2+.
Finally, the orbital ordering picture by Turner et al.
offers an interesting model to explain the observed mag-
netic ordering.48In this model, correlated local moments
and orbital degeneracy lead to a strong anisotropy to-
wards the b-direction. Furthermore, the structural dis-
tortion leading to the orthorhombic cell is proposed to
arise from orbital ordering rather than magnetic order-
ing. Double exchange leads to the ferromagnetic aligning
in the b-direction, and a kinetic energy term leads to anti-
ferromagnetic coupling in the a-direction. Electron dop-
ing from the interstitial iron leads to further occupation
of the orbital responsible for ferromagnetic coupling, and
the incommensurate spiral structure arises from the sys-
tem trying to lower the energy from the nearest neighbor
interaction (J1 in our model). Interestingly, this study
also predicts phase separation in the incommensurate or-
dering with the doped electrons separating into high- and
low-density regions. This is an appealing model to help
explain the phase separation observed in our samples for
x ≈ 12% since the temperature behavior of the magnetic
scattering implies that the phase separation is electronic
in nature.
The SDW observed in the phases Fe1+xTe for x ≈ 12%
could help explain some of the features observed in the
nonsuperconducting Se-doped phases. In several studies
undertaken to understand why the (π, 0) ordering gives
way to the spin resonance with (π, π) symmetry, several
studies have revealed a slightly incommensurate ordering
that it static and short-range ordered.21In some samples,
this short-range ordering with a weak moment for iron
(≈ 0.1µB) even seems to coexist with superconductivity.
Interestingly the propagation vector of k ≈ (0.45 0
found in some samples,49is close to that found in the
SDW presented in this paper.
Similarstudieson lightly
Fe1+xTe1−ySey show that the incommensurate short-
range magnetic ordering crosses over from static to
purely dynamic as a function of Se-doping.
a combination of inelastic neutron scattering measure-
ments and magnetization measurements,
et al. discovered a spin-glass transition that seems to
compete with long-range ordering.50Interestingly, the
1
2)
doped samplesof
Through
Katayama

Page 13

13
SDW is also centered at a propagation vector of (0.46,
0,
2), very close to that of the SDW found for Fe1+xTe
in this paper. Katayama et al. also find evidence for
crystallographic distortion, which would be consistent
with our observation that the short-range SDW was
only found in samples of with crystallographic phase
separation.
The similarities between our findings and those for Se-
doped samples implies that the critical amount of inter-
stitial iron plays a similar role to that of Se-doping in
modulating the bicollinear antiferromagnetic structure of
Fe1+xTe. The interstitial iron does this by increasing the
value of the nearest neighbor exchange interactions. Con-
versely, the Se substitution affects the nearest neighbor
interaction but seems to suppress rather than increase
this exchange interaction. Thus, in the superconducting
phases, the Se-doping destroys long-range magnetic or-
dering altogether while in the case of Fe1+xTe, interstitial
iron doping causes the long-range bicollinear ordering to
be replaced by other types of lower energy including the
incommensurate short-range SDW and the incommensu-
rate long-range helical ordering.
A significant difference between the two types of dop-
ing (interstitial iron vs. anion substitution) is that the
excess iron causes only short-range correlations along H,
1
while Se-doping leads to short-range correlations along L.
Thus, Fe1+xTe never becomes a two-dimensional magnet
within the ab-plane. Indeed, this is the opposite of what
what has been observed in some cuprate phases such as
YBa2Cu3O6.353 and La2−xSrxCuO4, which have short-
range correlations along the interplanar spacing and long-
range within the planes.51–53Likewise, when the super-
conducting state is reached in Fe1+xTe1−ySey the posi-
tion of the spin resonance in reciprocal space from in-
elastic neutron studies implies that it becomes strongly
two-dimensional in the ab-plane. Since the interstitial
iron chemically connects the layers, it could hinder super-
conductivity by maintaing long-range magnetic ordering
in the L-direction. Indeed, this deleterious effect of in-
terstitial iron on superconductivity has been observed in
several studies.11,54,55
V.ACKNOWLEDGEMENTS
This work has benefited from the use of the NPDF
beamline at the Lujan Center at Los Alamos Neutron
Science Center, funded by the US DOE Office of Basic
Energy Sciences.
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