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PhysRevB.85.024525 - Department of Physics

PHYSICAL REVIEW B 85, 024525 (2012)
Structural collapse and superconductivity in rare-earth-doped CaFe2 As2
S. R. Saha,1 N. P. Butch,1 T. Drye,1 J. Magill,1 S. Ziemak,1 K. Kirshenbaum,1 P. Y. Zavalij,2 J. W. Lynn,3 and J. Paglione1,*
Center for Nanophysics and Advanced Materials, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA
Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
(Received 3 November 2011; revised manuscript received 5 December 2011; published 13 January 2012)
Aliovalent rare-earth substitution into the alkaline-earth site of CaFe2 As2 single crystals is used to fine
tune structural, magnetic, and electronic properties of this iron-based superconducting system. Neutron and
single-crystal x-ray scattering experiments indicate that an isostructural collapse of the tetragonal unit cell
can be controllably induced at ambient pressures by the choice of substituent ion size. This instability is
driven by the interlayer As-As anion separation, resulting in an unprecedented thermal expansion coefficient
of 180 × 10−6 K−1 . Electrical transport and magnetic susceptibility measurements reveal abrupt changes in the
physical properties through the collapse as a function of temperature, including a reconstruction of the electronic
structure. Superconductivity with onset transition temperatures as high as 47 K is stabilized by the suppression of
antiferromagnetic order via chemical pressure, electron doping, or a combination of both. Extensive investigations
are performed to understand the observations of partial volume-fraction diamagnetic screening, ruling out extrinsic
sources such as strain mechanisms, surface states, or foreign phases as the cause of this superconducting phase
that appears to be stable in both collapsed and uncollapsed structures.
DOI: 10.1103/PhysRevB.85.024525
PACS number(s): 74.70.Xa, 74.90.+n
The interplay between structural, magnetic, and superconducting properties in the iron-based superconducting compounds has been a central theme in attempts to elucidate the
nature of Cooper pairing in this family of high-temperature
superconductors.1,2 Much focus has been paid to the intermetallic series of iron-based compounds with the ThCr2 Si2 type (122) crystal structure. With well over 700 compounds
known to take on this configuration,3 the 122 structure
forms the basis for a rich variety of physical phenomena
that stem from the fact that this lattice structure not only
supports a wide assortment of elemental combinations but
also harbors different mixtures of ionic, covalent, and metallic
The interesting chemistry of the AB2 X2 configuration was
highlighted in 1985 by R. Hoffman,4 who pointed out that
a segregation of this large family of materials occurs due to
the presence or absence of interlayer X-X bonding, which
results in, respectively, either a “collapsed” or “uncollapsed”
tetragonal structure. Despite an ∼20% change in unit cell
volume in traversing through Ba, Sr, and Ca-based series of
AFe2 As2 structures,5 this family of 122 materials remains
in the uncollapsed structure geometry at ambient pressures
through the entire range. However, it can be driven to collapse
by a modest external pressure applied to the smallest-volume
member of the series, CaFe2 As2 , resulting in a dramatically
abrupt ∼10% c-axis reduction of its tetragonal unit cell upon
Interestingly, a superconducting phase with a maximum Tc
of ∼10 K was first reported to straddle the critical pressure
where the collapse occurs in CaFe2 As2 8–10 but only under
nonhydrostatic experimental conditions,11 suggesting that the
change in electronic structure that occurs through the collapse
is not supportive of pairing. This was further confirmed by the
absence of superconductivity in the collapsed phase induced
by isovalent phosphorus substitution,12 and its importance
was heightened by first-principles calculations predicting a
quenched Fe moment in the collapsed structure.13
The nearness of the structural collapse instability to the
ambient pressure phase of CaFe2 As2 suggests that chemical
pressure is a viable alternative to applied pressure, as indeed
was shown by isovalent substitution directly into the FeAs
sublattice.12 We have stabilized the 122 collapsed phase at
ambient pressures by employing rare-earth substitution into
Ca1−x Rx Fe2 As2 to selectively induce a structural collapse via
the choice of rare earth.14 The close match between ionic
radii of the lighter rare earths such as La, Ce, Pr, and Nd
(130, 128.3, 126.6, and 124.9 pm, respectively15 ) with that of
Ca (126 pm) in the eight-coordinate geometry allows us to
selectively tune the structural parameters with both larger and
smaller relative radii, invoking a uniform chemical pressure
on the unit cell at a tunable rate of chemical substitution. In
parallel, electron doping via aliovalent substitution of trivalent
R3+ ions for divalent Ca2+ also tunes the electronic structure,
acting to suppress antiferromagnetic (AFM) order and induce
a superconducting phase with transition temperatures reaching
as high as 47 K.
In this article, we provide a comprehensive study of the
structural, magnetic, and electronic properties of the rareearth-doped CaFe2 As2 system throughout the antiferromagnetic, superconducting, and structural collapsed phases. We
show that the substitution of light rare earths provides an ideal
method of fine tuning the structure through collapse, while
simultaneously electron doping the system. In Secs. II and III,
we review the synthesis and characterization of our singlecrystal samples, providing chemical analysis and structural
refinements as a function of substitution and temperature.
Neutron-scattering and x-ray scattering experiments are used
to outline the systematic chemical pressure effects of rare-earth
substitution and the evolution of all structural parameters
through the collapse transition. Section IV presents the
temperature dependence of electrical transport and magnetic
©2012 American Physical Society
S. R. SAHA et al.
PHYSICAL REVIEW B 85, 024525 (2012)
susceptibility data, comparing the evolution of physical properties for different chemical pressures and dopings. Section V
reviews our systematic studies of the superconducting phase
induced by the suppression of the antiferromagnetic phase,
including annealing, etching, and oxidation effects. In Sec. VI
we build a composite phase diagram that segregates the effects
of electron doping and chemical pressure, and we finally
summarize our conclusions based on this work in Sec. VII.
actual substitutional concentrations do not exceed a solubility
limit that depends on the rare-earth species. This value can be
readily inferred from the value at which x(WDS) saturates in
Fig. 1 and appears to follow the tendency of a lower saturation
point for decreasing ionic radii of the heavier rare earths. The
limited solubility is likely due to ionic size mismatch between
Ca2+ and corresponding rare earth R, as also encountered in
the synthesis of Sr1−x Lax Fe2 As2 .17
Single-crystal samples of Ca1−x Rx Fe2 As2 were grown
using the FeAs self-flux method,16 yielding crystals as large
as ∼10 × 10 × 0.1 mm3 . Chemical analysis was obtained
via both energy-dispersive (EDS) and wavelength-dispersive
(WDS) x-ray spectroscopy, showing 1:2:2 stoichiometry
between (Ca,R), Fe, and As concentrations. For WDS analysis,
rare-earth concentrations were determined by recording the
concentration at eight separate scanned points across each
sample surface and averaging the result for each sample,
with standard deviation never found to be more than a few
percent (or within the accuracy of the technique). In the rest of
the paper, actual x concentrations are quoted based on WDS
Figure 1 presents the measured concentration x in
Ca1−x Rx Fe2 As2 single-crystal samples determined by WDS
spectroscopy as a function of nominal starting concentration.
Error bars are determined conservatively, taking the range in x
values determined in scanned WDS values across each sample.
At low values of x there is close to a one-to-one correspondence
between actual and nominal concentrations, indicating good
control of target and resultant substitution concentration. With
increasing x, it is apparent that saturation occurs whereby
Crystal structure determination was performed using
single-crystal x-ray-diffraction data measured on a Bruker
Smart Apex2 diffractometer equipped with a CCD detector, graphite monochromator, and monocap collimator using
MoKα radiation from a fine focus sealed tube. Due to strong
absorption and a highly anisotropic crystal shape, the full
sphere of reflections was collected with a redundancy of at least
eight and corrected for absorption effects using an integration
method (SADABS software18 ) based on a crystal shape (face
indices) yielding very good agreement between equivalent
reflections Rint (see Table I). The structure refinement was
performed using SHELXL software18 and included atomic
coordinates, anisotropic atomic displacement parameters, and
Ca:R occupation factors, assuming fully occupied sites and
using nine parameters in total.
Figure 2 presents the evolution of lattice constants with
rare-earth concentration determined from single-crystal x-ray
refinements performed at a fixed temperature of 250 K.
Data points determined by neutron-scattering experiments
are also included. The scatter in both data sets arises
due to uncertainties in the measured WDS concentration x
(∼ ±1%), measurement temperature (250 ± 5 K), and systematic variations in measurement platforms (i.e., x ray versus
neutron scattering), but is dominated by the uncertainty in
temperature due to the extremely large thermal expansion (see
At 250 K with increasing x, the a-axis lattice parameter for
all R increases at close to the same rate, while the variation
of the c axis shows a strong dependence on a type of rareearth substituent. As shown in Fig. 2(b), the c axis remains
constant with x for La substitutions, but decreases for Ce,
Pr, and Nd at a rate that increases for smaller/heavier rareearth species. Overall, it is clear that the progression of the
c-axis lattice parameter with rare-earth substitution presents a
unique opportunity to controllably apply chemical pressure by
the choice of rare-earth substituent. Below, we investigate the
effects of controlled c-axis reduction via this technique on the
crystal structure and its instability to collapse.
Neutron-diffraction experiments were performed on singlecrystal samples using the BT-7 and BT-9 triple axis spectrometers at the NIST Center for Neutron Research. The
incident energy was 14.7 meV using pyrolytic graphite (002)
monochromators and analyzers. Data were collected using
θ : 2θ scans to determine the temperature dependence of the
a and c lattice parameters, in steps of 2 K. Typically data
were taken upon warming and cooling through the range 2 to
300 K in order to properly capture the large hysteresis of the
structural collapse transition.
FIG. 1. (Color online) Chemical analysis of rare-earth concentration x in Ca1−x Rx Fe2 As2 obtained from wavelength-dispersive
(WDS) x-ray spectroscopy. Data points were determined by averaging
eight separate scanned WDS measurements across each sample,
and error bars express the range of values determined in each
measurement. Solid lines are guides to the eye.
PHYSICAL REVIEW B 85, 024525 (2012)
TABLE I. Crystallographic data for Ca0.91 Nd0.09 Fe2 As2 determined by single-crystal x-ray diffraction at 250 K [tetragonal structure (T),
above collapse transition], 105 K (T structure, just above collapse transition), and 80 K [collapsed tetragonal (CT) structure, just below
collapse transition]. Uncertainty in temperature values is ±5 K.
Space group
˚ 3)
V (A
Density (g/cm3 )
Refl. collected
Independent refl.
Rint a (%)
wR2 b , all refl.
R1 c , I 2σ I
Atomic parameters
Nd occupation factor
Atomic displacement
˚ 2)
parameters Ueq (A
Bond lengths (A)
Bond angles (deg)
80 K
105 K
250 K
z = 0.13328(11)
z = 0.13391(12)
z = 0.13339(14)
Rint = |Fo2 − Fc2 (mean)|/ [Fo2 ].
wR2 = [w(Fo2 − Fc2 )2 ]/ [w(Fo2 )2 ]1/2 .
R1 =
Fo | − |Fc / |Fo |.
A few select neutron-diffraction scans are shown in Fig. 3
for a Nd0.08 Ca0.92 Fe2 As2 crystal with a mass of 3 mg, measured
upon warming. At base temperature there is a resolution
limited peak on the high-angle side, which has a modest shift
to the left on warming as expected from thermal expansion.
On warming, there is a dramatic structural transition that
occurs between 80 and 84 K. In particular, at 82 K there is
a distribution of c-axis lattice parameters, while at 84 K the
peak has jumped to smaller angle, indicating that the c axis
has suddenly increased. Above 84 K the system undergoes
continuous thermal expansion as discussed below.
This abrupt shift in the (004) Bragg reflection arises from
a dramatic shift in the c-axis lattice constant as a function
of temperature, resulting from only 8% substitution of Nd
into CaFe2 As2 . As shown in Fig. 4, the substitution of a
similar amount of Pr into CaFe2 As2 is also enough to drive
the collapsed tetragonal (CT) transition, with the a-axis and
c-axis lattice parameters undergoing a discontinuous jump that
is hysteretic in temperature. In contrast, the substitution of up
to 28% La does not drive the system toward any observable
transition, consistent with the expectation that the larger ionic
radius of La is not amenable to inducing positive chemical
pressure. The temperature dependence of the c-axis unit cell
dimension upon cooling for a series of R-doped crystals, shown
in Fig. 5(a), presents a summary of this dramatic variation in
structural properties. As shown, small amounts of Nd and Pr
substitutions act in a quantitatively similar manner, achieving
an almost identical collapse transition, while crystals with
larger rare-earth size substitution (i.e., 19% La and 17% Ce)
fail to collapse through the entire temperature range studied.
Note that we have verified that the CT transition is intrinsic
to these crystals and not caused by strain fields induced by
growth conditions as observed in undoped CaFe2 As2 20 (see
Fig. 9 in the next section for more details).
S. R. SAHA et al.
PHYSICAL REVIEW B 85, 024525 (2012)
FIG. 3. (Color
Ca0.92 Nd0.08 Fe2 As2 summarized by a few selected θ : 2θ scans
across the (004) structural Bragg reflection, showing the abrupt
transition from the collapsed to the uncollapsed tetragonal phase
near 82 K. Data were obtained upon warming.
FIG. 2. (Color online) Characterization of Ca1−x Rx Fe2 As2 unit
cell lattice constants determined from single-crystal samples. Filled
symbols correspond to x-ray-diffraction data, while open symbols are
determined by neutron diffraction. Due to the large thermal expansion
(see text), uncertainties are dominated by the temperature stability of
the measurement apparatus estimated to be 250 ± 5 K, resulting in
(a) a-axis error values within the symbol sizes and (b) c-axis error
values. The dashed lines are least-squares fits to data for (a) all data
and (b) each rare-earth species.
The absolute change in the c axis upon collapse is nearly
identical to that observed in CaFe2 As2 under pressure,6 despite
subtle but important differences in charge doping effects.
This speaks to the dominant bonding interactions driving the
collapse, also apparent in the extremely large c-axis thermal
expansion observed in this series: even in the absence of a
collapse transition, a 22% Ce-doped crystal undergoes a 5.3%
expansion of the c axis between 0 and 300 K, giving a linear
thermal expansion coefficient of 180 × 10−6 /K. This value is
one of the largest for any metal (e.g., as compared to the largest
known thermal expansion values of 97, 83, and 71 × 10−6 /K
for elemental Cs, K, and Na, respectively, at 25 ◦ C),21 and
even rivals the largest known values for any solid as observed
in molecular crystals.22
The strong c-axis contraction and instability to collapse is
driven by an increasing overlap of interlayer As orbitals,4,13
controlled via the chemical pressure instilled by rare-earth
substitution. In fact, the As-As interlayer separation itself
appears to be the key parameter controlling the collapse: as
shown in Fig. 5(b), both CaFe2 As2 under 0.6 GPa pressure as
well as Pr- and Nd-doped CaFe2 As2 crystals collapse once the
interlayer As-As distance reaches a critical value of ∼3.0 A,
while La- and Ce-doped crystals which remain uncollapsed to
the lowest temperatures do not cross this value.
The highest-doped Ce compound is just on the verge of
collapse at ambient pressure. Applying a tiny amount of
external pressure to a 22% Ce crystal, whose As-As separation
˚ at zero temperature, confirms this scenario.
approaches 3.0 A
The c-axis lattice parameter of a 22% Ce sample was studied
via neutron diffraction as a function of applied hydrostatic
pressure achieved using an Al-alloy He-gas pressure cell as
described previously.7 As shown in Fig. 6, a collapse is induced
at only 0.05 GPa applied pressure at 50 K constant temperature.
This is an order-of-magnitude lower pressure than that required
to induce the collapse in undoped CaFe2 As2 ,7 which is easily
understood by the fact that 22% Ce substitution brings the
˚ interlayer As-As
crystal structure very close to the critical 3-A
distance at low temperatures, thereby only requiring a very
small additional pressure to induce the collapse.
Furthermore, it appears the critical distance has more to do
with the p-orbital bonding character than the exact chemical
makeup: phosphorus-based materials SrRh2 P2 and EuRh2 P2
both undergo a collapse of the c-axis dimension by ∼1.5 A
as a function of pressure (5 GPa) and temperature (800 K),
respectively, when they cross a similar critical interlayer P-P
˚ 23 The fact that 3 A
˚ is the average value
distance of ∼3 A.
between covalent and Van der Waals radii of both elemental
As and P21 suggests that this striking universal behavior can
be observed in any system with similar p-orbital overlap
approaching this critical value.
Full structural refinement data for 9% Nd at temperatures
above and below the collapse transition are tabulated in
Table I and presented graphically in Fig. 7 along with several
other characteristic samples for various temperatures and
rare-earth concentrations. For each characteristic doping, the
same crystal was measured at several fixed temperatures,
PHYSICAL REVIEW B 85, 024525 (2012)
FIG. 4. (Color online) Effect of structural collapse of the tetragonal unit cell of Ca1−x Rx Fe2 As2 by rare-earth substitution on
lattice parameters, determined by neutron-diffraction measurements
of (110) and (006) nuclear reflections represented as a- and c-axis
data, respectively. The contour plots highlight the structural collapse
of the tetragonal unit cell induced by rare-earth substitution upon both
warming (right arrows) and cooling (left arrows), that is present in (a)–
(d) Ca0.925 Pr0.075 Fe2 As2 but absent in (e) and (f) Ca0.81 La0.19 Fe2 As2 .
Data collected upon warming are displayed in panels (a) and (b) and
for cooling in panels (c) and (d), emphasizing the hysteretic nature of
the structural transition in the 7.5% Pr crystal.
providing a more systematic set of data that suffer from less
scatter than the x-dependent quantities shown in Fig. 2. Data
are presented for each rare-earth doping and compared to
available data for undoped CaFe2 As2 under 0.6 GPa applied
pressure.6 The intralayer Fe-As bond length, which remains
relatively rigid in all FeAs-based compounds, is shown to
decrease with decreasing temperature in 28% La, 16% Ce,
14.5% Pr, and 9% Nd from 250 to 100 K, as shown in
Fig. 7(e). Samples that undergo a structural collapse show
a large contraction of the Fe-As bond length in line with
the concomitant expansion of the a-axis plane. Interestingly,
as shown in Fig. 7(f), the As-Fe-As tetrahedral bond angle
shows an even stronger evolution with temperature in all
samples. While this angle also shows an abrupt increase
through the collapse transition in Pr- and Nd-doped samples
as expected by the strong c-axis contraction, even the noncollapsing samples show an ∼2% increase from 250 K to
FIG. 5. (Color online) (a) c-axis lattice parameters of
Ca1−x Rx Fe2 As2 with R = La, Ce, Pr, and Nd, determined from
neutron-diffraction measurements of (006) nuclear reflections upon
cooling. The evolution of the tetragonal-orthorhombic (T-O) and
tetragonal-collapsed tetragonal (T-CT) structural transitions is compared to undoped CaFe2 As2 at ambient pressure19 and undoped
CaFe2 As2 under 0.6 GPa of applied hydrostatic pressure (open
squares, from Ref. 6). (b) Comparison of the interlayer As-As separation distance for La-, Ce-, Pr-, and Nd-doped samples measured by
single-crystal x-ray diffraction (filled symbols, open diagonal square
from powder neutron diffraction) and CaFe2 As2 at 0.6 GPa.6 Dashed
lines are guides, with vertical portions indicating the measured CT
transition temperatures.
zero temperature, indicative of the strong thermal expansion
discussed above.
In addition to structural tuning, rare-earth substitution
introduces an important extra degree of freedom that applied
pressure does not: charge doping via aliovalent substitution
allows for fine tuning of both pressure and doping effects on
the physical properties. Here we use electrical resistivity ρ
measured with the standard four-probe ac method and magnetic susceptibility χ measured in a SQUID magnetometer, to
track the evolution of both structural and electronic properties
as a function of rare-earth substitution.
S. R. SAHA et al.
PHYSICAL REVIEW B 85, 024525 (2012)
FIG. 6. (Color online) Pressure-induced collapse of the c-axis
lattice parameter in a Ca0.78 Ce0.22 Fe2 As2 crystal, as obtained by
neutron-diffraction measurements of the sample under an applied
He-gas hydrostatic pressure at a constant temperature of 50 K. The
abrupt change above 0.5 kbar is the collapse of the tetragonal unit
cell, as discussed in the main text. Inset: ambient pressure c-axis
measurement of the same sample in the noncollapsed state, indicating
an unprecedented 5.3% thermal expansion (see text).
Figure 8(a) presents the progression of electrical resistivity
ρ of single crystals of Ca1−x Lax Fe2 As2 for various La
concentrations, normalized to 300-K values. In CaFe2 As2 , the
sharp jump at TN = 165 K is due to a structural phase transition
from tetragonal to orthorhombic upon cooling, and is known to
coincide with the onset of antiferromagnetic (AFM) order.24–26
The substitution of La into Ca1−x Rx Fe2 As2 suppresses the
feature associated with TN to lower temperatures, eventually
suppressing it completely with higher La concentrations. As
shown in Fig. 8(b), Pr substitution also acts to suppress TN to
lower temperatures in a similar manner.
This trend is also observed in magnetic susceptibility
data, shown in Figs. 8(c) and 8(d). Closest to the critical
La concentration for suppression of the AFM phase, such
as at x = 0.14, χ (T ) shows an extremely flat temperature
dependence that mimics the undoped compound above TN . A
moderate increase in χ (T ) is apparent at low temperatures,
and is attributed to the FeAs sublattice of the crystals given
the nonmagnetic nature of La substituents. In contrast, χ (T )
enhances strongly with Pr substitution due to the increasing
concentration of Pr localized 4f electrons and their contribution of a Curie-like susceptibility, as shown in Fig. 8(d).
Pr substitution gradually suppresses the steplike feature at TN
as with La, but an abrupt appearance of another first-order
transition occurs near 7.5%, coinciding with the structural CT
A comparison of crystals grown under different conditions
was performed to verify that strain mechanisms are not the
primary cause of the CT transition. This phenomenon was
recently reported to occur under different thermal treatments
in pure CaFe2 As2 , resulting in replication of conditions similar
to applied pressure that stabilize the structural collapse.20
Figure 9 presents a comparison of susceptibility data for
two crystals with the same Pr concentration but grown under
different conditions: one using the FeAs (self) flux technique
described above and another using Sn flux, known to provide
the least amount of strain during growth and cooling.20 As
shown in the χ (T ) curves, the structural collapse is evident in
both cases, and moreover is almost identical, thus indicating
that the collapse is caused by intrinsic chemical pressure due
to rare-earth substitution and not due to an extrinsic strain field
as found for undoped CaFe2 As2 .
A large hysteresis of ∼30 K between temperature cooling
and warming measurements is present in all structural, transport, and magnetic measurements, indicating the first-order
nature of this transition. The magnetic character of this
hysteresis does not appear to depend on the rare-earth species
(c.f. only present in Pr- and Nd-doped crystals), as indicated
by the abrupt, sharp transitions present in χ (T ) as highlighted
in Fig. 10. However, the change in absolute resistivity appears
to show a progression from a very large increase (decrease)
on warming (cooling) in undoped CaFe2 As2 (under applied
pressures) to an almost negligible change in magnitude at
large rare-earth concentration. As shown in Fig. 10, a change
in ρ(T ) of the order of 10% of the normalized resistivity is
observed in undoped CaFe2 As2 under pressure,11 as compared
to a much smaller change in a crystal with 9% Nd and an
almost negligible change in magnitude as shown for 14.5%
Pr. This appears to be related to the effect of electron
doping caused by trivalent rare-earth substitution, as the
magnitude of the change decreases with increasing rare-earth
Through the structural collapse, a dramatic change in
electronic structure is predicted to occur4,7,13 involving the
elimination of a cylindrical hole pocket centered at the point
in the Brillouin zone. This is confirmed by measurements
of the Hall coefficient RH in 14.5% Pr shown in Fig. 11,
which provide evidence for a dramatic and abrupt change
in electronic structure through the collapse transition, even
exhibiting hysteretic behavior identical to that observed in
structural (x-ray and neutron-scattering) and magnetic (susceptibility) data. The reduction of RH toward zero below
the CT transition suggests a transformation toward an almost
exact compensation of electron and hole bands. In contrast,
there is very little relative change in longitudinal resistivity
through the structural transition as noted above. For example,
note the contrast in behavior for 14.5% Pr, which shows
a dramatic order-of-magnitude drop in RH (T ) through the
CT transition as shown in Fig. 11, while there is an almost
negligible relative change in ρ(T ) as shown in Fig. 10(c). This
suggests that the change in band structure through the collapse
does not dramatically affect the bands that dominate intralayer
ab-plane transport, which is consistent with an iron plane that
expands but nevertheless remains intact through the collapse
with a lower electronic density of states.7,13 Moreover, because
electron doping decreases the amplitude of the jump in ρ(T )
at the CT transition, which is most pronounced in undoped
CaFe2 As2 under pressure11 and almost absent in the 14%
Pr crystal (c.f. Fig. 10), one can conclude that the enlarging
electron bands are more two-dimensional than the shrinking
hole band(s), leading to this effect. More work is required to
fully explore the change in the electronic structure through
the CT transition, but ambient-pressure access to both phases
PHYSICAL REVIEW B 85, 024525 (2012)
FIG. 7. (Color online) Structural characterization of the unit cell and substructure of Ca1−x Rx Fe2 As2 for several characteristic crystals,
including single-crystal neutron data (solid lines) extracted from Bragg reflections (see text), refinement of neutron powder diffraction for
14.5% Pr (open diagonal square), as well as refinement data from single-crystal diffraction (solid symbols). Dashed lines are guides to
single-crystal x-ray refinement results, with vertical portions indicating the temperature of the structural collapse transition determined from
magnetic susceptibility and arrows indicating cooling direction. Open squares are data for CaFe2 As2 under hydrostatic pressure reproduced
from Ref. 6 for comparison.
as a function of a continuously tunable parameter such as
temperature promises to provide much insight into the nature
of the bonding that dominates the electronic and magnetic
properties of these materials.
As evident in Fig. 8, the resistivity of Pr- and La-doped
samples exhibits high-temperature superconductivity, with the
highest observed onset temperature reaching 47 K as shown in
Fig. 12. This is much higher than values reported previously
in electron-doped intermetallic FeAs-based systems, including
both the commonly employed transition-metal doping and the
only other previously known case of electron doping via rareearth substitution in Sr1−x Lax Fe2 As2 .17 It also surpasses the
highest values found in hole-doped (e.g., K1+ for Ba2+ )27
122 compounds which have a maximum Tc of ∼38 K, and is
more comparable to that found in the fluorine-based materials
(Ca,R)FeAsF,28 where similar rare-earth electron doping with
Pr and Nd results in Tc values approaching the highest reported
for any noncuprate material.
The appearance of superconductivity in the Ca1−x Rx Fe2 As2
series is consistent with the generally accepted hypothesis
that the minimization of chemical disorder in the active FeAs
layers, by substitution in the alkaline-earth site, allows for
the highest possible Tc values in the iron-based materials.
What is most surprising, however, is that this superconducting
phase exists in both collapsed and uncollapsed structures.
As shown in Fig. 12, superconductivity is present both in
14% Pr and 8% Nd crystals which both undergo a collapse
transition, and in 27% La and 22% Ce crystals which do
not collapse. Given the evidence for a substantial change
in the electronic structure through the structural collapse
as shown by Hall data in Fig. 11, it is remarkable that
high-temperature superconductivity appears to occur in this
system regardless of the nature of the interlayer bonding: an
insensitivity of pairing in the iron layer to the configuration
of As p orbitals would provide strong constraints on a
microscopic model of superconductivity originating in the
iron sublattice. Furthermore, because theoretical calculations
predict a nonmagnetic ground state in the CT phase,13 it is
tantalizing to conclude that superconductivity is originating
S. R. SAHA et al.
PHYSICAL REVIEW B 85, 024525 (2012)
FIG. 8. (Color online) The normalized electrical resistivity of Ca1−x Rx Fe2 As2 crystals with various concentrations of (a) La
and (b) Pr tracking the evolution of magnetic, structural, and superconducting phase transitions. The tetragonal/paramagnetic-toorthorhombic/antiferromagnetic transition in CaFe2 As2 , indicated by a sharp rise in ρ(T ) near 165 K (x = 0 curves), is suppressed with
R substitution before entering a superconducting phase at higher x. Pr substitution also induces a collapse of the tetragonal structure at
x > 0.07, barely seen in the x = 0.14 sample as a kink in ρ(T ). Magnetic susceptibility data for (c) La and (d) Pr substitutions (measured in
fields 0.1 T for Pr and 1 T for La) exhibit sharp features associated with the AFM transition [drop in χ (T )] in both cases, in addition to the
collapsed tetragonal transition [hysteretic drops in χ (T )] for Pr substitutions. Data for Pr-doped samples x = 0.12, 0.14, and 0.145 are shifted
up for clarity.
in a phase void of spin fluctuations, providing an additional
pivotal constraint on the nature of the pairing mechanism.
However, the same calculation also predicts a second nearly
degenerate magnetic ground state for the CT phase, so the
perturbation introduced by charge doping must be properly
included before such conclusions are made.
Experimentally, the coexistence of a small fraction of
noncollapsed tetragonal phase cannot be ruled out below the
∼1% level from our elastic neutron-scattering data, although
it is highly unlikely due to the dramatic difference in lattice
constants between the two structural phases. Nevertheless,
the accessibility of the CT phase at ambient pressures in
Ca1−x Rx Fe2 As2 will allow for magnetism to be probed in
a manner similar to that done for undoped CaFe2 As2 under
pressure.7 Below, we investigate and rule out several possible
extrinsic causes of superconductivity that would point to other
Superconducting transitions are observed in all rare-earth
substitutions as evidenced by resistive transitions and the onset
of Meissner screening in magnetic susceptibility. As shown
in Fig. 13, three characteristic samples with La, Ce, and Pr
FIG. 9. (Color online) Comparison of structural collapse transition between crystals of Ca0.855 Pr0.145 Fe2 As2 grown using FeAs flux
and Sn flux. Arrows indicate warming/cooling directions.
PHYSICAL REVIEW B 85, 024525 (2012)
FIG. 11. (Color online) Temperature dependence of the Hall
effect in 14.5% Pr and 8% Nd crystals through their collapse
transitions, showing a dramatic change in the Hall coefficient through
the collapse, compared to a 19% La crystal that does not undergo a
collapse. Error bar denotes the resolution of the experiment, and
arrows indicate direction of warming/cooling during the experiment.
the AFM phase is suppressed, as shown in Fig. 8. For instance,
superconductivity with much lower Tc values often appears in
very low-doped samples such as Ca0.92 La0.08 Fe2 As2 , which
shows a resistive transition near ∼10 K [Fig. 8(a)]. This “10-K
phase” persistently appears at low rare-earth concentrations in
the Ca1−x Rx Fe2 As2 series and often shows traces in resistivity
FIG. 10. (Color online) Comparison of transport and susceptibility data on warming and cooling through the structural collapse
transition in three representative samples: (a) resistivity of undoped
CaFe2 As2 under 0.42 GPa applied hydrostatic pressure (reproduced
from Ref. 11); (b) Ca0.91 Nd0.09 Fe2 As2 at ambient pressure; and
(c) Ca0.855 Pr0.145 Fe2 As2 at ambient pressure. Note the normalized
resistivity (left) and susceptibility (right) vertical scales are equal for
each panel to allow comparison of relative change of ρ(T ) through
the collapse transition.
content exhibit an onset of Meissner screening in magnetic
susceptibility measured in low fields, observable more clearly
on the semilog scale of the inset figure. Full volume fraction
screening is not observed in these crystals, which exhibit
partial screening estimated to reach as high as ∼10% of full
volume fraction, as shown for the case of 14% Pr. While much
smaller than that expected for a bulk superconducting material,
this peculiar superconducting phase seems to be impervious
to annealing, strong surface etching, and surface oxidation,
suggesting that the superconducting fraction of these samples
is not obviously an extrinsic phase.
First, the persistent appearance of resistive transitions and
diamagnetic screening signals indicating Tc values between 30
and 47 K only occurs in samples sufficiently doped such that
FIG. 12. (Color online) Resistivity of representative samples of
Ca1−x Rx Fe2 As2 with La, Ce, Pr, and Nd substitution, as compared to
that of undoped CaFe2 As2 . The hysteretic structural transition, most
clearly observed in the 8% Nd crystal, is marked by arrows (warming
up, cooling down). Inset: characterization of transitions in a 14% Pr
crystal, showing both hysteretic features from the structural collapse
transition and the onset of superconductivity in resistivity near 45 K.
S. R. SAHA et al.
PHYSICAL REVIEW B 85, 024525 (2012)
FIG. 13. (Color online) Determination of superconducting volume fractions from diamagnetic screening estimation of three characteristic samples of Ca1−x Rx Fe2 As2 , with La (circles), Ce (diamonds),
and Pr (squares). Closed symbols indicate zero-field-cooled data, and
open symbols indicate field-cooled data. Inset: onset of diamagnetic
screening in magnetic susceptibility of a 14% Pr crystal at Tc = 44 K
(arrow), plotted on a semilog scale to expose the onset temperature.
data of pure CaFe2 As2 such as those shown in Fig. 12. The
origin of this phase is not known, but is likely related to
the strain-induced transition observed under nonhydrostatic
pressure conditions in undoped CaFe2 As2 .8–10 The high-Tc
state induced by rare-earth substitution appears to be a phase
distinct from the 10-K phase and occasionally exhibits distinct
partial resistive transitions as displayed in Fig. 8(a) for 18%
La. The higher-Tc phase in Ca1−x Rx Fe2 As2 is likely stabilized
by the extra carries introduced by aliovalent substitution, as
isovalent substitution fails to induce superconductivity.12
However, higher Tc transitions are never observed in
resistivity for x values below the concentrations necessary to
suppress the AFM phase, ruling out any randomly occurring
impurity or contaminant phase and suggesting that this pairing
mechanism is strongly tied to the suppression of magnetism.
It should also be noted that the presence of impurity or
contaminant phases has not appeared in any scattering or
chemical analysis experiments of these samples. In particular,
single-crystal x-ray scattering data refinements of over twenty
different crystals have not indicated the presence of any
crystalline phases other than the 122 structure, and have
consistently yielded residual fitting factors never greater than
∼3%. More detailed (i.e., synchrotron) scattering experiments
are required to further reduce the possible level of impurity
phase that may be present, but the consistent absence of this
phase in AFM samples statistically makes a strong case against
this possibility.
Second, the magnitude of the Tc values observed is far
above the transition temperatures that appear in undoped
CaFe2 As2 under nonhydrostatic pressure conditions (i.e., the
“10-K” phase)8–10 or in undoped SrFe2 As2 under strain
(i.e., the “20-K” phase),16 thus reducing the possibility of
superconductivity due to strain conditions in parts of the
sample. While we cannot rule out that strain is not playing any
role whatsoever, the fact that the dramatic change in lattice
constants through the collapsed structural transition does not
influence the effectiveness of this potential strain mechanism
is extremely challenging for such a scenario.
Nevertheless, to further reduce strain mechanisms as a concern we have performed annealing studies of superconducting
samples, both with and without structural collapse conditions present. Starting with as-grown La- and Pr-substituted
samples that exhibit Meissner screening, we first performed
susceptibility measurements of each sample to characterize
their as-grown properties and then subjected each sample
to an annealing treatment. This consisted of sealing each
sample in a separate quartz tube together with a Ta foil
oxygen getter under partial Ar gas pressure, heating to 700 ◦ C
and holding at that temperature for 24 h before cooling to
room temperature. Immediately after the annealing sequence,
the susceptibility of each sample was measured following the
same procedure as before. Figures 14(a) and 14(b) present the
results of the before- and after-anneal measurements. Although
there are finite changes in measured screening fractions,
the main result is that both samples still exhibit Meissner
screening after their annealing treatments. Furthermore, while
the La-substituted sample shows a reduction in diamagnetic
signal, the Pr-substituted sample in fact shows a small
enhancement, reflective of the absence of any systematic
trends to enhancing or reducing Meissner screening under
this heat treatment schedule. This is in stark contrast to
what happens in stoichiometric SrFe2 As2 , where annealing
completely removes any signature of superconductivity.16
Finally, to rule out the possibility that surface impurity
phases are responsible for partial Meissner screening, we
FIG. 14. (Color online) Effects of annealing heat treatments on
Meissner screening in noncollapsed [(a): La] and collapsed [(b): Pr]
phases showing superconductivity. Effects of etching on (c) electrical
resistivity (normalized to 200 K values) and (d) diamagnetic screening
are represented by the susceptibility offset from value above Tc and
normalized to a 2-K value in a 15% Pr-doped sample. Vertical arrows
indicate the position of the onset of the superconducting transition.
All susceptibility data are shown for zero-field-cooled conditions only
for clarity.
have checked the effect of both etching and oxidation on
the superconductivity in Ca1−x Rx Fe2 As2 . With Tc values
approaching those of the oxygen-based iron-pnictide superconductors, it is important to check for the possibility that
oxygenated surface phases somehow achieve optimal oxygen
doping for superconductivity and are providing the partial
screening observed here. As shown in Figs. 14(c) and 14(d),
we have measured both resistivity and magnetic susceptibility
of a 14.5% Pr sample both before and after etching the sample
in concentrated HNO3 for 30 s, which removes ∼25% of its
mass. It is clear that superconductivity survives this harsh
treatment, which results in no change in qualitative screening
behavior, as well as very little change in resistivity signatures of
both the collapse transition near 70 K and the superconducting
transition that onsets at 40 K.
To further verify that oxidation is not the cause of enhanced
screening, the susceptibility of a 16% Ce-doped sample
with Tc = 35 K was measured first as grown and then after
subsequent exposures to air under heated conditions on a
temperature-controlled hot plate. As shown in Fig. 15, there is
again no systematic trend observed after repeated oxidations,
with the onset of Meissner screening not changing significantly
even after visible oxidation from 300 ◦ C exposure. (The small
volume fraction variations, which are nonmonotonic with
exposure temperature, are likely due to uncertainty in mass
changes due to handling, as well as damage to the sample
from oxidation.)
Together, these tests strongly reduce the likelihood of the
observed high-Tc superconducting phase in Ca1−x Rx Fe2 As2
originating from extrinsic sources such as strain mechanisms,
surface states, or foreign phases such as oxides or other
contaminants. However, assuming this superconducting phase
is of the conventional type, the consistent observation of
FIG. 15. (Color online) Effect of surface oxidation on a
Ca0.84 Ce0.16 Fe2 As2 crystal, shown for the as-grown sample and for
repeated exposures to air under heated conditions. Closed symbols
indicate zero-field-cooled data, and open symbols indicate fieldcooled data. Inset: zoom of main panel demonstrating the insensitivity
of the onset of Meissner screening at Tc 37 K to different heated
PHYSICAL REVIEW B 85, 024525 (2012)
such small superconducting volume fractions points to a
phase that does not occupy the bulk of the samples. This is
extremely surprising, given that the majority of FeAs-based
superconducting compounds exhibit bulk superconductivity
upon suppression of the AFM phase.2 We can speculate on its
origin as having a localized nature tied to the low percentage of
rare-earth substitution, but further characterization is required
to elucidate the origin of this phase and its potential to be
stabilized in bulk form.
Because pressure29 and doping30 are both effective in
suppressing the AFM transition, the temperature-doping phase
diagrams of the Ca1−x Rx Fe2 As2 series appear qualitatively
similar but in fact evolve with different concentration rates
that depend on rare-earth ionic size. Figure 16 presents
the composite phase diagrams of Ca1−x Rx Fe2 As2 for each
rare-earth species, with antiferromagnetic transitions defined
by the minimum in ρ(T ) and the midpoint of the drop in χ (T ),
superconducting transitions determined by the onset of a drop
in ρ(T ), and CT transitions defined by abrupt features in χ (T )
upon warming and cooling as discussed in Sec. IV.
The suppression of the AFM phase with x is similar for
each species, but progresses at noticeably different rates.
Extrapolating a phenomenological fit of TN as a function
of x to T = 0 shows this explicitly: the resultant critical
concentration xc where TN vanishes is shown to vary with rare
earth. In the inset of Fig. 16, we show that xc actually scales
FIG. 16. (Color online) Rare-earth substitution phase diagrams of
Ca1−x Rx Fe2 As2 , showing antiferromagnetic (AF) transitions (solid
symbols), structural collapse transitions (half triangles), and superconducting transitions (open symbols) for Nd, Pr, Ce, and La
substitutions (all concentrations are determined by WDS; see text
for method of determination). Half triangles indicate the position
of structural collapse transition on warming (right-pointing) and
cooling (left-pointing) for Nd (open symbol) and Pr (closed symbol)
substitutions. Solid lines are fits to AF transitions for each rareearth set, extrapolated to zero temperature to identify the critical
concentration xc for each. Inset: scaling of xc with ionic radii of each
rare-earth species.
S. R. SAHA et al.
PHYSICAL REVIEW B 85, 024525 (2012)
linearly with the ionic radii values of the rare-earth species
for eight-coordinate geometry.15 Given the known sensitivity
of the lattice parameters to the choice of rare-earth substituent
as shown by the structural characterization in Sec. III, this
trend verifies that, in addition to electron doping, chemical
pressure also plays a role in shaping the phase diagram of the
Ca1−x Rx Fe2 As2 system.
To disentangle the doping and pressure effects, we utilize
the observations noted in Sec. III about the progression of
lattice constants—in particular the strong and weak dependencies of c- and a-axis lattice constants, respectively, on
rare-earth species (c.f. see Fig. 2)—to characterize chemical
pressure by the measured change in c-axis unit cell dimension.
For instance, substitution of La into CaFe2 As2 does not
change the c-axis unit cell length for concentrations up to
almost 30% La, while Nd substitution changes the c axis very
rapidly with x. However, for all rare-earth species the a-axis
length increases on average at the same rate with substitution
concentration regardless of ionic size. This is possibly due to
an expansion of the Fe sublattice caused by charge doping with
an effective adjustment of the Fe oxidation state, but such a
conclusion requires verification from a core-level spectroscopy
Therefore, we take the change in c-axis length as a measure
of the true chemical pressure. The value of the c-axis lattice
parameter at xc for each R is then used to project the individual
phase diagrams onto the x–c-axis plane, as shown in Fig. 17.
Note the smooth progression of the xc points across this
plane (i.e., the dash-dotted line), which also includes the
same extrapolated critical point for undoped CaFe2 As2 under
pressure.7 This indicates that a parameterized relation exists
between the suppression of AFM order via chemical pressure
and electron doping.
Also, the positions where the As-As interlayer distance
˚ are shown as a solid gray line, indicating the
equals 3 A
positions where the collapse transition onsets. This construction forms the basis for the universal phase diagram
for Ca1−x Rx Fe2 As2 shown in Fig. 18, which extends the
pressure-temperature phase diagram of CaFe2 As2 6,8,11 along
a third charge-doping axis. In this manner, it is seen that the
individual rare-earth species phase diagrams nicely straddle
the doping-pressure plane in a manner that allows access to
distinct parts of the phase diagram by the choice of rare-earth
Combining our transport, magnetic susceptibility, and
neutron-scattering data enables us to trace the progression of
the AFM, CT, and superconducting transitions as a function
of the segregated parameters of electron doping and chemical
pressure. In this way, it can be seen that the AFM phase is
effectively suppressed by both doping and chemical pressure,
similar to other established systems such as Ba1−x Kx Fe2 As2
and pressurized BaFe2 As2 .30 Furthermore, the AFM transition
line exhibits continuity through the doping-pressure plane,
demonstrating the symmetry between both methods of tuning.
This is in line with ideas about band-structure tuning, whereby
nesting features of the Fermi surface that may stabilize the
AFM phase in the parent compound are disrupted by either
FIG. 17. (Color online) The effective electronic doping-pressure
phase diagram for Ca1−x Rx Fe2 As2 and undoped CaFe2 As2 under
pressure (data from Ref. 7) used to construct the phase diagram
of Fig. 18. The individual rare-earth series are projections of finite
temperature data onto the T = 0 plane, showing the separation of
the effects of electron doping (x axis) and chemical pressure (c-axis
shift). The dash-dotted line is a guide to xc critical points denoting the
extrapolated suppression of the antiferromagnetic phase to T = 0.
The solid gray line indicates the projection of the doping-pressure
position where the As-As interlayer distance equals 3 A.
tuning parameter. However, the suppression of AFM order
with electron doping at the alkaline-earth site is in stark
contrast to recent first-principles calculations that predict an
enhancement of magnetism,31 demonstrating the failure of a
rigid band picture even at low charge doping. This is reflective
of a continued challenge to understand the true nature of the
magnetic order and its suppression by doping and pressure.
As in undoped CaFe2 As2 under pressure,7,11 where the CT
phase abruptly severs the continuous suppression of the AFM
transition under applied pressure, the suppression of the AFM
phase in Ca1−x Prx Fe2 As2 and Ca1−x Ndx Fe2 As2 is also shown
to be interrupted by the CT transition but at slightly lower
temperatures and effective pressures. This is understood as
being due to the occurrence of the CT transition exactly
˚ interlayer As-As separation, which follows both
at the 3-A
a pressure- and doping-dependent path through the phase
diagram as marked by the solid gray line in Fig. 18. What
is more unusual is the insensitivity of the observed high-Tc
superconducting phase to this boundary, raising important
questions regarding which elements of chemical, electronic,
and magnetic structure are important to Cooper pairing should
this superconducting phase prove to be intrinsic to both
the uncollapsed and collapsed structures that straddle this
Interestingly, high-temperature superconductivity in the
Ca1−x Rx Fe2 As2 series appears to exist only exclusively from
the AFM phase. This is strikingly similar to the segregation
of SC and AFM phases found in 1111 materials doped with
fluorine, such as in LaFeAsO1−x Fx 32 and CeFeAsO1−x Fx ,33
and should be contrasted with the well-known coexistence shown to occur in BaFe2−x Cox As2 .34,35 Further confirmation of the intrinsic nature of superconductivity in
PHYSICAL REVIEW B 85, 024525 (2012)
FIG. 18. (Color online) Phase diagram of the Ca1−x Rx Fe2 As2 series showing the evolution of the antiferromagnetic transition TN , the
appearance of superconductivity at Tc , and the isostructural collapse as a function of electron doping (x) and effective chemical pressure ( c,
the measured change in the c axis induced by doping relative to the value of undoped CaFe2 As2 at ambient pressure). Data for x = 0 are
taken from CaFe2 As2 measurements under pressure.7 Data points for the AFM transition are obtained from electrical resistivity (diamonds)
and magnetic susceptibility (squares). Superconducting transitions are taken from resistivity data (circles), and collapse transitions (triangles)
are from susceptibility data, indicating warming (up-triangle) and cooling (down-triangle) conditions. The solid gray line indicates the position
˚ coinciding with the onset of the structural collapse for each rare-earth series and for CaFe2 As2
where the interlayer As-As separation equals 3 A,
under pressure. The blue shaded T = 0 plane indicates the range where superconductivity is observed.
Ca1−x Rx Fe2 As2 will shed light on this interesting dichotomy,
possibly providing an explanation for this distinction between
phase diagrams in oxypnictide-based and intermetallic-based
In conclusion, we have shown that rare-earth substitution into the iron-based superconductor parent compound
CaFe2 As2 provides for a rich playground of phases that will
prove useful for studying various aspects of the physics of
iron-based superconductivity. Depending on the choice of
rare-earth substituent, varying degrees of chemical pressure
and electron doping can be utilized to tune both the electronic
and structural phases of this system, resulting in a remarkable
control over a large phase space of temperature, doping, and
We have shown that chemical pressure can drive CaFe2 As2
through a structural collapse of the tetragonal unit cell that
retains the crystal symmetry but dramatically changes the
bonding structure, dimensionality, and electronic properties.
The collapse is driven solely by the interlayer As-As p-orbital
separation, which prefers to form a covalent bond when the
˚ by chemical substitution
separation is driven to less than 3 A
or applied pressure, or a combination of both. This results in
an unprecedented thermal expansion of the unit cell due to
this instability and a controllable tunability of the crystal and
electronic structure as a function of temperature.
Interestingly, a very high superconducting transition temperature was observed in all rare-earth substitutions upon
complete suppression of the antiferromagnetically ordered
phase, with several extrinsic origins of this partial-volumefraction phase systematically ruled out. The presence of
this superconductivity regardless of the structural collapse
instability raises important questions regarding the sensitivity
of Cooper pairing in the iron-based materials to electronic
structure, bonding, and dimensionality, and access to this
dramatic structural collapse at ambient pressure conditions
will provide ample opportunity to study these effects in further
Note added: We note that the presence of superconductivity
in rare-earth-doped CaFe2 As2 has been independently verified
by two other groups.36,37
S. R. SAHA et al.
PHYSICAL REVIEW B 85, 024525 (2012)
The authors gratefully acknowledge B. Eichhorn, M. A.
Green, R. L. Greene, I. I. Mazin, J. Schmalian and I. Takeuchi.
Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am.
Chem. Soc. 130, 3296 (2008).
J. Paglione and R. L. Greene, Nat. Phys. 6, 645 (2010).
G. Just and P. Paufler, J. Alloys Compd. 232, 1 (1996).
R. Hoffmann and C. Zheng, J. Phys. Chem. 89, 4175 (1985).
S. R. Saha, K. Kirshenbaum, N. P. Butch, J. Paglione, and P. Y.
Zavalij, J. Phys.: Conf. Ser. 273, 012104 (2011).
A. Kreyssig et al., Phys. Rev. B 78, 184517 (2008).
A. I. Goldman et al., Phys. Rev. B 79, 024513 (2009).
M. S. Torikachvili, S. L. Budko, N. Ni, and P. C. Canfield, Phys.
Rev. Lett. 101, 057006 (2008).
T. Park, E. Park, H. Lee, T. Klimczuk, E. D. Bauer, F. Ronning, and
J. D. Thompson, J. Phys. Condens. Matter 20, 322204 (2008).
K. Prokes, A. Kreyssig, B. Ouladdiaf, D. K. Pratt, N. Ni, S. L.
Budko, P. C. Canfield, R. J. McQueeney, D. N. Argyriou, and A. I.
Goldman, Phys. Rev. B 81, 180506R (2010).
W. Yu, A. A. Aczel, T. J. Williams, S. L. Budko, N. Ni, P. C.
Canfield, and G. M. Luke, Phys. Rev. B 79, 020511R (2009).
S. Kasahara, T. Shibauchi, K. Hashimoto, Y. Nakai, H. Ikeda,
T. Terashima, and Y. Matsuda, Phys. Rev. B 83, 060505R (2011).
T. Yildirim, Phys. Rev. Lett. 102, 037003 (2009).
J. Paglione, Bull. Am. Phys. Soc. 56, W26.00004 (2011).
R. D. Shannon, Acta Crystallogr. A 32, 751 (1976).
S. R. Saha, N. P. Butch, K. Kirshenbaum, J. Paglione, and P. Y.
Zavalij, Phys. Rev. Lett. 103, 037005 (2009).
Y. Muraba, S. Matsuishi, S-W. Kim, T. Atou, O. Fukunaga, and
H. Hosono, Phys. Rev. B 82, 180512R (2010).
G. M. Sheldrick, Acta Crystallogr. Sect. A 64, 112 (2008).
N. Kumar, R. Nagalakshmi, R. Kulkarni, P. L. Paulose, A. K.
Nigam, S. K. Dhar, and A. Thamizhavel, Phys. Rev. B 79, 012504
S. Ran et al., Phys. Rev. B 83, 144517 (2011).
This work was supported by AFOSR-Multidisciplinary University Research Initiative Grant No. FA9550-09-1-0603 and
NSF-CAREER Grant No. DMR-0952716.
D. R. Lide, CRC Handbook of Chemistry and Physics, 88th ed.
(CRC Press, Boca Raton, 2007).
D. Das, T. Jacobs, and L. J. Barbour, Nat. Mater. 9, 36 (2010).
C. Huhnt, G. Michels, M. Roepke, W. Schlabitz, A. Wurth,
D. Johrendt, and A. Mewis, Physica B 240, 26 (1997).
F. Ronning, T. Klimczuk, E. D. Bauer, H. Volz, and J. D. Thompson,
J. Phys. Condens. Matter 20, 322201 (2008).
N. Ni, S. Nandi, A. Kreyssig, A. I. Goldman, E. D. Mun, S. L.
Budko, and P. C. Canfield, Phys. Rev. B 78, 014523 (2008).
A. I. Goldman, D. N. Argyriou, B. Ouladdiaf, T. Chatterji,
A. Kreyssig, S. Nandi, N. Ni, S. L. Budko, P. C. Canfield, and
R. J. McQueeney, Phys. Rev. B 78, 100506 (2008).
M. Rotter, M. Tegel, and D. Johrendt, Phys. Rev. Lett. 101, 107006
P. Cheng, B. Shen, G. Mu, X. Zhu, F. Han, B. Zeng, and H.-H. Wen,
Europhys. Lett. 85, 67003 (2009).
L. E. Klintberg, S. K. Goh, S. Kasahara, Y. Nakai, K. Ishida,
M. Sutherland, T. Shibauchi, Y. Matsuda, and T. Terashima, J. Phys.
Soc. Jpn. 79, 123706 (2010).
S. A. J. Kimber et al., Nat. Mater. 8, 471 (2009).
M. D. Johannes, I. I. Mazin, and D. S. Parker, Phys. Rev. B 82,
024527 (2010).
H. Luetkens et al., Nat. Mater. 8, 305 (2009).
J. Zhao et al., Nat. Mater. 7, 953 (2008).
N. Ni, M. E. Tillman, J.-Q. Yan, A. Kracher, S. T. Hannahs, S. L.
Budko, and P. C. Canfield, Phys. Rev. B 78, 214515 (2008).
J.-H. Chu, J. G. Analytis, C. Kucharczyk, and I. R. Fisher, Phys.
Rev. B 79, 014506 (2009).
Z. Gao, Y. Qi, L. Wang, D. Wang, X. Zhang, C. Yao, C. Wang, and
Y. Ma, Europhys. Lett. 95, 67002 (2011).
B. Lv, L. Denga, M. Goocha, F. Weia, Y. Suna, J. K. Meena, Y.-Y.
Xuea, B. Lorenza, and C.-W. Chu, Proc. Nat. Acad. Sci. 108, 15705
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