# Magetic and Superconducting Properties of Single Crystals of Fe1+δTe1-xSex
System

Jinhu Yang<EMAIL_ADDRESS>Department of chemistry, Graduate
School of Science, Kyoto University, 606 - 8502, Japan  Mami Matsui
Department of chemistry, Graduate School of Science, Kyoto University, 606 -
8502, Japan  Masatomo Kawa  Department of chemistry, Graduate School of
Science, Kyoto University, 606 - 8502, Japan  Hiroto Ohta  Department of
chemistry, Graduate School of Science, Kyoto University, 606 - 8502, Japan
Chishiro Michioka  Department of chemistry, Graduate School of Science, Kyoto
University, 606 - 8502, Japan  Chiheng Dong  Department of physics, Graduate
School of Science, Zhejiang University, Hangzhou 310027,China  Hangdong Wang
Department of physics, Graduate School of Science, Zhejiang University,
Hangzhou 310027,China  Huiqiu Yuan  Department of physics, Graduate School of
Science, Zhejiang University, Hangzhou 310027,China  Minghu Fang  Department
of chemistry, Graduate School of Science, Kyoto University, 606 - 8502, Japan
Department of physics, Graduate School of Science, Zhejiang University,
Hangzhou 310027,China  Kazuyoshi Yoshimura<EMAIL_ADDRESS>Department of chemistry, Graduate School of Science, Kyoto University, 606 -
8502, Japan

###### Abstract

The spin-fluctuation effect in the Se-substituted system Fe1+δTe1-xSex ($x$ =
0, 0.05, 0.12, 0.20, 0.28, 0.33, 0.45, 0.48 and 1.00; $0<\delta<0.12$) has
been studied by the measurements of the X-ray diffraction, the magnetic
susceptibility under high magnetic fields and the electrical resistivity under
magnetic fields up to 14 T. The samples with $x$ = 0.05, 0.12, 0.20, 0.28,
0.33, 0.45 and 0.48 show superconducting transition temperatures in the ranger
of 10 K$\sim$14 K. We obtained their intrinsic susceptibilities by the Honda-
Owen method. A nearly linear-in-$T$ behavior in magnetic susceptibility of
superconducting samples was observed, indicating the antiferromagnetic spin
fluctuations have a strong link with the superconductivity in this series. The
upper critical field $\mu_{0}H_{c2}^{orb}$ for $T\to$ 0 was estimated to
exceed the Pauli paramagnetic limit. The Kadowaki-Woods and Wilson ratios
indicate that electrons are strongly correlated in this system. Furthermore,
the superconducting coherence length and the electron mean free path were also
discussed. These superconducting parameters indicate that the
superconductivity in the Fe1+δTe1-xSex system is unconventional.

###### pacs:

74.70.-b,75.50.Bb,74.62.Dh

††preprint: APS/123-QED

##  I INTRODUCTION

Shortly after the discovery of the iron-based oxypnictide superconductor
LaFeAsO1-xFx with $T_{c}$ of 26 K, Hosono  another family of the iron-based
chalcogenide superconductor $\alpha$-FeSe with $T_{c}$ of about 8.5 K was
reported by Wu’s group. Wu  Later on, Fang’s group enhanced the $T_{c}$ up to
14 K by substituting Se for Te in the FeTe1-xSex system. Fang  Interestingly,
although both FeTe and FeS are not superconductors under ambient pressure, the
superconductivity can be induced by Se doping in FeTe1-xSex as well as S
doping in the FeTe1-xSx system. Fang ; STe ; Mizuguchi  While there is no sign
of superconductivity in pure FeTe under high pressure in contrast to that the
superconducting transition temperature was enhanced to 37 K, just below the
McMillan limit in FeSe under high pressure. 37K  Superconducting
$\alpha$-Fe1.01Se belongs to the tetragonal symmetry system at room
temperature and undergoes a structural transition to an orthorhombic phase at
90 K, while the non-superconducting Fe1.03Se does not. McQueen  FeSe has a
simpler structure by stacking only the conducting Fe2Se2 layers in contrast to
the Fe-As based superconductors having both the conducting Fe2As2 layers and
the blocking R2O2 layers (R = rare earth elements). FeTe has the same
structure as FeSe but with a rather complex magnetic structure. For example,
the stoichiometric sample FeTe has an commensurate antiferromagetic (AF)
ordering at low temperatures after suffering a structural phase transition,
while samples with excess iron Fe1+δTe has an incommensurate AF ordering. Bao
According to the result of density functional calculations, the spin density
wave (SDW) is more stable in FeTe than that in FeSe. Subedi  Therefore, the
doped sample FeTe is expected to have higher $T_{c}$. This was indeed observed
in S or Te substituted systems for Se in FeSe. SSe  The iso-valent
substitution does not directly introduce extra carriers but may change the
topology of the Fermi surface. Fang  Recently, a spin fluctuation spectrum and
a spin gap behavior were observed by neutron scattering. Bao ; nuclear  In
fact, the NMR results indicated that the AF spin fluctuations were enhanced
greatly toward $T_{c}$, indicating the importance of AF spin fluctuations for
the superconducting mechanism in FeSe. Cava

As for the sample preparations, the iron-based superconductors, as previously
reported, however, usually contain a very small amount of magnetic impurities,
e.g., Fe7Se8 and Fe3O4. Wu ; Fang ; Li ; Mizuguchi ; McQueen ; Kazumasa ;
Williams ; Taen  Therefore, in many cases the Verwey-phase like transition
happens around 120 K due to the existence of the magnetic impurity Fe3O4 which
causes a peak in the magnetic susceptibility. Fe3O4  To elucidate the
superconducting mechanism and its relation with the AF spin fluctuations, it
is vitally important to obtain the intrinsic susceptibility. In this study, we
successfully synthesized the single crystals of Fe1+δTe1-xSex and measured
their magnetic susceptibilities under high magnetic fields and obtained the
intrinsic susceptibilities by using the Honda-Owen plot. Honda  We have found
that the magnetic susceptibility of Fe1+δTe1-xSex ($0.12\leqslant x\leqslant
1.00$) decreases with decreasing temperature from 300 K to 20 K, similar to
the results in high temperature cuprate superconductor (La1-xSrx)2CuO4, or Fe-
As based superconductors. Takagi ; Klingeler  In addition, we conducted
electrical resistivity measurements of two single crystal samples with very
close composition $x\sim$ 0.3, both of which show the superconductivity at
$T_{c}$ $\sim$ 14 K under magnetic fields up to 14 T in order to estimate the
upper critical field $\mu_{0}H_{c2}^{orb}$ and the coherence length $\xi$. As
a result, the upper critical field is found to be much larger than the Pauli
limit, and the initial slope near $T_{c}$ is comparable with those of Fe-As
based superconductors. Kohama ; Terashima  Although Fe(Te-Se) is a layered
superconductor, both the upper critical field and the initial slope near
$T_{c}$ show weak anisotropies. In order to investigate the electron
correlation strength, we have estimated Kadowaki-woods and Wilson ratios which
indicate a strongly correlated electrons picture. The superconducting
coherence length and the electron mean free path are also discussed, leading
to the fact that Fe1+δTe1-xSex is a clean superconductor.

##  II EXPERIMENTAL

The high-quality single crystals of Fe1+δTe1-xSex ( $x$ = 0, 0.05, 0.12, 0.20,
0.28, 0.33, 0.45, 0.48 and 1.00; $0<\delta<0.12$) were prepared from Fe
powders (4N purity), Te powders (4N purity) and Se powders (5N purity).
Stoichiometric quantities of about 3g-mixtures were loaded into a small quartz
tube. This small tube was then sealed into second evacuated quartz tube, and
placed in a furnace at room temperature. The temperature was slowly ramped up
to 920∘C over for 36 hours and then held at that temperature for another 12
hours in order to obtain sample homogeneities. Then, the temperature was
reduced to 400∘C over for140 hours. On the other hand, the polycrystalline of
Fe1+δSe was synthesized by previously reported solid state reaction method. Wu

The obtained single crystal samples were ground into powders for measuring
powder X-ray diffraction (XRD) with Cu $K_{\alpha}$ radiation. The detailed
structural parameters were analyzed by Rietveld refinements. The compositions
of the single crystals were analyzed using SEM (JED-2300, JEOL) equipped with
an Energy Dispersive X-Ray (EDX) spectrometer. The DC magnetic measurements
were performed by using a Superconducting Quantum Interference Device (SQUID,
Quantum Design Magnetometer). For the observations of the superconducting
transitions, both the zero-field cooling (ZFC) and field cooling (FC )
measurements were performed under the magnetic field of 20 Oe. The temperature
dependence of resistivity was measured using a standard dc four-probe method
under dc magnetic fields up to 14 T with a Physics Property Measurements
System (PPMS, Quantum Design Magnetometer). The current direction was parallel
to the a- axis of the single crystal sample.

##  III RESULTS AND DISCUSSION

###  III.1 XRD and EDX Spectroscopy

The obtained single crystal has the layered planes held together by Van der
Waals force only, and thus the crystal can easily be cleaved. X-ray
diffraction pattern of a typical single crystal Fe1.12Te0.72Se0.28 measured
with the scattering vector perpendicular to the cleaved surface was shown in
Fig. 1 (a) and the image of the single crystal is in the inset. Only (00$l$)
reflections appear, indicating that the c-axis is perpendicular to the cleaved
surface. In order to get more structural information from the XRD pattern, the
singe crystal were ground into powders for powder XRD measurements. Figure 1
(b) shows XRD patterns of the selected samples of Fe1+δTe1-xSex( $x$ = 0,
0.05, 0.12, 0.20 and 0.33). The real compositions were analyzed by EDX
measurements as listed in Table I. The EDX spectroscopy results show that
there is a slight excess amount of Fe existing in each sample, and
furthermore, the Se content has a smaller ratio than the nominal one. All the
peaks are well indexed based on a tetragonal cell with the space group of
$P$4/$nmm$, except for a small amount of the magnetic impurity phase of
Fe7Se8-type, indicating that the samples are almost in a single phase. The
impurity phase exits in the surface or in the inter-layers of the single
crystal. It should be pointed out that there is a very small amount of Fe3O4
impurity in each sample, which cannot however be probed in the XRD patterns
but causes a peak in temperature dependence of magnetic susceptibility at
about 120 K due to the Verwey phase transition. Fe3O4  With increasing Se
doping level, the a-axis decreases slightly, while the c-axis shrinks
remarkably, which makes the (001) and (200) diffraction peaks shift to higher
angles monotonously, shown as enlarged views in the inset. The cell volume is
consequently decreased by substituting Te for Se from 92 Å3 to 78 Å3,
indicating that the samples are in a solid solution in which Se enters the
lattice as Fe1+δTe1-xSex successfully.

Figure 1: X-ray diffraction patterns of Fe1+δTe1-xSex. (a) A typical single
crystal XRD pattern for sample Fe1.12Te0.72Se0.28 as well as the single
crystal image in the inset. (b) Powder XRD patterns by using samples of ground
single crystal; the peaks marked by * are Fe7Se8 impurity phase. The enlarged
view of the (001) and (200) peaks and the lattice constants as functions of Se
content $x$ were shown in the inset.

Figure 2: (a) Isothermal magnetization ($M$) with magnetic field ($H$) in the
temperature range 60 K $\leqslant T\leqslant$ 200 K with the step of 10 K,
$M_{s}$ is saturation moment of the impurities. (b) Temperature dependence of
the intrinsic susceptibility for Fe1+δTe1-xSex ($x$ = 0, 0.05, 0.12, 0.20,
0.28 and 0.33) with $H$//c. The intrinsic susceptibility of Fe1.12Te was also
measured under $H$//a. (c) The Fe(I) site contribution to the magnetic
susceptibility: $\chi_{Fe(I)}$ as a function of temperature for
superconducting samples with $x$ = 0.12, 0.20, 0.28, 0.33, 0.45 and 0.48 with
$H$//c as well as the sample with $x$ = 0.28 with $H$//a. The anisotropy
susceptibility in this series is very weak: the susceptibility in sample of
$x$ = 0.28 showed only weak dependence on the magnetic direction of $H$//c or
$H$//a.

###  III.2 Magnetic Susceptibility

Since the presence of a small amount of ferromagnetic impurities which have a
profound effect on the low-field magnetization as shown in Fig. 2 (a) for
sample Fe1+δTe. A linear-in-$H$ term in high magnetic fields magnetization
appears in each curve for various temperatures; if we extrapolate the data
from high magnetic fields to $H$ = 0, all the extrapolation ends into almost
the same point, $M_{s}$, indicating the saturation magnitude moment of the
impurity. According to the Honda-Owen plot, by extrapolating the measured
susceptibility $M/H$ = $\chi$ \+ $C_{s}$$M_{s}/$$H$ for $1/H$ $\to$ 0, where
$M/H$ is the measured susceptibility, $\chi$ the intrinsic susceptibility,
$C_{s}$ the presumed ferromagnetic impurity content and $M_{s}$ its saturation
magnetization. The influence of ferromagnetic impurities must be avoided in
order to obtain the intrinsic susceptibility, $\chi$. Therefore, we use the
Honda-Owen method to obtain the $\chi$ of these samples as $\chi(T)$ = $\Delta
M\over\Delta H$. The magnetizations were measured between 5 K and 300 K
separately under magnetic fields of 3 and 4 T, or 4 and 5 T, above which the
magnetizations of the magnetic impurity were supposed to be saturated. Figure
2 (b) shows the temperature dependence of the intrinsic magnetic
susceptibility for samples with $x$ = 0, 0.05, 0.12, 0.20, 0.28, 0.33 and
1.00. The external field is applied parallel along the c-axis. For undoped
sample Fe1.12Te, the magnetic susceptibility $\chi(T)$ increases with
decreasing temperature, and decreases sharply near 69 K, due to the AF phase
transition accompanied by the structural phase transition, then becomes almost
the constant with decreasing temperature, in agreement with the previous
reports. Wang  The susceptibility does not show any anisotropy since it has
almost no distinct difference in the paramagnetic phase in cases of $H$//c and
$H$//a, and even at low temperatures $\chi^{H//c}$(5 K)/$\chi^{H//a}$(5 K)
$\sim$ 1.45 shows a weak anisotropy. For the superconducting sample, the
intrinsic susceptibility of the sample with $x$ = 0.28 under $H$//c and $H$//a
also shows a very weak anisotropy as displayed in Fig. 2 (c). On Se-doping,
the AF transition shifts to lower temperature and the peak is broadened, then
is hardly observed in the range $x>$ 0.12, where the superconducting phase
transition occurs at 10 K $\sim$ 14 K. The upturn of $\chi(T)$ at low
temperatures, indicating a Curie-Weiss like behavior, which is naturally
ascribed to a local moment effect. Here, we noticed that the Fe’s possibly
occupy two different sites in Fe1+δTe1-xSex, i. e., Fe(I) occupies (0, 0, 0)
site and has 1.6 $\sim$1.8 $\mu_{B}$ with itinerant characters and Fe(II)
occupies (0.5, 0, z) with a localized moment of 2.5$\mu_{B}$. Bao ; Chiba ;
Zhang  The localized moment has a strong competition with superconductivity,
making the superconductivity very sensitive to the excess amount of Fe in the
FeSe compound. Cava  Supposed by the band theory, the excess Fe occurs as Fe+,
donating one electron to the Fe(I) layer. Experimentally, there is always
excess iron in Fe(II) site and the number is lager in FeTe than that in FeSe,
Sales  which may be the reason for that FeSe has such a high $T_{c}$ under
high pressure while FeTe just changes to a metallic state at low temperatures
in the same situation. Okada  In contrast to the doped sample, the end parent
compound Fe1+δSe shows a very weak $T$-linear behavior in $\chi(T)$, in
agreement with the 77Se-nuclear magnetic resonance(NMR) measurement, Kotegawa
confirming a good reliability of Honda-Owen method. In NMR measurement, the
Fe(I) site contributes completely to the Knight shift, strongly indicating
that the Fe(I) site plays the key role to understand the superconducting
mechanism in this system. Kotegawa  Furthermore, density functional
calculations show that the electronic states near the Fermi level are mostly
of Fe $3d$ characters from the Fe(I) site and with a smaller contribution from
the excess Fe(II) site. Zhang  Herein, we ascribe the temperature dependence
of the magnetic susceptibility in Fe1+δTe1-xSex primarily originates from the
Fe(I) and Fe(II) sites. However, the magnetic susceptibility of Fe(II) will be
dominant since it has a larger local moment than that of Fe(I) site,
especially at low temperatures. We suggest that the upturn in $\chi(T)$ at low
temperatures comes from the excess Fe(II) site. In order to separate the
contributions from the two different Fe sites to the magnetic susceptibility,
We fitted the magnetic susceptibility data with the Curie-Weiss law at low
temperatures for sample with $x$ = 0.12, 0.20, 0.28 and 0.33 in the
temperature range of 20 K $\leqslant$ T $\leqslant$ 50 K as

$\chi(T)=\chi_{0}+\frac{C}{(T-\theta)},$ (1)

where the $T$-independent term $\chi_{0}$ contains the Pauli paramagnetic
susceptibility from itinerant-electron bands, the Van Vleck-orbital
susceptibility and the Larmor diamagnetic susceptibility from ionic cores, $C$
stands for the Curie constant, and $\theta$ the Weiss temperature. Here, the
Curie-Weiss term may be due to the Fe(II) site contribution. Therefore, the
magnetic susceptibility of the Fe(I) can be roughly estimated as
$\chi_{Fe(I)}$ = $\chi(T)$ \- $C_{II}\over(T-\theta_{II})$, as shown in Fig. 2
(c), where $C_{II}$ is Curie constant due to the Fe(II) site, $\theta_{II}$
the Weiss temperature due to the Fe(II) site. We also fitted the data with Eq.
(1) by using different temperature range of 100 K $\leqslant$ T $\leqslant$
300 K for samples with $x$ = 0 and 0.05 (the nominal composition is $x$ = 0
and 0.10). The fitting results are listed in Table I in detail.

Table 1: Fitted parameters using Eq. (1) for Fe1+δTe1-xSex system as well as the real compositions checked by EDXS. $C$ and $\theta$ are obtained from the wider temperature fitting. The units of $C$, $\theta$, $\mu_{eff}$, CII and $\theta_{II}$ are emu K/mol, K, $\mu_{B}$, emu K/mol and K, respectively. sample(nominal) | Fe | Te | Se | $C$ | $\theta$ | $\mu_{eff}$ | C(II) | $\theta_{II}$
---|---|---|---|---|---|---|---|---
0 | 1.12 | 1 | 0 | 2.24 | -319 | 4.2 | - | -
0.10 | 1.00 | 0.95 | 0.05 | 1.6 | -260 | 3.7 | - | -
0.20 | 1.01 | 0.88 | 0.12 | - | - | - | 0.10 | -52
0.30 | 1.07 | 0.80 | 0.20 | - | - | - | 0.02 | -5
0.40(I) | 1.12 | 0.72 | 0.28 | - | - |  | 0.12 | -24
0.40(II) | 1.04 | 0.67 | 0.33 | - | - | - | 0.05 | -23

After subtracting the Fe(II) contribution from the susceptibility, it is clear
that $\chi_{Fe(I)}$ decreases gradually from 300 K down to 20 K, as shown in
Fig. 2 (c), qualitatively consistent with our NMR results. Our  It is
important to note that there are other systems which also show the linear-
in-$T$ behavior: for example, the geometric frustrated system Na0.5CoO2, Maw
the high temperature cuprate superconductor La2-xSrxCuO2, Takagi  the simply
metal Cr as well as its alloys Fawcett  and even the new discovered Fe-As
based superconductors. Klingeler  All the above systems share a common
feature: having antiferromagnetic spin fluctuations on their backgrounds. Very
recently, Han and his colleagues studied the electronic structure and magnetic
interaction in Fe1+δTe. They found that the small amount of excess Fe played
an important role in determining the magnetic structure and drove the Fermi
surface nesting from ($\pi$, $\pi$) to ($\pi$, 0). Han  With increasing Se
doping, the ratio of Fe(II) was depressed in Fe1+δTe1-xSex system. Sales
Thus, the upturn at low temperatures will disappear in Se rich sample. It did
so in the samples with $x$ = 0.45 and 0.48 as shown in Fig. 2 (c) in which we
did not subtract the Fe(II) site contribution to the magnetic susceptibility
but only show the raw data. In LaFeAsO1-xFx, the linear-in-$T$ behavior is
considered to be a strong AF spin fluctuations with multi-orbital character.
Klingeler  Korshunov argued that it was universal for systems with the strong
($\pi$, $\pi$) SDW fluctuation. Korshunov  In fact, we observed the
$\mathbf{q}\neq 0$ modes of antiferromagnetic spin fluctuations were strongly
enhanced toward $T_{c}$ in the normal state. Our  Overall the linear-in-$T$
behavior of $\chi(T)$ observed in our single crystal samples strongly supports
the above model, suggesting the importance of the ($\pi$, $\pi$ ) AF spin
fluctuations originated from the Fe(I) site in superconducting mechanism of
this system.

###  III.3 Superconducting State and Upper Critical Field
$\mu_{0}H_{c2}^{orb}$

The superconducting transition temperature was found to be $\sim$10 K for the
sample with $x>$ 0.05 as shown in Figs. 3 (a), (b), (c), (d) and (e). Because
the excess Fe in the Fe(II) site has a localized moment, Chiba ; Zhang ; Liu
where there is the more excess amount of Fe(II), the less superconducting
volume fraction is observed, compared with Figs. 3 (d) and (e), where these
two samples have very close composition. With increasing the Se content $x$,
the superconducting volume fraction was enhanced greatly. The susceptibility
measured in the FC process shows no negative sign but a small positive value
in the superconducting state, indicating an intrinsic pinning effect in this
layered structure compound. Iye

Figure 3: Temperature dependence of susceptibility in superconducting samples
under magnetic field $H$ = 20 Oe applied along the c-axis $H$//c, for ZFC and
FC processes. (a) Fe1.00Te0.95Se0.05. (b) Fe1.01Te0.88Se0.12, (c)
Fe1.07Te0.80Se0.20. (d) Fe1.04Te0.67Se0.33. (e) Fe1.12Te0.72Se0.28.

In order to estimate the superconducting parameters, we selected two samples
with close composition Fe1.12Te0.72Se0.28 (simplified as R1) and
Fe1.04Te0.67Se0.33 (simplified as R2) for resistivity measurements. Figures 4
(a), (b), (c) and (d) show the suppression of the superconducting transition
in the electrical resistivity for $H$//c and $H$//a up to 14 T for the samples
of R1 and R2, respectively. With increasing the magnetic field, the
superconducting transitions shifted to lower temperatures, and became
broadened. The upper critical field $\mu_{0}H_{c2}^{orb}$ determined from the
onset $T_{c}$ were plotted in Figs. 5 (a) and (b) for the samples R1 and R2,
respectively. Here, the onset $T_{c}$ was defined as the resistivity falls to
90% of the $\rho_{0}$ value in the normal state just above $T_{c}$. The
initial slopes $\partial\mu_{0}H_{c2}/\partial T$ near $T_{c}$ are -6 T/K and
-3.9 T/K for the R1 sample with $H$//a and $H$//c, respectively, leading to an
estimation of the upper critical field extrapolated to zero-temperature as
$\mu_{0}H_{c2}^{orb}(0)$ = 57 T and 37 T, by using the Werthamer-Helfand-
Hohenberg (WHH) model as

$\mu_{0}H_{C2}^{orb}(0)=-0.693T_{c}(\frac{\partial\mu_{0}H_{C2}^{orb}}{\partial
T})_{T=T_{c}}.$ (2)

In contrast to the sample R1, the sample R2 shows larger initial slopes of
-8.7 T/K and -4.2 T/K as well as the upper critical fields of 85 T and 40 T
under $H$//a and $H$//c, respectively. The upper critical field in this system
is comparable with the cases of the Fe-As based superconductors
LaFeAsO0.93F0.03 Kohama  and KFe2As2. Terashima  In addition, the upper
critical field is much lager than the Pauli limit field
$\mu_{0}H_{\mathrm{P}}$ =1.84 $T_{c}$ $\sim$ 25 T. The anisotropy coefficients
$\Gamma$ determined from $\Gamma$ = $H_{c2}^{\perp}$/$H_{c2}^{\parallel}$ are
1.54 and 2.1 for the samples R1 and R2, respectively. In fact, the $\Gamma$ is
rather isotropic at low temperatures, indicating the three dimensional nature
of the Fermi-surface topology.Yuan  These results strongly suggest an
unconventional superconducting mechanism in this compound. The estimated
parameters are listed in Table II.

Figure 4: Temperature dependence of resistivity ($\rho$) under magnetic field
($H$) up to 14 T (0, 2, 4, 6, 8, 10, 12 and 14 T) for samples of R1 and R2:
(a) The sample R1 for $H$ // c. (b) The sample R1 for $H$ // a. (c) The sample
R2 for $H$ // c. (d) The sample R2 for $H$ // a.

Figure 5: Temperature dependence of the upper critical fields of (a) the
sample R1 and (b) the sample R2. The dashed line is the estimation by the WHH
theory.

The initial slope of $\mu_{0}H_{c2}^{orb}$ near $T_{c}$ is also weakly
anisotropic. The similar behavior was also observed in the 122-type compounds,
and was thought to be two-band superconductivity. Baily  The Sample R2 with
the less Fe shows a larger initial slope and a higher upper critical field in
compared with the sample R1, indicating the existence of Fe(II) affects the
electronic band structure and consequently the superconductivity greatly. The
initial slope near $T_{c}$ is proportional to the square of the electron
effective mass $m^{*2}$, in agreement with a large $\gamma\sim 39$ mJ/mol K2.
Sales  In strongly correlated electron systems, the Kadowaki-Woods ratio
$A/\gamma^{2}$ is expected to be a constant $\sim$ 1.0 $\times$
10-5$\mu\Omega$ cm (mJ/mol-K)2, where $A$ is the quadratic term of the
resistivity and $\gamma$ is the linear term coefficient of the specific heat,
so called the electronic specific heat coefficient. We obtained $A\sim 0.03$
$\mu\Omega$ cm /K2 by fitting the data with $\rho=\rho_{0}+AT^{2}$ in the
temperature range of 16 K $\leqslant$ T $\leqslant$ 20 K for the sample R2,
resulting in $A/\gamma^{2}\sim$ 2$\times$ 10-5$\mu\Omega$ cm/(mJ/mol K)2,
which is a little bit larger than the value of heavy fermion compound
UBe${}_{13}.$UBe13  The Wilson ratio
$R_{w}=\pi^{2}k_{B}^{2}\chi_{spin}/3\mu_{B}^{2}\gamma$ is estimated as 5.7 for
the sample R2 with $\chi_{spin}$ of $2\times 10^{-3}$emu/mol from our data,
well exceeding the unity for a free electron system. These results strongly
suggest that the electron in superconducting Fe1+δTe1-xSex is strongly
correlated, being in good agreement with our recent NMR investigation on the
same single crystal of Fe1.04Te0.67Se0.33 which strongly indicates the
unconventional d-wave superconductivity with spin singlet pairing-symmetry.
Our

It is also very important to know whether the Fe1+δTe1-xSex is a clean
superconductor or not. To solve this issue, we need to know the mean free path
$\ell$ and the Pippard coherence length $\xi_{0}$. On the basis of the
Bardeen-Cooper-Schrieffer (BCS) theory and the Drude model, $\ell$ = $\hbar$
(3$\pi^{2}$)1/3/e2$\rho_{0}$n2/3 and $\xi_{0}$ = $\hbar$VF/$\pi$$\Delta$,
where $n$ is the carrier concentration, $\rho_{0}$ the residual resistivity,
VF the Fermi velocity and $\Delta$ the superconducting gap. Giving the
superconducting gap 2$\Delta$/kB$T_{c}$ = 3.52 in the BCS theory, the
$\xi_{0}$ can be written as
$\hbar^{2}$(3$\pi^{2}$n)1/3/1.76$\pi$$m$$k_{B}$$T_{c}$, where $m$ is the free
electron rest mass. Very recently, the angle-resolved photoemission
spectroscopy (ARPES) measurement on Fe1.03Se0.3Te0.7 showed the Fermi velocity
$\sim$ 0.4 eV$\mathrm{\AA}$ for both the hole and the electron bands and the
superconducting gap $\Delta$ $\sim$ 4 meV. Nakayama  Therefore the $\xi_{0}$
is estimated as 33.5$\mathrm{\AA}$ and the carrier concentration estimated as
$\sim$ 6.8$\times$1023/m3. Since the composition is very close among the
samples of Fe1.12Te0.72Se0.28, Fe1.04Te0.67Se0.33 and Fe1.03Te0.70Te0.30 (in
ref Nakayama ), it is reasonable to consider that the carrier concentration
does not change very much among these three samples. The residual resistivity
was estimated as $\rho_{0}=0.70\times 10^{-5}\Omega m$, $0.65\times
10^{-5}\Omega m$ for the samples R1 and R2, respectively. Therefore, $\xi_{0}$
is estimated as $\sim$31 $\mathrm{\AA}$ and $\ell$ $\sim$ 2336 $\mathrm{\AA}$
for the sample R1 and $\xi_{0}$ $\sim$ 32 $\mathrm{\AA}$, $\ell$$\sim$ 2516
$\mathrm{\AA}$ for the case of the sample R2. The estimated parameters are
listed in Table II. Therefore, the ratio of $\ell$/$\xi_{0}$ $\sim$ 80 is well
exceeding the unity so that the Fe1+δTe1-xSex is thought to be a clean
superconductor and the estimated superconducting parameters are considered to
be intrinsic. For example, in a clean superconductor, $\xi_{GL}$ $\sim$ 0.74
$\xi_{0}$/(1-$T/T_{c}$)1/2. We estimated $\xi_{GL}$$\sim$ 24 $\mathrm{\AA}$
for sample R2 at T = 0 K along the c direction, in good agreement with the
value of 29 $\mathrm{\AA}$ derived from the upper critical field, where
$\xi_{GL}$ is expressed as $\xi_{GL}^{2}$ = $\phi_{0}$/2$\pi$$H_{c2}^{orb}$ (
$\phi_{0}$ = 2 $\times$ 10-7 Oe cm2). However, it should be pointed out that
those estimations based on the one band theory which may not valid for the
multi-band compound, and much information will be needed for further
discussion on superconductivity in this system.

Table 2: Estimated superconducting parameters for the samples R1 and R2. Tc = 13.7 and 14.1 K for the samples R1 and R2, respectively. sample |  $\partial\mu_{0}H^{orb}_{c2}$/$\partial$T |  $\mu_{0}$$H^{orb}_{c2}$ |  $\mu_{0}H_{\mathrm{P}}$(0) |  $\xi$0 |  $\xi$GL | $\ell$ |  $\ell$/$\xi_{0}$
---|---|---|---|---|---|---|---
($H$//a,c) | ($T/K$) | (T) | (T) | (Å) | (Å) | (Å) |
R1(a) | -6.0 | 57 | 25 | 32 | 24 | 2336 | 73
R1(c) | -3.9 | 37 | 25 | 32 | 30 |  |
R2(a) | -8.7 | 85 | 26 | 31 | 20 | 2516 | 79
R2(c) | -4.2 | 40 | 29 | 32 | 29 |  |

##  IV CONCLUSIONS

In summary, we successfully synthesized the single crystal of Fe1+δTe1-xSex
($x$ = 0, 0.05, 0.12, 0.20, 0.28, 0.33, 0.45, 0.48 and 1.00; $0<\delta<0.12$)
and measured their magnetic susceptibilities. The intrinsic magnetic
susceptibility was obtained though Honda-Owen method for the first time. The
nearly linear-in-$T$ behavior in susceptibility was observed in
superconducting samples with $x$ = 0.12, 0.20, 0.28, 0.33 0.45, 0.48 and 1.00,
indicating a close relationship between the AF spin fluctuations around
($\pi$, $\pi$) and the superconductivity. The excess Fe has a localized moment
which affects the superconducting state greatly. The intrinsic susceptibility
shows a weakly anisotropic behavior. Also, the initial slope near $T_{c}$ and
the upper critical field estimated by measuring the resistivity under high
magnetic fields show a weakly anisotropic behavior. The estimated coherence
length $\xi_{GL}$, the Pippard coherence length $\xi_{0}$ and the mean free
path $\ell$ by the BCS theory and the Drude model support a clean
superconductor scenario. The estimations of Kadowaki-Woods and Wilson ratios
indicate Fe1+δTe1-xSex belongs to a strongly electron-correlated system.
Consequently, the superconductivity in Fe1+δTe1-xSex is considered to be of
unconventional and in the strongly correlated one with the very high value of
$\mu_{0}H_{c2}^{orb}$, which are also supported by our recent NMR study. Our

## Acknowledgement

This research was supported by Grant-in-Aid for the Global COE Program
“International Center for Integrated Research and Advanced Education in
Materials Science” and for Scientific Research on Priority Area “Invention of
anomalous quantum materials”(16076210) from the Ministry of Education,
Culture, Sports, Science and Technology of Japan, and also by Grants-in-Aid
for Scientific Research (19350030) from the Japan Society for Promotion of
Science.

## References

  * (1) Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008).
  * (2) Hsu F. C., Luo. J. Y., Yeh K. W. Chen T. K. , Huang T. W. , Wu Philip M., Lee Y. C. , Huang Y. L. , Chu Y. Y. , Yan D. C. , and Wu M. K., Proc. Natl. Acad. Sci. U. S. A. 105, 14262 (2008).
  * (3) M. H. Fang, H. M. Pham, B. Qian, T. J. Liu, E. K. Vehstedt, Y. Liu, L. Spinu, and Z. Q. Mao, Phys. Rev. B 78, 224503 (2008).
  * (4) M. H. Fang, B. Qian, H. M. Pham, J. H. Yang, T. J. Liu, E. K. Vehstedt, L. Spinu and Z. Q. Mao, arXiv: 0811.3021
  * (5) Y. Mizuguchi, F. Tomioka, S. Tsuda, T. Yamaguchi, and Y. Takano, Appl. Phys. Lett. 94, 012503 (2009).
  * (6) S. Margadonna, Y. Takabayashi, Y. Ohishi, Y. Mizuguchi, Y. Takano, T. kagayama, T. Nakagawa, M. Takata, and K. Prassides, Phys. Rev. B 80, 064506 (2009).
  * (7) T. M. McQueen, A. J. Williams, P. W. Stephens, J. Tao, Y. Zhu, V. Ksenofontov, F. Casper, C. Felser, and R. J. Cava, Phys. Rev. Lett. 103, 057002 (2009).
  * (8) W. Bao, Y. Qiu, Q. Huang, M. A. Green, P. Zajdel, M. R. Fitzsimmons, M. Zhernenkov, M. Fang, B. Qian, E. K. Vehstedt, J. Yang, H. M. Pham, l. Spinu, and Z. Q. Mao, Phys. Rev. Lett. 102, 247001 (2009).
  * (9) A. Subedi, L. J. Zhang, D. J. Singh, and M. H. Du, Phys. Rev. B 78, 134514 (2008).
  * (10) Y. Mizuguchi, F. Tomiok, S. Tsuda, T. Yamaguchi, and Y. Takano, J. Phys. Soc. Jpn. 78, 074712 (2009).
  * (11) Y. Qiu, W. Bao, Y. Zhao, C. Broholm, V. Stanev, Z. Tesanovic, Y. C. Gasparovic, S. Chang, J. Hu, B. Qian, M. H. Fang, and Z. Q. Mao, Phys. Rev. Lett. 103, 067008 (2009).
  * (12) T. Imai, K. Ahilan, F. L. Ning, T. M. McQueen, and R. J. Cava, Phys. Rev. Lett. 102, 177005 (2009).
  * (13) L. Li, Z. R. Yang, M. Ge, L. Pi, J. T. Xu, B. S. Wang, Y. P. Sun, and Y. H. Zhang, J. Supercond. Nov. Magn. 22, 667 (2009).
  * (14) K. Horigane, H. Hiraka, and K. Ohoyama, J. Phys. Soc. Jpn. 78, 074718(2009).
  * (15) A. J. Williams, T. M. McQueen, and R. J. Cava, Solid State Commun. 149, 1507 (2009).
  * (16) T. Taen, Y. Tsychiya, Y. Nakajima, and T. Tamegai, arXiv: 0906.1951.
  * (17) E. J. W. Verwey, Nature(London) 144, 327 (1939).
  * (18) K. Honda, Ann. Phys. Lpz. 32, 1048 (1910). M. Owen, ibid. 37, 657 (1912).
  * (19) H. Takagi, T. Ido, S. Ishibashi, M. Uota, S. Uchida, and Y. Tokura, Phys. Rev. B 40, 2254 (1989).
  * (20) R. Klingeler, N. Leps, I. Hellmann, A. Popa, C. Hess, A. Kondrat, J. H-Borrero, G. Behr, V. Kataev and B.Buechner, arXiv : 0808.0708; J. Q. Yan, A. Kreyssig, S. Nandi, N. Ni, S. L. Budko, A. Kracher, R. J. Mcqueeney, R. W. McCalllum, T. A. Lograsso, A. I. Goldman, and P. C. Canfield, Phys. Rev. B 78, 024516 (2008).
  * (21) Y. Kohama, Y. Kamihara, S. A. Baily, L. Civale, S. C. Riggs, F. F. Balakirev, T. Atake, M.Jaime, M. Hirano, and H. Hosono, Phys. Rev. B 79, 144527 (2009).
  * (22) T. Terashima, M. Kimata, H. Satsukawa, A. Harada, K. hazama, S. Uji, H. harima, G. F. Chen, J. L .Luo, and N. L. Wang, J. Phys. Soc. Jpn. 78, 063702 (2009).
  * (23) G. F. Chen, Z. G. Chen, J. Dong, W. Z. Hu, G. Li, X. D. Zhang, P. Zheng, J. L. Luo, and N. L. Wang, Phys. Rev. B 79, 140509(R) (2009).
  * (24) S. Chiba, J. Phys. Soc. Jpn. 10, 837 (1955).
  * (25) L. J. Zhang, D. J. Singh, and M. H. Du, Phys. Rev. B 79, 012506 (2009).
  * (26) T. J. Liu, X. Ke, B. Qian, J. Hu, D. Fobes, E. K. Vehstedt, H. Pham, J. H. Yang, M. H. Fang, L. Spinu, P.Schiffer, Y. Liu, and Z. Q. Mao, Phys. Rev. B 80, 174509 (2009).
  * (27) B. C. Sales, A. S. Sefat, M. A. McGuire, R.Y. Jin, D. Mandrus. and Y. Mozharivskyj, Phys. Rev. B 79, 094521 (2009).
  * (28) H.Okada, H. Takahashi, Y. Mizuguchi, Y.Takano, and H. Takahashi, J. Phys. Soc. Jpn. 78, 083709 (2009).
  * (29) H. Kotegawa, S. Masaki, Y. Awai, H. Tou, Y. Mizuguchi, and Y. Takano, J. Phys. Soc. Jpn. 77, 113703 (2008).
  * (30) C. Michioka, H. Ohta, M. Matsui, J. H. Yang, K. Yoshimura, M. H. Fang, arXiv: 0911.3729. The Knight shift is proportional to the uniform spin susceptibility $\chi_{spin}$, reflecting the temperature dependence of $\chi_{spin}$. The nuclear spin-lattice relaxation rate1/T1 divided by temperature $T$ measures the weighted average for various q-modes of low frequency spin fluctuations. In our recent NMR measurement, the Knight shift in samples with $x$ = 0.28 and 0.33 decreases and 1/T1T was enhanced with decreasing temperature toward $T_{c}$. The 125Te nuclear spin-lattice relaxation rate strongly indicates that the d-wave superconductivity with spin singlet superconducting pairing-symmetry.
  * (31) M. L. Foo, Y. Y. Wang, S. Watauchi, H. W. Zandbergen, T. He, R. J. Cava, and N. P. Ong, Phys. Rev. Lett. 92, 247001 (2004).
  * (32) E. Fawecett, H. L. Alberts, V. G. Yu, R. D. Noakes, and V. J. Yakhmi, Rev. Mod. Phys. 66, 25 (1994).
  * (33) M. J. Han, S. Y. Savrasov, Phys. Rev. Lett. 103, 067001 (2009).
  * (34) M. M. Korshunov, I. Eremin, D. V. Efremov, D. L. Maslov, and A. V. Chubukov, Phys. Rev. Lett. 102, 236403 (2009).
  * (35) Y. Iye, S. Nakamura, and T. Tamegai, Physica C 159, 433 (1989); Y. Iye, T. Terashima, and Y. Bando, Physica C 184, 362 (1991).
  * (36) M. H. Fang, J. H. Yang, F. F. Balakirev, Y. Kohama, J. Singleton, B. Qian, Z. Q. Mao, H. D. Wang, and H. Q. Yuan, arXiv: 0909.5328V1.
  * (37) S. A. Baily, Y. Kohama, h. Hiramatsu, B. Maiorov, F. F. Balakirev, M. Hiranl, and H. Hosono, Phys. Rev. Lett. 102, 117004 (2009).
  * (38) K. Nakayama, T. Sato, P. Richard, T. Kawahara, Y. Sekiba, T. Qian, G. F. Chen, J. L. Luo, N. L. Wang, H. Ding, and T. Takahashi, arXiv: 0907.0763V1.
  * (39) K. Kadowaki, and S. B. Woods, Solid State Commun. 58, 507 (1986).