# Pauli limited upper critical field in Fe$_{1+}$$_{y}$Te$_{1}$$_{−}$$_{x}$Se$_{x}$ 

Hechang Lei, 1 Rongwei Hu, 1 , ∗ E. S. Choi, 2 J. B. Warren, 3 and C. Petrovic 1 

$^{1}$Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY 11973, USA 

$^{2}$NHMFL/Physics, Florida State University, Tallahassee, Florida 32310, USA and 

$^{3}$Instrumentation Division, Brookhaven National Laboratory, Upton, New York 11973, USA 

(Dated: November 1, 2018) 

In this work we investigated the temperature dependence of the upper critical field µ$_{0}$H c $_{2}$( T ) of Fe$_{1}$$_{.}$$_{02(3)}$Te$_{0}$$_{.}$$_{61(4)}$Se$_{0}$$_{.}$$_{39(4)}$ and Fe$_{1}$$_{.}$$_{05(3)}$Te$_{0}$$_{.}$$_{89(2)}$Se$_{0}$$_{.}$$_{11(2)}$ single crystals by measuring the magneto- transport properties in stable dc magnetic fields up to 35 T. Both crystals show that µ$_{0}$H c $_{2}$( T ) in the ab-plane and along the c-axis exhibit saturation at low temperatures. The anisotropy of µ$_{0}$H c $_{2}$( T ) decreases with decreasing temperature, becoming nearly isotropic when the temperature T → 0. Fur- thermore, µ$_{0}$H c $_{2}$(0) deviates from the conventional Werthamer-Helfand-Hohenberg (WHH) theoret- ical prediction values for both field directions. Our analysis indicates that the spin-paramagnetic pair-breaking effect is responsible for the temperature-dependent behavior of µ$_{0}$H c $_{2}$( T ) in both field directions. 

The discovery of superconductivity in REOFePn (RE=rare earth; Pn=P or As, 1111-system) 1 − 5 with high transition temperature T$_{c}$ has generated a great deal of interests. Shortly after, several other groups of iron-based superconductors have been discovered, such as AFe$_{2}$As$_{2}$ (A=alkaline or alkaline-earth metals, 122- system), 6 , 7 LiFeAs (111-system), 8 (Sr$_{4}$M$_{2}$O$_{6}$)(Fe$_{2}$Pn$_{2}$) (M=Sc, Ti or V, 42622-system), 9 , 10 and α -PbO type FeSe (11-system). 11 In particular, the discovery of su- perconductivity in FeSe, FeTe$_{1}$$_{−}$$_{x}$Se$_{x}$, 12 and FeTe$_{1}$$_{−}$$_{x}$S$_{x}$ 13 opened new directions. Simple binary Fe based super- conductors can help to understand the mechanism of superconductivity because they share the most promi- nent characteristics with other iron-based superconduc- tors, i.e., a square-planar lattice of Fe with tetrahedral co- ordination and similar Fermi surface topology. 14 Further- more, 11-type superconductors exhibit some distinctive features: absence of charge reservoir, significant pressure effect, 15 and excess Fe with local moment. 16 

In order to understand the mechanism of supercon- ductivity of iron-based superconductors, it is important to study the upper critical field µ$_{0}$H$_{c}$$_{2}$ . This is one of the most important superconducting parameters since it provides valuable information on fundamental super- conducting properties: coherence length, anisotropy, de- tails of underlying electronic structures and dimensional- ity of superconductivity as well as insights into the pair- breaking mechanism. 

There are two remarkable common characteristics in µ$_{0}$H$_{c}$$_{2}$ - T phase diagram in iron-based superconduc- tors. For 1111-system, µ$_{0}$H$_{c}$$_{2}$$_{,c}$ ( T ) shows pronounced upturn curvature at low temperatures. In contrast, µ$_{0}$H$_{c}$$_{2}$$_{,ab}$ ( T ) exhibits a downturn curvature with decreas- ing temperature. 17 The former can be explained by two band theory with high diffusivity ratio of electron band to hole band and the latter is mainly ascribed to 

PACS numbers: 74.62.Bf, 74.10.+v, 74.20.Mn, 74.70.Dd 

## I. INTRODUCTION 

the spin-paramagnetic effect. 18 − 19 For 122-system ((Ba, K)Fe$_{2}$As$_{2}$ and Sr(Fe, Co)$_{2}$As$_{2}$), the upturn curvature of µ$_{0}$H$_{c}$$_{2}$$_{,c}$ ( T ) present in 1111-system does not appear, but it still shows positive curvature of temperature far below T$_{c}$ without saturation. 20 − 22 It can also be interpreted us- ing two band theory with smaller diffusivity ratio of two bands when compared to 1111-system. 21 On the other hand µ$_{0}$H$_{c}$$_{2}$$_{,ab}$ ( T ) tends to saturate with decreasing tem- perature and it also originates from spin-paramagnetic effect. 23 However, for KFe$_{2}$As$_{2}$, both µ$_{0}$H$_{c}$$_{2}$$_{,ab}$ ( T ) and µ$_{0}$H$_{c}$$_{2}$$_{,c}$ ( T ) show saturation trend at low temperature with different negative curvature. The former can be ascribed to the spin-paramagnetic effect and the latter is mainly determined by orbital limited field in one band scenario. 24 

Previous research on polycrystalline FeSe$_{0}$$_{.}$$_{25}$Te$_{0}$$_{.}$$_{75}$ us- ing pulsed magnetic fields up to 55 T, indicated that spin-paramagnetic effect dominates µ$_{0}$H$_{c}$$_{2}$ ( T ). 25 How- ever, it is necessary to elucidate whether this kind of effect dominates the µ$_{0}$H$_{c}$$_{2}$$_{,ab}$ ( T ) or (and) µ$_{0}$H$_{c}$$_{2}$$_{,c}$ ( T ). In this work, we report the upper critical field anisotropy of Fe$_{1}$$_{.}$$_{02(3)}$Te$_{0}$$_{.}$$_{61(4)}$Se$_{0}$$_{.}$$_{39(4)}$ and Fe$_{1}$$_{.}$$_{05(3)}$Te$_{0}$$_{.}$$_{89(2)}$Se$_{0}$$_{.}$$_{11(2)}$ single crystals in stable dc high magnetic field up to 35T. We show that spin-paramagnetic effect is dominant in both of µ$_{0}$H$_{c}$$_{2}$$_{,ab}$ ( T ) and µ$_{0}$H$_{c}$$_{2}$$_{,c}$ ( T ). 

Single crystals of Fe(Te,Se) were grown by self- flux method with nominal composition FeTe$_{0}$$_{.}$$_{5}$Se$_{0}$$_{.}$$_{5}$ and FeTe$_{0}$$_{.}$$_{9}$Se$_{0}$$_{.}$$_{1}$. Stoichiometric elemental Fe (purity 99.98%, Alfa Aesar ), Te (purity 99.999%, Alfa Aesar), and Se (purity 99.999%, Alfa Aesar) were sealed in quartz tubes under partial argon atmosphere. The sealed am- poule was heated to a soaking temperature of 950 $^{◦}$C, then slowly cooled to 300-400 $^{◦}$C. Plate-like crystals up to 2 × 5 × 1 mm 3 can be grown. The powder X-ray diffrac- 

## II. EXPERIMENT 

