Strong anisotropy in nearly ideal-tetrahedral superconducting FeS single crystals
Christopher K. H. Borg, Xiuquan Zhou, Christopher Eckberg, Daniel J. Campbell, Shanta R. Saha, Johnpierre Paglione, Efrain E. Rodriguez
SStrong anisotropy in nearly ideal-tetrahedral superconducting FeS single crystals
Christopher K. H. Borg, Xiuquan Zhou, Christopher Eckberg,
2, 3
Daniel J.Campbell,
2, 3
Shanta R. Saha,
2, 3
Johnpierre Paglione,
2, 3 and Efrain E. Rodriguez*
1, 3 Department of Chemistry and Biochemistry, University of Maryland, College Park, MD 20742 Department of Physics, University of Maryland, College Park, MD 20742 Center for Nanophysics and Advanced Materials,University of Maryland, College Park, MD 20742
We report the novel preparation of single crystals of tetragonal iron sulfide, FeS, which exhibits anearly ideal tetrahedral geometry with S–Fe–S bond angles of 110.2(2) ◦ and 108.1(2) ◦ . Grown viahydrothermal de-intercalation of K x Fe − y S crystals under basic and reducing conditions, the silver,plate-like crystals of FeS remain stable up to 200 ◦ C under air and 250 ◦ C under inert conditions, eventhough the mineral “mackinawite” (FeS) is known to be metastable. FeS single crystals exhibit asuperconducting state below T c = 4 K as determined by electrical resistivity, magnetic susceptibility,and heat capacity measurements, confirming the presence of a bulk superconducting state. Normalstate measurements yield an electronic specific heat of 5 mJ/mol-K , and paramagnetic, metallicbehavior with a low residual resistivity of 250 µ Ω · cm. Magnetoresistance measurements performedas a function of magnetic field angle tilted toward both transverse and longitudinal orientationswith respect to the applied current reveal remarkable two-dimensional behavior. This is paralleledin the superconducting state, which exhibits the largest known upper critical field H c anisotropyof all iron-based superconductors, with H || abc (0) /H || cc (0) =(2.75 T)/(0.275 T)=10. Comparisons totheoretical models for 2D and anisotropic-3D superconductors, however, suggest that FeS is thelatter case with a large effective mass anisotropy. We place FeS in context to other closely relatediron-based superconductors and discuss the role of structural parameters such as anion height onsuperconductivity. I. INTRODUCTION
While the field of iron-based superconductors has fo-cused primarily on selenides, tellurides, and arsenides, recent developments show that sulfides are a possible newavenue for high- T c superconductors. The first iron-sulfidesuperconductor, BaFe S , has been reported to have asuperconducting critical temperature ( T c ) = 14 K at 11GPa. An even simpler sulfide, H S, under high pressure(90 GPa), has been found to exhibit superconductivity ashigh as 203 K, which is the highest reported T c thus far. Sulfides in general therefore merit closer inspection forexploring high temperature superconductivity, and ironsulfides in particular could point the way towards newsuperconducting compounds.Recently, Lai et al. found that the simple binary com-pound, FeS, in its tetragonal polymorph known as mack-inawite is a superconductor with a T c = 5 K. Similar tothe superconducting β -form of iron selenide, mackinawitealso adopts the anti-PbO structure where FeS tetrahe-dra edge-share to form two-dimensional (2D) layers (Fig-ure 1b inset). Unlike its heavier analogues, FeSe andFeTe, however, mackinawite is metastable and thereforecannot be synthesized from their respective elements us-ing solid state methods, unless it is alloyed with signifi-cant amounts of Co, Ni or Cu.
Due to the thermody-namic limitations in its preparation, single crystal growthof mackinawite is a challenge. Growing single crystals ofFeS is imperative, however, towards understanding itstrue physical properties.Before the report by Lai et al. on superconductiv-ity, several studies had found FeS to be a ferrimagnetic
FeSK0 10 20 30 40 50 60 700
P4/nmma = 3.683 Å c = 5.034 ÅRwp = 3.043 % Y calc Y obs Y calc-obs FeS
I4/mmma = 3.745 Å c = 13.627 ÅRwp = 3.783 % Y calc Y obs Y calc-obs I n t e n s i t y ( a r b . u n i t ) (a)(b) (001)(002) FIG. 1: Rietveld refinement with XRD powder diffraction onground single crystal samples. (a) Refinement of K x Fe − y S template’s body-centered tetragonal structure ( I /mmm ).(b) Refinement of the FeS product’s structure with a primi-tive tetragonal model ( P /nmm ). Fe (orange) ions are tetra-hedrally coordinated to S (yellow) anions, and the K (pur-ple) cations are located between two FeS layers. Tick markscorresponding to their respective phase are shown below thedifference curve. semiconductor. The conflicting reports on the prop- a r X i v : . [ c ond - m a t . s up r- c on ] J a n erties of polycrystalline FeS by different groups may bedue to impurities not observed through powder X-raydiffraction, especially since iron provides a high back-ground from fluorescence with Cu K- α radiation. Pow-der FeS samples prepared through aqueous methods mayform small crystallites as indicated by the broad Braggreflections in the diffraction patterns of past studies. The small particle size and polycrystalline nature of thesesamples impede accurate electrical resistivity and magne-tization measurements due to grain boundary effects andthe facile oxidation of surfaces of small particles.
De-spite their ground-breaking work on polycrystalline FeS,Lai et al. also called for high quality single crystal datafor definitive determination of the physical properties ofFeS.We report a method for the preparation of highquality single crystals of mackinawite FeS. Since FeSis metastable, single crystal growth through slowcooling of a melt is not possible. In the case ofFeSe − y Te y and Fe x Te, large single crystalswere grown through Bridgeman techniques allowing de-tailed transport and spectroscopic experiments. ForFeSe, which has limited window of phase stability, chem-ical vapor transport methods at elevated temperaturesis the only technique that has been reported.
Wepresent a general technique for the de-intercalation ofthe ternary phase K x Fe − y S Figure 1a inset), whichmelts congruently and can therefore be prepared in sin-gle crystal form.
We link how studying the materialschemistry of layered iron sulfides is key to discoveringthe underlying physics in new superconductors such asmackinawite FeS.
II. EXPERIMENTALA. Hydrothermal synthesis of FeS single crystals
In this work, superconducting FeS single crystals wereprepared by de-intercalation of potassium cations fromK x Fe − y S ( x ≈ . y ≈ .
4) single crystals under hy-drothermal condition. The growth of K x Fe − y S singlecrystals was modified by the method described by Lei et al. For a typical reaction, 1.00 g (11.4 mmol) ofhexagonal FeS powder (Alfa Aesar, 99.9%) was mixedwith 0.18 g (4.5 mmol) of potassium metal (Alfa Aesar,99%) to match the nominal composition of K . Fe S .The mixture was loaded in a quartz ampoule inside anargon-filled glovebox, and the ampoule was flame sealedunder vacuum (10 − Torr). In order to avoid oxidationof the sample due to the potassium-induced corrosion ofquartz, the sample containing ampoule was sealed in alarger ampoule under vacuum (10 − Torr).For crystal growth of K x Fe − y S , the mixture washeated to 1000 ◦ C over 10 hours and held at 1000 ◦ Cfor 3 hours to form a homogeneous melt. Subsequently,the melt was slowly cooled at a rate of 6 ◦ C/hour to650 ◦ C to allow crystal growth. After cooling to room temperature, K x Fe − y S single crystals approximately 3mm – 8 mm in diameter and approximately 0.1 mm inthickness were recovered.For the preparation of FeS single crystals, theK x Fe − y S precursor (0.2 g - 0.4 g), 0.28 g (5 mmol)Fe powder (Alfa Aesar, 99.9%), 0.84 g (5 mmol) Na S · O (dried from Na S · O, Sigma-Aldrich, 98%)and 0.20 g (5 mmol) NaOH (Sigma-Aldrich, 98%) wereadded to 10 mL water. The mixture was placed in aTeflon-lined stainless steel autoclave at 120 ◦ C for 3-4days. Silver colored FeS single crystals were recoveredby washing away excess powder with water and dryingunder vacuum overnight. Samples prepared in the ab-sence of excess iron powder were not superconducting,which could be due to either oxidation of the iron or va-cancy formation in the FeS layer. In the crystallographicstudies of layered iron selenide analogues such as FeSe and (Li x Fe − x OH)FeSe, iron vacancy formation is im-plicated in the loss of superconducting properties. B. X-ray diffraction and thermal stability analysis
Initial powder X-ray diffraction (XRD) data were col-lected using a Bruker D8 X-ray diffractometer with CuK α radiation, λ = 1.5418 ˚A (step size = 0.025 ◦ , with 2 θ ranging from 7 ◦ - 90 ◦ ). Temperature dependent X-raydiffraction on ground single crystals was performed usinga Bruker C2 diffractometer with a Vantec500 2D detec-tor, λ = 1.5418 ˚A (step size = 0.05 ◦ , with 2 θ rangingfrom 11 ◦ - 80 ◦ ). The sample was heated using an An-ton Paar DHS 1100 graphite-dome hot stage. Rietveldrefinements were carried out using TOPAS software.Differential scanning calorimetry (DSC) was con-ducted on a Mettler-Toledo TGA/DSC 3+ thermogravi-metric analyzer with high temperature furnace. Sampleswere heated from room temperature to 800 ◦ C. C. Magnetic susceptibility, electrical transport andheat capacity
Magnetic susceptibility measurements were performedusing a Quantum Design Magnetic Properties Measure-ment System (MPMS). Both field-cooled (FC) and zerofield-cooled (ZFC) measurements were taken from 2 K to300 K in direct current mode with an applied magneticfield of 10 Oe – 30 Oe. Hysteresis measurements werecarried out at 2 K with H = ± were usedfor this purpose.Electrical transport measurements were performed ona 14 T Quantum Design Dynacool Physical PropertiesMeasurement System (PPMS). Single crystal sampleswere mounted on a rotator AC transport sample boardand measured using the electrical transport option, ap-plying currents between 0.1-0.5 mA and frequencies near10 Hz.Heat capacity measurements were performed in a 14 TQuantum Design Dynacool PPMS System. The single-crystal sample of mass 2.9 mg was measured using therelaxation method with field applied perpendicular to thebasal plane. III. RESULTS: SYNTHESIS, THERMALSTABILITY AND STRUCTURALCHARACTERIZATIONA. Single crystal preparation by reductivede-intercalation
Our strategy for preparing single crystals of ametastable phase can be summarized as crystal-to-crystalconversion from a thermodynamically stable phase. Dur-ing the preparation of our FeS samples, we found thatmaintaining a reducing and basic hydrothermal envi-ronment was crucial to observing superconductivity inFeS. The de-intercalation of potassium cations fromK x Fe − y S resulted in the shift of alternating planes ofFeS along the a direction of the unit cell to form theprimitive layered FeS (Figure 1). Note that Lei et al. had found K x Fe − y S to be non-superconducting, soour reductive de-intercalation technique tunes this spinglassy material into a superconductor.A similar structural transformation from a body-centered tetragonal structure to a primitive tetragonalstructure has also been previously observed in the se-lenide analogue, K x Fe − y Se . When exposed to air ormoisture, oxidation of iron and formation of iron vacan-cies was suggested to be the driving force for the struc-tural transition. After the structural change inducedby oxidation in water, the superconducting K x Fe − y Se became non-superconducting. In contrast, our reduc-tive de-intercalation was driven by preference of potas-sium cations to solvate into solution under stronglybasic conditions, which consequently alters the non-superconducting K x Fe − y S , Figure S1 in Supplemen-tary Materials (SM), into superconducting FeS. Also, thereducing environment in the autoclave maintained by thepresence of Fe metal as a reagent prevented oxidation ofFe to Fe or the formation of iron vacancies.A more drastic structural change could be possi-ble under stronger oxidizing conditions. Neilson andMcQueen reported that KNi Se , a Ni analogue of theK x Fe − y Se , forms hexagonal NiAs-type, K − y Fe − z Se ,by oxidative de-intercalation of K + by CuI in acetoni-trile. This caused a complete structural reconstructionfrom edge-sharing layered NiSe tetrahedra to corner-
50 150 250 350 450-1.5-1.0-0.50 DSC h e a t fl o w ( W g - ) T ( o C) Argonair I ( ) ( n o r m . ) (a)(b) 00.20.40.60.81 FeS single crystal FIG. 2: (a) Normalized integrated intensity of the (001) peak(top) from temperature dependent XRD. Under Argon (redcurve), the loss of the (001) peak is gradual and is absentabove 250 ◦ C. Under air (blue curve), the loss of (001) peakis more abrupt and the peak is absent above 200 ◦ C. (b) DSCresults, plotted as heat flow as a function of temperature, forsingle crystal FeS. The sudden change in heat flow at 300 ◦ Cis associated with an endothermic reaction. sharing NiSe octahedra. Such a reconstruction wasnot seen in our de-intercalation reaction of K x Fe − y S since we did not utilize strong oxidizing environmentbut rather maintained reducing conditions. We simi-larly found this strategy in achieving the highest T c ’sfor the (Li − x Fe x OH)FeSe and (Li − x Fe x OD)FeSe sin-gle crystals in their single crystal-to-single crystal con-version also utilizing K x Fe − y Se as the template. Asimilar method was used for ion exchange in the single-crystal conversion of the selenide analogues K x Fe − y Se to (Li x Fe − x OH)FeSe, which demonstrates how power-ful this technique is for exploring new layered iron chalco-genides. B. X-ray diffraction and crystal structure
The XRD powder pattern of ground single crystalsof K x Fe − y S , presented in Figure 1a, shows pure crys-talline product before the de-intercalation reactions. Thepattern for K x Fe − y S was fit with a body-centeredtetragonal structural model with space group I /mmm and lattice parameters a = 3.745(1) ˚A and c = 13.627(9)˚A (Table I, Figure 1). Full structural parameters fromthe fits are presented in Table I and are in good agree-ment with those presented in an earlier study. Recently,Pachmayer et al. found that FeS powders prepared byhydrothermal methods remain tetragonal down to lowtemperatures; while the heavier congeners, FeSe and FeTe, are known to have a crystallographic phasetransitions.After hydrothermal de-intercalation of potassiumcations, the XRD pattern of the newly formed super-conducting FeS crystals were fit to a primitive unit cellwith space group P /nmm and lattice parameters a =3.6286(5) ˚A and c = 5.03440(9) ˚A. These values wereconsistent with values previously reported for tetragonalFeS. Due to the layered nature of the samples, theXRD powder patterns for K x Fe − y S and FeS were re-fined with preferred orientation along the [002] and [001]directions, respectively. Table I presents the parametersof our structural refinements for ground single crystals ofK x Fe − y S and FeS as well as the powder samples of FeSprepared as a side reaction during the single-crystal-to-single-crystal conversion. This powder consisted primar-ily of the product from the reaction of the iron powderin the presence of sodium sulfide and NaOH during thehydrothermal preparation (Figure S2 in SM). For com-parison, we have also prepared a powder sample of FeSthrough a modified method employed by Lai et al. , andthe results from our diffraction measurements of a powdersample with T c = 4 K are presented in the SM (FiguresS3–S5 and Table S1 in SM). C. Thermal stability of FeS single crystals
To test the thermal stability of our new FeS single crys-tals, samples were heated under inert Argon atmospherein steps ranging from 25 ◦ C, 50 ◦ C, and 100 ◦ C. The 001peak is visible up to 250 ◦ C (Figure S6 in SM), and itsintegrated intensity versus temperature under an Argonatmosphere is presented in Figure 2a along with a plotof the DSC. The decomposition of mackinawite FeS asdetermined by the integrated intensity of the (001) peakbegin above 100 ◦ C and disappeared completely above250 ◦ C. Due to the geometry of the XRD experiment,the (00 l ) reflections in the single crystal sample were ob-served while other reflections were not. Therefore, it islikely that if greigite were to form above T = 100 ◦ C, itwould not have been detected in our experiment.DSC measurements of FeS in Argon up to 600 ◦ C,shown in Figure 2b, give some clues on the thermal be-havior during the decomposition of mackinawite. The dipin the heat flow around 300 ◦ C indicates an endothermicreaction that could be associated with the crystalliza-tion of a phase such as pyrrhotite not seen in our tem-perature dependent diffraction studies. The appearanceof this transition in the DSC after the disappearance ofthe (001) reflection in the XRD, indicates that the twoare related. XRD analysis on the residue from the DSCexperiment indicated formation of hexagonal pyrrhotite(Figure S7 in SM). The higher than expected thermal sta-bility of the mackinawite compared to past studies couldbe due to the single crystalline nature of our samples,which have larger surface areas and are therefore less re-active than a polycrystalline product with small particle sizes.From their high-resolution X-ray diffraction study,Lennie et al. reported that mackinawite begins to de-compose to greigite (Fe S ) above 100 ◦ C and that allFeS reflections disappear above T = 200 ◦ C under a Heatmosphere. Above 260 ◦ C, greigite decomposes andhexagonal pyrrhotite begins to emerge. Lennie et al. also reported that mackinawite-FeSrapidly oxidizes under air. . To test the air stabilityof our single crystals, we heated samples under ambientatmosphere in steps ranging from 25 ◦ C, 50 ◦ C, and 100 ◦ C. As presented in Fig 2b, the (001) peak is visible up to200 ◦ C. As this level of air stability has not been reportedfor mackinawite before, it could imply that there may besome alkali metal incorporation that could passivate thesurface and prevent oxidation of FeS. EDS mapping onthe surface of FeS single crystals shows up to 9% totalalkali (K and Na) on the surface of the FeS crystals (Fig-ure S8 in SM). Due to the similarity of the c -parameterto those previously reported FeS, it is unlikely that largecations such as sodium or potassium intercalate between TABLE I: Structural parameters for ground single crystals ofK x Fe − y S and FeS along with FeS obtained through powdermethods. Rietveld refinements with XRD data are of theroom temperature structures. In the FeS samples, we foundfull occupancy for the iron and sulfur sites. In the case of theK x Fe − y S single crystals we found x = 0 . y wasfixed to zero. Relevant bond distances and angles are alsoincluded for each structural refinement. FeS (298 K, ground single crystal), P /nmm , R wp = 3 . a = 3 . c = 5 . U iso (˚A )Fe1 2a 0 0 0 0.016(3)S1 2c 0 0.5 0.266(2) 0.029(5)S-Fe-S ( ◦ ) S-Fe-S ( ◦ ) Fe-S (˚A) Fe-Fe (˚A) anion height (˚A)108.1(2) 110.2(2) 2.275(5) 2.6040(5) 1.34(1)FeS (298 K, powder preparation) , P /nmm , R wp = 2 . a = 3 . c = 5 . U iso (˚A )Fe1 2a 0 0 0 0.034(3)S1 2c 0 0.5 0.253(2) 0.033(4)S-Fe-S ( ◦ ) S-Fe-S ( ◦ ) Fe-S (˚A) Fe-Fe (˚A) anion height (˚A)110.7(4) 108.9(2) 2.239(5) 2.6051(4) 1.27(1)K x Fe − y S (298 K, single crystal) , I /mmm , R wp = 3 . a = 3 . c = 13 . U iso ˚A K1 2a 0 0 0 0.006(2)Fe1 4d 0 0.5 0.25 0.019(7)S1 4e 0 0 0.352(2) 0.006(8)S-Fe-S ( ◦ ) S-Fe-S ( ◦ ) Fe-S (˚A) Fe-Fe (˚A) anion height (˚A)110.8(3) 106.8(3) 2.33(2) 2.6481(6) 1.39(3) layers. IV. RESULTS: PHYSICAL PROPERTIESA. Magnetic susceptibility
The temperature-dependent FC and ZFC magneticsusceptibilities of FeS crystals measured in a constantfield of 1 mT are presented in Figure 3, for fields appliedboth parallel and perpendicular to the crystallographic c -axis. The volume susceptibility 4 πχ under ZFC con-ditions exhibits an onset superconducting transition at T c = 3 . πχ ≈ H // c T (K)-0.8-0.6-0.4-0.20-0.8-0.6-0.4-0.20 π Χ π Χ (a)(b) H =
H // cH // ab T = 2 K H (T) M ( e m u ) (c) -1-0.8-0.6-0.4-0.20 H // abH = FIG. 3: Magnetic susceptibility of an FeS single crystal. (a)Temperature-dependent volume susceptibility 4 πχ of an FeScrystal with a H || ab shows Pauli paramagnetic behavior in thenormal state and transitions to the superconducting at T c =3.5 K. (b) Susceptibility for H || c with an increased diamag-netic response with a relative volume fraction increase of 30%(c) Magnetization M as a function of applied field at 2 K.The diamagnetic response weakens for fields greater than 4mT ( H || ab ) and 5 mT ( H || c ). FeS is a bulk superconductor. In both cases of the fieldorientation, the ZFC and FC curves in the normal stateabove T c are largely temperature independent, indicativeof Pauli paramagnetism and therefore metallicity in FeS.Figure 3c presents magnetization ( M ) as a function ofapplied field ( H ) along two different directions for theapplied field. The M ( H ) isotherms indicate the valuesof the lower critical field H c to be 4 mT and 5 mT at1.8 K for H || ab and H || c , respectively. One differencebetween our single crystal results and those of Lai et al. is the maximum critical temperature observed. Lai et al. reported the superconducting powder samples of FeS tohave a T c = 4.5 K, which is approximately 1 K greaterthan found for our single crystals. Magnetic susceptibil-ity of our own prepared powder samples show T onsetc =4 K (Figures S4 and S5 in SM). B. Heat capacity
Heat capacity was measured on a large single crystal inboth the superconducting (0 T) and normal (3 T) states.As shown in Figure 4, a 3 T field is large enough tosuppress the superconducting state in the crystal, makingfor a good comparison with the 0 T curve.In zero applied field, a clear signature of the supercon-ducting transition develops at T c =3.9 K, consistent withmagnetic susceptibility and resistivity (below) measure-ments, confirming bulk superconductivity in single crys-tal FeS. Fitting the 3 T data to a standard electron andphonon contribution specific heat model, C = γT + βT ,yields a normal state Sommerfield coefficient to be γ =5.1mJ/mol-K and phonon term β =0.23 mJ/mol-K , thelatter corresponding to a Debye temperature Θ D = 257 K.Unlike reports for FeSe where the specific heat was fit to C = γT + β T + β T , , for FeS a plot for C/T vs T is linear in the normal state. FeS does share somesimilarities with FeSe, however, as γ was estimated to be5.4(3) mJ/mol-K , , which is within error to the valuewe found for γ in FeS. C. Magnetoelectric transport
Temperature dependent electrical resistivity of single-crystal FeS is presented in Figure 5a. The resistivityexhibits metallic character down to the superconductingstate with T onsetc = 3.5 K and T zeroc = 2.4 K. The residualresistivity of FeS was determined to be ρ = 240 µ Ω · cmbased on an average of the values measured for severalsamples (Figure S9 in SM), all of which exhibit a roomtemperature to residual resistivity ratio (RRR) of ap-proximately 10, indicative of the high quality of our crys-talline samples and the low uncertainty in geometric fac-tors that may vary widely due to the micaceous natureof the crystals.Figure 5b presents the normalized magnetoresistance(MR) as a function of applied magnetic field at 1.8 K. C p / T ( m J / m o l - K - ) T (K ) FIG. 4: Low temperature specific heat of single crystal FeSfor 0 T and 3 T applied magnetic fields. The arrow indicatesthe onset of a superconducting feature at T = 3.9 K. As shown, a significant anisotropy appears in both thenormal state high-field MR as well as the H c transition,with the latter ranging from 0.16 T for H (cid:107) c to 1.6 T for H (cid:107) ab . The full angular dependence of these featuresare presented in Figure 6. Panels (a) and (b) present theangular variation of MR for both longitudinal ( H (90 ◦ ) (cid:107) I ) and transverse ( H ( θ ) ⊥ I ) orientations, respectively.Indeed, as shown in Figure 6c, the MR angular variationis well represented by a cosine-like dependence for bothlongitudinal and transverse orientation angles.A very large anisotropy is also evident in the uppercritical field H c as the field angle is rotated away fromthe c -axis. In both longitudinal and transverse orienta-tions, H c is observed to diminish strongly as the fieldrotates toward the basal plane, as shown in the insets ofFigure 6a-b. Taking the two extremes, one can define an H c anisotropy Γ ≡ H || abc /H || cc , which is a value of 10at 1.8 K. A more complete evaluation of the full H c ( T )dependence allows for an extrapolation of Γ to zero tem-perature. As shown in Figure 7a-d, extracting the H c ( T )values from the resistive transitions at several angles (alltransverse to current direction, with T c values chosenat the 50% resistance midpoint) leads to a full H c ( T )plot given in Figure 7e. For all field directions, H c (0) was estimated using the Werthamer-Helfand-Hohenberg(WHH) formula ( H c = 0 . − ( dH c /dT )] | T c T c ). Fit-ting results give H || abc (0) = 2.75 T and H || cc (0) = 0 .
275 T,yielding nearly the same anisotropy value Γ(0)=10 as for1.8 K. The coherence lengths calculated from the esti-mated H c (0) values ( ξ = (cid:112) Φ ◦ / (2 πH c ) where Φ is theflux quantum) are calculated to be ξ H || ab = 343 ˚A and ξ H || c = 104 ˚A.These large changes in H c with field angle and theconcomitant coherence length anisotropy are in line withthe strong anisotropy observed in the normal state MRas discussed above. To determine whether the large H c ρ ( μ Ω - c m ) T (K) 0 T1.8 K H // abH // c H (T)FeS single crystal0 1 2 3050100150200250 ρ ( μ Ω - c m ) FIG. 5: Electrical resistivity of single crystalline FeS. (a)Temperature-dependent resistivity with inset highlighting lowtemperature transition to the superconducting state at T =3.5 K. The geometry of the resistivity measurement for thesingle crystal also shown as inset. (b) Resistivity as a functionof applied magnetic field for both H || ab and H || c orientations(always transverse to current direction). anisotropy is indicative of a truly two-dimensional andnot a strongly anisotropic three-dimensional supercon-ducting system, we performed detailed measurements ofthe angular dependence of H c at 1.8 K. Figure 8 presentsthe angle dependence of H c (1.8 K) as determined frommidpoints of field sweep resistive transitions. (Using dif-ferent criterion to define H c results in slight variation inabsolute anisotropy, but the shape of the H c ( θ ) curveremains constant). The shape of the H c ( θ ) curve, espe-cially near the H (cid:107) ab ( θ = 90 ◦ ) orientation, is indicativeof the true dimensionality of the superconductor withrespect to the coherence length. Tinkham’s model forthin-film superconductors incorporates the effect of re-duced dimensionality, yielding an angular dependence (a)(b) o o o o o o o o o ρ ( μ Ω - c m ) M R ( % ) o o o o o o o o o H (T) (c) 051015202530 51015200longitudinaltransverseangle ( o ) L o n g i t u d i n a l M R ( % ) T r a n s v e r s e M R ( % ) θ H I θ I H ρ ( μ Ω - c m ) H (T) H (T) M R ( % ) FIG. 6: Constant temperature scans of magnetoresistance(MR) of FeS as a function of field angle θ , defined as thedeflection from c -axis direction. Angular dependence of (a)longitudinal ( H (90 ◦ ) (cid:107) I ) and (b) transverse ( H ( θ ) ⊥ I ) MRtaken at 1.8 K are presented. Insets in each figure display azoom of the superconducting H c transition. (c) Comparisonof angular dependence of transverse and longitudinal MR at1.8 K and 14 T. given by (cid:12)(cid:12)(cid:12)(cid:12) H c ( θ )sin θH ⊥ c (cid:12)(cid:12)(cid:12)(cid:12) + (cid:32) H c ( θ )cos θH (cid:107) c (cid:33) = 1 , (1)whereas Ginzburg Landau (GL) theory can be used todetermine the effect of an anisotropic effective mass m ∗ o (b) θ = 30 o (d) θ = 90 o (c) θ = 60 o ρ ( μ Ω - c m ) ρ ( μ Ω - c m ) T (K) T (K) (e) H c ( T ) T c (K)0 0.5 1 1.5 2 2.5 300.511.522.53 FeS single crystal90 o o o o o FIG. 7: Superconducting transition of FeS single crystal as afunction of magnetic field applied along different angles θ withrespect to the crystallographic c -axis (transverse to current di-rection). Panel e) presents the compiled H c ( θ ) temperaturedependences for all angles measured. T c values were deter-mined by the resistance transition midpoint. Solid lines rep-resent the WHH orbital pair-breaking expectation for H c ( T )in each case (see text for details). on the angular dependence as (cid:18) H c ( θ )sin θH ⊥ c (cid:19) + (cid:32) H c ( θ )cos θH (cid:107) c (cid:33) = 1 . (2)As shown in the inset of Figure 8, the H c ( θ ) data ismuch better represented by the anisotropic GL theory,suggesting a highly anisotropic 3D environment for thesuperconductivity in FeS. This can be quantified by usingthe calculated anisotropy for this sample Γ (cid:39) . m ∗(cid:107) /m ∗⊥ =Γ =164. Thisis believed to be the largest upper critical field anisotropyobserved in any Fe based superconductor reported so far. H c ( T ) θ ( o )86 88 90 92 9411.11.21.31.41.51.6H c2 ( T = 1.8 K)2D fit3D fit0 30 60 90 FIG. 8: Angular dependence of the superconducting uppercritical field H c at 1.8 K. Black diamonds represented mea-sured transition fields (defined as the resistive transition mid-point), and lines represent fits to the theoretical expectationfor the angular dependence: solid line represents the GinzburgLandau expectation for a 3D system with anisotropic effec-tive mass, and dashed line represents the Tinkham’s modelexpectation for 2D superconductors. Inset displays zoomeddata near 90 ◦ ( H (cid:107) ab ). All data were collected with mag-netic field direction always transverse to the current direction. V. DISCUSSIONA. Strongly anisotropic electronic properties
The previous report for powder samples of FeS found H c (0) to be 0.4 T, which is much lower than that ofFeSe and other iron-based superconductors. H c for FeSehas been reported to be 16.3 T in powder samples. Thisdifference between the upper critical fields in FeSe andFeS has significant effects on their coherence lengths aswell. Coherence lengths calculated from H c (0) for FeSpowders and FeSe powders are 287 ˚A and 45.0 ˚A,respectively. We confirm Lai’s report of a much lower H c (0) and higher coherence length in FeS compared toother iron-based superconductors, but also demonstratethat these properties are highly anisotropic.As important as the comparatively smaller criticalfields in FeS, the anisotropy also appears to be muchlarger in this system. We find an anisotropy ratio ofΓ ∼
10, and to our knowledge this is the largest re-ported Γ yet for an iron-based superconductor. ForFeTe − y S y single crystals, the field dependence on T c ismostly isotropic with a reported Γ = H || abc /H || cc = 18 T/ 19 T = 0.95. . Recent studies on Fe(Se − x S x ) singlecrystals has shown sulfur to increase T c from 8.5 K for x = 0 to 10.7 K for x = 0.11, and the anisotropy is alsomore pronounced in crystals with higher sulfur contentas Γ = H || abc /H || cc = 2 for x = 0 and 3.5 for x = 0 . Surprisingly, in our studies of angular dependence ofMR, both longitudinal and transverse rotation studiesshow a diminishment of MR as the field is rotated towardthe crystallographic basal plane, irrespective of whetherthe field direction is rotated parallel or perpendicular tothe current direction (Figure 6a,b). This is consistentwith either a projection-like orbital MR of a very thinspecimen ( i.e. , with a large MR when H is perpendic-ular to the plane where orbital motion is allowed andzero MR when orbital motion of charge carriers is pro-hibited by geometric confinement), or with a very strongelectronic anisotropy as found in other materials with re-duced electronic dimensionality.Given the micaceous nature of FeS single crystals, theanisotropic behavior of the MR may arise due to a micro-scopic physical separation of crystalline layers resultingin effectively two-dimensional layers that would act muchas in a thin film. Such a description of our sample’s be-havior would imply that it contains a slab thickness thatis less than the characteristic magnetic length scale. Ourstudies of H c anisotropy and its angular variation (Fig-ure 8) suggest that the measured superconducting stateof FeS is in fact inhabiting a three-dimensional environ-ment with strong anisotropy, given the lack of a cusp in H c ( θ ) near the 90 ◦ field alignment (Figure 8). The resultfor our case is in good agreement with GL theory. There-fore, the appropriate length scale to consider is the super-conducting coherence length which is 104 ˚A for ξ H || ab . Inother words, our single-crystal samples must entail crys-talline slabs of at least 104 ˚A thickness in order to ex-hibit the GL-type behavior of H c that follows from Eq.2. An estimate of the mean free path of quasiparticles yields l mfp ≈
30 ˚A, which is much smaller than 104 ˚A,suggesting the scattering length is at least much smallerthan the known slab thickness. At the very least, the factthat the effective thickness must be at least ∼
20 unit cellssuggests quasiparticles are not artificially confined, andthat the the observed two-dimensional behavior in MRmay be intrinsic to the electronic structure.
B. True ground and normal state properties of FeS
The tetragonal FeS system was originally predicted tobe semiconductor in nature by Bertaut et al. This claimwas recently supported by resistivity measurements per-formed by Denholme et al. , which showed that theirsamples were non-superconducting with ferrimagnetic-like behavior. Similarly, samples prepared by Sines et al. were also exhibited semiconducting and ferri-magnetic behavior. Contrary to experimental evidencepublished before the work of Lai et al. , several othergroups had predicted tetragonal FeS to be metallic. Vaughan and Ridout proposed that the bonding in thetetragonal FeS was metallic in nature due to delocalized d electrons in iron sublattice. Recent density functionaltheory (DFT) calculations also supported metallicity, intetragonal FeS. Geochemists studying mackinawite have suggestedthat the ferrimagnetic-like behavior from earlier mag-netization data might have risen from the well-knownthiospinel ferrimagnetic impurity, Fe S , considering theease of conversion of mackinawite FeS to Fe S . Sev-eral of our powder FeS samples prepared through thesynthesis detailed by Lennie et al. form with an Fe S impurity as revealed by combined magnetization mea-surements and neutron powder diffraction (Figures S10-12 in SM). Even Denholme et al. acknowledged that thesemiconductor behavior of FeS could be attributed to thesurface oxide layers of FeS, as suggested by Bertaut etal. Indeed, similar oxidation has been observed in theFeSe system, as Greenfield et al. reported that amor-phous surface oxide layers of FeSe particles suppressedthe superconductivity in FeSe. Our single crystal re-sults definitively support a metallicity in the normal stateproperties and superconductivity in the ground state. C. Structural trends concerning T c Compared to tetragonal FeSe, mackinawite FeS con-tains more regular tetrahedral Ch –Fe– Ch bond angleswhere Ch = chalcogenide. In FeSe, the Se–Fe–Se out-of-plane bond angle is 112.32(6) ◦ and the Se–Fe–Se in-planebond angle is 103.91(7) ◦ . The respective bond anglesfor our FeS powder and single crystal samples were cal-culated to be close to 108.1(3) ◦ and 110.2(2) ◦ (Table I).Several studies have suggested that higher T c could beachieved from more regular bond angles, as is with ironpnictide superconductors. However, this structuralparameter does not seem to be as important an indicatorin the iron chalcogenides since FeSe exhibits a higher T c (8 K) than FeS ( T c = 4 K) even though it is comprisedof more distorted tetrahedra. This suggests that struc-tural factors controlling T c in iron pnictides may not beidentical to those of the iron chalcogenides.Anion height has also been implicated as a reliable pre-dictor for T c in iron-based superconductors. For ironpnictides, T c increases with increasing anion height asFeP-based superconductors have lower anion height andlower T c than FeAs-based superconductors. However, T c begins to drop off for anion heights greater than 1.38 ˚A,which suggests there is an optimal anion height for max-imizing T c . For FeSe with T c = 8 K, the Se height is1.45 ˚A, and upon application of physical pressure, the Seheight decreases to 1.425 ˚A, which leads to an increase in T c up to 37 K (8 GPa). For larger anions, i.e. FeTe,the anion height is larger than that of FeSe and whileFeTe is not superconducting at ambient pressure isova-lent anionic substitution as in FeTe . S . induces super-conductivity (anion height = 1.75 ˚A, T c = 10 K). From this anion height principle, we should expect thesmaller anionic radius of sulfide to lead to a larger T c .However, the anion height in FeS was found in the rangefrom 1.27(1) to 1.34(1) ˚A (Table I), which is below the op-timal height of 1.38 ˚A. This result for FeS could therefore c T c ( K ) P (kbar) m o m e n t ( - e m u ) T (K) FIG. 9: Applied pressure dependence of the superconduct-ing transition temperature of an FeS crystal as extractedfrom magnetic susceptibility measurements performed using aBeCu piston-cylinder clamp cell. Inset displays the measuredsusceptibility data (presented with a vertical offset for clar-ity). Pressure values are determined at room temperature. explain why the T c is remains low and between 3.5 and5 K despite having more regular tetrahedra than FeSe orFeTe.As a preliminary study on modifying the anion heightin FeS to affect T c , we have performed magnetizationmeasurements as a function applied pressure. As shownin Figure 9, measurements of magnetic susceptibility ina clamp-cell setup show that the transition temperaturedecreases with increasing pressure, at least up to 10 kbar.While it is known that T c in the related superconductorFeSe undergoes a dramatic enhancement under pressure,the increase in T c for FeSe occurs at much higher pres-sures than currently reached in the present experimentfor FeS (on the order of 10 GPa). Further work to studythe relation between T c ( P ) and the crystallographic pa-rameters as a function of applied pressure will shed morelight on the relation between structure and superconduc-tivity in FeS. VI. CONCLUSIONS
In conclusion, we have synthesized superconductingsingle crystals of FeS and characterized their thermal,magnetic, and electrical properties. The synthesis ofFeS single crystals was accomplished through the novelmethod of reductive de-intercalation of K x Fe − y S singlecrystals under hydrothermal conditions. The FeS crys-tals are stable up to 250 ◦ C in argon and 200 ◦ C inair. At 4 K the FeS crystals transition from a metallic,Pauli paramagnetic state to the superconducting state.In both the normal state and superconducting states, we0observe a large anisotropy in the properties of FeS. Theupper critical field expresses a large anisotropy with aΓ = H || abc (0) /H || cc (0) = (2 . T ) / (0 . T ) = 10, thelargest reported for any iron-based superconductor thusfar. Magnetoresistance measurements for the normalstate performed as a function of applied field angle reveala remarkable two-dimensional behavior in FeS. Overall,the physical property results indicate that the Fermi sur-face of FeS may be highly two-dimensional, and perhapseven more so than other closely-related iron-based super-conductors. Since the metastable system, mackinawite-type FeS, is now confirmed as a superconductor and not amagnetic semiconductor, this system could be a template for the preparation of new sulfide-based superconductorsthat exhibit strong anisotropic behavior. VII. ACKNOWLEDGEMENTS
Research at the University of Maryland was supportedby the NSF Career DMR-1455118, AFOSR Grant No.FA9550-14-10332, and the Gordon and Betty MooreFoundation Grant No. GBMF4419. We acknowledge thesupport of the National Institute of Standards and Tech-nology, U. S. Department of Commerce, in providing theneutron research facilities used in this work. J. Paglione and R. L. Greene,
Nat. Phys. , 2010, , 645–658. D. C. Johnston,
Adv. Phys. , 2010, , 803–1061. A. Ivanovskii,
Physica C , 2011, , 409–427. H. Takahashi, A. Sugimoto, Y. Nambu, T. Yamauchi,Y. Hirata, T. Kawakami, M. Avdeev, K. Matsubayashi,F. Du, C. Kawashima, H. Soeda, S. Nakano, Y. Uwatoko,Y. Ueda, T. J. Sato and K. Ohgushi,
Nat. Mater. , 2015, , 1008–1012. A. P. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontovand S. I. Shylin,
Nature , 2015, , 73–76. X. Lai, H. Zhang, Y. Wang, X. Wang, X. Zhang, J. Lin andF. Huang,
J. Amer. Chem. Soc. , 2015, , 10148–10151. O. Kouvo, J. Long and Y. Vuorelainen,
Am. Mineral. ,1963, , 511. E. Bertaut, P. Burlet and J. Chappert,
Solid State Com-mun. , 1965, , 335 – 338. H. T. Evans Jr, C. Milton, E. Chao, I. Adler, C. Mead,B. Ingram and R. A. Berner,
US Geol. Survey Prof. Paper ,1964, , 1312 – 1318. A. Lennie, S. Redfern, P. Schofield and D. Vaughan,
Min-eral. Mag. , 1995, , 677–684. D. Rickard and G. W. Luther,
Chem. Rev. , 2007, ,514–562. S. Denholme, S. Demura, H. Okazaki, H. Hara, K. Deguchi,M. Fujioka, T. Ozaki, T. Yamaguchi, H. Takeya andY. Takano,
Mater. Chem. Phys. , 2014, , 50 – 56. I. T. Sines, D. D. Vaughn II, R. Misra, E. J. Popczun andR. E. Schaak,
J. Solid State Chem. , 2012, , 17–20. A. K. Dutta, S. K. Maji, D. N. Srivastava, A. Mondal,P. Biswas, P. Paul and B. Adhikary,
ACS Appl. Mater. &Interfaces , 2012, , 1919–1927. A. R. Lennie, K. E. England and D. J. Vaughan,
Am.Mineral. , 1995, , 960–967. D. Csakberenyi-Malasics, J. D. Rodriguez-Blanco, V. K.Kis, A. Recnik, L. G. Benning and M. Posfai,
Chem. Geol. ,2012,
294 - 295 , 249 – 258. W. Bao, Y. Qui, Q. Huang, M. A. G. a. P. Zajdel, M. R.Fitzsimmons, M. Zhernenkov, S. Chang, M. Fang, B. Qian,E. K. Vehstedt, J. Yang, H. M. Pham, L. Spinu and Z. Q.Mao,
Phys. Rev. Lett. , 2009, , 247001. T. J. Liu, J. Hu, B. Qian, D. Fobes, Z. Q. Mao, W. Bao,M. Reehuis, S. A. J. Kimber, K. Prokes, S. Matas, D. N.Argyriou, A. Hiess, A. Rotaru, H. Pham, L. Spinu, Y. Qiu,V. Thampy, A. T. Savici, J. A. Rodriguez and C. Broholm,
Nat. Mater. , 2010, , 716–720. V. Bhatia, E. E. Rodriguez, N. P. Butch, J. Paglione andM. A. Green,
Chem. Comm. , 2011, , 11297. E. E. Rodriguez, C. Stock, P. Zajdel, K. L. Krycka, C. F.Majkrzak, P. Zavalij and M. A. Green,
Phys. Rev. B , 2011, , 064403. C. Stock, E. E. Rodriguez, M. Green, P. Zavalij andJ. Rodriguez-Rivera,
Phys. Rev. B , 2011, , 045124. Y. Hara, K. Takase, A. Yamasaki, H. Sato, N. Miyakawa,N. Umeyama and S. Ikeda,
Physica C , 2010, , S313 –S314. A. E. B¨ohmer, T. Arai, F. Hardy, T. Hattori, T. Iye,T. Wolf, H. v. L¨ohneysen, K. Ishida and C. Meingast,
Phys.Rev. Lett. , 2015, , 027001. R. Hu, K. Cho, H. Kim, H. Hodovanets, W. E. Straszheim,M. A. Tanatar, R. Prozorov, S. L. Bud’ko and P. C. Can-field,
Supercond. Sci. Tech. , 2011, , 065006. X. G. Luo, X. F. Wang, J. J. Ying, Y. J. Yan, Z. Y. Li,M. Zhang, A. F. Wang, P. Cheng, Z. J. Xiang, G. J. Ye,R. H. Liu and X. H. Chen,
New J. Phys. , 2011, , 053011. H. Lei, M. Abeykoon, E. S. Bozin and C. Petrovic,
Phys.Rev. B , 2011, , 180503. T. M. McQueen, Q. Huang, V. Ksenofontov, C. Felser,Q. Xu, H. Zandbergen, Y. S. Hor, J. Allred, A. J. Williams,D. Qu, J. Checkelsky, N. P. Ong and R. J. Cava,
Phys. Rev.B , 2009, , 014522. H. Sun, D. N. Woodruff, S. J. Cassidy, G. M. Allcroft, S. J.Sedlmaier, A. L. Thompson, P. A. Bingham, S. D. Forder,S. Cartenet, N. Mary, S. Ramos, F. R. Foronda, B. H.Williams, X. Li, S. J. Blundell and S. J. Clarke,
InorganicChemistry , 2015, , 1958–1964. T. F. Smith and C. W. Chu,
Phys. Rev. , 1967, , 353–358. H. Lei, M. Abeykoon, E. S. Bozin, K. Wang, J. B. Warrenand C. Petrovic,
Phys. Rev. Lett. , 2011, , 137002. D. P. Shoemaker, D. Y. Chung, H. Claus, M. C. Francisco,S. Avci, A. Llobet and M. G. Kanatzidis,
Phys. Rev. B ,2012, , 184511. J. R. Neilson and T. M. McQueen,
J. Amer. Chem. Soc. ,2012, , 7750–7757. X. Zhou, C. K. H. Borg, J. W. Lynn, S. R.Saha, J. Paglione and E. E. Rodriguez, http://arxiv.org/abs/1512.03399 . X. Dong, K. Jin, D. Yuan, H. Zhou, J. Yuan, Y. Huang,W. Hua, J. Sun, P. Zheng, W. Hu, Y. Mao, M. Ma,G. Zhang, F. Zhou and Z. Zhao,
Phys. Rev. B , 2015, , U. Pachmayr, N. Fehn and D. Johrendt,
Chem. Commun. ,2016, –. S. Margadonna, Y. Takabayashi, Y. Ohishi, Y. Mizuguchi,Y. Takano, T. Kagayama, T. Nakagawa, M. Takata andK. Prassides,
Phys. Rev. B , 2009, , 064506. E. E. Rodriguez, D. A. Sokolov, C. Stock, M. A. Green,O. Sobolev, J. A. Rodriguez-Rivera, H. Cao and A. Daoud-Aladine,
Physical Review B , 2013, , 165110. A. R. Lennie, S. A. T. Redfern, P. E. Champness, C. P.Stoddart, P. F. Schofield and D. J. Vaughan,
Am. Mineral. ,1997, , 302–309. N. R. Werthamer, E. Helfand and P. C. Hohenberg,
Phys.Rev. , 1966, , 295–302. M. Tinkham,
Phys. Rev. , 1963, , 2413–2422. J. Ketterson and S. Song,
Superconductivity , CambridgeUniversity Press, 40 West 20th Street, New York, NY10011-4211, USA, 1999, pp. 45–46. F.-C. Hsu, J.-Y. Luo, K.-W. Yeh, T.-K. Chen, T.-W.Huang, P. M. Wu, Y.-C. Lee, Y.-L. Huang, Y.-Y. Chu, D.-C. Yan et al. , P. Natl. Acad. Sci. USA , 2008, , 14262–14264. R. Hu, E. S. Bozin, J. B. Warren and C. Petrovic,
Phys.Rev. B , 2009, , 214514. M. Abdel-Hafiez, Y.-Y. Zhang, Z.-Y. Cao, C.-G. Duan,G. Karapetrov, V. M. Pudalov, V. A. Vlasenko, A. V.Sadakov, D. A. Knyazev, T. A. Romanova, D. A. Chareev,O. S. Volkova, A. N. Vasiliev and X.-J. Chen,
Phys. Rev. B , 2015, , 165109. A. J. Millis, S. Sachdev and C. M. Varma,
Phys. Rev. B. ,1988, , 4795. D. Vaughan and M. Ridout,
J. Inorg. Nucl. Chem. , 1971, , 741 – 746. A. Subedi, L. Zhang, D. J. Singh and M. H. Du,
Phys.Rev. B , 2008, , 134514. K. D. Kwon, K. Refson, S. Bone, R. Qiao, W.-l. Yang,Z. Liu and G. Sposito,
Phys. Rev. B , 2011, , 064402. A. J. Devey, R. Grau-Crespo and N. H. de Leeuw,
J. Phys.Chem. C , 2008, , 10960–10967. J. Brgoch and G. J. Miller,
J. Phys. Chem. A , 2012, ,2234–2243. J. T. Greenfield, S. Kamali, K. Lee and K. Kovnir,
Chem.Mater. , 2015, , 588–596. C. Lee, K. Kihou, A. Iyo, H. Kito, P. Shirage and H. Eisaki,
Solid State Commun. , 2012, , 644 – 648. Y. Mizuguchi, Y. Hara, K. Deguchi, S. Tsuda, T. Yam-aguchi, K. Takeda, H. Kotegawa, H. Tou and Y. Takano,
Supercond. Sci. Tech. , 2010, , 054013. T. Imai, K. Ahilan, F. L. Ning, T. M. McQueen and R. J.Cava,
Phys. Rev. Lett. , 2009, , 177005. Y. Mizuguchi, F. Tomioka, S. Tsuda, T. Yamaguchi andY. Takano,
Appl. Phys. Lett. , 2009, , –. P. Zajdel, P.-Y. Hsieh, E. E. Rodriguez, N. P. Butch, J. D.Magill, J. Paglione, P. Zavalij, M. R. Suchomel and M. A.Green,
J. Amer. Chem. Soc. , 2010,132