⇦Chinese Physics Letters, 2019, Vol. 36, No. 7, Article code 077402Express Letter Observation of Two-Level Critical State in the Superconducting FeTe Thin Films * Hao Ru (茹浩), Yi-Shi Lin (林一石), Yin-Cong Chen (陈寅聪), Yang Feng (冯洋), Yi-Hua Wang (王熠华)** Affiliations Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai200438 Received 12 June 2019, online 22 June 2019 *Supported by the National Key Research and Development Program of China under Grant Nos 2016YFA0301002 and 2017YFA0303000, and the National Natural Science Foundation of China under Grant No 11827805.
**Corresponding author. Email: wangyhv@fudan.edu.cn Citation Text: Ru H, Lin Y S, Chen Y C, Feng Y and Wang Y H et al 2019 Chin. Phys. Lett. 36 077402    Abstract FeTe, a non-superconducting parent compound in the iron-chalcogenide family, becomes superconducting after annealing in oxygen. Under the presence of magnetism, spin-orbit coupling, inhomogeneity and lattice distortion, the nature of its superconductivity is not well understood. Here we combine the mutual inductance technique with magneto transport to study the magnetization and superconductivity of FeTe thin films. It is found that the films with the highest $T_{\rm C}$ show non-saturating superfluid density and a strong magnetic hysteresis distinct from that in a homogeneous superconductor. Such a hysteresis can be well explained by a two-level critical state model and suggests the importance of granularity to superconductivity in this compound. DOI:10.1088/0256-307X/36/7/077402 PACS:74.25.Ha, 74.25.F-, 74.78.-w, 74.70.Xa © 2019 Chinese Physics Society Article Text Iron-chalcogenide is an important family of iron-based high $T_{\rm C}$ superconductors (Fe-SCs). It has the simplest crystal structure with one layer of Fe square lattice sandwiched between two layers of chalcogen atoms. Despite the simplicity of its crystal structure, a single layer of FeSe grown on SrTiO$_{3}$ displays the highest $T_{\rm C}$ among Fe-SCs.[1] While the electronic structures are similar across Fe-SCs, the magnetic structure in the Fe square lattice is complex and intriguing,[2,3] and is believed to be essential for the pairing interaction in Fe-SCs.[4] As spin-fluctuations on the FeSe side evolve into an antiferromagnetic ordering on the FeTe side, superconductivity disappears. Furthermore, in the presence of stronger spin-orbit coupling at higher Te concentration, the band structure of iron-chalcogenides has shown non-trivial topology[5] and the vortex cores of the superconducting compounds have shown signs of zero-bias peaks.[6] Inducing superconductivity in FeTe is therefore useful for both the understanding of its relation with magnetism and utilizing even stronger spin-orbit coupling in iron-chalcogenide family. It has been reported that FeTe films may become superconducting after annealing in oxygen[7] or simply being exposed to air for a long time.[8] The oxygen atoms occupy the interstitial sites in the Te planes and substituting Te with O would only suppress superconductivity.[9] Exposing a bulk crystal to oxygen could not show the similar effect,[10] suggesting that the substrate plays a role in inducing superconductivity. Nevertheless, superconductivity has been found in FeTe films grown on different substrates,[7,8,10] even those that do not necessarily match the crystal symmetry and lattice constant of FeTe.[7,10] The exact roles of oxygen and substrate in inducing the superconductivity in FeTe and whether such superconductivity bears any resemblance to other compounds in the iron-chalcogenide family remain largely unknown. In this Letter, we report the observation of two-level critical state in the superconducting FeTe thin films grown on Al$_{2}$O$_{3}$. We combine the mutual inductance technique with magneto transport to uncover the surface resistance change over 8 decades when the superconductivity is tuned by temperature and magnetic field. Despite a $T_{\rm C}$ of around 13 K, superfluid density does not saturate down to 2 K. Furthermore, the films show magnetic hysteresis in surface resistance distinctively different from what one might expect from a homogeneous superconductor with vortex pinning. The hysteresis decreases with increasing temperature and with reducing maximum magnetic field in a way consistent with the two-level critical state model. These observations suggest the importance of granularity for the superconductivity in FeTe thin films induced by oxygen. In experiment, we grew FeTe thin films using molecular-beam-epitaxy on both Al$_{2}$O$_{3}$ and SrTiO$_{3}$ substrates and annealed the sample in situ in an oxygen pressure of about 10$^{-2}$ Torr (see the supplementary materials). The films on the latter substrate show better morphology (see the supplementary materials) but much lower or even zero $T_{\rm C}$. The current study focuses on the films grown on Al$_{2} $O$_{3} $ and use a film of 49 nm thick as a representative throughout this paper. Its resistance shows a superconducting transition around 13 K (Fig. 1(a)) and shows a down turn at around 70 K (Fig. 1(a) inset). The latter one is also present in the non-superconducting FeTe bulk crystals and is associated with the antiferromagnetic transition.[11] In order to investigate the superconducting regime below 10 K where the resistance of the film would be too small to be reliably measured using charge transport (Fig. 1(a)), we employed the mutual inductance technique, which is sensitive to the superconductivity even in monolayer films.[12,13] The in-phase component of the ac voltage on the pickup coil $V_{\rm p} $ increases whereas the out-of-phase component decreases with temperature below 10 K (Fig. 1(b)), in consistent with a diamagnetic response.[14–17] However, unlike the diamagnetic response of a BCS bulk superconductor, the in-phase component exhibits a broad peak and the out-of-phase component does not saturate down to 2 K (Fig. 1(b)). Such behavior has been observed in other unconventional superconducting films.[14,17]
cpl-36-7-077402-fig1.png
Fig. 1. Unsaturated superconductivity in FeTe films after annealing in oxygen. (a) The sheet resistance $R_{\Box}$ of a 49-nm-thick FeTe sample after annealed in oxygen. Inset: resistance over a larger temperature range showing a transition around 70 K similar to the antiferromagnetic transition in the non-superconducting FeTe bulk crystals. (b) The mutual inductance signal of the same sample. Blue and orange are the in-phase and out-of-phase components of the ac voltage signal on the pickup coil (see the supplementary materials), respectively. The data were obtained at a drive frequency of 10 kHz and drive current of 10 µA.
As a function of the external magnetic field applied perpendicular to the film, our sample shows strong hysteresis both from transport and from mutual inductance measurement (Fig. 2). The overall signal is symmetric about zero field, and therefore we focus our discussion on the positive field. At 2 K, resistance in the down-sweep (Fig. 2(a) blue) is lower than that in the up-sweep (Fig. 2(a) orange), leading to an enhanced critical field in the down-sweep. Similarly, the out-of-phase component of the mutual inductance signal is also lower in the down-sweep than in the up-sweep (Fig. 2(b)), leading to a peak value in the down-sweep occurring at $\sim $0.2 T before the field returning to zero. The magnitude of the hysteresis as represented by the difference between up and down sweeps decreases as temperature increases (Fig. 2(d)). Due to the reduced in-phase and out-of-phase signals close to $T_{\rm C}$, no hysteresis is observable from the mutual inductance signal above 9 K (Figs. 2(b)–2(d)). Nevertheless, it is still present in the resistance data up to 11 K (Fig. 2(a) inset).
cpl-36-7-077402-fig2.png
Fig. 2. Magnetic hysteresis of the film in the superconducting state. (a) Resistance at 2 K (inset: 11 K) showing hysteresis under up-sweep (orange) and down-sweep (blue) of the perpendicular magnetic field. The sample was cooled under nominally zero field to 2 K. Similar hysteresis is observed from the mutual inductance measurement on the out-of-phase (b) and in-phase (c) components. The yellow and purple curves, which overlap, represent up and down sweeps, respectively, at 15 K. (d) Difference between the down and up field sweeps of out-of-phase component of the mutual inductance signal as a function of temperature.
We find that the magnetic hysteresis in the superconducting state obtained from both transport and mutual inductance signal could be unified if we transform the mutual inductance voltage $V_{\rm p}=X+iY$ into surface impedance $Z_{\rm s}=R_{\rm s}+i\omega L$ according to $$ V_{\rm p}=i\omega I_{\rm d}\int_0^\infty {dx\frac{M(x)}{1-(\frac{2xi}{{\mu \mu }_{0}h\omega })Z_{\rm s}}}, $$ where $R_{\rm s}$ is the surface resistance, $L$ is the inductance with $L^{-1}=(\frac{2e^{2}}{m})n_{\rm s}$ proportional to superfluid density $n_{\rm s}$, $I_{\rm d}$ and $\omega$ is the amplitude and frequency of the drive current, respectively, and $M(x)$ is determined by the specific geometry of the mutual inductance coils.[16,17] We used frequencies around 10 kHz for both transport and mutual inductance measurements to keep them in a similar quasi-dc regime. As we can see from Fig. 3(a), $R_{\rm s}(T)$ can be connected with $R(T)$ from transport up to a scaling constant. They overlap in the temperature window of 10–11 K, below which the resistance in the superconducting state is too small to be measured by charge transport and above which the surface impedance is dominated by normal inductance. Combining $R_{\rm s}(T)$ and $R(T)$, we can cover 8 decades of variation in resistance from the first sign of superconductivity at 13 K. From the imaginary part of $Z_{\rm s}$, we obtain $L^{-1}$, which shows that the superfluid density is almost kept in a linear temperature dependence deep into the superconducting state and is unsaturated at 2 K (Fig. 3(b)). Such a linear dependence of $n_{\rm s} (T)$ has been observed in cuprate superconductors.[14,18]
cpl-36-7-077402-fig3.png
Fig. 3. Obtaining surface impedance and the magnetic hysteresis in the surface resistance. (a) Surface resistance $R_{\rm s}$ of the superconducting film as a function of temperature, measured by transport (magenta) and extracted from mutual inductance (purple). (b) Inverse of the surface inductance (which is proportional to the superfluid density) extracted from the mutual inductance data. See text for the details for extracting the surface impedance from mutual inductance data. (c) $R_{\rm s}$ as a function of magnetic field. Again, the data in the high field region are obtained from transport and the data in the low field region are extracted from surface impedance. The maximum applied field (${\mu}_{0}H_{\max}$) is 8 T. (d) Field down-sweep of $R_{\rm s}$ as a function of temperature with ${\mu}_{0}H_{\max}=8$ T. The 12 K data (grey) are scaled down by a factor of 10. Here ${\mu}_{0}H_{\rm m}$ is defined as the field at which the lowest $R_{\rm s}$ occurs in the down sweep.
Applying the same method on the mutual inductance data under sweeping external magnetic field $H$ at various fixed temperatures (Figs. 2(b), 2(c) and 2(d)), we are able to connect $R_{\rm s}(H)$ from the mutual inductance with $R(H)$ from transport (Fig. 3(c) and 3(d)) using the same scaling constant for connecting the temperature data (Fig. 3(a)). The combined $R_{\rm s}(H)$ hysteresis loop (Fig. 3(c)) clearly illustrates two abnormal features: (1) The surface resistance is lower in the down sweep, and (2) the minimum of the surface resistance occurs at a field $H_{\rm m}$ before the field crosses zero. These features are quite opposite to those expected from the hysteresis loop of a homogeneous superconductor with vortex pinning. Because $R_{\rm s}$ is caused by motion of the free vortices, such features in hysteresis suggest the existence of different levels of pinning strength which may be a result of granularity.[19] According to the two-level critical state model, the intergranular regions have a higher penetration field $H_{\rm g}$ and much stronger pinning than the grain boundaries. When the field is swept upward, flux penetrates into grain-boundaries to first form Josephson vortices, which causes large increase in $R_{\rm s}$ due to a lower viscosity. In the down sweep, intergranular fluxons disappear first, leaving the more strongly pinned intragrain fluxons that contribute less $R_{\rm s}$ per fluxon than their intergranular counterparts. The validity of the two-level critical state model can be further seen from the variation of hysteresis with the variation of temperature and maximum applied field $H_{\max}$. As we increase temperature, both the magnitude of hysteresis in $R_{\rm s}$ and $H_{\rm m}$ reduce and both disappear at 12 K (Fig. 3(d)). $H_{\rm m}$ follows a linear temperature dependence (Fig. 4(a)), which suggests that the penetration field in the grains and the critical current density decrease linearly with increasing temperature. At the lowest temperature, $H_{\rm m}$ follows a linear dependence of $H_{\max}$ when it is small and tends to a constant when $H_{\max}$ is large (Fig. 4(b)). The turning point of these two regions is nothing but the grain's penetration field $H_{\rm g}$, which can be determined by fitting $H_{\rm m}$ in the low field and by finding its interception point with the constant level at high field.[19] All these behaviors are in good agreement with the two-level critical state model.[19]
cpl-36-7-077402-fig4.png
Fig. 4. Determination of the characteristic field in the two level critical state and its film thickness dependence. (a) The lowest field at which the lowest resistance occurs in the magnetic hysteresis $H_{\rm m}$ as a function of temperature obtained from Fig. 3(d). The red line is a linear fit. (b) $H_{\rm m}$ as a function of $H_{\max}$ measured at 2 K. The two red lines are linear fits in the high and low field regions, respectively. We can obtain the penetration field $H_{\rm g}$ from the crossing point between these two lines (see text). (c) $H_{\rm g}$ at 2 K as a function of film thickness. Films under comparison have similar $T_{\rm C}$. The dashed line is a linear fit to guide the eyes.
We find that such a two-level critical state invariably occurs in the superconducting FeTe films we studied. Films of same thickness with higher $T_{\rm C}$ tend to have stronger hysteresis at same temperature, which unsurprisingly gives the temperature dependence of $H_{\rm m}$ (Fig. 4(a)). What is a bit surprising is that $H_{\rm g}$ decreases in thicker films that have very similar $T_{\rm C}$ with the others under comparison (Fig. 4(c)). In the two-level critical state model, $H_{\rm g}$ is proportional to the grain size.[19] Our observation suggests that superconducting grains are much bigger in thinner FeTe films, which is in contrast to the roughness from topography (see the supplementary materials). This points suggestively to the role of both oxygen and interface in inducing superconductivity in FeTe: thinner films allow oxygen to permeate uniformly towards the bottom layers, whose lattice is likely distorted from the FeTe bulk, and this combination facilitates larger superconducting grains to form. It is well known that granularity strongly affects the electromagnetic properties of superconductors. Even in high quality cuprate high $T_{\rm C}$ superconductors, granularity plays a crucial part in determining the critical density,[20,21] magnetization,[19] superfluid density[18] and superconducting gap inhomogeneity.[22] In some cases, granularity in thin films may appreciably enhance $T_{\rm C}$.[23,24] Our finding of the two-level critical state in the superconducting FeTe films after oxygen annealing suggests that granularity may also play an essential role in inducing superconductivity from an antiferromagnetically ordered iron-chalcogenide. References Interface-Induced High-Temperature Superconductivity in Single Unit-Cell FeSe Films on SrTiO 3Antiferromagnetic order and spin dynamics in iron-based superconductorsConcepts relating magnetic interactions, intertwined electronic orders, and strongly correlated superconductivityPhotoionisation cross section and spin polarisation of photoelectrons from thalliumObservation of a robust zero-energy bound state in iron-based superconductor Fe(Te,Se)Superconductivity induced in iron telluride films by low-temperature oxygen incorporationSuperconductivity in epitaxial thin films of Fe 1.08 Te : O x Impact of interstitial oxygen on the electronic and magnetic structure in superconducting Fe 1 + y Te O x thin filmsSuperconductivity in Iron Telluride Thin Films under Tensile StressFrom (π,0) magnetic order to superconductivity with (π,π) magnetic resonance in Fe1.02Te1−xSexHigh-Temperature Superconductivity in a Single Copper-Oxygen PlaneOnset of the Meissner effect at 65 K in FeSe thin film grown on Nb-doped SrTiO 3 substrateDependence of the critical temperature in overdoped copper oxides on superfluid densityMetallic and superconducting surfaces of YBa 2 Cu 3 O 7 probed by electrostatic charge modulation of epitaxial filmsVortex dynamics in a type-II superconducting film and complex linear-response functionsPenetration depths of high T c films measured by two‐coil mutual inductancesMicrowave conductivity and superfluid density in strongly overdoped Tl 2 Ba 2 CuO 6 + δ Magnetic-field-dependent surface resistance and two-level critical-state model for granular superconductorsTheory for the hysteretic properties of the low-field dc magnetization in type-II superconductorsNonlinear surface impedance for YBa 2 Cu 3 O 7 − x thin films: Measurements and a coupled-grain modelResonance Raman Study of the Superconducting Gap and Low Energy Excitations in Tl 2 Ba 2 CuO 6 + δ SuperconductorsSuperconductivity in Granular Aluminum FilmsSuperconducting Thin Films
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