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Anisotropy of superconducting single crystal SmFeAsO_(0.8)F_(0.2) studied by torque magnetometry

Single crystals of the oxypnictide superconductor SmFeAsO_(0.8)F_(0.2) with T_c=45(1) K were investigated by torque magnetometry. The crystals of mass~0.1 mug were grown by a high-pressure cubic anvil technique. The use of a high-sensitive piezoresistive torque sensor made it possible to study the anisotropic magnetic properties of these tiny crystals. The anisotropy parameter was found to be field independent, but varies strongly with temperature ranging from 8 at T=T_c to 23 at T=0.4T_c. This unusual behavior signals unconventional superconductivity.


I. INTRODUCTION
The search for novel superconductors recently lead to the discovery of the Fe-based oxypnictide layered superconductor LaFeAsO 1−x F x with a transition temperature of T c ≃ 26 K [1]. By substituting La with other rare earth ions like Sm, Ce, Nd, Pr, or Gd a series of novel superconducting materials was synthesized with T c 's up to 55 K [2,3,4,5,6,7].
These compounds have a layered crystal structure consisting of LaO and FeAs sheets, where the Fe ions are arranged on simple square lattices [1]. According to theoretical predictions superconductivity takes place in the FeAs layers, whereas the LaO layers are charge reservoirs when doped with F ions [8,9].
The anisotropic behavior of layered superconductors can be characterized by their effective mass anisotropy γ, which in the framework of the classical anisotropic Ginzburg-Landau theory is given by γ = m * c /m * ab = λ c /λ ab = B ab c2 /B c c2 [10]. Here m * ab and m * c are the effective carrier masses related to supercurrents flowing in the ab-planes and along the c−axis, respectively, λ ab and λ c are the corresponding magnetic penetration depths, and B ab c2 and B c c2 the corresponding upper critical fields. In order to determine reliable values of γ high-quality single crystals are required.
An estimation of γ ≥ 30 at T = 0 K was made for SmFeAsO 0.82 F 0.18 from measurements of the c-axis plasma frequency using infrared ellipsometry [11]. From point-contact spectroscopy [12] and resistivity experiments [13] on LaFeAsO 0.9 F 0.1−δ the anisotropy parameter was estimated to be γ ≃ 10. Recent resistivity measurements on single crystal NdFeAsO 0.82 F 0.18 revealed a value of γ 5 [14] close to T c .
Band structure calculations for LaFeAsO 1−x F x yield a resistivity anisotropy of ∼ 15 for isotropic scattering, corresponding to γ ≃ 4 [8]. For comparison, in MgB 2 γ ranges from 1 to 8 and shows a strong temperature and field dependence [15,16]. This unconventional behavior of γ is well described within the framework of two-band superconductivity [17,18].

II. EXPERIMENT
Here we report magnetic torque experiments on a single crystal of SmFeAsO 0.8 F 0.2 with a T c ≃ 45(1) K performed in the temperature range of 19 K to 45 K and in magnetic fields up to 1.4 T. From these measurements the magnetic anisotropy γ was extracted in the framework of the anisotropic London model [19,20]. Single crystals of nominal composition SmFeAsO 0.8 F 0.2 [21] with masses of only ≈ 0.1 µg were grown from NaCl/KCl flux using a high-pressure cubic anvil technique [22,23]. The plate-like crystals used in this work are of rectangular shape with typical dimensions of 70×25×3 µm 3 , corresponding to an estimated volume of V ≃ 5 · 10 −15 m 3 . The crystal structure was checked by means of X-ray diffraction revealing the c-axis to be perpendicular to the plates. especially designed for measurements on micro crystals with masses smaller than 1 µg using micro-machined sensors of high sensitivity (∼ 10 −14 Nm) developed in our group [24]. To collect angular dependent torque data τ (θ) we used a measurement system with a turnable Bruker NMR iron yoke magnet with a maximum magnetic field of 1.4 T, allowing a rotation of the magnetic field direction of more that 360 • with respect to a crystallographic axis of the sample. Temperatures down to 10 K can be achieved with a flow cryostat between the poles of the magnet. The possibility of rotating the magnetic field around a fixed sample increases the sensitivity again because background effects to the torque are minimized.
Below T c we observe a torque signal arising from the interaction of the applied magnetic field with vortices in the sample. Based on the 3D anisotropic London model, the free energy of an anisotropic superconductor in the mixed state was calculated by Kogan et al. [19,20] V is the volume of the crystal, Φ 0 is the elementary flux quantum, B c c2 is the upper critical field along the c-axis of the crystal, η denotes a numerical parameter of the order unity depending on the structure of the flux-line lattice, and ǫ(θ) = [cos 2 (θ) + γ −2 sin 2 (θ)] 1/2 . By measuring the angular dependence of the torque in the mixed state of a superconductor, three fundamental parameters can be extracted from the data: the in-plane magnetic penetration depth λ ab , the c-axis upper critical field B c c2 , and the effective mass anisotropy γ . In this work we performed angle dependent measurements of the torque over more than 180 • in order to investigate the full angular dependent magnetization in terms of Eq. (1).
The torque was measured with a clockwise and a counterclockwise rotating magnetic field and then averaged according to τ rev = (τ (θ + ) + τ (θ − ))/2 to reduce vortex pinning effects (see upper panel of Fig. 2). To further minimize the influence of pinning, we partly applied a vortex-lattice shaking technique [25]. With this technique the relaxation of the vortex-lattice towards its thermal equilibrium is strongly enhanced by using an additional small magnetic AC field perpendicular to the static external field B. The magnitude of the  [8,11,12,13,14]. At low temperatures pinning effects give rise to the rather large errors in the anisotropy parameter, preventing a reliable determination of γ for T < 19 K. In order to demonstrate that the strong temperature dependence of γ is not an artefact of the increasing pinning strength at low temperatures, we compared shaked and unshaked torque data. One would expect that the shaked data are close to the reversible thermal equilibrium state. However, as indicated by the open and closed symbols in Fig. 3 there is within error bars no difference between the values of γ determined with and without shaking, attesting that the used procedure to determine γ below the irreversibility line is still reliable [25]. Furthermore, the field dependence of γ was studied at T = 36.3 K. As shown in the inset of Fig. 3, for 0.6 T B 1.4 T no field dependence of γ could be detected, suggesting that the measured anisotropy parameter in this work is γ = λ c /λ ab = B ab c2 /B c c2 . Since γ is field independent its determination is not appreciably affected by weak intrinsic pinning present in the sample.
The only parameter which is difficult to extract from Eq. (1) in the presence of weak pinning is the upper critical field B c c2 as it enters only logarithmically into the formula. For this reason we fitted B c c2 (T ) above 28 K according to ηB c c2 (T ) ≈ 88 T−(1.9 T/K)·T and extrapolated values of B c c2 (T ) down to 19 K in order to follow the temperature dependence of γ further down in temperature (note that the fitted slope of dB c c2 /dT ≈ −2 T/K agrees well with the slope close to T c reported in [28]). The values obtained from the extrapolated values of B c c2 are displayed in Fig. 3 as squares, whereas the values evaluated by the free fits are represented by circles.
The temperature dependencies of the upper critical field B c c2 and the in-plane magnetic penetration depth λ ab as extracted from the torque data are displayed in Fig. 4. B c c2 follows a linear temperature dependence down to 28 K. The dashed line represents a linear fit in order to extrapolate B c c2 down to 19 K. Using the WHH approximation [29] yields B c c2 (0) ≃ 60 T. λ ab was also estimated from the torque data using Eq. (1). In the lower panel of Fig. 4 the temperature dependence of 1/λ 2 ab is displayed. As shown by the solid curve in Fig. 4 [31]. The exponent n = 3.8(4) is close to n = 4 for the two-fluid model, characteristic for a superconductor in the strong-coupling limit [32]. However, the present data are too limited to draw definite conclusions. SmFeAsO 0.8 F 0.2 exhibits a similar temperature dependence of the anisotropy parameter γ as MgB 2 for which γ varies between 1 and 8, depending on temperature and magnetic field [15,16,18]. Therefore, the unusual temperature dependence of γ of SmFeAsO 0.8 F 0.2 , which cannot be explained by conventional Ginzburg-Landau theory, indicates a possible two gap scenario [18]. Note that other experiments such as recent resistivity measurements of the upper critical field on LaFeAsO 0.89 F 0.11 [28] and NMR studies of PrFeAsO 0.89 F 0.11 [33] also suggest that the novel class of Fe-based oxypnictide superconductors exhibit two-band superconductivity. Nevertheless, other possibilities of a temperature dependent γ should be mentioned here [26,27,34].

III. CONCLUSIONS
In conclusion, the magnetic anisotropy parameter γ, and the in-plane magnetic penetration depth λ ab were determined by high-sensitive magnetic torque experiments for a single crystal of SmFeAsO 0.8 F 0.2 . The parameter γ extracted from the reversible torque signals was found to be strongly temperature dependent, ranging from γ ≃ 8 at T T c to γ ≃ 23 at T ≃ 0.4T c . However, no field dependence of γ could be detected. For the in-plane magnetic penetration depth at zero temperature a value of λ ab (0) ≃ 210(30) nm was estimated, in agreement with values reported in the literature [30,31]. The unusual temperature dependence of γ suggests that SmFeAsO 0.8 F 0.2 is probably a multi-band superconductor, similar to MgB 2 [18] and the cuprate superconductors [35]. However, other explanations for this unusual behavior such as e.g., the possibility of an anisotropic s-wave gap [34], cannot be ruled out. More detailed experimental work is required to clarify this point. Lower panel: In-plane magnetic penetration depth λ ab (T ) obtained from the torque data and plotted as 1/λ 2 ab versus temperature. The solid line represents a fit of the data to the power law 1/λ 2 ab (T ) = 1/λ 2 ab (0) · (1 − (T /T c ) n ) with all parameters free. The exponent of n = 3.8(4) is close to n = 4 characteristic for the two-fluid model. The meaning of the symbols is the same as in Fig. 3