Unique interplay between superconducting and ferromagnetic orders in EuRbFe{}_{4}As{}_{4}

Unique interplay between superconducting and ferromagnetic orders in EuRbFeAs

V. S. Stolyarov vasiliy@travel.ru Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia Institute of Solid State Physics (ISSP RAS), 142432, Chernogolovka, Russia Kazan Federal University, 18 Kremlyovskaya str., Kazan 420008, Russia    A. Casano 1. Physikalisches Institut, Universität Stuttgart, 70569 Stuttgart, Germany    M. A. Belyanchikov Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia    A. S. Astrakhantseva Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia    S. Yu. Grebenchuk Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia    D. S. Baranov Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia LPEM, ESPCI Paris, PSL Research University, CNRS, 75005 Paris, France    I. A. Golovchanskiy Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia    I. Voloshenko 1. Physikalisches Institut, Universität Stuttgart, 70569 Stuttgart, Germany    E. S. Zhukova Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia    B. P. Gorshunov Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia    A. V. Muratov Lebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia    V. V. Dremov Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia    L. Ya. Vinnikov Institute of Solid State Physics (ISSP RAS), 142432, Chernogolovka, Russia    D. Roditchev Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia LPEM, ESPCI Paris, PSL Research University, CNRS, 75005 Paris, France Sorbonne Université, CNRS, LPEM, 75005 Paris, France    Y. Liu Department of Physics, Zeijiang University, Hangzhou, 310027, China    G.-H. Cao ghcao@zju.edu.cn Department of Physics, Zeijiang University, Hangzhou, 310027, China    M. Dressel Moscow Institute of Physics and Technology, Dolgoprudny, 141700 Moscow, Russia 1. Physikalisches Institut, Universität Stuttgart, 70569 Stuttgart, Germany    E. Uykur ece.uykur@pi1.physik.uni-stuttgart.de 1. Physikalisches Institut, Universität Stuttgart, 70569 Stuttgart, Germany
July 16, 2019
Abstract

Transport, magnetic and optical investigations on EuRbFeAs single crystals evidence that the ferromagnetic ordering of the Eu magnetic moments at  K, below the superconducting transition ( K), affects superconductivity in a weak but intriguing way. Upon cooling below , the zero resistance state is preserved and the superconductivity is affected by the in-plane ferromagnetism mainly at domain boundaries; a perfect diamagnetism is recovered at low temperatures. The infrared conductivity is strongly suppressed in the far-infrared region below , associated with the opening of a complete superconducting gap at  meV. A gap smaller than the weak coupling limit suggests the strong orbital effects or, within a multiband superconductivity scenario, the existence of a larger yet unrevealed gap.

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New members of the iron-pnictide family, the so-called 1144-compounds, attract interest recently because the alternating layers of alkaline and alkaline-earth cations produce two different kinds of As sites (Hao et al., 2013; Kawashima et al., 2016; Iyo et al., 2016; Liu et al., 2016a). These materials can be viewed as the intergrowth of -122 and -122 iron-pnictides and they are naturally hole doped. The parent compounds are superconducting with transition temperatures around 35 K, higher than most of the 122-materials; no spin-density-wave order has been observed. Among all possible candidates, Eu-based 1144-systems are even more intriguing, since the Eu-sublattice orders ferromagnetically below a critical temperature  K Liu et al. (2016b, 2017), similar to the 122-counterpart EuFeAs Wu et al. (2009); Zapf et al. (2011, 2013); Zapf and Dressel (2017); Jannis and Philipp (2017). Ferromagnetic order deep inside the superconducting state is very rare, in general Sonin and Felner (1998); Lorenz and Chu (2005); hence the “ferromagnetic superconductor” EuRbFeAs might pave the way towards realization of a “superconducting ferromagnet” Nachtrab et al. (2006); Mineev (2017); Jiao et al. (2017a). However, the exact nature of the Eu magnetic order and its effect on superconductivity is unresolved Liu et al. (2016b, 2017) because single crystals have been synthesized only recently.

In this Letter we focus on the interplay between superconductivity and ferromagnetism in EuRbFeAs single crystals. We report comprehensive investigations comprising transport, magnetic and optical measurements combined with microscopic studies of the vortex dynamics. The infrared spectra show a clear gap opening around 80 cm below  K that is slightly reduced compared to the value expected from the BCS theory. We relate this small value to the multiband character of superconductivity as well as to the depairing (orbital) effects of supercurrents screening the ferromagnetic domains. A surprisingly weak effect on the superconducting condensate has been observed upon magnetic ordering indicating a rather weak interaction between Eu- and Fe- sublattices.

Single crystals of EuRbFeAs are obtained according to Ref. Liu et al. (2016b, a); Meier et al. (2017); Liu and Cao (2018); they exhibit shiny -faces of approximately 1 mm in size. The structure of the compound is presented in Fig. 1(a). The crystals are characterized by x-ray, electrical transport, and magnetic susceptibility measurements. In Fig. 1(a) we plot the dc resistance vs. temperature together with the extrapolation of the infrared (IR) measurements. The residual resistivity ratio (RRR) of 15.7 is significantly higher than reported for polycrystals Liu et al. (2016b, 2017). The transition to the superconducting state takes place within a fraction of a degree [see inset in Fig. 1(a)]. No effect of the ferromagnetic ordering at  K on resistivity is observed.

Fig. 1(b) displays the temperature dependence of the magnetization probed in the field cooling (FC) and zero-field cooling (ZFC) protocol, for (black circles) and (red triangles). The high quality of the crystals and the three-dimensional nature of the superconducting state are confirmed by the perfect diamagnetism rapidly reached below for both field orientations. Below the ferromagnetic ordering of the Eu-sublattice gives a kink-like anomaly in magnetic susceptibility (indicated by the red arrow) that is only visible for . The absence of ferromagnetic signature for is taken as evidence that the ferromagnetic order of the Eu-sublattice at  K results in domains oriented within the -plane. The magnetization data presented in Fig. 1(c) confirm this conclusion: a pronounced hysteresis is observed within the plane, while the -axis response is solely determined by the vortex dynamics Liu and Cao (2018). The behavior is very much in contrast to the phenomena observed in the EuFeAs-family where canted A-type antiferromagnetism dominates with a reentrant spin glass behavior at lower temperatures Zapf et al. (2011, 2013); Zapf and Dressel (2017).

Figure 1: (a) Temperature-dependent dc-resistance (blue curve) of EuRbFeAs single crystals measured within the -plane. The red dots correspond to the resistivity extracted from the Hagen-Rubens fit of the reflectivity normalized to dc resistance at room temperature, with . The sharp superconducting transition at  K is magnified in the inset. The structure of the unit cell illustrates the two spacing layers: Eu in blue and Rb in magenta. (b) Magnetization at low temperatures measured by applying a magnetic field  Oe within the -plane and perpendicular to it, . The phase transitions are indicated by a sharp drop at superconducting and a pronounced feature around the magnetic order , marked by a red arrow. The distinct behavior of field cooled (FC) and zero-field cooled (ZFC) susceptibility characterizes the superconducting state. (c) The completely different field-dependent magnetization for both orientations hallmarks the confinement of the magnetic moments to the -plane.

The -plane optical reflection measurements are performed in a frequency range from 25 to 20 000 cm and down to  K, using several Fourier-transform spectrometers complemented by IR microscopes and helium cryostats. The optical conductivity is obtained via the Kramers-Kronig analysis, using a Hagen-Rubens behavior in the normal state and Mattis-Bardeen fit in the superconducting state as low-frequency extrapolations; ellipsometric spectra collected up to 45 000 cm and x-ray scattering functions were supplemented at higher frequencies.

Figure 2: (a) Temperature evolution of the infrared reflectivity of EuRbFeAs; at the lowest temperature the spectra approach unity around 80 cm. The inset displays the overall behavior at ambient and low temperatures. (b) The corresponding conductivity spectra reveal the opening of the superconducting gap when the temperature drops below  K. The solid lines correspond to fits by the Drude-Lorentz model and Mattis-Bardeen equations, respectively. The inset shows the complete behavior at and 4 K.

In Fig. 2 the IR reflectivity and conductivity are plotted for selected temperatures. At a first glance the overall optical response of this new class of 1144-iron-pnictide resembles that of the 122-type systems Wu et al. (2010); Barišić et al. (2010); Nakajima et al. (2010); Uykur et al. (2015, 2017).

In the normal state, optical data presented in Fig. 2 can be described by two Drude components and series of Lorentzians, as demonstrated in Fig. 3(a). The decomposition of the itinerant carriers into a narrow and a broad Drude term accounts for the multiband scenario of iron-pnictides Wu et al. (2010); Barišić et al. (2010). Similar to the observations in Eu-based 122-compounds Wu et al. (2009); David et al. (2017); Baumgartner et al. (2017), the mid-IR band and higher-energy interband transitions are also visible. Fig. 2(b) clearly shows that by decreasing the mid-IR absorption is suppressed and spectral weight transferred to higher energies; we interpret this behavior as an indication of Hund’s rule coupling Schafgans et al. (2012). The low-energy absorption features [orange bands in Fig. 3(a) and (b)] observed in EuRbFeAs are unprecedented and their origin is not completely clear at this point. The temperature evolution of these bands summarized in Fig. 3(c) reveals the splitting below and the redistribution at .

Figure 3: (a) Drude-Lorentz fits to the room-temperature optical conductivity of EuRbFeAs. (b) In the superconducting state the two Drude modes are replaced by BCS terms Dressel and Grüner (2002). Note the drastic changes in the low-energy bands. (c) The temperature and frequency dependences of the low-lying absorption modes highlight the effects of the phase transitions.

The superconducting state is characterized by a distinct upturn of the reflectivity Dressel and Grüner (2002) reaching unity at around 80 cm. As a consequence, the optical conductivity drops and disappears for  cm with basically no in-gap absorption. This evidences the presence of a complete gap throughout the Fermi surface, which might only have a small anisotropy Schachinger and Carbotte (2011). The opening of the superconducting gap in can be well described by the Mattis-Bardeen equation Wu et al. (2010); Gorshunov et al. (2010) adding two contributions, corresponding to the Drude terms in the normal state; the result is summarized in the solid lines of Figs. 2(b) and 3(b). From the fits at 4 K we determine a gap value of that is about 10 below predictions by weak-coupling theory. The obtained frequency is in line with the small gap values detected for other 122-iron pnictides with a similar Dressel et al. (2011); Inosov et al. (2011). Since in EuRbFeAs several electronic bands cross the Fermi level, one may expect other gap(s) to be present, having the ratio Suhl et al. (1959), similar to what is reported in 122 iron-based superconductors Dressel et al. (2011). For CaKFeAs with -36 K, for instance, indications of two gaps, at 1-4  meV and at 6-9 meV have been reported Biswas et al. (2017). The narrow Drude component of EuRbFeAs, however, suggests that here we fall in the clean limit since ; while the broad Drude term allows a small gap: Dai et al. (2016); David et al. (2017).

It is remarkable that the gap in the IR spectra does not open gradually, as expected for a second-order transition, but rises sharply at , as depicted in Fig. 4(a). Similar observations have been reported for other iron-pnictides such as electron-doped Eu122 Baumgartner et al. (2017), Co-doped Ba122 Lobo et al. (2010) and Sm-1111 thin films Charnukha et al. (2018). Further theoretical effort is required to explain this behavior.

Figure 4: (a) The superconducting gap of EuRbFeAs deviates from the prediction of a mean-field transition. (b) Temperature evolution of the superfluid density; the - and -wave behavior is shown for comparison. A dip in the dependence is marked by red arrow

Upon the gap opening in the optical conductivity, the missing area between the normal and superconducting states, and , respectively, is condensed to the -function at , according to the Ferrell-Glover-Tinkham sum rule Dressel and Grüner (2002). Hence, the spectral weight analysis allows us to evaluate the penetration depth  nm at  K, comparable to similar iron-pnictides, and the superfluid density ; the results are consistent with calculations based on the imaginary component . In Fig. 4(b) is plotted together with predictions for isotropic (-wave) and anisotropic (-wave) gap symmetries. The -wave model seems more appropriate, consistent with the observed full gap opening in the IR spectra.

At first glance, there is no effect of the ferromagnetic order on superconductivity of EuRbFeAs. Indeed, unlike in Eu-122 systems, where reentrant superconductivity has been reported Miclea et al. (2009); Paramanik et al. (2013); Jiao et al. (2017b); Baumgartner et al. (2017), we cannot detect any indication of ordering at on the resistivity curve [Fig. 1(a)] or any noticeable in-gap absorption due to vortices in IR spectra; instead, a fully developed superconducting gap and -wave characteristic of the superfluid density is observed. However, several signatures of the ferromagnetic order are unveiled by our investigations. First, the magnetization curve in Fig. 1(b) measured with a magnetic field within the -plane shows a clear kink around  K – the perfect diamagnetism is destroyed; it is recovered only at significantly lower temperatures. Second, the superfluid density in Fig. 4(b) manifests a weak dip in the range -15 K, followed by the recovery of superfluid density at lower temperatures (red arrow). Both experimental results suggest that the superconductivity is substantially weakened at the ferromagnetic transition but somehow “recovers” at lower temperatures.

This “weakening/recovery” of superconductivity in EuRbFeAs is confirmed by local MFM investigations, in which the influence of ferromagnetic ordering on the Abrikosov vortex lattice is studied. Since the MFM probes the -component of the local magnetic field, the vortex lattice is created by applying an external field along the -axis of the crystal. The magnetic map in Fig. 5(a), acquired just above , shows a lattice of Abrikosov vortices emerging out of the -plane. The vortex organization, their surface density, and inter-vortex distances are typical of disordered type-II superconductors. The images displayed in Fig. 5(b) and (c) correspond to the same region of the sample; the maps were acquired at  K, right below , and at  K, respectively. In these maps an additional magnetic contrast appears on a larger spatial scale, which is associated with a -oriented component of the local field due the domain walls between neighboring -plane oriented ferromagnetic domains. The fact that the vortices continue to exist below without any significant deformation of the vortex lattice evidences a rather weak local field generated by the ferromagnetic domains. This behavior is in contrast to the stark effect of ferromagnetism on superconductivity observed in other ferromagnetic superconductor EuFe(AsP) in which a -oriented ferromagnetic ordering takes place, leading to novel magnetic superconducting phases Nowik et al. (2011); Veshchunov et al. (2017); Stolyarov et al. (2018).

A detailed analysis of MFM data demonstrates that the ferromagnetic order does influences the vortex lattice, albeit weakly. Near the integrated vortex density is reduced as demonstrated in Fig. 5(d). On a local scale, the vortex distribution becomes inhomogeneous: domains with unchanged vortex density coexist with regions where the density becomes significantly higher or lower. This indicates that below the vortex lattice is affected by ferromagnetism, but the intensity of the additional field remains rather low, as it is not able to alter the vortex lattice significantly. The weak coupling of ferromagnetism and superconductivity may imply the existence of a rather weak exchange fields between the Eu- and Fe- sublattices, where such effects have been discussed previously for the Eu-122 systems with Eu-bands located far away from the Fermi energy Jeevan et al. (2008).

Figure 5: Abrikosov vortex lattice in EuRbFeAs revealed by magnetic force microscopy. A field of  Oe is applied along the -direction, perpendicularly to the scanned sample surface. (a) For the main magnetic contrast comes from quite uniformly distributed vortices. (b, c) For a large scale magnetic contrast due to ferromagnetic domain walls adds to the vortex signal; the positions of the vortices are modified. The white scale bars correspond to 2 m. (d) The temperature dependence of the vortex density integrated over the scanned area shows a minimum below the ferromagnetic transition, marked by red arrow.

From our investigations on single crystals, we conclude that EuRbFeAs is a ferromagnetic multiband superconductor, in which superconductivity overcomes the -plane oriented ferromagnetic order of the Eu ions. A single excitation gap at is observed below a sharp superconducting transition at  K; it reveals an unconventional temperature dependence. The gap energy is below the weak coupling limit, suggesting the existence of another larger superconducting gap. The reduction of the gap energy can also be associated with the depairing effect of spontaneous Meissner currents screening the ferromagnetic domains in the -plane below .

Acknowledgements.
We acknowledge the fruitful discussions with F. Hütt, D. Günther, and A.V. Pronin and the technical support by G. Untereiner, and R. Aganisyan. V.S., D.B. and D.R. acknowledge the partial supports by the French Nat. Agency for Res. via grant SUPERSTRIPES and by the Ministry of Educ. and Sci. of the Russian Federation via grant 14.Y26.31.0007. D.R. acknowledge the COST project “Nanoscale coherent hybrid devices for SC quantum technologies” – Action CA16218. The Magnetic Force Microscopy studies were funded by the Russian Sci. Fou. (project no 18-72-10118). Part of the work was supported by RFBR project 14-02-00255 and the Nat. Nat. Sci. Fou. of China (No. 11474252). B.G, E.Z. thank support of the RAS Program of Fund. Res. “Fundamental Problems of High-Temperature Superconductivity” and Program “5-top100”. We also acknowledge funding of the MIPT grant for visiting professors and of the DFG via DR228/42-1. E.U. acknowledges the support by the ESF and by the Ministry of Sci. Res. and the Arts Baden-Württemberg.

References

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