Visualization of Magnetic Flux Structure in Phosphorus-Doped EuFe$_2$As$_2$ Single Crystals

TL;DR

This study visualizes magnetic flux and domain structures in phosphorus-doped EuFe$_2$As$_2$ single crystals, revealing vortex and magnetic domain formations across different temperature ranges using advanced microscopy techniques.

Contribution

It provides the first detailed visualization of magnetic flux and domain structures in phosphorus-doped EuFe$_2$As$_2$ single crystals, highlighting their behavior in superconducting and ferromagnetic phases.

Findings

Vortex structures observed between 17.7 K and 22 K.

Magnetic domain structures appear below 17.7 K.

Flux structures are typical for type-II superconductors.

Abstract

Magnetic flux structure on the surface of EuFe$_2$(As$\rm_{1-x}$P$\rm_x$)$_2$ single crystals with nearly optimal phosphorus doping levels $x=0.20$, and $x=0.21$ is studied by low-temperature magnetic force microscopy and decoration with ferromagnetic nanoparticles. The studies are performed in a broad temperature range. It is shown that the single crystal with $x=0.21$ in the temperature range between the critical temperatures $T_{\rm SC}=22$ K and $T_{\rm C}=17.7$ K of the superconducting and ferromagnetic phase transitions, respectively, has the vortex structure of a frozen magnetic flux, typical for type-II superconductors. The magnetic domain structure is observed in the superconducting state below $T_{\rm C}$. The nature of this structure is discussed.

Full text

ferromagnetic superconductor; spontaneous vortex phase; magnetic force microscopy

I Introduction

The coexistence of superconductivity and magnetic ordering has been a subject of a strong interest.Huxley Currently, the electric transport and magnetic properties are well studied for a number of single-crystalline compounds of the so-called magnetic superconductors: borocarbides,Gupta ; Canfield ; Canfield1 ; Kawano ; Chia ; Gammel uranium compounds,Huy high-temperature cuprate superconductors,Lavrov_PRB_79_214523 and iron-based superconductors.Kamihara

An important issue of the coexistence of superconductivity and magnetism from both theoretical Ng ; Buzdin1 ; Faure ; Sonin and experimental perspectives Iavarone ; Tamegai ; Xing ; Yang relates to the microstructure of the magnetic flux, as well as to its dynamics upon variation of the temperature and external magnetic field. Until recently, low temperatures of superconducting and magnetic phase transitions of known single crystals, as well as the requirement of a high spatial resolution, have limited experimental capabilities for visualization of the magnetic flux structure employing e.g. magnetic force microscopy (MFM),Bluhm scanning Hall probe imaging,Bluhm1 and decoration with magnetic nanoparticles. Vinnikov_Springer_23_89 ; March ; decor

Recently, new iron-based compounds AFe2(As1-xPx)2 (where А = Ba, Sr, Ca, Eu) have been synthesized. Superconductivity in these compounds can be induced by doping with phosphorus.Ren Superconductivity in EuFe2(As1-xPx)2 single crystals occurs in a rather narrow doping range $x=0.14-0.25$ (or in the phosphorus content range $7.0-12.5$ at%) with the maximum superconducting transition temperature $T_{\rm SC}^{\rm max}=27$ K.Jeevan ; Adachi The magnetic transition in the Eu2+ subsystem is observed at temperatures $T_{\rm C}\sim 17-20$ K and depends moderately on the phosphorus content (doping level) in the specified range of contents.Jeevan ; Nandi1 ; Zapf ; Zapf1 ; Pogrebna ; Goltz ; Kadowaki

Previously, the magnetic flux structure was visualized with the MFM on artificial thin-film superconductor/ferromagnet (Nb/FeNi) hybrid structures,Iavarone where the domain structure and Abrikosov vortices frozen in the superconductor were observed simultaneously. However, in Ref. Iavarone, the Curie temperature $T_{\rm C}$ of ferromagnetic layers was much higher than the critical temperature of the superconducting transition $T_{\rm SC}$ in niobium films. Also, vortex structures were observed in spatially homogeneous ErNi2B2C bulk superconducting single crystals ($T_{\rm SC}=10.5$ K) in Ref. Veschunov, using the decoration method, and interpreted as an evidence of presence of domain boundaries in a weakly ferromagnetic phase with $T_{\rm C}=2.3$ K.

In this work, the structure of the magnetic flux in EuFe2(As1-xPx)2 single crystals with $x=0.20$ and $x=0.21$ is studied with MFM and Bitter decoration technique in a broad temperature range. Stripe and maze domain structures typical for ferromagnets with perpendicular magnetic anisotropy, are observed in the superconducting state below $T_{\rm C}$. In contrast to artificial hybrid systems, in EuFe2(As1-xPx)2 an interface is absent and superconductivity and ferromagnetism coexist on the atomic scale.

II Experimental details

EuFe2(As1-xPx)2 single crystals were synthesized using the self-flux method.Zhou The actual composition of synthesized single crystals was determined by energy dispersive X-ray (EDX) microanalysis employing Carl Zeiss Supra 50 VP SEM microscope. For MFM and decoration studies, single crystals of EuFe2(As0.8P0.2)2 and EuFe2(As0.79P0.21)2 of $1\times 1\times 0.012$ mm3 size with an atomically smooth surface were obtained by mechanical cleavage. Temperature and field dependences of the magnetization were measured on Quantum Design MPMS-XL5 SQUID magnetometer at fields up to 5 T. The surface structure and the distribution of magnetic flux were studied using AttoCube AttoDry 1000 atomic force microscope (AFM) with a closed-cycle cryogenic system, and a base temperature of 4 K. For AFM and MFM studies silicon cantilevers were used coated by magnetic CoCr layer (MESP, Bruker) with the following characteristics at 4.2 K: the resonance frequency of the cantilever 87 kHz, the stiffness constant 2.8 N/m, and the coercive field $\approx 1400$ Oe. AFM/MFM imaging was performed in an atmosphere of exchange gas (helium) at pressure $P\sim 0.5$ mbar in the temperature range from 4 to 30 K, controlled with exceptional precision of 1 mK. Prior to MFM imaging, probes were magnetized at $H=2$ kOe above the superconducting transition temperature $T_{\rm SC}=22$ K of EuFe2(As0.79P0.21)2 sample. The topography of the surface was studied in the tapping mode and magnetic flux structure was imaged in the MFM lift mode at 110 nm above the sample surface with the feedback switched off and fast scanning direction along the $Y$ axis. The MFM contrast was provided by the phase shift in the cantilever oscillation. The decoration of the surface of EuFe2(As0.8P0.2)2 single crystal was performed with magnetic iron particles ($\sim 10$ nm) in the field cooling (FC) regime at liquid helium temperatures.Vinnikov_Springer_23_89

III Results

Fig. 1 shows typical magnetic properties of EuFe2(As0.79P0.21)2 single crystal. Fig. 1(a) demonstrates temperature dependences of the magnetization measured in the FC and zero-field cooling (ZFC) regimes. The superconducting transition temperature $T_{\rm SC}=22$ K is indicated by the right arrow. Step features on the ZFC and FC temperature dependences of the magnetization are attributed to a ferromagnetic phase transition. It is noteworthy that a transition to the superconducting state is also accompanied by the appearance of residual magnetization upon cooling in an external field of 10 Oe. Fig. 1(b) shows the dependence of the magnetization on the applied magnetic field parallel to the $c$-axis of the crystal. For the sample with $x=0.20$ the temperature dependence of the magnetization and magnetization curve at 4 K are similar but with a higher superconducting transition temperature and a wider hysteresis loop.

Fig. 2 shows the results of the AFM/MFM studies. Fig. 2(a) demonstrates the AFM topography of the $8\times 8\,\rm\mu m^{2}$ surface area of EuFe2(As0.79P0.21)2 single crystal with the step of $\sim 100$ nm height. Fig. 2(b) shows the distribution of the magnetic flux over the surface shown in Fig. 2(a) at $T=17.27$ K. This structure is typical for the entire temperature range below the Curie temperature and disappears after heating above $T_{\rm C}$. Thus, the observed sign-alternating contrast can be attributed to the magnetic domain structure. Importantly, the domain structure is observed not only at zero external magnetic field, but also upon cooling in weak fields $H<100$ Oe. Fig. 2(c) shows the distribution of the magnetic flux in the superconducting state in a narrow temperature range above $T_{\rm C}$. The observed contrast (light spots) corresponds to Abrikosov vortices with the magnetic flux density $\Phi_{0}/a^{2}\sim 6$ G, where $\Phi_{0}$ is the magnetic flux quantum and $a$ is the average distance between vortices.

Fig. 3 shows the typical magnetic flux structure observed by the decoration method on the (001) surface of EuFe2(As0.80P0.20)2 single crystal with the superconducting transition temperature $T_{\rm SC}=24$ K. With MFM only a small $\sim 8\times 8\,\rm\mu m^{2}$ surface area of the sample was studied, whereas the decoration method reveals the magnetic structure on the almost entire surface. According to the principle of the image contrast formation in the decoration method,Veshchunov_JETP_88_758 ; Sakurai the region of higher density of magnetic particles (light) is treated as a domain with the magnetization along the applied field direction, whereas the region with lower density or without magnetic particles (dark) is interpreted as a domain with the opposite sign of the magnetization. As can be seen, the decorated domain structure (Fig. 3(b)) agrees with MFM imaged one (Fig. 2(b)) at corresponding scales. The period of the domain structure is about 0.9 $\rm\mu m$. At the same time, finer details of the decorated domain structure can be resolved (Fig. 3(b)). The magnetization measurements and both MFM imaged and decorated magnetic structure define explicitly EuFe2(As0.79P0.21)2 and EuFe2(As0.80P0.20)2 single crystals as superconductors with ferromagnetic ordering and the superconducting transition temperature $T_{\rm SC}$ above the Curie temperature $T_{\rm C}$.

IV Discussion

The experimental results can be interpreted as follows. According to the dependences shown in Fig. 1(a), the ZFC magnetization is negative below the superconducting transition temperature $T_{\rm SC}=22$ K. In the temperature range below $T_{\rm C}$, the diamagnetic response is weakened by the ferromagnetic transition in the Eu2+ subsystem. The exact determination of the Curie temperature using the observed features on the ZFC and FC temperature dependences of the magnetization is complicated due to competing mechanisms of superconducting and ferromagnetic orderings. In particular, maxima on the FC and ZFC temperature dependences of the magnetization are observed in Ref. Jeevan, at $T\sim 17.7$ K, whereas according to measurements of the specific heat, the Curie temperature is $T_{\rm C}=19$ K. In this work, the transition temperature to the ferromagnetic state $T_{\rm C}$ is defined as a temperature at which the domain structure is first observed, i.e., $T_{\rm C}=17.7$ K. The dependence of the magnetization on the applied magnetic field (Fig. 1(b)) is the superposition of a typical hysteresis loop of a type-II superconductor (within the Bean model the critical current density $J\rm_{c}$ is proportional to the width of the hysteresis loop) and the magnetization curve of the Eu2+ ferromagnetic subsystem.Jeevan

The magnetic origin of the domain structure contrast (Figs. 2(b) and 3(a)) is confirmed by insensitivity of the MFM probe to small details of the surface topography, e.g. to the 100 nm step. Sign-alternating (phase) contrast on domains indicates perpendicular magnetic anisotropy and corresponds to the antiparallel direction of the magnetization in neighboring domains.

Individual vortices could not be resolved with decoration since the expected magnetic flux density within domains is about 0.9 T ($M\rm_{s}=714$ cgs units/cm3) at liquid helium temperatures,Jeevan whereas the resolution of the decoration method is limited by 0.2 T.Vin3 The spatial resolution of MFM also cannot identify individual vortices if the local magnetic flux density in domains is much higher than 10 mT.Volodin ; Auslaender At the same time, the fine structure of domains, which is shown in Fig. 3(b), can be explained within the framework of domain branching in ferromagnets.Hubert An alternative origin of the fine domain structure is the so-called intermediate-mixed state,Golubok_JETP_35_642 which appears if the thickness of the superconducting crystal is much larger than the width of domains and is characterized by a mixture of flux-free domains (Meissner phase) and domains with Abrikosov vortices. In contrast to the structure of the intermediate-mixed state, the fields of vortices in neighboring branching domains should be oppositely oriented. Such a possibility was theoretically considered in Ref. Faure, . According to this model, different types of domain configurations can be formed in a ferromagnetic superconductor depending on the parameters (magnetic and superconducting): the saturation magnetization ($M\rm_{s}$), London penetration depth ($\lambda$), the lower critical field ($H_{\rm c1}$), and the domain wall width $w$. Precise measurements of these parameters and studies of the fine structure of domains will provide further clarification of the mechanisms of the coexistence and mutual influence of superconductivity and ferromagnetism in EuFe2(As1-xPx)2 single crystals.

V Concluding remarks

The main result of this work is the observation of the magnetic domain structure in EuFe2(As1-xPx)2 superconducting single crystals with $x=0.20$, and $x=0.21$. This domain structure disappears in EuFe2(As0.80P0.20)2 single crystal after heating above the Curie temperature $T_{\rm C}=17.7$ K. Thus, the magnetic domain structure has been observed for the first time in spatially homogeneous single crystals with the superconducting transition temperature $T_{\rm SC}$ exceeding the Curie temperature $T_{\rm C}$, $T_{\rm SC}>T_{\rm C}$, which unambiguously indicates the coexistence of ferromagnetism and superconductivity in this material. The observations of the magnetic flux structure using low-temperature MFM and decoration methods in real space (in contrast to X-ray and neutron diffraction studies) provide important information on the topology, real sizes, and shape of domains. At the same time, only further combined studies employing, e.g. diffraction methods and scanning probe microscopy, in particular high-resolution scanning tunneling microscopy, as well as decoration with ferromagnetic nanoparticles in a broad range of temperatures and magnetic fields can clarify the mechanism of the coexistence of superconductivity and ferromagnetism in these ferromagnetic superconductors.

VI Acknowledgments

I.S.V, L.Ya.V., and V.S.S. are grateful to V.V. Ryazanov, L.S. Uspenskaya, S.I. Bozhko, and A.I. Buzdin for stimulating discussions. We are grateful to V.V. Dremov, E.Yu. Postnova, A.G. Shishkin, and L.G. Isaeva for assistance. N.Z., Z.X.S., X.F.X., W.J., and G.C. acknowledge the support by the National Science Foundation of China (No. 11474252, 11611140101 and U1432135). The work of V.S.S., D.S.B., and I.A.G. was supported by the Russian Foundation for Basic Research (project No. 16-32-60133 mol-a-dk and 16-32-00309 mol-a). The MFM studies were supported by the Ministry of Education and Science of the Russian Federation (project No. 14.Y26.31.0007).