Introduction

Magnetism is believed to play an important role in high-temperature superconducting pairing, e.g., the Fe-related antiferromagnetism (Fe-AFM) in the iron-based superconducting family1,2,3. The competition between superconductivity (SC) and Fe-AFM in the charge-lightly doping region has been widely revealed4,5,6,7,8, however, the systems with unusual phase diagrams are also worth our concern. Typically, in the 112-type (Ca,La)FeAs29, the Fe-AFM exhibits robustness and is abnormally enhanced by La doping in the overdoped region, with SC gradually suppressed10. Lately, a series of the homogenous (Eu,La)FeAs2 compounds were discovered11. The transport and magnetic measurements suggested a structural transition (110 K), a Fe-related antiferromagnetic (Fe-AF) transition (98 K), and an Eu-AF transition (46 K) for single-crystalline EuFeAs212. A recent Mössbauer spectroscopy investigation on the polycrystalline EuFeAs2 sample confirmed an incommensurate spin-density-wave-type (SDW-type) AFM ordering of Fe2+ around 106 K13. The transport measurements on the underdoped Eu1−xLaxFeAs2 (x = 0–0.15) suggest that the Fe-AFM exists in the studied doping region11. Hence, the unusual relationship between Fe-AFM and SC in (Eu,La)FeAs2 is anticipated in a broader doping region, than that of (Ca,La)FeAs2 with lightly-doped samples unavailable.

On the other hand, various Eu-related magnetic properties were revealed in polycrystalline EuFeAs2 under a low magnetic field of 10 Oe, including a spin glass (SG) transition, reentrant magnetic modulation, and moment canting induced by transition metal doping in the Fe site14,15. The SG and the moment canting indicate a tunable competition and coexistence of the ferromagnetic and AF interactions between the Eu2+ ions, which was proposed to mainly originate in the Ruderman–Kittel–Kasuya–Yosida (RKKY) indirect exchange.

More intriguing is that the coupling between the two magnetic sublattices (see the crystal structure12 in Fig. 1a) would lead to anisotropic interaction between Eu2+ and Fe2+ in EuFeAs2. Magnetic systems with anisotropic interactions exhibit various magnetic properties, including sign-reversible exchange bias (EB)16, spin reorientation (SR)17, thermal magnetic hysteresis18, etc. The most studied EB effect is an exchange anisotropy with a shift of the magnetic hysteresis loop along the magnetic-field axis, which was first discovered in oxide-coated cobalt particles with moment compensation in the ferromagnetic/AF interface of Co/CoO19. Later, single-phase compounds with double magnetic sublattices have been found to exhibit the EB effect due to the existence of anisotropic interactions20,21. One explanation is that when a net moment is induced in one of the sublattices by the anisotropic interaction, a circumstance analogous to the FM/AFM interface generates compensation in between. The moment compensation between FM and SDW-type AFM could also trigger the EB effect in alloys or interfaces22,23. However, the EB effect associated with SDW-type AFM in a stoichiometric compound system is rare. (Eu,La)FeAs2 with robust SDW-type AFM and doping-modifiable Eu-related magnetism is a suitable compound system for exploring the EB anisotropy. Furthermore, the interplays of exotic magnetism and SC have shown interesting physics and application prospects in layered or wire-like heterostructures24,25,26,27,28,29. Hence, the (Eu,La)FeAs2 system is worth deeper investigation, not only for the unusual relationship between SDW and SC but also for the underlying physics originating from the interplay between anisotropic magnetism and SC.

Fig. 1: Crystal structure and magnetic properties of EuFeAs2.
figure 1

a Schematic diagram of the crystal structure12. b Magnetization against temperature under a magnetic field of 100 Oe. c, d Magnetization against the magnetic field at different temperatures with fields parallel to the c direction and the ab plane, respectively. The stars to the right axis in (b) represent the EB fields of the hysteresis loops in (c). The original curve in (d), solid, is the obtained M–H curve. The inverted curve, dashes, is the centrosymmetric one of the original.

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In this article, we first illuminate the magnetic anisotropy in the parent EuFeAs2. Then, the La-doping-induced magnetic evolution and the coupling between anisotropic magnetism and SC are studied. The nature of the robust Fe-AFM is discussed and examined in the superconducting state. Finally, a La-doping phase diagram on structure, magnetism, and SC is established.

Results and discussion

Magnetic anisotropy in EuFeAs2

The phase transitions of EuFeAs2 are reexamined by heat capacity, high-field magnetization, and single-crystal X-ray diffraction (SXRD) analyses, detailed in Supplementary Fig. 1. Based on the phase transitions, zero-field-cooling (ZFC), field-cooling (FC), and field-cooled-warming (FCW) magnetization measurements were performed on single-crystalline EuFeAs2 under a low magnetic field of 100 Oe below 50 K. The temperature-dependent magnetization (M–T) curves, depicted in Fig. 1b, exhibit Eu-related AF moment canceling in the ab plane and moment canting in the c direction below \(T_{\mathrm{N}}^{{\mathrm{Eu}}}\) ~45 K. Considering that the RKKY interaction in a conducting system30 and the anisotropic interaction in an insulating system31 can both induce net moment, we ascribe the moment canting in EuFeAs2 to the collaboration of the RKKY interaction between Eu2+ ions and the anisotropic interaction between Eu2+ and Fe2+. An SR-like upturn of the magnetization appears below TSR ~7 K in both directions, corresponding to the reentrant magnetic modulation proposed in the polycrystalline sample14, while, the SG behavior around 15.5 K is absent in single-crystalline EuFeAs2, even with the magnetic field decreased to 10 Oe, see Supplementary Fig. 2. The hysteresis below \(T_{\mathrm{N}}^{{\mathrm{Eu}}}\) for the FC and FCW curves in the c direction is reminiscent of the behavior observed in magnetically anisotropic SmCr1−xFexO3, which is attributed to the lower temperature SR32. Though the temperature interval of the hysteresis in EuFeAs2 is well above TSR, the hysteresis still implies a metastable spin state probably fixed by the magnetic anisotropy.

The net moment of Eu2+ encourages us to explore the EB anisotropy in undoped EuFeAs2. The magnetization versus magnetic field (M–H) is studied at different temperatures in the thermal-hysteresis interval with magnetic fields parallel to the c direction, shown in Fig. 1c (full curves presented in Supplementary Fig. 2). A magnetic hysteresis behavior appears in the M–H curves, with EB discernible from the comparison between the coercivities HC+ and HC−. The EB fields, defined as

$$H_{\mathrm{EB}} = (H_{{\mathrm{C}} + } + H_{{\mathrm{C}} - })/2,$$
(1)

are summarized in Fig. 1b. The non-monotonic temperature dependence of HEB, is similar to the oscillation behavior associated with incommensurate SDW in the (100)Cr/Ni81Fe19 bilayers23. We ascribe this EB behavior in EuFeAs2 to the anisotropic interaction between Eu2+ and Fe2+. Besides, a sign reversal of EB occurs in the thermal hysteresis interval, which may be related to the metastable spin state. We also performed a magnetization measurement on EuFeAs2 with H//ab at 3 K, as shown in Fig. 1d. Similar to the scenario of H//c, a weak EB is observed for H//ab below TSR, as seen from the comparison between the original and inverted curves. Thus, a weak net moment and a moment compensation emerge in the ab plane as well. The FCW measurement below TSR with H//ab has also been conducted, while, the magnetization curve basically overlaps with the FC and ZFC curves due to the measurement error of the physical property measurement system (PPMS).

In a word, the single-crystalline EuFeAs2 shows various magnetic properties, mainly associated with magnetic anisotropy. The EB behaviors related to SDW-type AFM in a stoichiometric compound system enrich the EB effect and the platforms for investigating the mechanism of EB anisotropy.

La-doping effects in Eu0.79La0.21FeAs2

La-doping effects are investigated in overdoped single-crystalline Eu0.79La0.21FeAs2, of which the doping level is determined by an energy-dispersive X-ray spectroscopy (EDXS) analysis, detailed in Supplementary Fig. 5. The electrical transport measurement was carried out to check the structural and Fe-AF transitions in this overdoped sample, as demonstrated in Fig. 2a. The resistivity curve exhibits an anomaly around 80 K, similar to that around 100 K in the parent EuFeAs212. According to the phase transitions of the parent EuFeAs2 (see Supplementary Fig. 1), the derivation of the R–T curve indicates that the structural and Fe-AF transitions are suppressed to TS ~82 K and \(T_{\mathrm{N}}^{{\mathrm{Fe}}}\) ~73 K, respectively. The slight resistivity decreasing below 8 K indicates that SC is greatly destroyed, despite the remaining of the robust Fe-AFM.

Fig. 2: Physical properties of Eu0.79La0.21FeAs2.
figure 2

a Normalized in-plane resistivity against temperature with part of the first derivation curve. b, c Magnetization against temperature with magnetic fields parallel to different directions. d First derivation of the M–T curves (10 Oe) and the EB fields in different directions. e, f Magnetization against the field in different directions. The inset in c is the enlarged view of the thermal hysteresis of the FC and FCW curves in the shadow area.

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The M–T curves, demonstrated in Fig. 2b, c, exhibit a dramatic ferromagnetic transition at \(T_{\mathrm{M}}^{{\mathrm{Eu}}}\) ~32 K for both directions, and an SR-like transition at TSR ~26.5 K (determined from the derivation of M–T in Fig. 2d) in the ab plane. The magnetic susceptibility can be suppressed by larger fields (not demonstrated), manifesting the canted AF nature of the Eu-FM with field-modifiable competing ferromagnetic and AF interactions. Thermal hysteresis of the FC and FCW processes exists in both directions below \(T_{\mathrm{M}}^{{\mathrm{Eu}}}\), which is probably associated with magnetic anisotropy. No superconducting diamagnetic behavior appears below 8 K.

For comparison, a series of Pr-doped (Eu,Pr)FeAs2 samples are synthesized, of which Pr doping introduces equal electrons but with less magnetic dilution comparing to equally La doping. All the Pr-doped samples exhibit weak moment canting behaviors, even in the overdoped region, detailed in Supplementary Fig. 8. Thus, the emergence of the stronger FM in (Eu,La)FeAs2 can be mainly attributed to the La-doping-induced magnetic dilution effect, rather than simply the doping-introduced extra electrons modifying the RKKY interaction. We consider the origin of the net moment in Eu0.79La0.21FeAs2 the same as that in the parent phase discussed above. Then, there are two possible ways to trigger the magnetic dilution effect on enhancing the magnetic anisotropy and generate FM: (1) The anisotropic exchange between Eu2+ and Fe2+ is adjusted by introducing nonmagnetic La3+, which leads to the change of the ferromagnetic-AF competition, similar to the dilution effect in (Sm,La)FeO333. (2) The nonmagnetic La3+ will not participate the RKKY interaction, which results in the doubling of the interaction distance between the Eu2+ moments beside the La3+ ion and might change the proportion of the ferromagnetic term of the RKKY interaction.

To further illuminate the La-doping effect on the exchange anisotropy, isothermal magnetization measurements were performed at different temperatures in the thermal-hysteresis interval, as shown in Fig. 2e, f (full curves seen in Supplementary Fig. 3). The areas of the magnetic loops are reasonably larger than those of the parent EuFeAs2. EB emerges in both the ab and c directions, with a longitudinal shift along the magnetization axis. The EB fields for different temperatures are summarized in Fig. 2d. The increased HEBs from those of the parent EuFeAs2, and the longitudinal shift of the loop support the enhancement of the magnetic anisotropy in Eu0.79La0.21FeAs2. A sign reversal of EB occurs below \(T_{\mathrm{M}}^{{\mathrm{Eu}}}\) for H//c, while, below TSR for H//ab.

It is worth mentioning that higher magnetic fields are needed to reverse the partially frozen moment at a lower temperature. Hence, a lower magnetic field only results in M–H curves with a loop area close to zero at a low temperature, shown in Supplementary Fig. 3. The almost linear M–H curve shows an upward shift with bias in the field direction, which is similar to that observed in (Sm,La)FeO333. The upward shift can be ascribed to the pinning between the partially frozen magnetic moment and the reversible magnetic moment.

Briefly, La doping greatly affects the competing balance between the ferromagnetic and AF interactions of the Eu2+ sublattice and enhances the magnetic anisotropy in Eu1−xLaxFeAs2.

The interplay of the anisotropic magnetism and SC

To explore the interplay of the anisotropic magnetism and SC, an overdoped sample with a sharper superconducting transition is requisite. Here, a series of Eu1−xLaxFeAs2 (x = 0.2, 0.25, and 0.3) polycrystalline samples are prepared and investigated. The chemical phase and quality of the samples are examined by powder X-ray diffraction (PXRD), detailed in Supplementary Fig. 6. For these polycrystalline samples, we use the nominal doping levels to represent the La-doping contents. From the resistivity curves depicted in Fig. 3a, the anomaly related to the structural and Fe-AF transitions remains in these overdoped samples. As magnified in the inset of Fig. 3a, a sharp superconducting transition at Tc ~11 K is realized for x = 0.2, which is suppressed with further doping. Zero resistivity is realized below Tzero ~8.5 K for Eu0.8La0.2FeAs2. Hence, Eu0.8La0.2FeAs2 is the expected superconducting compound.

Fig. 3: Physical properties of overdoped Eu1−xLaxFeAs2.
figure 3

a, b Normalized resistivity and magnetization against temperature, respectively. c, d Magnetization against the field for different field intervals of −6 to 6 T and −500 to 500 Oe, respectively, obtained at 2.5 K. The inset in a is a close view of the superconducting transition. Parts of the inverted M–H curves, dashes in c and d, are for comparison with the original ones.

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Temperature dependences of magnetization were measured for these overdoped samples, as depicted in Fig. 3b. Eu-related ferromagnetic transition occurs in all the samples, different from the AF behavior of the compounds with x ≤ 0.1511. The magnetization increases from x = 0.2 to 0.25, indicating an enhancement of the ferromagnetic interaction. Then, it is suppressed by further La doping, implying an excessive magnetic dilution. Meanwhile, the SR-like behavior gradually disappears in these overdoped samples. A diamagnetic transition appears at 7 K for Eu0.8La0.2FeAs2 in the ZFC process, with a superconducting volume fraction estimated to be 0.15–0.2 at 2.5 K. The broad superconducting transition for Eu0.75La0.25FeAs2 in the R–T curve disappears in the M–T curve, which probably originates in the slight inhomogeneity nature for the polycrystalline sample and/or the filamentary SC.

ZFC isothermal magnetization was studied at 2.5 K for Eu0.8La0.2FeAs2. The magnetic hysteresis loop obtained in a large field interval of −6 to 6 T is enlarged in Fig. 3c. The full and less-enlarged M–H curves can be seen in Supplementary Fig. 4. The misalignment of the first quarter (0 → 6 T) and the last two quarters (−6 → 6 T) of the loop are due to the superposition of the superconducting and ferromagnetic loops. The superposed loop exhibits an EB behavior with HEB ~−19 Oe, as seen from the comparison between the original and inverted curves.

As mentioned above, a lower magnetic field results in bias curves with a loop area close to zero at lower temperatures. Thus, to eliminate the component of the ferromagnetic loop, the isothermal magnetization in a smaller field interval is studied, as shown in Fig. 3d. The first quarter and the fifth quarter of the loop coincide fast when passing the lower critical field HC1, indicating that the superconducting loop is no longer superposed on the ferromagnetic loop. Meanwhile, an enhanced EB with HEB ~−54 Oe is obtained.

In short, combining of the anisotropic magnetism and SC leads to an EB behavior of the superposed magnetic and superconducting loop for Eu0.8La0.2FeAs2. This compound with the interplay between SC and anisotropic magnetism may serve as a prototype for application exploration. Also, seeking emergent physical phenomena from the interplay between multiple magnetic and superconducting orders is promising in this material.

Nature of the Fe-AFM, and the FM/AFM/SC coexisting state

To understand the nature of the robust Fe-AFM, we performed a density functional theory (DFT) calculation on the band structure of EuFeAs2. Without considering the magnetic order of Eu2+, seen in Fig. 4a, the band structures near the Fermi level are mainly attributed to the Fe-3d orbitals, of which the t2g orbitals contribute to the hole pockets at the Γ point and the electron pockets at the M point, similar to the band structure of LaFeAsO34. Following the magnetic structure of EuFe2As235, an assumed A-type AF order of Eu2+ was considered in the calculation, as seen in Fig. 4b. The band structures near the Fermi level barely changes, and the Eu-4f orbitals are below the Fermi level. Figure 4c shows the Fermi surface (FS) of EuFeAs2 with Fermi level Ef = 0 lying at the charge neutral point. Similar to that in the Ca112 system36, a reasonable FS nesting exists between the electron pockets at the M site and the hole pockets at the Γ point, suggesting the appropriate origin of the SDW-type AFM in EuFeAs2. In order to further explore the influence of electron doping, we artificially raise the Fermi level to examine the changes of the FS. The FSs with Fermi level Ef = 30 and 50 meV (corresponding to 0.07 and 0.12 electron doping per Fe) are displayed in Fig. 4d, e, respectively, where the FS nesting is gradually weakened by electron doping but always exists.

Fig. 4: DFT calculations on EuFeAs2.
figure 4

a, b Band structures without and with A-type AF order at the Eu2+ site, respectively, where the areas of the symbols represent the weights of the Fe d- and Eu f-orbitals. c–e Fermi surfaces with corresponding Fermi levels Ef = 0, 30, and 50 meV, respectively.

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The SDW-type Fe-AFM of (Eu,La)FeAs2 in the underdoping region can be explained by the FS nesting, despite the La- doping induced structural transformation11,12, as discussed in Supplementary Fig. 10. Whereas the FS nesting is gradually destroyed with electron doping exceeding 0.12 (Supplementary Fig. 11). A dual itinerant and localized nature is proposed for the Fe-AFM in Ca0.73La0.27FeAs236 and other iron-based systems37. Given that the ordered magnetic moment of Fe2+ in EuFeAs2 \(\left( {0.78\mu _{\mathrm{B}}} \right)\)13 is relatively larger than many other iron-pnictide parents38,39,40, we consider that the Fe-AFM in this Eu112 system is also dual-natured. Thus, with the FS nesting in (Eu,La)FeAs2 weakened by La doping, the Fe-AFM in the overdoped region is probably contributed increasingly by the local superexchange interaction.

To further reveal the nature of the Fe-AFM in the overdoped area, as well as to check if it survives in the superconducting state, we performed a 57Fe Mössbauer spectroscopy investigation on the superconducting Eu0.8La0.2FeAs2 polycrystalline sample. The fit of the 57Fe Mössbauer spectrum obtained at 300 K, detailed in Supplementary Fig. 12, reveals a nearly single iron-containing phase. The fitted isomer shift (IS) and quadrupole splitting (QS) are 0.432(1) and 0.157(4) mm s−1, respectively, which are close to the corresponding values for the parent EuFeAs2 and the Ni-doped EuFe0.97Ni0.03As213.

The spectrum collected at 6 K (<Tc), as shown in Fig. 5a, is similar to that of the undoped EuFeAs213 in the form of a broadened, asymmetric, six-line Zeeman pattern, which can be explained by the distribution of hyperfine magnetic field due to the SDW-type AF order. To fit the spectrum of 6 K in the main text, we follow the procedure reported in ref. 41. In general, the hyperfine magnetic field of the spin-density-wave order can be expressed as

$$H\left( {qX} \right) = \mathop {\sum }\limits_{n = 1}^N h_{2n - 1}{\mathrm{sin}}[\left( {2n - 1} \right)qX],$$
(2)

where h2n−1 denote the amplitudes of subsequent harmonics, q stands for the wavenumber of the SDW, and X denotes the relative position of the resonant nucleus along the propagation direction of the stationary SDW. The root-mean-square value of the hyperfine magnetic field \(\sqrt {\langle{H^2}\rangle}\) can be obtained as

$$\sqrt {\langle{H^2}\rangle} = \sqrt {\frac{1}{2}\mathop {\sum }\limits_{n = 1}^N h_{2n - 1}^2},$$
(3)

which is proportional to the ordered magnetic moment \(\mu _{{\mathrm{Fe}}}\) carried by the Fe atoms. It is generally accepted that the magnetic moment is approximately proportional to the measured hyperfine magnetic field. The obtained hyperfine parameters are listed in Supplementary Table 1, and the resulting SDW shape and the corresponding hyperfine field distribution are shown in Fig. 5b, c, respectively. The magnetic moment is determined to be 0.84(1) \(\mu _{\mathrm{B}}\) by using the same proportionality constant of a = 63 kOe \(\mu _{\mathrm{B}}\)−1 as was used for the calculation of the magnetic moment of the parent compound EuFeAs213. The ordered magnetic moment is much larger than those of other iron-based superconducting samples with suppressed Fe-AFM42,43,44. Another interesting result is that the SDW shape is almost rectangular rather than quasi-triangular as found in most iron-based superconductors13,42,43. The rectangular SDW shape at a low temperature has been observed in some of the parent compounds with relatively large magnetic moments and less pronounced itinerant character41. Besides, the ratio of the third and first amplitudes h3/h1 ~0.36, which outclasses the range of 10−3–10−2 expected from the itinerant-electron model45,46,47, implies that the Fe-AFM in Eu0.8La0.2FeAs2 cannot be accurately described merely by the itinerant picture. All these unusual Mössbauer spectroscopy results put our sample closer to the localized-AFM nature with the itinerant character of the magnetic order less prominent. Also, the magnetic moment is enhanced from that of the parent EuFeAs213, which is in agreement with the increasing prominence of the local superexchange interaction suggested by the DFT calculation.

Fig. 5: 57Fe Mössbauer spectroscopy analysis on Eu0.8La0.2FeAs2.
figure 5

a The spectrum (blue crosses) obtained at 6 K and the fit (red solid line) with the SDW model detailed in the main text. b the SDW shape, and c the resulting hyperfine field distribution.

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On the other hand, the Mössbauer spectrum obtained at 6 K manifests a microscopic coexistence of the Fe-AFM and SC. Given the relatively small superconducting volume fraction of Eu0.8La0.2FeAs2, the robust Fe-AFM remains in the superconducting state probably with a cost of suppression on SC. Anyhow, Eu0.8La0.2FeAs2 exhibits a microscopic coexistence of Eu-FM, Fe-AFM, and SC at low temperatures, similar to the Co-doped EuFe2As2 system30,44.

Finally, combining the results above and the data we previously reported on the lightly-doped compounds11, a La-doping electronic phase diagram on structure, magnetism, and SC for Eu1−xLaxFeAs2 is assembled in Fig. 6. All the values of the transition temperatures included in the phase diagram are listed in Supplementary Table 2. The La-doping-induced structural transformation occurs around x ~0.05–0.1 (detailed in Supplementary Fig. 7), which barely impacts the property evolution. The structural and Fe-AF transition temperatures are obtained from the derivation of the R–T curves, see Supplementary Fig. 9. The Fe-AF transition temperature of Eu0.8La0.2FeAs2 obtained from the Mössbauer spectroscopy investigation (Supplementary Fig. 13) is included for comparison, which manifests the reliability of the Fe-AF transition temperatures extracted from the R–T data. Both the structural and Fe-AF transitions are slightly suppressed by La doping but robustly remain. The slight suppression of the Fe-AFM by La doping in (Eu,La)FeAs2 is likely due to the weakened FS nesting, which is contrary to the overdoped (Ca,La)FeAs2 with stronger FS nesting and doping-enhanced Fe-AFM10,36. Consequently, the Fe-AFM phase with doping-adjustable dual nature is unusually adjacent to the whole superconducting dome. The robustness of the Fe-AFM is universal for electron doping in the Eu site, see the phase diagram of (Eu,Pr)FeAs2 in Supplementary Fig. 8. On the other hand, the Eu2+ magnetic moments in EuFeAs2 start to order below 45 K with a weak moment canting, leading to the coexistence of the Fe2+ and Eu2+ magnetic orders. The moment canting of the Eu2+ sublattice is tunable by La doping, with the AF transition temperature suppressed with doping level increasing in the underdoped region. FM originating from the canted AF order of the Eu2+ sublattice is realized for x ≥ 0.2, with a higher ordering temperature than that of the AF transition temperature for x = 0.15, indicating the domination of the ferromagnetic interaction. With temperature further dropping, a superconducting dome is obtained by La doping. Under the dome, the superconducting order coexists with the Fe- and Eu-magnetic orders.

Fig. 6: Electronic phase diagram of Eu1−xLaxFeAs2.
figure 6

The structural, Fe-AF, Eu-related magnetic, and superconducting transition temperatures as functions of the nominal La doping content x for the polycrystalline samples. The open symbols for x ≤ 0.15 represent the data extracted from our previous work11, and the solid symbols for x ≥ 0.15 the data obtained in the present work. The structural transition temperatures (TS), the Fe-AF transition temperatures \(\left( {T_{\rm{N}}^{\rm{Fe}} - {{RT}}} \right)\), and the superconducting transition temperatures (Tc − RT) are obtained from the transport measurements. The Fe-AF transition temperature \(\left( {T_{\rm{N}}^{\rm{Fe}} - {\rm{MS}}} \right)\) for x = 0.2 is obtained from the Mössbauer spectroscopy investigation, where the error bar represents the s.e.m. The Eu-magnetic transition temperatures \(\left( {T_{\rm{N}}^{\rm{Eu}}\,{\rm{and}}\,T_{\rm{M}}^{\rm{Eu}}} \right)\) and the diamagnetic transition temperatures (Tc − MT) are obtained from the magnetization measurements.

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In summary, we systematically investigated the electrical and magnetic properties of the 112-type (Eu,La)FeAs2. Due to the magnetic anisotropy, various exceptional magnetic phenomena are discovered in the parent EuFeAs2. Nonmagnetic La substitution modifies the balance of the ferromagnetic-AF competition and enhances the magnetic anisotropy. Several related physical phenomena are further revealed, including the EB effect of the superposed ferromagnetic/superconducting loop; the robustness of the Fe-AFM with doping-adjustable dominance of the dual itinerant and localized nature; and the coexisting state of Eu-FM, Fe-AFM, and SC. We call for further theoretical explanations for the SDW-associated magnetic exchange anisotropy. The incorporation of superconducting electrons and anisotropic spin states may trigger explorations of applications in electronics and spintronics, for example, in the cross-control field. Experimental investigations of the underlying physical phenomena in the FM/AFM/SC coexisting state are promising, given the coexistence of the multiple orders and the strong couplings. Most importantly, SC adjacent to the Fe-AFM with doping-adjustable itinerant/localized characters may host different threads to the nature of high-temperature SC in different doping regions.

Methods

Sample preparation

Single crystals of EuFeAs2 and Eu0.79La0.21FeAs2 were grown from a CsCl flux. A mixture of elementary Eu/La, Fe, and As in ratio of 1:1:4 (or 2:1:6) with 10- to 20-fold of dehydrated CsCl was sealed in a vacuum quartz tube, heated slowly to 800 °C, and held for 2 weeks before quenching. Polycrystalline Eu1−xLaxFeAs2 (x = 0.2, 0.25, and 0.3) samples were synthesized following our previous work11. The reaction temperature in the last step was modulated to 850 °C to improve the La-doping homogeneity in the overdoped samples.

Phase and property characterization

The SXRD experiments were carried out on a Single-crystal X-ray Diffractometer (Bruker). The PXRD patterns were collected on a Powder X-ray Diffractometer (PAN-analytical). The EDXS experiment was performed using a Scanning Electron Microscope (SEM) equipped with an energy dispersive X-ray spectrometer. Electrical transport, heat capacity, and magnetic measurements were conducted on a PPMS and a magnetic property measurement system (MPMS) (Quantum Design).

Transmission 57Fe Mössbauer spectra were recorded by using a conventional spectrometer working in constant acceleration mode. A 50 mCi of 57Co embedded in an Rh matrix moving at room temperature was used as the γ-ray source. The absorber was prepared with a surface density of ~8 mg cm−2 natural iron. The drive velocity was calibrated with sodium nitroprusside at room temperature and all the ISs quoted in this work are relative to that of the α-Fe.

Theoretical calculations

Theoretical calculations were performed using the DFT as implemented in the Vienna ab initio simulation package code48,49,50. The generalized-gradient approximation for the exchange-correlation functional was used. The cutoff energy was set to be 400 eV for expanding the wave functions into a plane-wave basis. In the calculation, the BZ was sampled in the k space within Monkhorst–Pack scheme51.