⁵⁷Fe and ¹⁵¹Eu Mössbauer studies of 3d-4f spin interplay in EuFe_2−xNi_xAs₂

Abstract

The EuFe_2−xNi_xAs₂ (with 0 ≤ x ≤ 0.4) compounds exhibiting 3d and/or 4f magnetic order were investigated by means of ⁵⁷Fe and ¹⁵¹Eu Mössbauer spectroscopy. Additionally, results for EuNi₂As₂ are reported for comparison. It was found that spin-density-wave order of the Fe itinerant moments is monotonically suppressed by Ni-substitution. However, the 3d magnetic order survives at the lowest temperature up to at least x = 0.12 and it is certainly completely suppressed for x = 0.20. The Eu localized moments order regardless of the Ni concentration, but undergo a spin reorientation with increasing x from alignment parallel to the a-axis in the parent compound, toward c-axis alignment for x > 0.07. Change of the 4f spins ordering from antiferromagnetic to ferromagnetic takes place simultaneously with a disappearance of the 3d spins order what is the evidence of a strong coupling between magnetism of Eu²⁺ ions and the conduction electrons of [Fe_2−xNi_xAs₂]^2- layers. The Fe nuclei experience the transferred hyperfine magnetic field due to the Eu²⁺ ordering for Ni-substituted samples with x > 0.04, while the transferred field is undetectable in EuFe₂As₂ and for compound with a low Ni-substitution level. It seems that the 4f ferromagnetic component arising from a tilt of the Eu²⁺ moments to the crystallographic c-axis leads to the transferred magnetic field at the Fe atoms. Superconductivity is not observed down to 1.8 K, although a comparison with ⁵⁷Fe and ¹⁵¹Eu Mössbauer data for EuFe₂As₂-based superconductors indicates a similar magnetic structure.

Introduction

The EuFe₂As₂-based compounds are unique laboratory for investigations of interplay between magnetism and superconductivity (SC), as well as they are a playground for peculiar competition between itinerant 3d magnetic order of the spin-density-wave (SDW) type and the localized 4f magnetic moments. EuFe₂As₂ belongs to the “122” family of parent compounds of iron-based superconductors, the same as AFe₂As₂ (A = Ca, Sr, Ba)¹. It crystallizes in the tetragonal ThCr₂Si₂-type structure with a space group I4/mmm at room temperature, distorted into orthorhombic structure with space group Fmmm upon cooling. Structural transition is accompanied by the Fe-3d itinerant SDW ordering at T_SDW = 190 K with saturation moment M_sat = 0.99 µ_B along a-axis. The Eu-4f localized magnetic moments order in an antiferromagnetic (AFM) A-type structure at T_N = 19 K with effective moment µ_eff = 7.94 µ_B². The neutron diffraction studies suggest rather weak coupling between the Fe and Eu magnetism, but it was found that the strength of interplay between 3d and 4f electrons can be tunable by chemical doping. The Fe magnetic order drives the structural phase transition, which indicates a strong coupling between structural and magnetic components². The Eu²⁺ ions are located in the planes perpendicular to the c-axis separating [Fe₂As₂]^2- layers. They are in a divalent ⁸S_7/2 state without orbital contribution to the 4f magnetic moments and a spin-only moments are aligned along the crystallographic a-axis. The A-type order of Eu²⁺ moments means that they are coupled ferromagnetically within the plane and antiferromagnetically between the planes. Adjacent europium planes are about 6 Å apart², hence direct overlap of interplanar 4f orbitals can be neglected. It can be assumed that the charge carrier mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is responsible for the AFM exchange between interplanar Eu moments. An interesting observation is a field-induced spin reorientation in the presence of a magnetic field along both the a and c axes, which causes that the ground-state AFM configuration of Eu²⁺ moments transforms into a ferromagnetic (FM) structure with moments along the applied field direction³. Another interesting effect for EuFe₂As₂ is that the SDW transition is suppressed by applied pressure and bulk superconductivity appears in the pressure range from 2.5 to 3 GPa^4,5. The Eu²⁺ AFM order and the Néel temperature T_N reveal no changes up to 3 GPa, then the applied pressure above 6 GPa causes a 4f spin reorientation and the Eu²⁺ FM order, while further pressure increase above 8 GPa results in suppression of the FM state, which is connected with the Eu valence change from a divalent state to a nearly trivalent state^6,7.

Superconductivity in EuFe₂As₂-based compounds can be achieved by substitutions on either one of three lattice sites as well as by pressure. There are many possibilities for hole and electron doping or isovalent substitution leading to SC, e.g. Eu_1−xA_xFe₂As₂ with A = K, Na, La, and EuFe_2−xT_xAs₂ with T = Co, Ru, Ir, or EuFe₂(As_1−xP_x)₂¹. It is interesting to note, that 4f magnetic order occurs within superconducting material as well, and doping leading to superconductivity usually causes some 4f magnetic moment reorientation (canting) with a generation of the 4f FM component^8,9,10. The iron-based superconductors are known as materials for which the SC occurs in proximity to a magnetic instability and the magnetic fluctuations could play a key role in the Cooper pairs formation. Hence, it is important to establish the nature of magnetism in these materials.

The electron doping is achieved by partial substitution of the Fe by Ni in EuFe_2−xNi_xAs₂ system with structural stability up to x = 0.4, while the Eu sublattice remains chemically intact. Although Ni-substitution causes suppression of the SDW, nevertheless the SC has not been observed down to 2 K¹¹.

The Mössbauer spectroscopy for ⁵⁷Fe and ¹⁵¹Eu isotopes is a useful local probe for simultaneous investigations of the mutual interaction between the magnetic Fe and Eu sublattices. It has also been shown that the Mössbauer hyperfine parameters are sensitive to change of the electronic charge modulations in the iron-based superconductors^12,13,14. A previous ⁵⁷Fe and ¹⁵¹Eu Mössbauer investigations have found a significant coupling between the 3d and 4f magnetic subsystems in the EuFe₂As₂-based compounds^{8,10,15,16,17,18,19,20}. The transferred magnetic hyperfine field from the 4f-Eu order to the Fe nuclei even in the superconducting state was reported for the first time by Nowik and Felner for EuFe₂(As_1−xP_x)₂¹⁰. An enhancement of Fe spin dynamics closely above superconducting critical temperature and related to enhanced Eu spin fluctuations was reported for superconducting EuFe₂(As_0.81P_0.19)₂¹⁵ and EuFe₂(As_0.7P_0.3)₂¹⁶. EuFe_2−xT_xAs₂ with the same substitution level x ≈ 0.2 for T = Co (superconductor) and T = Ni (non-superconductor) show practically the same Mössbauer spectra, confirming that only the Fe magnetic state affects the ordered Eu sublattice direction¹⁷ and the 4f electronic system is unaffected by the SC transition. Substitution of Eu site by K atoms gives rise to superconductivity, but long-range 4f magnetic order is suppressed due to the magnetic moment dilution at the rare-earth site in Eu_0.5K_0.5Fe₂As₂ system¹⁸. In Eu(Fe_0.86Ir_0.14)₂As₂, the SDW order is fully suppressed and the Eu²⁺ moments order magnetically with an appreciable FM component, which causes resistivity reentrance below the superconducting transition temperature¹⁹. These brief examples of Mössbauer spectroscopy studies show peculiar phenomena existing in the EuFe₂As₂-based systems due to the 3d-4f spin interplay.

On the other hand, the electron doping by the Ni atoms substituting the Fe atoms causes interesting effects in the iron-pnictide superconducting compounds. In (Eu_0.5K_0.5)Fe_2−xNi_xAs₂, the compensation of holes (K doping at the Eu site) by the electrons (Ni doping at the Fe site) leads to the reappearance of the resistivity anomaly presumably due to the SDW transition²¹, which is fully suppressed for (Eu_0.5K_0.5)Fe₂As₂. In particular, the anomaly associated with the SDW is observed at about 200 K for x = 0.24, which is close to the SDW transition temperature for parent EuFe₂As₂. It means that the electron doping almost compensates holes in (Eu_0.5K_0.5)Fe_1.76Ni_0.24As₂²¹. The itinerant FM ordering associated with the Co/Ni spins was discovered in Eu(Co_1-xNi_x)₂As₂²², while it is known that the Co atoms do not participate in the magnetic ordering in EuCo₂As₂. The same phenomenon occurs in CaK(Fe_1-xNi_x)₄As₄ where the itinerant SDW magnetism and superconductivity coexist, while no magnetic hyperfine field (e.g. no static magnetic order) was detected for CaKFe₄As₄ superconductor²³. The Ni doping leads to superconductivity of the “112” compound EuFeAs₂, i.e. the magnetism of the 4f-Eu order at 44 K and the 3d-Fe SDW order at 57 K coexist with the superconducting transition at 14 K for EuFe_0.97Ni_0.03As₂^24,25.

The Ni doping of the “122” iron-pnictide parent compounds AFe₂As₂ (A = Ca, Sr, Ba) changes these systems in the same following way: 1) the SDW is suppressed with increasing Ni concentration, 2) the SC appears. The maximum critical temperature and optimal substitution level x for AFe_2−xNi_xAs₂ (A = Ca²⁶, Sr²⁷, Ba²⁸) are as follows: 15 K for x = 0.06, 10 K for x = 0.18, and 21 K for x = 0.10, respectively. The same effect of the SDW suppression is observed in the fourth member of “122” family, i.e. EuFe_2−xNi_xAs₂¹¹. Hence, it raised the question “why is it not a superconductor?”. Of course the suspect culprit is the 4f magnetism.

The EuFe_2−xNi_xAs₂ system was studied by means of Mössbauer spectroscopy in early years of a fascination with the iron-based superconductors and the results for one composition with x = 0.20 and for selected temperatures were reported^17,29,30. The present contribution reports Mössbauer results obtained by means of ⁵⁷Fe and ¹⁵¹Eu spectroscopy applied to systematic investigations of the magnetic properties of the Ni-substituted EuFe₂As₂ compounds with an emphasis on study of the 3d-4f spin interaction.

Experiment

Single crystals of EuFe_2−xNi_xAs₂ were grown using the Sn flux method. The starting materials, high-purity elements of Ca, Fe, Ni, As, and Sn, were taken in the atomic ratio of Eu:Fe:Ni:As:Sn = 1:(1−x):10x:2:30²⁶. The constituent components were loaded into alumina crucibles and placed in silica ampules sealed under vacuum. The ampules were heated to 1050 °C and kept at this temperature for 10 h to ensure complete dissolving of all components in molten Sn. Next, the ampules were slowly (2–3 °C/h) cooled down to 600 °C, then the liquid Sn flux was removed by centrifugation. The chemical composition of the obtained crystals was determined using the energy-dispersive x-ray spectroscopy (EDX) and the following Ni content has been received: x = 0, 0.04, 0.07, 0.08, 0.10, 0.12, 0.20, and 0.40. Crystal lattice constants and phase purity were characterized by powder x-ray diffraction (XRD) using PANalytical X’Pert Pro diffractometer. Resistivity measurements were performed by the four probe technique using Quantum Design PPMS system.

⁵⁷Fe Mössbauer spectroscopy measurements were performed in transmission mode for 14.41-keV transition. The samples with x = 0, 0.04, 0.07, 0.10, 0.12, and 0.40 were selected for this investigation. The RENON MsAa-4 spectrometer operated in the round-corner triangular mode and equipped with the LND Kr-filled proportional detector was applied. The He–Ne laser based interferometer was used to calibrate a velocity scale. A single line commercial ⁵⁷Co(Rh) source made by RITVERC GmbH was kept at room temperature. The source linewidth Γ_s = 0.106(5) mm/s and the effective source recoilless fraction were derived from fit of the Mössbauer spectrum of 10-μm-thick α-Fe foil. The absorbers were prepared using 31 mg of the EuFe_2−xNi_xAs₂ samples in the powder form and mixed with a fine powder of B₄C carrier. The absorber thickness (surface density) for ⁵⁷Fe Mössbauer measurements amounted to 15 mg/cm² of investigated material. The SVT-400 cryostat by Janis Research Inc. was used to maintain temperature of absorbers.

¹⁵¹Eu Mössbauer transmission spectra for 21.6-keV resonant transition were collected applying ¹⁵¹SmF₃ source kept at room temperature and a scintillation detector. The samples with x = 0, 0.07, and 0.10 were selected for this investigation. Additionally, the sample of EuNi₂As₂ was measured. The absorbers were made in the same way, albeit they contained about twice as much the EuFe_2−xNi_xAs₂ material per unit area. Data for ⁵⁷Fe and ¹⁵¹Eu Mössbauer hyperfine parameters were processed by means of the Mosgraf-2009 software within the transmission integral approximation. Europium and iron nuclei in EuFe_2−xNi_xAs₂ experience almost axially symmetric electric field gradient (EFG) with the principal component aligned with the c-axis of the crystallographic unit cell. The ⁵⁷Fe spectra with SDW component were processed by treating the electric quadrupole interaction in the first order approximation. Remaining spectra were processed by application the full Hamiltonian diagonalization in both nuclear states. The europium hyperfine anomaly (the Bohr-Weisskopf effect) was accounted for ¹⁵¹Eu spectra. The spectral center shifts are reported with respect to the center shift of the room temperature α-Fe or room temperature ¹⁵¹SmF₃ source, respectively.

Mössbauer spectra evaluation within SDW model

A transmission integral approximation has been applied to fit Mössbauer spectra exhibiting magnetic hyperfine interaction. The SDW magnetism should be viewed as modulations of the spin polarization of the itinerant electrons. The absorption profile of the SDW spectral component was processed by applying a quasi-continuous distribution of the magnetic hyperfine field B. For the Fe magnetic moment being collinear with the hyperfine filed, the amplitude of SDW along the direction parallel to the SDW wave vector can be expressed as a series of odd harmonics^31,32,33,34:

$${B(qx) = \sum\limits_{n = 1}^{N} {h_{2n - 1} \, \sin [(2n - 1)qx]} ,}$$

(1)

where B(qx), q, x, and qx denote respectively the magnetic hyperfine field arising from SDW, the wave number of SDW, relative position of Fe atom along the propagation direction of stationary SDW, and phase shift. The symbols h_2n−1 denote the amplitudes of subsequent harmonics. The index N enumerates maximum relevant harmonic. Amplitudes up to seven subsequent harmonics (N = 7) have been fitted to the spectral shape. The constant number of N harmonics was chosen in such a way as to obtain a good-quality fit of the experimental spectrum represented by the parameter χ² per degree of freedom of the order of 1.0. The argument qx satisfies the following condition: 0 ≤ qx ≤ 2π due to the periodicity of the SDW. Further details of the Mössbauer spectra evaluation within SDW model can be found in Ref.³¹. Because the average amplitude of SDW described by expression (1) equals zero, thus the root-mean-square amplitude of SDW expressed as < B >  = ${\sqrt {\left\langle {B^{2} } \right\rangle } = \sqrt {\frac{1}{2}\sum\limits_{n = 1}^{N} {h_{2n - 1}^{2} } } }$ was used as the average magnetic hyperfine field of the SDW³³. Here, the parameter < B > is proportional to the value of the electronic magnetic moment per unit volume.

Results and discussion

Lattice parameters and electrical resistivity

Lattice parameters of the tetragonal unit cell of EuFe_2−xNi_xAs₂ at room temperature are shown in Fig. 1. In the range from x = 0 to x = 0.40, the lattice constant a increases slightly by about 0.3%, while the constant c contracts by 1.1%. Hence, the volume of the unit cell decreases by 0.5%, leading to the more compact packing of the [Fe₂As₂] layers and a decrease in the distance between Eu planes.

Figure 1

Lattice parameters of the tetragonal unit cell (space group I4/mmm) at room temperature for obtained EuFe_2−xNi_xAs₂ samples.

Figure 2 shows relative resistivity plotted versus temperature for various nickel concentrations x. A sharp uplift of resistivity is visible for x = 0 and 0.04 at about 190 K and 165 K, respectively, while a broad hump appears for x = 0.07, 0.10 and 0.12 starting at about 130 K, 90 K and 65 K respectively. Both behaviors are caused by the iron magnetism, but with a gradual ordering of 3d spins in the second case. Upon entering the magnetic state, the metallic behavior changes due to partial gapping of the Fermi surface leading to decrease of the carrier concentration. On the other hand, the spin scattering is reduced owing to the increasing spin order. The first mechanism leads to the upturn, while the second to the downturn of the resistivity with lowering of the temperature. The resistivity anomaly associated with SDW order is invisible for x = 0.20 and x = 0.40 due to lack of this type of magnetism for such high nickel concentration. The europium magnetic ordering is seen as much less pronounced kink on the resistivity at about 20 K. The SC is not observed down to 1.8 K for any of these compounds.

Figure 2

Temperature dependencies of the relative resistivity (normalized to the resistivity at 300 K) for EuFe_2−xNi_xAs₂ samples. The current was applied perpendicular to the c-axis. The resistivity anomaly associated with the iron magnetism is clearly visible for all studied samples, except the highest Ni-substitution levels x = 0.20 and 0.40.

⁵⁷Fe Mössbauer measurements

Magnetic hyperfine interactions

⁵⁷Fe Mössbauer spectra measured at selected temperatures of 4.2, 25, 80 and 300 K are shown in Fig. 3. The 25 K was chosen because it was the lowest temperature of our measurements without europium magnetic order. Spectra were fitted with the SDW model in the magnetically ordered region and with a quadrupole doublet otherwise. Apart from the spectra for the parent compound and the spectra for the compound with the highest Ni content, all other spectra were fitted with superposition of two components. Spectra at 300 K have a shape of pseudo-single line due to small electric quadrupole hyperfine interaction. The precise case is that they are unresolved spectral doublets with small average quadrupole splitting ranging from about 0.1 mm/s for the parent compound to about 0.2 mm/s for the compound with the highest substitution level x = 0.40. An asymmetrical spectral broadening is observed with increasing x due to doping-induced disorder and perturbation of the Fe plane site by the Ni atoms. Spectra at 25 K and 80 K have a shape resulting from the coexistence of the magnetic component and the “non-magnetic” second component. The magnetic spectral component associated with SDW order is described by the average magnetic hyperfine field < B > . The second spectral component is described by the average quadrupole splitting < Δ > and has significantly broadened line-width. The latter component at the low temperatures was fitted applying some hyperfine magnetic field B_Q with a low value of about 1 – 2 T. Further broadening of spectra and change of their shape are observed at 4.2 K and it results from the hyperfine transferred field B_t from ordered magnetic moments of the Eu²⁺ atoms. The presence of two spectral components is somewhat similar to the so-called double-Q magnetic phase with spatially non-uniform magnetization caused by a coherent superposition of two SDWs, leading to both constructive and destructive interference of the SDWs on alternate Fe sites³⁵. The spin amplitudes at the Fe sites are nonuniform, vanishing on half of the sites and doubling on the others. But this scenario requires a constant ratio between contribution of both spectral components, which, as will be shown further in the article, is not the case of EuFe_2−xNi_xAs₂ system.

Figure 3

The ⁵⁷Fe Mössbauer spectra of EuFe_2−xNi_xAs₂ measured at 4.2, 25, 80 and 300 K. (Inserted values in blue) The relative contribution of the SDW spectral component A, the average magnetic hyperfine field of SDW < B > , and the hyperfine transferred magnetic field due to the Eu²⁺ ordering for iron in the SDW state. (Inserted values in green) The hyperfine transferred field due to the Eu²⁺ ordering for iron in the “non-magnetic” state (the second spectral component), and the angle θ between the principal component of EFG at Fe nuclei (i.e. the crystallographic c-axis) and the Eu²⁺ magnetic moment. The spectral center shift δ and the quadrupole splitting Δ at 300 K are shown. Errors for all values are of the order of unity for the last digit shown.

Spectra of EuFe_1.96Ni_0.04As₂ compound across magnetic transition are shown in Fig. 4. The magnetic component with low hyperfine field of 1.5 T appears at 200 K. Its contribution and the magnetic field increase with decreasing temperature. Half of the iron moments are magnetically ordered at about 175 K and the complete order of all iron spins is observed at 4.2 K with < B >  = 7.1 T, which is comparable to < B >  = 8.1 T for the parent compound. The transferred hyperfine field at iron due to the magnetic ordering of europium is undetectable for EuFe_2−xNi_xAs₂ with x = 0 and 0.04. Since the Fe plane is in the middle of the distance along the c-axis between adjacent Eu planes, hence, in the case of θ = 90°, the B_t is zero due to a cancellation of the internal magnetic induction from the nearest-neighbor Eu planes of FM-aligned moments corresponding to an A-type collinear AFM state. However, it should be mentioned that some small increase of the Fe hyperfine field of about 0.2 T around temperature of the Eu order in the parent compound EuFe₂As₂ was reported by Ikeda et al.³⁶. Processing of our spectra for x = 0.07, 0.10, and 0.12 at 4.2 K gives the transferred field with fairly similar values for both spectral components and with clearly visible difference in the shape of the spectra compared to the temperature of 25 K, i.e. before the Eu magnetism.

Figure 4

Selected ⁵⁷Fe Mössbauer spectra of EuFe_1.96Ni_0.04As₂ versus temperature across the SDW order. (Inserted values) The contribution of the SDW spectral component A, and the average magnetic hyperfine field of SDW < B > . Spectra were measured at the same conditions during non-interrupted series and they are shown for comparison on the same scale, except that the left column scale is twice the scale of the right one. The influence of the magnetic SDW order on the shape of the spectra is clearly visible.

The contribution of SDW magnetic component A together with its average magnetic field < B > versus temperature are shown in Fig. 5. The EuFe_2−xNi_xAs₂ compounds with x = 0.07, 0.10, 0.12 contain a predominant contribution of the SDW phase at the lowest measured temperature reaching of about 90%, 80%, 70% respectively. Moreover, a significant reduction of the hyperfine field of the SDW magnetic component to < B >  = 5.5, 4.8, 4.6 T at 4.2 K was observed, respectively. Temperature evolution of the SDW hyperfine field < B > (T) for EuFe_1.96Ni_0.04As₂ was fitted within the model described in Ref.³¹ and compared with the results for EuFe₂As₂³¹. The static critical exponent of 0.130(4) and the coherent SDW order temperature of 184(2) K were obtained. We note that the critical exponent in the substituted system EuFe_1.96Ni_0.04As₂ is almost the same as that in the parent compound³¹. The value close to 1/8 indicates that the universality class (1, 2) is retained and it means that the electronic spin system with SDW obeys the Ising model (one-dimensional spin space) and has two dimensions in the configuration space (magnetized planes). It is difficult to draw such conclusions for compounds with x = 0.07, 0.10, 0.12, but one can see that the magnetic ordering starts at about 160, 130 and 100 K, respectively. These temperatures are significantly higher than a temperatures of the resistivity anomaly associated with iron magnetism which are shown in Fig. 2. This is because the Mössbauer spectroscopy is much more sensitive to the electron spin density and even to an incoherent spin density wavelets typical for a critical region of the SDW. The low panel of Fig. 5 shows temperature dependence of a low hyperfine field B_Q resulting from broadening of the second spectral component. Due to the small contribution of this component, the origin of such weak magnetism and even its existence is doubtful.

Figure 5

(a) Temperature dependence of the contribution of the SDW spectral component A for Ni-substituted compounds with x = 0.04, 0.07, 0.10, 0.12. (b) The average magnetic hyperfine field of SDW < B > versus temperature. The solid lines for x = 0 and 0.04 represent the best-fit to experimental data using the model described in Ref.³¹. The dashed line for x = 0.07 is for the view clarity only. (c) The low hyperfine field of the second spectral component B_Q arising from the broadening of spectral lines.

The average hyperfine field of SDW < B > for the EuFe₂As₂ at 4.2 K is 8.1 T and this value is related to 0.99 µ_B magnetic moment determined from the neutron-diffraction measurements². Such small moment results from itinerant character of iron magnetism. The Ni-substitution causes decreasing of the hyperfine field < B > and related magnetic moment can be estimated as < B >  = α μ_Fe, where μ_Fe is the on-site magnetic moment of iron atom and α denotes the constant, which is specific for a given compound³⁷. To convert the hyperfine magnetic field to the iron magnetic moment, we used α = 8.18 T/μ_B. The average hyperfine field of SDW at 4.2 K and related 3d itinerant magnetic moment of iron versus Ni-substitution x in EuFe_2−xNi_xAs₂ system are shown in Fig. 6. The magnetic moment of SDW is halved for the Ni substitution x = 0.12 and it decreases linearly in this dopant concentration range. Taking into account the decreasing contribution of SDW component A with increasing Ni content, the weighted average field and corresponding weighted average magnetic moment was presented by triangles in Fig. 6.

Figure 6

The average hyperfine field of SDW < B > at 4.2 K and corresponding itinerant magnetic moment versus Ni-substitution level x for EuFe_2−xNi_xAs₂ system. Triangles represent the weighted average values of both quantities with taking into account the contribution of SDW phase.

Transferred magnetic field from Eu to Fe

The EuFe_1.60Ni_0.40As₂ displays no magnetic dipole hyperfine interaction in the whole studied temperature range, as the SDW does not develop for such high concentration of nickel. One has sole non-magnetic component with clearly visible influence of the transferred magnetic hyperfine field B_t = 1.38(2) T at 4.2 K from europium order. It gives an opportunity to estimate the angle θ between the principal component of the electric field gradient (EFG) at the Fe nuclei (i.e. the crystallographic c-axis in the present case) and the Eu²⁺ localized magnetic moment. It is assumed that the transferred field points in the same direction as that of the Eu magnetic moment. The angle θ = 39(1)° is determined reliably for this spectrum and indicates canting of europium moments from ab-plane of about 90° − θ = 51°. The lack of iron magnetism and almost the same angle θ = 36° for B_t = 1.37 T at 4.2 K was found previously for EuFe_1.80Ni_0.20As₂ by Nowik and Felner^29,30. The Eu²⁺ spin reorientation phenomenon will be also discussed later in this article based on data from the ¹⁵¹Eu Mössbauer spectroscopy.

It seems that the transferred field of about 1 T is typical for the EuFe₂As₂-based compounds with suppressed SDW magnetism and even in the superconducting state. The transferred magnetic hyperfine field acting in the superconducting layer was observed for the first time in the EuFe₂(As_1−xP_x)₂ system with x > 0.2¹⁰. The advantage of this discovery was that the coexistence of SC and magnetic field in the Fe–As based layer was observed on the same sample under the same experimental conditions, by the local probe, i.e. ⁵⁷Fe Mössbauer spectroscopy. The value of B_t = 0.93(5) T was reported for optimally doped superconductor with x = 0.3, while B_t = 0.85(2) T for x = 0.75, and 0.97(2) T for x = 1, i.e. EuFe₂P₂¹⁰. For the latter case, the angle θ = 15(5)° was obtained. Another report shows B_t = 1.2(1)T and θ = 40° for the optimally doped EuFe₂(As_1-xP_x)₂ superconductor with x = 0.28¹⁵. Almost the same values of the B_t for different substitution level x indicate that the electron spin density at the position of the Fe nucleus is the same whether the system is normal or superconducting. Another examples of the Eu to Fe magnetic field transfer and the Eu canting are: Eu(Fe_0.71Co_0.29)₂As₂ with B_t = 1.27(2)T and θ = 40(1)°⁸, or Eu(Fe_0.75Ru_0.25)₂As₂ with B_t = 0.71(2) T³⁸. An interesting results of the B_t = 0.6 T were reported for the ferromagnetic superconductors AEuFe₄As₄ (A = Rb³⁹ and Cs⁴⁰) with Eu moments laying in the ab-plane.

Electric hyperfine interactions and relative spectral area

Temperature dependencies of the spectral center shift δ and the quadrupole splitting Δ for both spectral components (if present) are shown in Fig. 7. The SDW phase seems to have a lower value of the δ (i.e. a higher value of the s-electron charge density) than the “non-magnetic” phase in cases of compounds and temperature ranges where both components occur. But some effect of a fitting artifact can’t be excluded due to a low content of one of the components in the temperature ranges discussed. Hence, the weighted average value of spectral center shift should be considered as a reliable parameter. Generally, the δ is almost insensitive to Ni-substitution level x and keeps the value of about 0.41 and 0.54 mm/s at temperature of 300 and 4.2 K, respectively. The same insignificant Ni-concentration dependence of the δ was found for CaK(Fe_1-xNi_x)₄As₄ superconductors²³. It means that Ni-doping does not noticeably affect the s-electron charge density at the Fe nuclei. From this Mössbauer spectroscopy point of view, the Ni should be considered as isovalent dopant in the EuFe_2−xNi_xAs₂ system. However, other effects leading to such an outcome, such as opposite influence of the lattice volume effect and the d-electrons shielding effect, cannot be ruled out. Hence, based on these results, the Ni atoms commonly recognized as electron dopant in the EuFe_2−xNi_xAs₂ can’t be called into question. The value of δ indicates that Fe atoms are in a low-spin Fe(II) electronic configuration.

Figure 7

Temperature dependencies of the Mössbauer spectroscopy parameters: the spectral center shift δ relative to the shift of room temperature α-Fe, and the electric quadrupole splitting Δ. Values for the SDW spectral component and the second spectral component are shown in blue and in green, respectively. The weighted average spectral center shift < δ > is marked in red along with the solid lines representing the best-fit to experimental data using the Debye model for < δ > (T). The Debye temperature Θ_D and the spectral shift at the ground state δ₀ are shown. The symbols δ₃₀₀, Δ_4.2 and |Δ₃₀₀| stand for measured values of the spectral shift, the quadrupole splitting, and the absolute value of the quadrupole splitting, at 4.2 K and 300 K, respectively. For x = 0.40, point of Δ_4.2 with the positive sign determined in presence of the Eu²⁺ transferred hyperfine field isn’t shown. Note: for ⁵⁷Fe the sign of the quadrupole coupling constant cannot be determined without the hyperfine field or applied external magnetic field.

The temperature evolution of weighted average spectral center shift < δ > , shown in Fig. 7, represents a typical second-order Doppler shift dependence on temperature and it could be treated in terms of the Debye model for the lattice vibrations of iron atoms. The Debye temperatures Θ_D obtained on the basis of this model are typical for a strongly bound metal-covalent system. It increases with Ni substitution level x from about 400 K for the parent compound to about 500 K for x = 0.10. On the other hand, further increasing x to 0.40 causes the return to the almost initial value of Θ_D. It means that the (Fe/Ni)−As bonds become stiffer with increasing Ni content up to x = 0.10. The x = 0.10 is close to the critical substitution level for the AFM-FM transition. It seems that some magneto-elastic effect accompanies this critical Ni concentration resulting in lattice hardening and jump of Θ_D.

The right panel of Fig. 7 shows the parameter of the electric quadrupole hyperfine interaction, i.e. the quadrupole spitting Δ. At 300 K, the Δ systematically increases from about 0.12 mm/s for the parent compound to about 0.23 mm/s for the Ni-substitution x = 0.40. It means that the EFG at iron site increases with x in EuFe_2−xNi_xAs₂ system. This is a symptom of an increase in disorder and perturbation of the Fe atoms surrounding in Fe-plane caused by the Ni atoms. The absolute value of Δ for the “non-magnetic” phase increases as the temperature decreases. At 4.2 K, the Δ of the SDW phase keeps almost constant and negative value of about −0.10 mm/s. This is a manifestation of a greater strength of the magnetic dipole hyperfine interaction than the electric quadrupole interaction, which masks the EFG perturbation caused by increasing Ni substitution. It should be noted that additional magnetic transferred field form europium order perturbs the Mössbauer spectra at 4.2 K. Accordingly, when the 3d magnetism of SDW is weakened by Ni-substitution x > 0.04, the 4f transferred magnetism causes difference of the Δ between 4.2 and 25 K. For x = 0.40, for which the iron 3d magnetism was not observed in whole studied temperature range, the 4f magnetism at 4.2 K causes a positive sign of the Δ =  +0.224(7) mm/s (point not shown in Fig. 7).

The Mössbauer recoilless fraction can be approximated by the relative spectral area (RSA), which is defined as:

$${RSA = \left( \frac{1}{C} \right)\sum\limits_{n = 1}^{C} {\frac{{N_{0} - N_{n} }}{{N_{0} }}} },$$

where C denotes the number of data channels for folded spectrum, N₀ is the average number of counts per channel far-off resonance, namely the baseline, and N_n stands for the number of counts in the channel n. The RSA can be directly evaluated from measured spectra as a quantity independent of any physical model. The temperature evolutions of the relative spectral areas for EuFe_2−xNi_xAs₂ with x = 0.04, 0.10, 0.40 are displayed in Fig. 8. Here, the RSAs are calculated for the Mössbauer spectra recorded versus increasing temperature in the non-interrupted series of measurements carried out in the same experimental conditions (radioactive source, geometry, velocity scale, number of data channels, background under the resonance line, and linear response range of the detector system) and for the same mass of each of the samples. The RSA slightly increases with decreasing temperature due to the thermal effect. Some slight jump of RSA at about 180 K for x = 0.04 is observed due to an increase in the recoilless fraction probably arising from the weak magneto-elastic effect, which results in a fine hardening of lattice vibrations upon development of the magnetic order. Such an effect, but much stronger, is observed upon magnetic transition for other compounds with the iron–pnictogen bonds^41,42. In this case, it may be suppressed due to the Ni perturbation of the Fe-plane. For comparison, the compound with x = 0.40 without any 3d magnetism has almost flat temperature dependence of RSA and without any irregularity.

Figure 8

Temperature dependencies of the relative spectral area (RSA) for EuFe_2−xNi_xAs₂ with x = 0.04, 0.10, 0.40. Vertical dashed lines at 184 K and 130 K denote the SDW order temperatures for x = 0.04 and x = 0.10, respectively. Each RSA set is derived from series of measurements performed at constant conditions (see text for details). Note: despite the identical weights of samples the sets of RSA differ due to difference in the resonant thickness (⁵⁷Fe content) between particular absorbers.

¹⁵¹Eu Mössbauer measurements

It should be noted that ¹⁵¹Eu Mössbauer spectroscopy is very sensitive to the angle between principal component of EFG and hyperfine magnetic field B on the ¹⁵¹Eu nucleus, i.e. for the angle between the c-axis (in this case of tetragonal or orthorhombic structure) and the Eu²⁺ magnetic moment. The spin reorientation phenomenon can be easily recognized (even by eye) due to characteristic change of the relative intensity of spectral lines, see Fig. 9.

Figure 9

Simulated ¹⁵¹Eu Mössbauer spectra for two extreme values of the θ angle, i.e. 90° and 0°. The other hyperfine parameters are constant and their values are close to those for EuFe₂As₂, i.e. δ = −11.4 mm/s, V_zz = −0.49 (10²² V/m²), and B = 26.6 T. The spectral linewidths are equal to the natural width and the optimal effective absorber thickness was applied. Clearly visible change of the relative intensity of spectral lines illustrates the high sensitivity of ¹⁵¹Eu Mössbauer spectroscopy to the phenomenon of spin reorientation. On the other hand, the ϕ angle is undetectable for the quadrupole asymmetry parameter η = 0, i.e. V_xx = V_yy, which is a case of tetragonal structure with V_zz along c-axis of the unit cell.

¹⁵¹Eu Mössbauer spectra for the parent compound and the Ni-substituted compounds with x = 0.07 and 0.10 are shown in Fig. 10, while obtained hyperfine parameters are listed in Table 1. The symbol $\varepsilon = \tfrac{1}{4}(c/E_{0} )eQ_{g} V_{zz}$ stands for the quadrupole coupling constant for Eu²⁺ under assumption that the EFG is axially symmetric with the main axis aligned with the c-axis of the unit cell. The symbol c stands for the speed of light in vacuum, the symbol E₀ denotes transition energy, while the symbol e stands for the positive elementary charge. The symbol Q_g =  +0.903 b denotes spectroscopic nuclear electric quadrupole moment in the ground state of ¹⁵¹Eu, while the symbol V_zz stands for the principal component of EFG on Eu²⁺ nucleus. For spectra with the europium hyperfine magnetic field one obtained the quadrupole shift $\varepsilon = \tfrac{1}{4}(c/E_{0} )eQ_{g} V_{zz} (3\cos^{2} \theta - 1)/2$.

Figure 10

source and the quadrupole shift, respectively. The arrow on spectrum of x = 0.10 at 300 K shows position of the Eu³⁺ component with ε =  +0.8(2) mm/s and Γ_a = 1.6(6) mm/s. (Lower panel) Sketches of the corresponding magnetic structures of EuFe_2−xNi_xAs₂ system at the ground state emerging from the ⁵⁷Fe and ¹⁵¹Eu Mössbauer results at 4.2 K. The gray line outlines the orthorhombic unit cell.

The ¹⁵¹Eu Mössbauer spectra of EuFe_2−xNi_xAs₂ with x = 0, 0.07, 0.10. The hyperfine magnetic field for Eu²⁺ is denoted by B, while the symbol θ stands for the angle between the principal component of the EFG (c-axis of the unit cell) and the Eu²⁺ hyperfine field (4f-Eu magnetic moment). The symbols δ and ε stand for the spectral center shift relative to room temperature ¹⁵¹SmF₃

Table 1 The ¹⁵¹Eu Mössbauer spectroscopy parameters for EuFe_2−xNi_xAs₂ and EuNi₂As₂.

The hyperfine magnetic field B on the Eu²⁺ ions in the spectrum collected at lowest temperatures for the parent EuFe₂As₂ and for x = 0.07 are almost the same. The angle θ equal to or close to the right angle indicates that AFM order of europium 4f spins between subsequent ab-planes is preserved for these compounds. However, it must be admitted that by fitting the Mössbauer spectra at 4.2 K for EuFe₂As₂ and EuFe_1.93Ni_0.07As₂ one obtained a slight canting of the Eu²⁺ moments out of the ab-plane of 13(3)° and 7(6)°, respectively. The same result of 13(7)° and ~ 10° was indicated for EuFe₂As₂ studied by means of Mössbauer spectroscopy¹⁰ and magnetic torque measurements⁴³, respectively. To our knowledge, the canting of Eu²⁺ moments out of the ab-plane for EuFe₂As₂ has not been observed (yet) by the neutron diffraction and resonant x-ray measurements. Hence, a wary notation θ ~ 90° is used in Fig. 10.

On the other hand, for x = 0.10 the angle θ between hyperfine field on Eu²⁺ and the main component of EFG on the same ion amounts to 31(2)° at 4.2 K. The main component of EFG is oriented along the crystallographic c-axis, while the hyperfine field is aligned with the Eu²⁺ magnetic moment. Hence, the magnetic moment of europium is tilted by 90° – θ = 59(2)° from the ab-plane, while in the parent compounds is perpendicular to the c-axis. It means that in EuFe_1.90Ni_0.10As₂ magnetic moments of Eu²⁺ tend to rotate on the c-axis in similarity to the superconducting EuFe₂As₂-based compounds with some canting leading to the ferromagnetic component of the 4f origin^8,10.

Another proof of the AFM to FM transition in EuFe_1.90Ni_0.10As₂ is the hyperfine field B = 27.5 T, hence about 1 Tesla higher than for the parent compound and the compound with a slightly lower substitution level x = 0.07. Increased hyperfine field for Eu²⁺ spins almost aligned along c-axis was observed for EuFe₂As₂-based substituted compounds¹⁰.

Both phenomena, i.e. the spin reorientation and the accompanying increase in the hyperfine field, were previously observed by means of the ¹⁵¹Eu Mössbauer spectroscopy for other substituted EuFe₂As₂-based compounds. For Eu(Fe_0.75Ru_0.25)₂As₂ superconductor with T_sc = 23 K, the Eu²⁺ spins order ferromagnetically below 19.5 K with the hyperfine field 28.8 T at 5 K tilted away from the c-axis by 20(3)°³⁸, while for EuRu₂As₂ one obtained B = 30.2 T and θ ~ 0°⁴⁴. For Eu(Fe_0.86Ir_0.14)₂As₂ superconductor with T_sc = 22.5 K and double reentrance at lower temperature, the Eu²⁺ moments order magnetically at 18 K with an appreciable FM component and the Eu hyperfine field of 28.5 T at 4.2 K¹⁹. The EuFe₂(As_1−xP_x)₂ system preserves the AFM order for x ≤ 0.2 with the angle θ = 77(7)° and the hyperfine field B = 26.2 T^10,15. While, the canting effect and Eu hyperfine field increase with accompanying the Eu to Fe transferred field (~ 1 T) have been observed for x > 0.2, with reported values of θ = 12(8)° and B = 28.4 T for x = 0.3¹⁶, or θ = 22(3)° and B = 30.8 T for x = 1, i.e. EuFe₂P₂^10,45.

It can be additionally noted that the FM order of Eu magnetic moments laying in the ab-plane was detected by ¹⁵¹Eu Mössbauer measurements for superconducting AEuFe₄As₄ (A = Rb³⁹ and Cs⁴⁰) with the europium hyperfine field of 22.5 T and 22.4 T, respectively. In this case, the sheets of Eu atoms are separated by the AFe₄As₄ unit which rules out the possibility of any strong interaction between the Eu planes. In particular, no magnetic coupling is expected to exist between the Eu atoms along the c-direction. On the other hand, the AFM order was reported for parent EuFeAs₂ and superconductor EuFeNi_0.03As₂²⁴ with B = 29.4 T and 29.1 T, respectively.

Traces of Eu³⁺ makes about 2.6% contribution to the spectra of EuFe_1.90Ni_0.10As₂ in similarity to the superconducting and/or overdoped EuFe₂As₂-based compounds studied previously by ¹⁵¹Eu Mössbauer spectroscopy⁸. The Eu³⁺ component of spectra was usually assigned to a unidentified foreign phase or a result of oxidation. But some change in valence of the Eu²⁺ belonging to the main phase due to local chemical pressure induced by nickel substitution cannot be ruled out^8,46. However, in the present case one cannot prove that trivalent europium is in the main phase of the sample.

The magnetic structures resulting from ⁵⁷Fe and ¹⁵¹Eu Mössbauer spectra are shown in lower panel of Fig. 10. For parent compound, the Fe-SDW itinerant moments align along a direction and order antiferromagnetically in both a and c directions, while the Eu localized moments align along a direction and order antiferromagnetically in c direction only. The reduction of the Fe moments follows for x = 0.07 without changes of the 3d and 4f spins order directions. The further lowering of 3d moment by almost half for x = 0.10 results in the 4f spin reorientation.

EuNi₂As₂

Additionally, ¹⁵¹Eu Mössbauer spectra for compound with iron fully replaced by nickel, i.e. EuNi₂As₂, are shown in Fig. 11 and the hyperfine parameters are listed in Table 1. We used exactly the same EuNi₂As₂ single crystal sample (from the same batch) that was used in Ref.⁴⁷, only powdered for our use. This compound possess a tetragonal structure (space group I4/mmm with a = 4.1145 Å and c = 10.091 Å) at room temperature, similar to EuFe₂As₂, but without structural phase transition and magnetic ordering of the 3d transition metal (i.e. Ni). The neutron diffraction measurements of this sample⁴⁷ found that the Eu²⁺ moments form an incommensurate antiferromagnetic spiral-like structure below the Néel temperature of T_N = 15 K. They align ferromagnetically in the ab-plane and rotate spirally by 165.6° around the c-axis from layer to layer⁴⁷. It must be noted, however, that our ¹⁵¹Eu Mössbauer investigation indicates some canting of the europium moments out of the ab-plane and θ = 65(2)° was obtained. On the other hand, we note that ¹⁵¹Eu Mössbauer spectroscopy is not sensitive to the rotation of the Eu²⁺ moments around the c-axis in this case due to axially symmetric EFG in EuNi₂As₂ (c-axis is the main axis of the EFG) and, therefore, a spiral-like order of Eu²⁺ moments cannot be seen by this method. The EuNi₂As₂ was studied by ¹⁵¹Eu Mössbauer spectroscopy in the past⁴⁸, but unlike our results, negligible quadrupole interaction and some different value of the hyperfine field was reported⁴⁸.

Figure 11

The ¹⁵¹Eu Mössbauer spectra of EuNi₂As₂. The meaning of the symbols is the same as in Fig. 10. Description of the magnetic structure of this sample can be found in Ref.⁴⁷.

Conclusions

⁵⁷Fe Mössbauer measurements on EuFe_2−xNi_xAs₂ show that Ni doping monotonically suppresses the SDW ground state of itinerant magnetic moments and iron diamagnetism is achieved for x > 0.12, i.e. certainly for x = 0.20. While, ¹⁵¹Eu Mössbauer spectra indicate that Eu²⁺ magnetic moments order regardless of the Ni-substitution level. However, for the parent EuFe₂As₂ and for low Ni-substituted compounds up to about x ≤ 0.07, the localized 4f spins order perpendicular to the c-axis, whereas from about x ≥ 0.10, the magnetic ordering of europium changes from AFM to FM with the angle of deviation from the c-axis of about 30°. It seems that the FM order of Eu²⁺ spins causes the transferred hyperfine magnetic field sensed by ⁵⁷Fe nuclei. But, it should be noted that some transferred field was also detected for ⁵⁷Fe spectrum at the lowest temperature for x = 0.07, hence close to the range border of the europium AFM order. However, due to broad magnetic ⁵⁷Fe spectrum for x = 0.07 at 4.2 K, the transferred field may be somewhat doubtful for this compound and a hypothesis that mainly FM component of the Eu order is responsible for the transferred field seems reasonable. Another explanation that can possibly be proposed is some shielding effect, i.e. the disclosure of the transferred field only after a significant weakening of the iron SDW magnetism caused by the Ni dopant. Also note that Ni substitution in EuFe_2−xNi_xAs₂ reduces c lattice constant of the unit cell (see Fig. 1) and shortens the distance between the Eu planes, which can strengthens the coupling between them.

Based on these and previous results, it can be concluded that the 4f-Eu magnetism in the EuFe₂As₂-based systems is strongly affected by the magnetic behavior of the Fe-As layer. As long as Fe-plane remains unperturbed, for the parent EuFe₂As₂ and a low substituted compounds for which the 3d-SDW order is present, the Fe magnetic anisotropy pulls the Eu magnetic moment direction to be parallel to the ab-plane. On the other hand, a chemical substitution leads to a continuous suppression of the SDW ordering and for the sufficiently substituted compounds (specific to a particular substituent), when the Fe magnetism is strongly suppressed or absent, the direction of the Eu moments tend to turn parallel to the c-axis and the FM order is partly or fully achieved. The disappearance of the SDW changes the RKKY interaction and increases interplanar coupling which leads to a FM arrangement of the Eu moments. This rearrangement of the 4f spins as the result of the disappearance of the 3d spins magnetism proves a strong coupling between the magnetism of Eu²⁺ ions and the conduction electrons of [Fe_2−xNi_xAs₂]^2- layers. Additionally, the transferred magnetic hyperfine field with value of about 1 Tesla at 4.2 K from the magnetically ordered Eu sublattice to the Fe atoms is observed for substituted samples, but it is undetected for the parent and a low-substituted samples. This effect may result in competition between magnetism and superconductivity in EuFe₂As₂-based superconductors, because the Zeeman effect, which arises due to the FM order, strongly disfavors formation of the Cooper pair. However, as shown for many EuFe₂As₂-based compounds, this does not prevent the occurrence of superconductivity^10,39,40. Eventually, the reentrant effect in some cases was observed^19,20. Another effect is the anisotropic resistivity when the interplay between Eu-ferromagnetism and Fe-superconductivity causes zero resistance and diamagnetism only when the supercurrent flows within ab-planes, but in comparison, the out-of-plane resistivity does not go to zero³⁸.

When trying to answer the question posed in introduction of this article “why is EuFe_2−xNi_xAs₂ not a superconductor?”, it must be said that the phenomena seen by the Mössbauer spectroscopy and described above for this system are the same as for many other EuFe₂As₂-based superconductors. This indicates a similar magnetic structure regardless of whether the system is normal conducting or superconducting. Hence, the reason for the lack of superconductivity in EuFe_2−xNi_xAs₂ (at least above 1.8 K) is an open question.