Introduction

In the iron-based superconductors family1,2 EuFe2(As,P)23 and Eu(Fe,Co)2As24 offer an interesting experimental possibility to study the competition between the ferromagnetic (FM) and superconducting (SC) order parameters that can lead to nonuniform magnetic and SC states4,5,6,7 since the optimal superconducting critical temperature Tc ~ 28 K8 is comparable to the FM Eu2+-spin ordering temperatures TC ~ 18 K3,9.

The strength and nature of the coupling between the carriers in the FeAs planes, responsible for superconductivity and localized Eu2+ f-orbitals spins, responsible for ferromagnetism, is expected to influence strongly any possible magnetic as well as SC modulated state6. To enable coexistence of the singlet superconductivity with ferromagnetism in the case of strong exchange-interaction-dominated coupling the magnetization modulation period should be short on the lengthscale below the SC coherence length5,6, which is a few10,11 tens of nm in 122 iron based compounds. On the other hand, in the case of weaker long-range magnetic-dipole dominated coupling a longer lengthscale FM domain structure can effectively minimize the internal magnetic field enabling coexistence of the singlet superconductivity and FM state12. Alternatively a spontaneous SC vortex state6 might form as proposed recently13 for EuFe2(As,P)2.

In the literature opposing claims regarding the coupling between the carriers in the FeAs planes and localized Eu2+ spins exist. A weak coupling between Fe and Eu magnetic orders was initially suggested by Xiao et al.14, while recently a strong coupling was suggested from the in-plane magnetoresistance15 and NMR16.

The strength of the coupling between the carriers in the FeAs planes and localized Eu2+ f-orbitals spins should be reflected also in the energy transfer speed between the two subsystems upon photoexcitation. We therefore systematically investigated the ultrafast transient reflectivity (ΔR/R) dynamics and time resolved magneto-optical Kerr effect (TR-MOKE) in EuFe2(As1−xPx)2 in both, the undoped spin-density wave (SDW) and doped SC state. In addition to the relaxation components, that were observed earlier in related non-FM Ba(Fe,Co)2As2,17,18 we found another slow-relaxation component associated with Eu2+-magnetization dynamics. The relatively slow 0.1-1 nanosecond-timescale response of the Eu2+ spins to the optical excitation of the FeAs itinerant carriers indicates a rather weak coupling between the two subsystems suggesting the magnetic-dipole dominated coupling between SC and FM order parameters.

Moreover, the antiferromagnetic (AFM) Eu2+-spin order in the undoped SDW EuFe2As2, where the spins are aligned ferromagnetically in the ab plane with the A-type AFM order of the adjacent Eu2+ planes along the c axis, is rather well understood9,14. Contrary, no coherent picture of Eu2+-spin ordering upon P or Co doping exists. In addition to the proposal of a SC induced helimagnetic ordering4 in Eu(Fe,Co)2As2 a canted AFM was proposed by Zapf et al.19 in superconducting EuFe2(As1−xPx)2, while a pure FM ordering13 at x = 0.15 coexisting with superconductivity was reported by Nandi et al.13. A spin-glass state over the all P doping range was also suggested by Zapf et al.20 recently.

The observed time-resolved magnetooptical transients in the presence of an in-plane magnetic field reveal an additional coherent magnon response in the superconducting sample. The polarization dependence of the coherent magnon oscillations points towards a FM domain state consistent with results of Nandi et al.13.

Results

Temperature dependence of photoinduced reflectivity

In Fig. 1 a)–d) we show temperature dependence of the transient reflectivity (ΔR/R) measured with the probe pulses polarized in the ab-plane in undoped nonsuperconducting EuFe2As2 (Eu-122) and doped superconducting EuFe2(As0.81P0.19)2 (EuP-122). The transient reflectivity is anisotropic in the ab-plane, consistent with the orthorhombic crystal structure. We indicate the two orthogonal polarizations and according to the sign of the subpicosecond transient reflectivity. In addition to the anisotropic fast component associated with the SDW order discussed elsewhere21 we observe in both samples, concurrently with emergence of the Eu2+-spin ordering14,19, appearance of another much slower relaxation component with a risetime of ~ 1 ns in Eu-122 and ~ 100 ps in EuP-122 (at T = 1.5 K) and the decay time beyond the experimental delay range. The amplitude, A, of the slow component, corresponding to the long-delay extremum of ΔR/R shown in Fig. 2 is clearly correlated with the Eu2+ magnetic moment. In the vicinity of the Eu2+ magnetic ordering temperature a marked increase of the risetime is observed in both samples. In Eu-122 the slow component is rather anisotropic, while in EuP-122 it appears almost isotropic.

Figure 1
figure 1

Temperature dependence of the ab-plane transient reflectivity.

Photoinduced reflectivity transients at low-T in EuFe2As2 (a), (c) and EuFe2(As0.81P0.19)2 (b), (d) for two probe-photon polarizations. Inset to (c) represents a schematic of the probe beam configuration. and correspond to two orthogonal in-plane probe-photon polarizations.

Full size image
Figure 2
figure 2

Temperature dependence of the slow transient-reflectivity component amplitude.

The amplitude of the photoinduced reflectivity transients at long delays as a function of temperature in EuFe2As2, (a) and EuFe2(As0.81P0.19)2, (b), compared to the magnetic moment along the c-axis. and correspond to two orthogonal in-plane probe-photon polarizations while ZFC and FC correspond to cooling in the presence and absence of magnetic field, respectively.

Full size image

The probe-photon-energy dependence of the transients in Eu-122 is shown in Fig. 3. The dispersion of the fast component21 is much broader than that of the slow one, which shows a relatively narrow resonance around ~1.7 eV.

Figure 3
figure 3

Photoinduced reflectivity transients at low-T in EuFe2As2 as a function of probe photon energy for the polarization.

The spectral dependencies of the fast and slow response amplitude are shown as red and dark-grey lines, respectively.

Full size image

Metamagnetic transitions

Upon application of magnetic field lying in the ab-plane the Eu2+ AFM order in Eu-122 is destroyed above µ0H ~ 0.8 T in favor of an in-plane field-aligned FM state22,23,24. In EuP-122 a similar field-induced spin reorientation from the out-of-plane FM into the in-plane field-aligned FM state was observed around µ0H ~ 0.6 T13. These metamagnetic transitions have remarkable influence on the transient reflectivity as shown in Fig. 4. While the fast picosecond response associated with the SDW state21 shows virtually no dependence on the magnetic field, the slow response shows a marked change in the field-induced FM state13,22,23,24.

Figure 4
figure 4

In-plane magnetic field dependence of the transient reflectivity.

(a), (b) The reflectivity transients in EuFe2As2 with the magnetic field parallel to the polarization. (c), (d) The reflectivity transients in EuFe2(As0.81P0.19)2 with the magnetic field field paralel to the polarization. All transient were measured at T = 2 K, and 1.55-eV pump-photon energy. Insets show shematically magnetization reorientation in magnetic field.

Full size image

In undoped Eu-122 the -polarization slow response is suppressed above the metamagnetic transition [Fig. 4 (a)] and is magnetic-field independent above 2 T. Concurrently, for the polarization, which is parallel to the magnetic field, [Fig. 4 (b)] the slow response is first enhanced at low magnetic field above the transition, resembling a rotation of the anisotropy by π/2 and then slightly suppressed upon increasing the field to 7 T.

In EuP-122 the initially positive rather isotropic slow response [Fig. 4 (c), (d)] switches to a negative anisotropic one along the polarization, parallel to the magnetic field. Similar to Eu-122 the slow response is slightly suppressed at the highest field with a faster relaxation.

Coherent spin waves

In EuP-122 at low magnetic fields below ~ 0.5 T additional damped oscillations appear on top of the slow relaxation in ΔR/R [see Fig. 5 (a), (b)]. These oscillations appear rather isotropic. The amplitude of the oscillations, shown in Fig. 6 (d), is strongly peaked around ~ 0.25 T and vanishes at 0.5 T. The frequency of the oscillations, as determined by a damped oscillator fit, ΔRosc/R = Aosc exp(−t/τ) cos(ω0t), shown in Fig. 6 (a), is H independent at low fields and starts to decrease with increasing field above µ0H ~ 0.3 T. The damping, on the other hand, is magnetic-field independent at τ−1 ~ 10 GHz.

Figure 5
figure 5

(a), (b) The reflectivity transients in EuFe2(As0.81P0.19)2 in low magnetic fields at T = 2 K, and 1.55-eV pump photon energy. Transient Kerr ellipticity, (c), (d) and rotation, (e), (f), upon reversal of the magnetic field at T = 1.5 K and . Odd and even part of the responses correspond to the difference an the sum of the responses measured at different signs of the magnetic field, respectively.

Full size image
Figure 6
figure 6

(a) The oscillatory part of the isotropic ΔR/R component in EuFe2(As0.81P0.19)2 at low magnetic fields, and 1.5-eV pump photon energy. Thin lines represent the damped oscillator fits discussed in text. The frequency (b), decay time (c) and amplitude (e) of the oscillations as functions of the magnetic field. The points (open symbols) at B = 0.15 T were obtained from the polarization fit due to the lack of data at the polarization. The red squares were obtained from TR-MOKE fits. The lines in (b) are uniaxial ferromagnet25 fits discussed in text. The inset to (a) schematically shows magnetization precession in small magnetic fields with corresponding projections onto the z-axis.

Full size image

Another oscillation with a higher frequency (~ 14.5 GHz at 0.3 T) is revealed by the transient magnetooptical Kerr effect (TR-MOKE) shown in Fig. 5 (c)–(f). The oscillatory part of the transient rotation and ellipticity is polarization independent and almost even with respect to the reversal of magnetic field.

Discussion

Eu2+ ions have [Xe]4f76s2 (8S7/2) electronic configuration. The lowest excited states of a free Eu2+ ion are ~ 3.5 eV above the ground state26. In oxides, however, this splitting can be reduced down to ~ 1 eV26,27. In Eu-122 the position of f-derived states was calculated to be ~ 2 eV below the Fermi energy28, close to the observed Eu2+-spin ordering related slow-component resonance around 1.7 eV [see Fig. 3 (b)]. It is therefore plausible that the coupling of the Eu2+ magnetism to the dielectric constant at the probe photon energy of 1.55 eV is through the resonant magneto-optical Cotton-Mouton effect with the location of the Eu2+-4f states ~ 1.7 eV below the Fermi level.

On the other hand, a large magnetostriction is indicated from the realignment of the crystal twin domain structure in magnetic field23, suggesting a possibility of the indirect contribution to the optical dielectric function through the magnetoelastic effect. The rather narrow probe-photon-energy resonance of the slow component does not support this mechanism.

We should also note that the realignment of the twin domain structure23 was not observed in our experiment, since the anisotropy of the fast component, which is associated with the structural twin domains18, shows no dependence on magnetic field in both samples (see Fig. 4) up to µ0H = 7 T. Moreover, the realignment of the twin domain structure observed in Ref. 23 might be related to the Fe spin ordering as indicated by observation of a partial magnetic field detwinning also in non-ferromagnetic Ba(Fe1−xCox)2As229.

The strong in-plane anisotropy of the slow component in Eu-122 indicates that the response corresponds to the dynamics of the in-plane component of the sublattice Eu2+ magnetizations. The presence of qualitatively same response in the in-plane field-aligned FM state suggests that the observed slow dynamics is not dominated by the orientational dynamics of the AFM sublattice magnetizations, but rather by the longitudinal dynamics of the individual sublattice magnetizations. The response can therefore be associated with a decrease of the Eu2+ magnetization upon photoexcitation in both, the zero-field AFM and the field-induced in-plane FM state.

To understand the change of the anisotropy between weak and strong magnetic fields in EuP-122 let us look at the symmetric part of the in-plane dielectric tensor components . Within the orthorhombic point symmetry can be expanded in terms of magnetization to the lowest order as:

with i ∈ {x, y}. Here M would correspond to the Eu2+ sublattice magnetization in the case of a canted AFM ordering, or the total Eu2+ magnetization in the case of FM ordering. In EuP-122 in low magnetic fields M is predominantly oriented along the c-axis13,30 leading to the nearly isotropic response, since axxzz ~ ayyzz due to the small orthorhombic lattice distortion. In the field-induced FM state and the zero-field AFM state of Eu-122 M lies in the ab-plane leading to an anisotropic response since it is quite unlikely that aiiii ~ ajjii, with i ≠ j.

The photoinduced Eu2+ demagnetization is therefore slow, on a nanosecond timescale in Eu-122 and a ~ 100 ps timescale in EuP-122. It can not be due to a direct emission of incoherent Eu2+ magnons by the eV-energy photoexcited Fe-d-bands electron-hole pairs since it has been shown, that in the case of iron-based pnictides in the SDW state the Fe-d-bands quasiparticle relaxation occurs on a picosecond timescale21,31,32 and goes through emission of Fe-d-spin magnons21 followed by relaxation to phonons. It can therefore be assumed that the Fe-d-bands quasiparticle and lattice degrees of freedom are fully thermalized beyond ~ 10 ps when the slow component starts to emerge. This suggests that the energy transfer from the excited quasiparticles in the Fe-d bands to the Eu2+ magnons is rather inefficient. The incoherent Eu2+ magnons are therefore excited indirectly via the spin-lattice coupling only after the initial excitation energy was thermally distributed between the Fe-d-bands quasiparticles and phonons. The Eu2+ spins therefore appear only weakly coupled to the Fe-d-bands quasiparticles with the coupling increasing with the P doping. The rather large in-plane magnetoresistance observed by Xiao et al.15 in Eu-122 can therefore be attributed to slow magnetostriction effects modifying the lattice twin domain structure.

The light penetration depth at the probe-photon energy of ħωpr = 1.55 eV is ~ 27 nm33, while the beam diameters are in a 100 µm range. Irrespective of the excitation mechanism, which can be either nonthermal impulsive34 inverse Cotton-Mouton effect or thermal displacive non-Raman35 like, it can be assumed that the relevant wavevectors are and dominantly a uniform coherent magnetization precession is excited and detected. (In the case of helical magnetic order with the propagation vector q0, spin waves at q = ±mq0, , also need to be considered36.)

The low frequency mode observed in the transient reflectivity response softens with increasing temperature and vanishes in the field induced in-plane FM state so it can definitely be assigned to a magnetic mode. The high frequency mode has also a magnetic origin since it appears in the TR-MOKE configuration only.

Analyzing contributions of the magnetization displacements, δMi, to the symmetric part of the optical response it follows from (1),

The low-frequency mode is very strong in ΔR/R and rather isotropic in the ab-plane indicating that is either associated with the out of-plane terms (i) 2aiizzMzδMz or (ii) both, Mx and My, are finite such as in the case of a helimagnetic ordering. In the latter case the local magnetization needs to be considered since the average of the terms <MiδMi>, i ∈ {x, y}, over Eu2+ planes is finite despite <Mi> = 0. Concurrently, it is weak in the TR-MOKE configuration, which is sensitive to δMz. Since δMz ≠ 0 for both (i) and (ii) (see Supplemental information for case (ii)) this indicates that the measured volume is composed from the “up” and “down” magnetic domains magnetized along the c-axis. The sign of δMz varies in different magnetic domains leading to a vanishing TR-MOKE response averaged over many magnetic domains, while the sign of MzδMz does not depend on the domain orientation and averages to a finite value.

For the high-frequency mode observed in the TR-MOKE configuration, on the other hand, the averaged δMz is finite while the averaged MzδMz is rather small in comparison to the low frequency mode. This indicates that in addition to the c-axis magnetized domains in-plane magnetized regions exist with Mz ~ 0. The in-plane magnetization leads to an out of plane magnetization displacement with δMz ≠ 0 and MzδMz ~ 0, consistent with the observed magnetic field dependence of the mode frequency. The invariance of the oscillatory TR-MOKE response [see. Fig. 5 (c)–(f)] with respect to the inversion of the magnetic field is also consistent with the in-plane magnetization orientation.

A fit of the frequency magnetic-field dependence [see Fig. 6 (b)] using the standard uniaxial ferromagnet formula for a parallel magnetic field25 ignoring demagnetization factors, ω = γab(Hab + H), yields µ0Hab = 0.3 T and γab/µ0 = 182 GHz/T. The obtained gyromagnetic ratio gab = 2.06 is consistent with 8S7/2 state of Eu2+ ions. The absence of demagnetization factors suggests that the response does not originate from the domain walls between the c-axis oriented domains but rather from planar shaped domains. Due to surface sensitivity (~ 30 nm) of the optical probe these are very likely surface domains, however, the bulk nature of these domains can not be entirely excluded.

The observed behaviour is compatible with the simple ferromagnetic order (within the domains) proposed by Nandi et al.13. In the absence of the in-plane magnetic field the static magnetization in the c-axis domains is along the c-axis and δMz = 0, consistent with the vanishing amplitude of the low frequency mode near the zero field. Upon application of the in-plane magnetic field the magnetization is tilted away from the c-axis (see inset to Fig. 6) leading to a finite δMz and the observed decrease of the mode frequency25. The decrease of the transient-reflectivity amplitude, when approaching to the metamagnetic transition, can be associated with the vanishing Mz.

A fit of the frequency magnetic-field dependence using the standard uniaxial ferromagnet formula for the perpendicular magnetic field25 ignoring demagnetization factors, , results in µ0Hc = 0.52 T and γc/µ0 = 119 GHz/T. The small value of γc leading to a small gyromagnetic ratio (gc = 1.35) can be attributed to the ignored unknown demagnetization factors of the c-axis magnetized domains. Moreover, it suggests that the c-axis magnetized domains have a flat shape with the normal perpendicular to the c axis.

On the other hand, the presence of two distinct modes and the magnetic field dependence of the mode frequencies [see Fig. 6 (b)] resembles the standard uniaxial AFM cases with the magnetic field perpendicular to the easy/hard axis25,37 indicating a possible canted AFM19 (CAFM) order. The polarization dependence of the modes is, however, not compatible with the CAFM picture since both, the quasi-AFM mode38 and the quasi-FM mode, contribute to δMz (see Supplemental) and should, contrary to the observations, contribute concurrently to the transient reflectivity and the TR-MOKE with identical relative amplitudes.

In the case of the conical helimagnetic ordering4,30,39 the in-plane isotropy naturally appears for certain modes (see Supplemental). However, since, as in the case of the CAFM state, contributions of more than one magnetic mode to δMz are expected, our data do not support the conical helimagnetic ordering.

In conclusion, our data point towards the simple FM Eu2+-spin order in superconducting EuFe2(As,P)2 proposed by Nandi et al.13. The observed weak coupling between the FeAs-plane quasiparticles and Eu2+ spins indicates a weak magnetic-dipole dominated coupling between the SC and FM order parameters. This indicates that the coexistence of the singlet superconductivity with ferromagnetism in EuFe2(As1−xPx)2 is possible without necessity of the magnetic structure modulation on the lengthscale shorter than the SC coherence-length. The presence of the FM domain structure on longer lengthscales, which is inferred from the coherent-spin-wave response, might additionally contribute to stability of the coexisting state.

Methods

Sample preparation

Single crystals of EuFe2(As1−xPx)2 were grown by a flux method, similar to a previous reports21,40 The out-of-plane magnetic susceptibilities shown in Fig. 1 are consistent with previous results20,22. From the susceptibility we infer Eu2+ spin ordering temperatures TN = 19 K and TCur = 17.6 K in EuFe2As2 (Eu-122) and EuFe2(As0.81P0.19)2 (EuP-122), respectively. EuP-122 also shows the onset of superconductivity at Tc = 22.7 K.

Optical measurements

Measurements of the photoinduced transient reflectivity, ΔR/R, from ab facets of freshly cleaved samples at nearly normal incidence were performed using a standard pump-probe technique, with 50 fs optical pulses from a 250-kHz Ti:Al2O3 regenerative amplifier seeded with an Ti:Al2O3 oscillator18. We used the pump photons with both, the laser fundamental () and the doubled () photon energy and the probe photons with the laser fundamental () photon energy.

Magnetooptical measurements

Transient Kerr rotation, ΔϕK, was also measured on ab facets of freshly cleaved samples at nearly normal incidence by means of a balanced detector scheme using a Wollaston prism and a standard homodyne modulation technique in a 7-T split-coil optical superconducting magnet. To measure the transient Kerr ellipticity, ΔηK, a π/4-waveplate was inserted in front of the Wollaston prism. In order to minimize the pollution of the Kerr signals with the photoinduced reflectivity signal the detector was carefully balanced prior to each scan.