Local magnetic behavior of 54Fe in EuFe2As2 and ...

Local magnetic behavior of 54 Fe in EuFe2 As2 and Eu0.5 K0.5 Fe2 As2 : Microscopic study using time differential perturbed angular distribution (TDPAD) spectroscopy S.K. Mohanta,1 S.N. Mishra,1 S.M. Davane,1 S. Layek,2 and Z. Hossain3 1

Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400005, India 2 Department of Physics, Indian Institute of Technology, Kanpur-208016, India (Dated: April 30, 2013)

We report time differential perturbed angular distribution measurement of 54 Fe on a polycrystalline EuFe2 As2 and Eu0.5 K0.5 Fe2 As2 . The hyperfine field and nuclear spin-relaxation rate are strongly temperature dependent in the paramagnetic state suggesting strong spin fluctuation. The local susceptibility show Curie-Weiss like temperature dependence and Korringa like relaxation is observed in the tetragonal phase indicating the presence of local moment. In the orthorhombic phase, the hyperfine field behaviour suggesting quasi two dimensional magnetic ordering. The experimental results are in a good agreement with first principle calculations based on density functional theory. PACS numbers: 75.20.Hr;74.70.Xa;74.25.Jb

I.

INTRODUCTION

EuFe2 As2 is a peculiar member of the ternary iron arsenides having chemical formula XFe2 As2 (X = Ca, Ba, Sr, Eu),1 since the X site is occupied by Eu2+ which is a s state ( L = 0) rare-earth ion possessing 4f7 state.12 It menifests a structural phase transition from high temperature tetragonal to low temperature orthorhombic phase at 190 K as well as concomitant anti-ferromagnetic and/or spin density wave (SDW) magnetic phase transition.8 Partial substitution of the X site with alkali metals or the Fe site with transition metals also induce superconductivity with suppressed magnetic and structural phase transition.1,8 Furthermore, application of pressure also induces superconductivity in these materials.13–15 These results suggest that superconductivity in these class of materials is intimately linked with structural as well as magnetic degrees of freedom. It is now widely believed that AFM spin fluctuations play an important role in pairing mechanism.16 In this regard, it is important to understand the magnetism of Fe, above and below the structural transition. Although magnetic properties has been studied up to a large extent using techniques like neutron diffraction, M¨ ossbauer and NMR, the detail behavior is still unclear. Neutron diffraction measurements show first order antiferromagnetic ordering with Fe atom carrying a moment of ≈ 0.8 µB .17 NMR measurements in these kind of compounds also reveals a single frequency below TN .18,19 On the other hand recent M¨ ossbauer and time differential perturbed angular distribution measurements on CaFe2 As2 yield multiple hyperfine components indicating a wide variety variation of the Fe moment.20,21 As far the tetragonal phase is concerned, whether the Fe atoms carry a local moment or not is still a mystery. Determination of Fe moment in the tetragonal (paramagnetic) phase and its behaviour is yet to be unveiled. Although M¨ ossbauer measurements in external magnetic field can provide information on Fe local moment in paramagnetic state, such a study has not done so far. Furthermore, the calculated Fe moment from density functional theory is always larger compared to experimental

values. In view of these multifaceted magnetic behavior and diversity in available results, further microscopic investigations are desirable. Time differential perturbed angular distribution (TDPAD) technique is a very sensitive tool to study magnetic interaction in very short length and time scale and have been successfully applied to study static and dynamic magnetic interactions in a variety of solids from decades. We have applied the TDPAD spectroscopy to study the magnetic properties of EuFe2 As2 and Eu0.5 K0.5 Fe2 As2 . The local susceptibility measured in the paramagnetic region shows a Curie-Weiss temperature dependence reflecting a local Fe moment ≈ 1.3 µB . Below the magnetic phase transition (orthorhombic phase) we observed two hyperfine fields components with distinctly different field. The experimental results are supported by ab initio calculations based on density functional theory.

II.

EXPERIMENTAL DETAIL

Polycrystalline samples of EuFe2 As2 and Eu0.5 K0.5 Fe2 As2 were synthesized by solid state reaction method as described in ref. 7. Phase purity and composition of the samples were checked by x-ray diffraction and energy dispersive x-ray analysis (EDAX). TDPAD experiments were performed on a pellet of 10 mm diameter and 0.5 mm thickness obtained by griding and pressing the sample. The TDPAD experiments were performed at 14UD Pelletron accelerator facility at TIFR, Mumbai. The magnetic response of Fe atoms in the EuFe2 As2 and Eu0.5 K0.5 Fe2 As2 hosts were studied via the hyperfine interaction of 10+ isomeric state of 54 Fe nucleus (T1/2 = 360ns, gN = 0.728(1) and nuclear quadrupole moment Q = 0.29(4)).22 Because of the long half life and high g-factor, TDPAD measurements with 54 Fe provides much better sensitivity compared to 57 Fe. The probe nuclear state was produced via the reaction 45 Sc(12 C, p2n)54 Fe using 40 MeV pulsed 12 C beam. The 54 Fe nuclei recoiling out of the thin Sc target foil were implanted inside the hosts at a concentration

2 well below 1 ppm. Measurements were performed within a time window of 10 ns to 2 µs immediately after implantation. These experimental condition ensures negligible impurity-impurity interaction and the results reflect the magnetic response of truly isolated impurity. Observations were made in the temperature range of 5-300 K in a transverse applied magnetic field of 1 Tesla. The PAD time spectra were recorded using four high-purity Germanium detectors (HPGe) placed at ±450 and ±1350 with respect to the beam direction. The time resolution was ≈ 5 ns for Eγ 500 keV. From the normalized coincidence counts, N(±1350 , t), of each detectors the ratio function R(t) =

N (+θ, t) − N (−θ, t) N (+θ, t) + N (−θ, t)

(1)

were generated and fitted to the function R(t) = (3/4)A22 e−λt sin(2ωL t − ϕ)

(2)

to extract the Larmor precession frequency ωL and damping factor λ. Here A22 is the anisotropy of the angular distribution pattern and ϕ is the phase factor arising from finite bending of the incoming beam due to applied field. Using the relation ωL = (gN µN Bef f /¯ h), one could calculate the effective magnetic field Bef f = Bext -Bhf and hence the hyperfine field, Bhf at a nuclear probe site. For paramagnetic systems, the Bhf is proportional to the external field and the ratio β = Bef f /Bext gives a measure of the local susceptibility χloc of the probe. The details of TDPAD can be found elsewhere.23,24

III.

RESULTS AND DISCUSSION

Figure 1 shows the typical spin rotation spectra R(t) of Fe in EuFe2 As2 and Eu0.5 K0.5 Fe2 As2 ranging from 5 K to 300 K. The R(t) spectra show high anisotropy and well defined oscillations at all measured temperature ranges indicating that 54 Fe comes to rest at unique lattice site in the host, probably substitutional site due to the compact symmetry of the ThCr2 Si2 structure. The geometry used in our experiment, presence of weak quadrupole interaction, if any, at most will give rise to an increased damping of the R(t) but would not have serious influence on the accuracy of ωL values extracted. The spectra measured for the parent host above 200 K could be fitted with a single frequency with amplitude close to to the full anisotropy (A22 = 0.13) observed in liquid metals. Near the phase transition (180 < T < 205), the R(t) spectra show beat patterns indicating superpositions of two or more frequencies. Fourier transform of the time spectra show two well defined frequencies with relative amplitudes 70 % and 30%. The majority comonent show large hyperfine field (Bhf ), steeply varying with temperature, while, the minority component show much smaller Bhf . Below 180 K the Bhf value for the majority comonent becomes quite large resulting very fast precession, 54

FIG. 1. Spin rotation spectra for 54 Fe in EuFe2 As2 and Eu0.5 K0.5 Fe2 As2 at different temperatures and an transverse external field of 1 Tesla.

compared to the time resolution of our setup. Combined with damping due to spin relaxation rate, the amplitude attenuated significantly. Thus at low temperatures (below 170 K) we again observe sigle frequency with 30% of the total amplitude. The possibilities of multiple hyperfine fields have been discussed in many papers.21,26 . The spectra of the doped sample on the other hand show a single frequency throughout the temperature range of measurements confirming no phase transition. Figure 2 shows the temperature dependence of the inverse of local susceptibility in the paramagnetic region. The measured local susceptibility χloc (β - 1) data could be fitted to the Curie-Weiss (CW) law above 200 K: χloc = C/(T+θp ), where the Curie constant C = gµB (S+1)B(0)/3KB provides a measure of the Fe magnetic moment, µF e = gS. B(0) is the magnetic hyperfine field at T = 0 and S is the effective spin on Fe. The Curie constant for the parent compound estimated to be C = 11(4)K and θp = -30 K. The data also indicate the negligible contribution from orbital contributions. Using B(0) =-100 kG, taken from M¨ ossbauer measurements27 and ab initio calculations as discussed below, the mag-

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FIG. 2. Inverse of local susceptibility (1/β-1) as a function of temperature.Circles and trangles are data obtained for parent and doped compound. Filled and open symbols correspond to the minority and majority component discussed in text.

netic moment in the paramagnetic tetragonal phase is estimated to be ≈ 1.3 (2)µB , expectedly small compared to Fe moment, suggesting large spin fluctuation. This experimental observation is also consistent with density functional calculations discussed below. The negative θp value derived from CW fit is consistent with antiferromagnetic interaction between Fe moments. Below 190 K local susceptibility drops suddenly due to the structural (magnetic) phase transition. We now discuss about the hyperfine field and magnetic moment of Fe below the phase transition. As discussed above, close to TN , the magnetic response of Fe shows two hyperfine field components. The Bhf values for both the components come out to be negative. Fig. 3 shows the temperature dependence of hyperfine fields. For the majority component, the Bhf values increases rapidly below 190 K, indicating the first order nature of magnetic transition. Below 180 K the majority component becomes too large, thus making the precession much faster and limiting us to measure in experimental time resolution limit. In contrast, the minority component comes out to be much smaller, whose value at 15 K was found to be 0.30 T. Both the hyperfine field components at the onset of antiferromagnetic order could be fitted to a simple power law dependence Bhf (T) = Bhf (0)(1T/TN )β , yield a critical exponent β = 0.23(2) (explicitely not shown, see ref Mohanta). The critical exponents extracted from our data suggest quasi two dimensional magnetic ordering of Fe moments in EuFe2 As2 is in agreement with the recent MS and NMR measurements.18,21 The nuclear spin-lattice relaxation rate (τN ) is very sensitive to the electron density at Fermi level (EF ). Fig. 4 shows τN , obtained from the nuclear damping as a function of temperature. At high temperature T>TN , τN follows linearly with temperature, i.e. Korringa-type behavior as expected in metallic systems and may reflect the coupling of the nuclei to the conduction electrons.18,19

FIG. 3. Hyperfine field as a function of temperature. Solid circles below 200 K reprsent the low field component (see text) and the hollow circles, the high field component

FIG. 4. Nuclear spin relaxation time τN with temperature. The solid line above 200 K is liner fit reflecting Korringa like behaviour.

With decreasing temperature τN decreases. The high value of spin relaxation rates imply strong hybridization between Fe-d and ligand orbitals, which also supports the small moment observed from Curie-Weiss fit. In an attempt to explain the experimental results, we present ab initio density functional theory (DFT) study of the magnetic moment and hyperfine field (Bhf ) and electric field gradient (Vzz ) at Fe site on both phases. We have chosen the experimental lattice parameters.29 The calculations were performed using full potential, all electron, spin polarized electronic structure calculations utilizing the augmented plane wave (APW)+local orbital (lo) method within the WIEN2K code.30 For exchange correlation potential, we used generalizedgradient approximation (GGA) in the Perdew-BurkeErnzerhoff (PBE) scheme.31 The muffin-tin radii for Eu, Fe and As were selected as 2.5 a.u., 2.3 a.u and 2 a.u respectively achieving convergence for a cutoff value of

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FIG. 5. Density of states in different configurations: (a) TPM (b) T- FM (c) T-AFM (d) O-FM (e) O-AF1 (f) black-OAF2a, pink-O-AF2b. All the cases represents the d-density except for the case a; where it represents the total density.

RMT KMAX = 9.0. All atoms are fully relaxed until the change in energy upon ionic displacement was less than 0.1 meV. Adequate K point sampling in the irreducible wedge of the Brillouin zone was checked and the convergence in energy, charge and force criteria are set to be 0.01 mRy, 0.0001 and 1 mRy/˚ A respectively. Let us first discuss the magnetism and hyperfine fields of Fe in tetragonal phase of EuFe2 As2 . Here we first address the question: Do Fe atoms in tetragonal phase have local moment? Within band-structure theories, the existence of local moment is mainly governed by Stoner criterion INl (EF )≥ 1 where, I is the Stoner exchange parameter and Nl (EF ) is paramagnetic local density of states (LDOS) at the Fermi energy EF on a per atom of Fe per spin basis. Taking I = 0.9 eV for Fe,32 the Fe atoms are expected to develop a local moment only if the density of states at EF is higher than 1.08 states/eV-atom. Fig 5.a shows the non-spin polarized LDOS of Fe in tetragonal phase with the lattice parameters at 250 K taken from Ref. 27. The LDOS come out to be much larger than the Stoner limit, justifying the Curie-Weiss behavior. The large exchange splitting for the spin polarized DOS (See Fig. 5b) further supports the result. In both the PM and AFM states the dxz and dyz remain degenerate and the energy difference between PM, FM and AFM states are less than 0.5 mRyd, suggesting the system is close to magnetic instability and possible spontaneous symmetry breaking on lowering the temperature.33,34 The moment values obtained for AFM and AFM come out to be 2

µB and 1.4 µB respectively while, ferromagnetic hyperfine field come out to be -135 kG. Spin fluctuations in tetragonal phase likely to be large, making Fe moment unstable. Next we discuss the magnetic moment and hyperfine field of Fe calculated in orthorhombic phase. AF234 is the most stable configuration in orthorhombic phase. The Fermi level (EF ) lies on the edge of the of a peak in the density of states (DOS). In either AFM phase, the Fe majority states are more or less completely filled; thus, the moment is determined by occupation of the minority states. The calculated magnetic moment and hyperfine field come out to be 2 µB and -130 kG (mainly coming from the core contributions). AF1 is the next stable configuration, where we observed a reduced moment of 1.4 µB , and a hyperfine field of -33 kG. The observed experimental moment is much smaller compared to calculated value, which we tentatively ascribe to strong paramagnetic fluctuation. From the results of tetragonal and Orthorhombic phases, one can draw a conclusion that magnetic moment should be present at all times in undoped case.33,34 It is clear from experimental results and ab initio calculations that, moment should present in the paramagnetic region. Then a natural question arises why it has not been observed in experiments like NMR, M¨ ossbauer and bulk magnetization measurements ? As spin-fluctuations are expected to be large in these systems, the above mentioned experiments see only the time average. While, TDPAD is site specific and can see each of the excited states. Though muon-spin rotation measurement can observe these possibilities, we did not come across such a measurement in the paramagnetic region. Our results are also consistent with the multiple hyperfine field components of recent M¨ ossbauer measurements.20,26 The power law behavior showing quasi two dimensional nature of magnetism. As it is evident that spin fluctuations are present also in doped superconducting compound, and may be playing a vital role in superconducting pairing.

IV.

CONCLUSION

In summary, a systematic measurement of hyperfine field employing TDPAD technique has been carried out using 54 Fe as probe. We confirm the existence of magnetic moment above TN and the fact that the local susceptibility follows a Curie-Weiss like temperature dependence. In the orthorhombic phase the spin rotation spectra show rwo hyperfine field components, both exhibiting quasi two dimensional first order magnetic transition at TN ≈ 190 K. The TDPAD measurements reported here, especially on this ferro-pnictide, EuFe2 As2 compound is an excellent tool to have an insight into the microscopic properties in atomic environment. We emphasize that the spin fluctuations are inherent in these compounds and may possibly be playing an important role in superconducting pairing. The results reported here, are com-

5 patible with M¨ ossbauer and NMR measurements. The basic feature of the hyperfine field measured here is anal-

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