57 Fe Mössbauer study of new multiferroic AgFeO 2

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1 Hyperfine Interact DOI /s Fe Mössbauer study of new multiferroic AgFeO 2 I. Presniakov V. Rusakov A. Sobolev A. Gapochka M. Matsnev A. A. Belik Springer Science+Business Media Dordrecht 2013 Abstract The present work reports results of the 57 Fe Mössbauer measurements on AgFeO 2 powder sample recorded at various temperatures including the points of both magnetic phase transitions. The 57 Fe Mössbauer spectra of AgFeO 2 measured in the paramagnetic range (T > T N1 ) consist of one quadrupole doublet with rather high quadrupole splitting of 300K = 0.66 ± 0.01 mm/s for Fe 3+ ions. In order to predict the sign of electric field gradient (EFG) at 57 Fe nuclei, we calculated the lattice contribution to the electric field gradient (EFG) at 57 Fe nuclei, which emphasized the importance of the dipolar contributions, with resultant oxygen polarizabilities in the range of α O = 0.83 Å 3, in agreement with the results obtained previously for other delafossite-like oxides. In the temperature range of T N2 <T <T N1,Mössbauer spectra gave clear evidence for the existence of a distribution of the hyperfine magnetic fields H hf at 57 Fe nuclei. We present the results of a model fitting of the spectra based on an assumption of the cycloid magnetic structure of AgFeO 2 at T < T N2. The obtained data were analysed in comparison with published data on Mössbauer studies of oxide multiferroics. Keywords Mössbauer spectroscopy Multiferroics Frustrated magnetic interactions Iron oxides Non-collinear spin configurations Proceedings of the 32nd International Conference on the Applications of the Mössbauer Effect (ICAME 2013) held in Opatija, Croatia, 1 6 September 2013 I. Presniakov ( ) V. Rusakov A. Sobolev A. Gapochka M. Matsnev M. V. Lomonosov Moscow State University, Moscow, Russia ipresniakov@rambler.ru A. A. Belik International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki , Japan

2 I. Presniakov et al. 1 Introduction AgFeO 2 ferrite with a quasi-two-dimensional delafossite structure presents an opportunity to study the effects of geometrical spin frustration in triangular lattice of antiferromagnetic systems [1, 2]. The lattice of this oxide, having rhombohedral space group R3m at room temperature, consists of Fe 3+ hexagonal layers along the c h axis, which are separated by intervening two layers of oxygen and one layer of Ag + ions with linear coordination. This ferrite exhibits two successive magnetic phase transitions at T N1 14 K and T N2 9K [3, 4]. Below T N1 the paramagnetic AgFeO 2 phase turns to be the sinusoidally modulating partially disordered states (PD) [3, 4]. The recent neutron diffraction experiments [4] have shown that the magnetic ordering in AgFeO 2 (T T N2 ) exhibits elliptical cycloid with the incommensurate propagation wave vector Q = ( 1/2,q,1/2) m, q It was concluded [4] that the resulting ferroelectric polarization in AgFeO 2 is perpendicular to the monoclinic b axis and is driven by the inverse Dzyaloshinskii-Moriya mechanism [4]. It should be noted that many issues including those related to the nature of the magnetic ordering of this ferrite in the T N2 <T <T N1 region and driving forces of the both phase transitions observed are still a subject of numerous discussions. In this work, we present the results of the first Mössbauer study of ferrite AgFeO 2.The spectra of 57 Fe nuclei were measured in a wide range of temperatures including the points of both magnetic phase transitions (at T N1 and T N2 ). The profile and parameters of the hyperfine magnetic structure of 57 Fe spectra were shown to experience significant changes when the type and character of spin ordering of the iron sublattice change. We present the results of a model fitting of spectra based on an assumption of the cycloid magnetic structure of AgFeO 2 at T < T N2 [4]. The obtained data are analysed in comparison with published Mössbauer data for oxide multiferroics CuFeO 2 [5 9], CuFe 1 x Ga x O 2 [10]and BiFeO 3 [11]. 2 Experimental The powder AgFeO 2 sample was synthesized by the solid-state reaction method as described elsewhere [3]. For Rietveld refinement Jana 2006 software package was used. Analysis of the powder diffraction data shows that the obtained compound crystallizes in the rhombohedral structure (space group R3m). The refined unit cell parameters a h = b h = (2) Åandc h = (1) Å are in good agreement with literature data [3, 4]. The 57 Fe Mössbauer spectra were recorded at K using a conventional constantacceleration spectrometer. The radiation source 57 Co(Rh) was kept at room temperature. All isomer shifts refer to the α-fe at RT. The experimental spectra were processed and analyzed using methods of model fitting and reconstruction for distribution hyperfine parameters corresponding to partial spectra implemented in the SpectrRelax program [8]. 3 Results and discussions The Mössbauer spectrum of AgFeO 2 measured in the paramagnetic temperature range at T = 300 K (Fig. 1a) consists of a single quadrupole doublet with an isomer shift δ = ± mm/s that corresponds to high-spin Fe 3+ ions in an octahedral oxygen environment [12]. The presence in the spectrum of a single doublet with narrow components (Ɣ = ± mm/s) is an indication that at T > T N1 all Fe 3+ ions occupy in

3 57 Fe Mössbauer study of new multiferroic AgFeO 2 V contributions (e/a 3 ) el (mon + dip) (1-R)V + (1-γ )V el (1-R)V mon (1-γ )V dip (1-γ )V Dipole Total Experimental Electronic Monopole Δ(mm/s) a Polarizability (α Ο ) for O 2- (Α 3 ) b Fig. 1 a 57 Fe Mössbauer spectrum of AgFeO 2 recorded at T = 300 K (T >> T N1 ). The solid line is the result of( simulation of the) experimental spectra as described in the text. b Dependences of partial contributions V mon,vdip,vov to the total EFG and quadrupole spitting calc versus the oxygen polarizability (α o ) in the AgFeO 2 structure the ferrite structure equivalent crystallographic positions. The high quadrupole splitting of the doublet = ± mm/s shows that the 57 Fe nuclei are located in crystal positions with a strong electric field gradient (EFG). This result seems to be rather unexpected since octahedral polyhedrons (FeO 6 ) in the structure of AgFeO 2 ferrite are characterised by nearly zero value of distortion parameter d [13]. We calculated the main component V of the EFG tensor using crystallographic data for the AgFeO 2 ferrite [13]. The obtained results show that, in addition to the monopole lattice contribution ( V mon ) that usually dominates in case of high-spin Fe 3+ ions with a spherically symmetric d 5 shell, large weight is also attributable to the dipole ( ) contribution that parametrically depends on the polarizability of oxygen ions (α) and to the electronic contribution ( V) ov related to overlapping of (ns, np, 3d)Fe and (2s, 2p) O orbitals [14]: { V = (1 γ ) V mon + V dip } V dip + (1 R)V ov, (1) where γ = 9.1 andr = 0.32 [14] are Schterheimer s antishielding and shielding factors. Calculated dependence of the dipole contribution V dip as a function of the polarizability of oxygen anions (α O ) in the AgFeO 2 structure shown in Fig. 1b. The best agreement between the theoretical and experimental values of quadrupole splitting = eqv /2 was found for the polarizability α O 0.83 Å 3 (for nominal charges Z O = 2, Z Ag =+1, and Z Fe =+3and the quadrupole moment of the 57 Fe atom nucleus of Q = 0.15 barns [15]). The obtained high value of α O agrees well with the data for other oxides possessing the delafossite structure [16]. The calculations show that the principle V component of the EFG tensor is directed along the c h axis of the hexagonal AgFeO 2 unit cell.

4 I. Presniakov et al. Below T < T N1, a complex magnetic structure appears in the Mössbauer spectra (Fig. 2) indicating the existence of a continuous distribution of hyperfine magnetic fields H hf at 57 Fe nuclei. At the first stage of the analysis of this series of the spectra, distributions p(h hf ) were reconstructed assuming linear correlation of isomeric shift δ and quadrupole shift ε with the value of H hf [11] (Fig.2). An analysis of the temperature dependence of average field H hf (T ) (Fig. 3a) that corresponds to distributions p(h hf ) enabled us to determine the value of the temperature at which the magnetic hyperfine structure of the spectra completely disappears. The obtained value 19 ± 1Kissomewhat higher than the Neel temperature T N = 16 K derived from the magnetic measurements of AgFeO 2 [3]. Such disagreement may be related to persistence, in a narrow temperature range ( T 4K)atT T N, of short-range magnetic correlations between Fe 3+ ions that are characteristic features of layered systems with frustrated magnetic interactions [2]. Asymmetric profile of the experimental spectra (Fig. 2a) reflects a high degree of correlation between the values of magnetic hyperfine field H hf and isomer (δ) and/or quadrupole (ε) shifts. Figure 3b displays temperature dependences of the correlation coefficients δ/ H hf and ε/ H hf obtained from the distributions p(h hf ) (Fig. 2). The strongest positive correlation ( ε/ H hf > 0) is observed for the magnetic hyperfine field and the quadrupole shift of the Zeeman components. The linear temperature dependence ε/ H hf (T ) experiences a clear kink at T 8.5 K(Fig.3b) that almost completely coincides with the point T N2 = 9 K of the second magnetic phase transition [3]. According to [4], in the temperature range T < T N2 the magnetic moments of Fe 3+ ions form an elliptic cycloid with a period of 500 Å that propagates along the [010] direction in the hexagonal lattice. Such change in the character of magnetic ordering within iron sublattice of the AgFeO 2 ferrite induces non-zero electric polarization [4]. It is important to note that the complex magnetic hyperfine structure for ferrite AgFeO 2 (at T = 4.7 K) significantly differs from a single Zeeman sextet for CuFeO 2 ferrite having the same crystal structure [5, 7]. At T T N2,CuFeO 2 is characterized by a collinear magnetic ordering [1, 17, 18] excluding any possibility of spontaneous electric polarization [1]. Thus, the individual features of the electronic structure and crystal chemistry of two formally isovalent ions Cu + (3d 10 4s 0 ) and Ag + (4d 10 5s 0 ) are not only manifested in the significant difference of the magnetic ordering in CuFeO 2 and AgFeO 2 oxides but also affect the parameters of combined hyperfine structure of the 57 Fe spectra. In particular, the complex magnetic structure of the Mössbauer spectra of ferrite AgFeO 2 reflects noncollinear spatially modulated spin ordering, which is one of the most important intrinsic characteristics of magnetic systems with multiferroic properties [1]. For model fitting of the Mössbauer spectra in the T < T N2 range, we used a procedure similar to that applied earlier to ferrite BiFeO 3 that also possesses a non-collinear magnetic structure of the cycloid type [11]. We took into account the dependence of the quadrupole shift and hyperfine magnetic field on polar angle ϑ between the direction of H hf (collinear, in first approximation, with the direction of the Fe 3+ spins) and the principal component V that coincides, according to our calculations, with the hexagonal axis of the AgFeO 2 lattice: 4ε Q (ϑ) = eqv par (3cos2 ϑ 1)/2 + eqv mag, (2a) H hf (ϑ) = H cos 2 ϑ + H sin 2 ϑ, (2b) where V par is the value of the principal components of the EFG tensor related to local distortion of Fe 3+ positions in paramagnetic temperature range (T > T N ); V mag is a part of

5 57 Fe Mössbauer study of new multiferroic AgFeO 2 Fig Fe Mössbauer spectra (experimental hollow dots) ofagfeo 2 recorded at the indicated temperatures. The solid line is simulation of the experimental spectra as described in the text. The hyperfine field distributions p(h hf ) resulting from simulation of the spectra are shown on the left

6 I. Presniakov et al. a b Fig. 3 a Temperature dependence of the average field H hf (T ) of the distributions p(h hf ). b Temperature dependences of the coefficients of correlation of δ/ H hf and ε/ H hf obtained as a result of reconstructing distributions p(h hf ) EFG which follows the electronic spin direction due to a possible strong local magnetoelastic coupling T < T N [11]; and H and H are the values of H hf oriented along and perpendicular to the direction V par. Thus, the angular dependences of parameters ε(θ) and

7 57 Fe Mössbauer study of new multiferroic AgFeO 2 H hf (θ) in Eq. 2a reflect the changes in the spatially-modulated magnetic structure along the length of cycloid with respect to the hexagonal reference system. To take into account anharmonicity of the spatial distribution of the magnetic moments of Fe 3+ in the cycloid (along the axis), Jacobian elliptic function [8, 19] was used: cosϑ(x) = sn[(±4k(m)/λ)x, m], (3) where K(m) is the complete elliptic integral of the first kind, m is the anharmonicity parameter, and λ is the period of cycloid. Within the above model, the best description of all spectra measured at 4.2 κ T 8K (Fig. 4) may only be attained with sufficiently high values of the anharmonicity parameter that remains almost unchanged in the entire range of temperatures (m = 0.78 ± 0.03). The anharmonicity is related to the constant of uniaxial anisotropy (K u ) [19]: K u = 16mAK 2 (m)/λ 2, where A is the magnetic exchange rigidity the value of which can be estimated using the relation A 3/2(k B T N /R Fe Fe ) [4]. If corresponding parameters for AgFeO 2 (λ = 500 Å[4], T N1 = 14 K, K(m = 0.78) = 2.21, R Fe Fe = 3.04 Å[13]) are substituted into these formulas, we get K u = erg/cm 3 ( mev). It should be noted that the estimated value of the anisotropy constant for AgFeO 2 proves to be smaller than the value K u = mev for ferrite CuFeO 2 obtained in other studies [20, 22]. This result may be indicative of another possible reason for the different character of magnetic ordering in the isostructural CuFeO 2 and AgFeO 2 ferrites. According to the theoretical studies [23], collinear spin ordering becomes energetically unfavourable at insignificant decreasing constant K u and is replaced with more stable non-collinear spin configurations as it is observed, for example, in case of the ferrites CuFe 1 x M x O 2 (M = Al, Ga, Rh) [17, 18, 24]. According to our calculations, V > 0 meaning that the maximum value of quadrupole shift is attained at ϑ = 0 0 (see Eq. 2a). Given the positive value of correlation coefficient ε/ H hf > 0(Fig.2), one may conclude that maximum hyperfine field H hf is attained for the spins of Fe 3+ ions that are directed along the V (H ) axis, i. e. H >H. Note that a similar character of hyperfine field anisotropy (H >H ) is observed in NMR spectra for BiFeO 3 ferrite with hexagonal crystal cells (V c) [19]. The analysis of the spectra shows the strong anisotropy of hyperfine field H = 499 ± 1kOeandH = 476 ± 1 koe (at 4.7 K); the difference H hf = H H increases with temperature to 39 ± 1 koe at 7 K. Note that magnetic disordering in the ( sublattice of iron does not induce an additional magnetic contribution to the EFG mag eqv = 0.08 ± 0.12 mm/s). At the same time, the local contribution eqv par = 1.24 ± 0.02 mm/s related to the symmetry of lattice proves to be very close to the value eqv = ± mm/s obtained in the paramagnetic temperature range. Thus, the transition to the magnetically-ordered region T < T N1 does not cause any significant distortions in the local environment of iron ions. Usually the anisotropy of hyperfine field H hf is related to the dipole contribution H dip which maximum and minimum values may be evaluated using the following formulas: H max dip = μ Z,Fe D and H min dip = μ X,FeD XX,where{D ii } i=x,z are the components of the matrix of lattice sums and μ i,f e are the projections of the magnetic moment of Fe 3+ ions ( onto corresponding principle axes of the EFG tensor. The structural data for AgFeO 2 [13] D = Å 3 and D XX = Å 3) were used to calculate the maximum value ( ) of H dip = Hdip max H dip min = 15 koe that appear to be significantly smaller than the experimental value H Fe = koe. Therefore, the observed very strong anisotropy

8 I. Presniakov et al. Fig Fe Mössbauer spectra of AgFeO 2 at the indicated temperatures fitted using a modulation of the hyperfine interactions as the Fe 3+ magnetic moment rotates with respect to the principal axis of the EFG tensor, and the anisotropy of the magnetic hyperfine interactions at the Fe 3+ sites of hyperfine coupling in AgFeO 2 cannot be explained on the basis of dipole contribution H dip alone. The transition to the temperature range 9K T T N1 results in significant changes in the profiles of AgFeO 2 spectra (Fig. 2). All components of the Zeeman structure become broader and the structure of spectra becomes more symmetric. According to the

9 57 Fe Mössbauer study of new multiferroic AgFeO 2 recent diffraction data [4], at T N2 T T N1 AgFeO 2 has the collinear sinusoidally modulated spin structure almost identical to that found in the partially disordered state of CuFeO 2 [17]. However, our attempts to describe the experimental spectra in the IC SDW approach, as it was done e.g. in [25], were not successful. Thus the results of the Mössbauer measurements obtained in this work convincingly show a more complex character of the magnetic reordering of Fe 3+ ions in the T N2 T T N1 temperature range [4]. 4 Conclusions The 57 Fe Mössbauer studies of ferrite AgFeO 2 have shown that the Fe 3+ ions occupy equivalent crystallographic sites in the structure of the ferrite. The value and sign of the principal component of the EFG tensor on 57 ( Fe nuclei )(V > 0) could only be explained with consideration the dipole contribution V dip > 0 from O 2 ions with polarizability α O 0.83 Å 3 and the electronic contribution ( V ov > 0) that is due to overlapping of the valence orbitals of iron and oxygen ions. At T < T N1, a non-uniform magnetic hyperfine structure is observed in 57 Fe spectra that is related to the anisotropic character of the mutually correlating ε and H hf values. It was shown that these line broadenings and spectral asymmetry in the space modulated cycloidal type magnetic structure of AgFeO 2 (T T N1 ) arise from the slight modulation of the electric hyperfine interactions as the Fe 3+ magnetic moment rotates with respect to the principal axis of the EFG tensor V, and from the intrinsic anisotropy of the magnetic hyperfine interactions at the Fe 3+ sites along the cycloid propagation vector. A model deconvolution of spectra at T < T N1 yielded the high degree of the anharmonicity of the cycloid (m 0.78) with a magneto-crystalline anisotropy constant K u = erg/cm 3. The hyperfine field H hf was shown to include a large anisotropic contribution ( H hf = H H 30kOe) that cannot be related to only the dipole contribution ( H dip 15 koe) from the nearest magnetic neighbours. References 1. Wang, K.F., Liu, J.-M., Ren, Z.F.: Adv. Phys. 58, 321 (2009) 2. Diep, H.T.: Frustrated Spin Systems. World Scientific, Singapore (2004) 3. Vasiliev, A., Volkova, O., Presniakov, I., et al.: J. Phys. Condens. Matt. 22, (2010) 4. Terada, N., Khalyavin, D.D., Manuel, P., et al.: Phys. Rev. Lett 109, (2012) 5. Muir, A.H., Wiedersich, H. Jr.: J. Phys. Chem. Solids 28, 65 (1967) 6. Xu, W.M., Pasternak, M.P., Taylor, R.D.: Phys. Rev. B 69, (2004) 7. Mekata, M., Yaguchi, N., Takagi, T., Sugino, T., et al.: J. Phys. Soc. Jpn. 62, 4474 (1993) 8. Choi, D.H., Shim, I.-B., Kim, C.S.: J. Magn. Magnet. Mater. 320, e575 (2008) 9. Xu, W.M., Rozenberg, G.Kh., Pasternak, M.P., et al.: Phys. Rev. B 81, (2010) 10. El Ataoui, K., Doumerc, J.-P., Ammar, A., Fournes, L., et al.: J. Alloys Comp. 368, 79 (2004) 11. Palewicza, A., Szumiatab, T., Przeniosło, R., et al.: Solid State Commun. 140, 359 (2006) 12. Menil, F.: J. Phys. Chem. Solids 46, 763 (1985) 13. Doumerc, J.-P., Ammar, A., Wichainchai, A., et al.: J. Phys. Chem. Solids 48, 37 (1987) 14. Sharma, R.R.: Phys. Rev. B 6, 4310 (1972) 15. Rusakov, V.S., Khramov, D.A.: Izv. Akad. Nauk SSSR, Ser. Fiz. 56, 201 (1992) 16. Taft, C.A.: J. Phys. C Solid State Phys. 10, L369 (1977) 17. Nakajima, T., Mitsuda, S., Takahashi, K., et al.: Phys. Rev. B 79, (2009) 18. Terada, N., Nakajima, T., Mitsuda, S., et al.: Phys. Rev. B 78, (2008)

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