Lattice dynamics of iron chalcogenides : Raman scattering study

The discovery of superconductivity in FeSe led to a new subclass of high-temperature superconductors – iron chalcogenides. Materials from this group exhibit variety of specific features, from superconductivity with relatively high critical temperatures to low-dimensional magnetic properties. This review presents the most important results regarding the iron chalcogenides, with special emphasis on their vibrational properties investigated by means of Raman spectroscopy. Temperatureand/or doping-dependent Raman scattering spectra of iron chalcogenides provide a valuable insight into the complex relationships between the vibrational, electronic and magnetic properties of these materials. The results presented in this review demonstrated that Raman spectroscopy provides new insights which may significantly improve our understanding of the fundamental properties of iron chalcogenides.

FeSe is the first discovered material from one of the newest subclasses of iron-based superconductors -iron chalcogenides. 22Its physical properties are extremely sensitive to doping on the chalcogen site, as well as to the Fe concentration, and T c can be enhanced by applying pressure. 23,24Intercalation of alkali metal between the FeSe layers led to the formation of A x Fe 2-y Se 2 (A = alkali metal) crystals with the defect 122  structure. 256][27][28] Absence of hole pockets at the Fermi surface suggests that the pairing mechanism may differ from the one in the pnictides.By cutting the layers of FeSe 4 tetrahedra, e.g., removing every third Fe atom from these layers, one obtains a basic building block of the so-called spin-ladder compounds BaFe 2 Se 3 (BaFe 2 S 3 ). 29][32][33] In this article an overview of iron-chalcogenides is presented, but instead of a comprehensive review of their features, we focus our attention on the vibrational properties studied by Raman spectroscopy, as a suitable technique for investigating lattice and magnetic excitations of crystalline solids.[36] 2. 11-TYPE MATERIALS

Crystal structure
Materials with the general formula FeCh (Ch = Se or Te), belonging to this group, have the simplest structure among all iron chalcogenides.They are built of edge-sharing FeCh 4 tetrahedra stacked along the crystallographic c-axis, see Fig. 1.At room temperature, they adopt the tetragonal crystal structure of the PbO type, space group P4/nmm. 22,37,38he crystal structure of FeSe at low temperatures is orthorombic, space group Cmma, 24,37,39 although it was initially proposed that FeSe 0.88 below T s ≈ ≈ 100 K changes symmetry into triclinic, space group P-1 . 22Structural transition temperature T s for FeSe differs between various papers, depending strongly on the strain and sample stoichiometry. 37,40,41Based on the temperature evolution of synchrotron X-ray diffraction profiles of FeSe 0.92 , 37 it is concluded that T s is about 70 K, whereas elsewhere 40 is showed that the phase transition in SC Fe 1.01 Se occurs at 90 K.
With Te-doping of FeSe crystals, the tetragonal-to-orthorombic structural transition moves toward lower temperatures and finally disappears for FeTe 0.507 Se 0.493 . 42For low Te-content a miscible region with the local phase separation between two phases emerges. 23,43These two phases have the same space group (P4/nmm) but different lattice parameters.With further increasing Te-concentration, the monoclinic structure appears at low temperatures (space group P2 1 /m), instead of orthorombic. 38Martinelli et al. 38 reported tetragonal-to-monoclinic phase transition in Fe 1+y Te 1-x Se x crystals for x ≤ 0.1, with increasing T s as x decreases.For the end member Fe 1+y Te, the structural transition occurs around 70 K.

Physical properties
FeSe exhibits metallic behavior of electrical resistivity (ρ) from room temperature down to T c ≈ 8 K, where a sharp drop to zero resistance occurs. 22,23,43Some authors 22 noticed a weak anomaly at about 100 K, which coincide with the anomaly in magnetic susceptibility χ(T), and attributed them to the structural transition.They observed almost temperature independent magnetic susceptibility for T > T c , which led them to conclude that FeSe does not order magnetically. 22owever, recent inelastic neutron scattering experiments revealed stripe and Neel spin fluctuations over a wide energy range. 44Susceptibility measurements also showed SC transition at about 8 K. 22,43 Temperature dependence of resistivity under various pressures is analyzed, 24 and the SC transition was noticed below 13.4 K for low pressures.With the increasing pressure, T c rapidly increases and reaches maximal value of 37 K at about 6.6 GPa.With further pressurization, T c decreases and at 13.9 GPa T c ≈ 6 K. 24 It was recently shown that an electronic nematic state develops below T s , 45,46 suggesting that structural transition in FeSe may be driven by the orbital, magnetic and/or charge instability.
FeTe does not exhibit the SC transition. 38,43Its resistivity weakly increases with decreasing temperature and exhibits an upturn at about 77 K, with rapid drop.Below the structural phase transition temperature T s = 70 K FeTe has metallic behaviour. 38,43Structural transition is followed by the AFM spin ordering, with T N ≈ T s . 42For FeTe 0.82 single crystals, magnetic susceptibility curve χ(T) exhibits two anomalies, at 65 and 125 K. Anomalous peak in ρ(T) also appears at 65 K. 23 It was later shown that this behaviour is connected with the structural and Available on line at www.shd.org.rs/JSCS/_________________________________________________________________________________________________________________________ (CC) 2017 SCS VIBRATIONAL PROPERTIES OF IRON CHALCOGENIDES 961 AFM phase transition. 47Hall constant, R H , is negative in the temperature range 10 K ≤ T ≤160 K, indicating that charge carriers are dominantly electrons. 23omprehensive study of physical properties of Fe(Se 1-x Te x ) 0.82 , 0 ≤ x ≤ 1, alloys is performed. 23Maximal T c of about 14 K is achieved for the sample with x = 0.6, and SC disappears in the end member (x = 1).Anomaly in the susceptibility at 125 K, similar to that in FeTe 0.82 , persists for all samples with x > 0.4.It was shown that, 47 for the (FeSe 0.4 Te 0.6 ) 0.82 sample, short range magnetic correlations appear below 75 K and rapidly enhance below 40 K, which coincide with anomalous temperature dependence of R H in this temperature range, indicating the strong interplay between spin and charge degrees of freedom. 23Samples with 0 ≤ x ≤ 0.15 have metallic resistivity from room temperature down to T c , whereas samples with 0.3 ≤ x ≤ 1 have a weak upturn before approaching the SC transition temperature. 23This is consistent with the results for FeTe 1-x Se x , 0< x ≤ 0.2, alloys, 38 where all samples show an upturn in ρ(T) below 100 K, which weakens and shifts to lower temperature as x increases, and metallic behavior at lower temperatures.For x ≥ 0.05, material become SC, and T c increases with increasing Se content. 38Similar resistivity curves were also obtained for FeSe 1-x Te x samples with low Se content, where it was found that T c increases with x for x ≤ 0.75, and T c,max = 15.3K for x = 0.25. 43

Raman scattering studies
According to the factor group analysis (FGA) for the P4/nmm space group, four Raman active modes (A 1g +B 1g +2E g ) could be observed in the room-temperature Raman spectra of FeCh (Ch = Se or Te) materials.A 1g mode represents vibrations of the Ch-ions, whereas B 1g one represents Fe-ion vibrations along the z-axis.Twofold degenerate E g modes originate from Fe-and Ch-ion vibrations within the ab-plane. 39,489][50][51][52] Almost all authors observed and assigned, at room temperature, two Raman active modes, of A 1g and B 1g symmetry, allowed by the selection rules when measuring from the (001)-plane of the sample.The A 1g mode was not observed in Fe 1.03 Se 0.3 Te 0.7 sample, 49 although in FeTe 0.92 sample it is present; it was suggested that it may be due to the vacancies introduced into the system with Se doping, or slightly different excess of Fe-ions.Energies of the A 1g and B 1g modes for different samples are compared in Table I.As can be seen, they are rather close.However, temperature dependence of Raman mode energy, ω(T), and linewidth, Γ(T), differs substantially between various papers.The spectrum of FeSe single crystal, 39 is shown in Fig. 2.
Magnetic transition that exists in FeTe leaves a clear fingerprint on the behavior of B 1g mode energy and linewidth. 48,50,52Namely, the B 1g mode exhibits significant softening and narrowing below T N ≈ 70 K (where it changes the sym-962 OPAČIĆ and LAZAREVIĆ metry to A g 52 ) for all samples except Fe 1.09 Te.Besides that, both the B 1g mode energy and linewidth decrease with decreasing temperature 48,50,52 (Fig. 3) and it was shown 52 that they scales well with the normalized magnetic susceptibility, confirming that spin-phonon coupling substantially influence the behaviour of the B 1g (Fe) mode.Absence of the B 1g phonon softening below T N for Fe 1.09 Te single crystal 50 was ascribed to the significant Fe excess, which contributes to the filling up the gap in the spin-wave excitation spectrum with the low-energy spin fluctuations.Unlike the B 1g one, behaviour of the A 1g symmetry mode differs substantially.The only common feature is the large intrinsic linewidth, which is attributed 48 to the spin-orbital frustration, whereas elsewhere 52 is suggested that electron-phonon interaction may also play an important role.
The A 1g mode for Fe 1.051 Te 48 hardens and broadens with decreasing temperature, showing a weak anomaly in ω(T) at T s , followed by more rapid increase of Γ(T) below T s .Authors believe that the A 1g mode energy renormalization is caused by the phonon modulation of the magnetic interactions and by the antiphase motion of Te-ions surrounding Fe-ions, which modulates exchange interaction.Rapid increase of the A 1g mode linewidth is attributed to the spin-orbital Available on line at www.shd.org.rs/JSCS/_________________________________________________________________________________________________________________________ (CC) 2017 SCS VIBRATIONAL PROPERTIES OF IRON CHALCOGENIDES 963 frustration.Energy and linewidth of the A 1g mode for Fe 1.02 Te and Fe 1.09 Te 50 remains almost constant at the temperatures up to 300 K.The A 1g mode energy and linewidth were analyzed 52 using phonon anharmonicity model and good agreement is obtained between experimental data and calculated spectra, indicating that they follow anharmonic temperature dependence.Effect of Se doping on FeTe Raman spectra has also been investigated. 49,50,52Um et al. 50analyzed Raman spectra of Se-doped FeTe single crystals and showed that in the sample with the highest Se content (Fe 0.95 Te 0.56 Se 0.44 ) change of the A 1g and B 1g mode energy and linewidth with temperature is in agreement with the anharmonic picture: the phonon energy increases and the linewidth decreases with the decreasing temperature.By decreasing Se content, the energy and the linewidth of these modes gradually moves away from the conventional behaviour and for the Fe 1.00 Te 0.78 Se 0.22 crystal the B 1g phonon even broadens with decreasing temperature (Fig. 4).Absence of phonon renormalization at T c for these SC samples is expected because their energies are much larger than the energy of the SC gap.More detailed analysis of the B 1g mode linewidth temperature dependence for Se-doped samples revealed that with decreasing Se content its intrinsic linewidth increases, which is attributed to the influence of the spin-phonon coupling, since lower Se (higher Te) content means stronger magnetic interactions.Raman spectra of Se-doped Fe 1+y Te crystals were analyzed 52 with respect to the undoped case.It was observed that the A 1g and B 1g modes have opposite behaviour of energy and linewidth with Se doping: A 1g mode hardens and narrows whereas the B 1g one softens and broadens with increasing Se content.A 1g mode hardening is explained by the mass effect, whereas decreased linewidth is attributed to the lower electron-phonon interaction and/or to the excess Fe-ions.On the other Available on line at www.shd.org.rs/JSCS/_________________________________________________________________________________________________________________________ (CC) 2017 SCS VIBRATIONAL PROPERTIES OF IRON CHALCOGENIDES 965 hand, B 1g mode broadening in Fe 1.02 Te 0.6 Se 0.4 compared with Fe 1.07 Te authors ascribed to the induced structural disorder, whereas phonon softening could be explained with the change in excess iron in these two single crystals.Qualitatively similar behaviour is presented 50 for the A 1g mode, whereas for the B 1g one the situation is almost opposite.
Temperature-dependent phonon Raman spectra of FeSe were analyzed in detail. 39Room-temperature spectra consist of A 1g and B 1g modes, as expected from the selection rules.Due to the structural transition into the ortorhombic phase (e.g., lowering of the rotational symmetry from C4 to C2), A 1g mode changes symmetry becoming A g one, but without energy change, and three new modes appearing at higher energies can be of B 2g /B 3g symmetry, according to the Cmma space group.They emerge due to the splitting of E g mode from the tetragonal phase.Both A 1g and B 1g mode energies vary smoothly with temperature, and large B 1g mode hardening with decreasing temperature is argued to be a consequence of the dynamical crossover from Fe spin state S = 2 to S = 0 with the lowering of temperature. 39They suggested that smooth temperature dependence of the phonon linewidth at T s indicates that orbital fluctuations do not have significant impact on the behavior of Raman modes.Highly polarized quasi-elastic response emerging in Raman spectra of the tetragonal phase, with maximal intensity at T s , is considered as a fingerprint of electronic nematic fluctuations. 39,53E g mode splitting to B 2g +B 3g phonons in FeSe, as a consequence of C4-symmetry breaking, is found to be only about 2.6 cm -1 , which is small in comparison to Ba(Fe 1-x Co x ) 2 As 2 , probably due to the lack of the magnetic order (Fig. 5). 54This

966
OPAČIĆ and LAZAREVIĆ splitting sets in below 65 K, where the spin-lattice relaxation rate is found to increase, which led to the conclusion that spin correlations have stronger influence to the lattice than the orbital interactions. 46 122  -TYPE MATERIALS

Crystal structure
The SC in this class was firstly discovered in a sample with the nominal composition K 0.8 Fe 2 Se 2 , with the proposed tetragonal crystal structure of the ThCr 2 Si 2 -type, space group I4/mmm. 25It consists of FeSe layers and K atoms stacked alternatively along the z-axis (Fig. 6a).Intercalation of the K atoms between the FeSe slabs significantly increases the lattice parameter c (decreasing )). 28ailable on line at www.shd.org.rs/JSCS/_________________________________________________________________________________________________________________________ (CC) 2017 SCS VIBRATIONAL PROPERTIES OF IRON CHALCOGENIDES 967 dimensionality of the system), as well as the interlayer Fe-Fe spacing.(Fe 2 Se 2 ) δ- layers serve as conducting layers, whereas K + are charge carriers.Fe-Se-Fe bond angle is very close to the angle of the ideal tetrahedra (109.47°). 25owever, the appearance of additional peaks in the neutron powder diffraction (NPD) spectra indicated that symmetry lowering to I4/m phase occurs, due to the Fe vacancies ordered into the √5×√5 superlattice in the FeSe plane (Fig. 6b). 26Zavalij et al. 55 and Wang et al. 56 also suggested √5×√5 order of the iron vacancies.Fe vacancy order disappears at very high temperature (500 K ≤ T s ≤ ≤ 578 K), depending on the sample composition, 26,57 and I4/mmm symmetry is achieved.
The application of the transmission electron microscopy, Chen et al. 58 showed that K x Fe 2-y Se 2 single crystals exhibit a mesoscopic phase separation between an insulating phase with √5×√5 vacancy order and SC/semiconducting phase free of vacancies (i.e., with composition KFe 2 Se 2 , space group I4/mmm).This is also seen by Li et al. 27 on K x Fe 2-y Se 2 thin films.PXRD measurements confirmed 28 the phase separation: experimental data were well described with the mixture of I4/m and I4/mmm space groups.0][61] On the other hand, Bao et al. 62 reported phase separation between three phases (I4/m, I4/mmm and Pmna) in K x Fe 2-y Se 2 samples for 1.4 ≤ 2-y ≤ 1.6 and x > 0.85 (the samples have general formula K 2 Fe 3 Se 4 ) between T s and T * ≈ 350 K, whereas below T * only I4/m phase with ordered Fe vacancies persists.For Fe content 1.6 ≤ 2-y ≤ 1.7 the sample composition is described with K 2 Fe 4 Se 5 and below T s their space group is I4/m. 62oping of K x Fe 2-y Se 2 crystals on either chalcogen or transition metal site significantly affects their properties.It was recently shown 60 that the phase separation persists in Co-doped K x Fe 2-y Se 2 single crystals.However, when Co content is significant (z ≥ 0.92 in K x Fe 2-y-z Co z Se 2 ), vacancy order was not observed and these samples belong to the I4/mmm space group. 60,63,64Doping of K x Fe 2-y Se 2 with small Ni content also preserves the phase separation. 59Similarly to the Co--doped case, in K x Fe 2-y-z Ni z Se 2 samples with z ≥ 0.73 low symmetry I4/m phase disappears. 59Pure K x Ni 2-y Se 2 crystallizes in the tetragonal crystal structure with I4/mmm space group, without any indications of vacancy ordering, [65][66][67] as well as his Co-counterpart.K x Fe 2-y Se 2 samples doped with S on chalcogen site exhibit iron vacancy order for all doping levels. 68,69

Physical properties
Detailed investigations revealed that the physical properties of K x Fe 2-y Se 2 strongly depend on the sample composition, i.e., K-and Fe-stoichiometry.Bao et al. 62 systematically studied few samples having general formula K x Fe 2-y Se 2 and obtained different properties for various sample compositions.Two samples with higher Fe and lower K content exhibit SC with T c ≈ 30 K and large resistivity just 968 OPAČIĆ and LAZAREVIĆ above T c .These samples show poor diamagnetic response below T c .With the gradually increasing K content, a bump in ρ(T) appears, which is attributed to the metal-insulator crossover, similarly to the results presented elsewhere: 25 above the peak, samples show semiconducting behaviour, whereas below the bump down to T c , ρ(T) has typical metallic character.Peak position is strongly dependent on the sample composition. 25,62With the further increasing of K and the decreasing of Fe content, the gradual opening of transport activation gap was observed in the resistivity. 62arly studies of the magnetic properties of alkali metal iron selenides revealed that AFM order appears at T N ≈ 560 K, slightly below the Fe vacancy ordering temperature T s . 26,62The four magnetic moments from the nearest neighbouring Fe atoms order ferromagnetically (FM), whereas these FM blocks form the block-checkerboard AFM order, with very high magnetic moment (3.31 μ B /Fe at 11 K). 26SC transition strongly affects the magnetic order parameter, suggesting significant interaction between SC and AFM order. 26ecent studies indicated that SC in K x Fe 2-y Se 2 was highly influenced by the connectivity between SC phases and the proximity effects. 70,71Three K x Fe 2-y Se 2 samples with different microstructure exhibited different T c , 71 although they all have approximately the same fractional ratio of the SC area and similar resistive and magnetic properties.Huang et al. 71 showed that proximity effects, that is, the interlayer hopping and interlayer spin coupling, reduce T c from the theoretically predicted 65 K to the experimentally observed 32 K. On the other hand, large AFM order results in a large SC order, thus explaining relatively high T c . 71he chemical doping is an appropriate way to tune and control physical properties of materials, since it introduces changes in the structure and carrier density.Doping on the Fe site with other transition metals is detrimental for SC. 72amely, Cr-, Co-and Zn-doping rapidly suppresses SC in the K 0.8 Fe 2-y Se 2 , by inducing a large effective magnetic moment, thus destroying SC via a magnetic pair-breaking effect. 72Recently reported study of Ni-doped K x Fe 2-y Se 2 single crystals 59 shows that small Ni content destroys SC, leading to the insulating behaviour, whereas with further Ni-doping metallic character of crystals gradually increases.It was also shown that these materials exhibit spin glass behaviour below critical temperature T f of 10-50 K, depending on the Ni concentration. 59 x Ni 2-y Se 2 have a local charge-density-wave state persisting up to 300 K. 65 Some authors 66 reported the metallic resistivity of K x Ni 2-y Se 2 single crystal up to the room temperature, without SC transition or bump in the ρ(T), unlike the K x Fe 2-y Se 2 .SC is suppressed probably due to the K and Ni deficiency, indicating the strong sensitivity to the sample composition.Magnetic measurements revealed that this material is Pauli paramagnet, with local magnetic moments much lower than in K x Fe 2-y Se 2 . 66Co-doped K x Fe 2-y Se 2 single crystals behave similarly to its Ni-counterparts. 60 73 When S completely replaces Se in K x Fe 2-y Se 2 , single crystal becomes a small-gap semiconductor, which is ascribed to the random scattering potential introduced by the Fe deficiency, and exhibits a spin glass behaviour below 32 K. 68,69

Raman scattering studies
FGA for the I4/m space group predicts 9A g , 9B g and 9E g modes to be observed in the Raman scattering experiments, 28,61 whereas for the I4/mmm space group only four phonon modes (A 1g +B 1g +2E g ) are expected to be observed. 28,61,64,675][76] These spectra are very similar to each other; characteristic K x Fe 2-y Se 2 Raman spectrum is shown in Fig. 6.However, the symmetry analysis of the phonon spectra was performed assuming the different space groups in various papers.Temperature analysis of Raman spectra, as well as the line shape of some modes, also differs, as will be discussed.
First Raman study of K x Fe 2-y Se 2 was done by Zhang et al. 74 They assumed the I4/m space group for the single phase and thus assigned phonons which appeared in the parallel polarization configuration only as A g symmetry modes, whereas those modes appearing in both polarization configurations were assigned as B g ones.In that way 6 A g and 5 B g modes were assigned, with energies coinciding well with the lattice dynamics calculations.The most intriguing fact is a frequency jump at T c for the Raman mode appearing at about 180 cm -1 in parallel polarization configuration, of unknown origin, since its energy did not match with any of the calculated A g mode energies.Authors interpreted this behaviour as an evidence of specific connection between phonons and SC.This hardening was also observed, 75 where Raman spectra of three SC (K 0.8 Fe 1.6 Se 2 , Tl 0.5 K 0.3 Fe 1.6 Se 2 and Tl 0.5 Rb 0.3 Fe 1.6 Se 2 ) and one non-SC sample (KFe 1.5 Se 2 ) were analyzed in terms of I4/m space group (Fig. 7).It is suggested that this mode is local, originating from the nanoscopic region of filled Fe vacancies.By comparing the Raman spectra of K 0.8 Fe 1.6 Se 2 and KFe 1.5 Se 2 single crystals, frequency shift of the Raman modes originating from Fe-and Se-ion vibrations was observed, due to the differences in the FeSe plane induced by the change of Fe content.Doping on the K site did not influence phonon spectra above 60 cm -1 , but induces additional modes in the low energy range, attributed to the change of local symmetry in the K layer. 75I4/m space group is assumed also for K x Fe 2-y Se 2 . 7616 Raman modes at room temperature was observed, some of them with Fano line shape, attributed to the coupling of the vibrations with AFM spin fluctuations.Authors agreed that three new phonon modes appear below 250 K, due to the structural transition, i.e. symmetry lowering from the I4/m to the I4 phase. 76Unlike to the presentations by some authors, [74][75][76] Raman spectra of K x Fe 2-y Se 2 were analyzed 28,61 in terms of both I4/m and I4/mmm space groups.Raman modes from the I4/mmm space group were assigned. 28It was determined that the A 1g mode appears at about 180 cm -1 , whereas energy of the B 1g mode is 207 cm -1 .It is interesting to note that this A 1g phonon is probably the same Raman mode as that of the unknown origin, 74,75 with frequency jump at T c .Large number of modes from the low symmetry I4/m phase were assigned 28 by means of detailed symmetry analysis and measurements in various polarization configurations.A g and B g mode energies coincide with other data, 74 which can be seen from Table II.Detailed temperature-dependent Raman scattering study of SC K x Fe 2-y Se 2 and non-SC K x Fe 1.8 Co 0.2 Se 2 is given. 61Similar spectra of the two crystals indicate that phase separation is preserved with small amount of Co doped at the Fe-site.Analysis of the temperature-dependent Raman spectra revealed the phonon energies temperature dependence is dominantly driven by the lattice thermal expansion, whereas the impact of phonon anharmonicity is negligible.The renormalization of the A 1g phonon energy below T c was observed only for the SC sample (Fig. 8), which led to the conclusion that it is induced by the SC gap opening, in line with the theoretically expected behaviour. 77oom temperature Raman spectra of Ni-and Co-doped K x Fe 2-y Se 2 crystals give valuable insight into the structural changes of K x Fe 2-y Se 2 with doping.Recent Raman studies 59,60 revealed that increasing Co and Ni content have similar influence on phonon spectra of these materials.When Ni (Co) content is low, large number of modes are present in Raman spectra (Fig. 9), in accordance with the symmetry lowering due to the Fe-vacancy ordering, i.e., presence of I4/m phase, Available on line at www.shd.org.rs/JSCS/_________________________________________________________________________________________________________________________ (CC) 2017 SCS VIBRATIONAL PROPERTIES OF IRON CHALCOGENIDES 971 TABLE II.Comparison of experimentally observed wavenumbers (in cm -1 ) at room temperature for the selected A g and B g symmetry modes of K x Fe 2-y Se 2 single crystals 28,74 Ref.  64 only two modes can be observed in Raman spectra, confirming the lack of any vacancy order.Appearance of the A 1g mode in the whole series gives a clear evidence that I4/mmm phase persists for all Ni (Co) concentrations. 59,60Detailed Raman scattering studies of K x Ni 2-y Se 2 67 and K x Co 2-y Se 2 single crystals 64 support the findings given elsewhere. 59,60As opposed to the A 1g phonon that appears at similar energies in these two compounds, 64,67 the B 1g phonon energy (representing vibrations of the transition metal ions) differs substantially (Table III).Besides that, by measuring from the (010)-plane of K x Ni 2-y Se 2 , one E g mode is clearly observed (Fig. 10) whereas the other, low intensity E g mode, was confirmed by numerical calculations.Large intrinsic line-Fig.9. Raman spectra of K x Fe 2-x-y Ni y Se 2 single crystal series measured from the (001)-plane at 100 K. 59 width of the B 1g phonon, together with the mode asymmetry, is believed to originate from the structural disorder, although the impact of the electron-phonon interaction cannot be excluded. 67Similar features of the B 1g phonon are also observed in K x Co 2-y Se 2 , where it was argued that they are mainly caused by the spin fluctuations coupled to the electronic structure via lattice vibrations. 64Temperature dependence of A 1g and B 1g mode energy in K x Co 2-y Se 2 in the paramagnetic phase is governed by the lattice thermal expansion and phonon anharmonicity, whose relative importance is not yet firmly established.Change of phonon linewidths is well described with the lattice anharmonicity model.Both phonon modes have energy jump below the FM transition temperature T c , but the A 1g mode exhibits sharpening with further cooling, whereas the B 1g mode broadens (Fig. 11).Sudden frequency change of the observed Raman mode energies as the sample gets magnetized can occur due to the magnetostriction effects, spinphonon coupling and/or changes in the electron-phonon interaction caused by the spin polarization and changes in the electronic spectrum. 64s opposed to K x (Co, Ni) 2-y Se 2 , phonon spectra of K 0.88 Fe 1.63 S 2 consists of large number of modes, originating from the I4/m phase.This confirms symmetry lowering due to the Fe-vacancy order, but without phase separation, unlike the Available on line at www.shd.org.rs/JSCS/_________________________________________________________________________________________________________________________ (CC) 2017 SCS VIBRATIONAL PROPERTIES OF IRON CHALCOGENIDES 973 K x Fe 2-y Se 2 . 786 A g and 8 B g modes were assigned by measuring the spectra from the (001)-plane of the sample.

Crystal structure
The most studied materials among the iron-containing spin-ladder compounds with the general formula AFe 2 X 3 (A = K, Rb, Cs, Ba and X = Ch) are barium-iron-chalcogenides, BaFe 2 (S,Se) 3 .The ladder structure of these compounds can be considered as obtained by cutting the layers of edge-sharing FeSe 4 tetrahedra of the two-dimensional 11-iron chalcogenides, i.e., removing every third Fe atom from the FeSe layers.BaFe 2 (S,Se) 3 crystals consists of one-dimensional FWHM: measure of the electron-phonon coupling (1/q) of the B 1g mode as a function of temperature. 64e 2 (S,Se) 3 ] 2-double chains, propagating along the long ladder direction (,,lag'') and Ba 2+ as separators (Fig. 12).In BaFe 2 S 3 the double chains extend along the aaxis, whereas in BaFe 2 Se 3 the ladder lag is along the b-axis. 33,79There are two important structural differences between these two materials.Namely, two different Fe-Fe distances along the ladder lag exist in BaFe 2 Se 3 , whereas in BaFe 2 S 3 all Fe-Fe distances are the same.Moreover, [Fe 2 Se 3 ] 2-double chains are tilted off the bc-plane, with opposite tilting directions of the two neighbouring layers, whereas in BaFe 2 S 3 there is no tilting.Due to the slight structural differences, BaFe 2 Se 3 and BaFe 2 S 3 crystals, although both orthorombic, are not isostructural.BaFe 2 S 3 has Cmcm space group, whereas space group of BaFe 2 Se 3 is Pnma, both with four formula units per unit cell. 79aFe 2 Se 2 O is the first layered iron-oxychalcogenide with alkali earth metal.It consists of Fe-Se(O) layers and Ba 2+ , stacked alternatively along the c-axis, similar with BaFe 2 Se 3 and BaFe 2 S 3 .Fe-Se(O) double chains are bridged by the oxygen atoms along the a-axis and propagate along the b-axis.However, the intralayer structure differs from those in previously described spin-ladder materials.Different Fe-Se and Fe-O distances cause Fe atoms to be located in highly dis-Available on line at www.shd.org.rs/JSCS/_________________________________________________________________________________________________________________________ (CC) 2017 SCS VIBRATIONAL PROPERTIES OF IRON CHALCOGENIDES 975 torted (asymmetric) tetrahedra, whose angle significantly deviates from the ideal value.Crystal structure is orthorombic (Pmmn space group), with two formula units per unit cell. 80 010) plane.w and w * denote Fe-Fe distances along short ladder directions ("rungs"), whereas u, v and v * represent Fe-Fe distances along the ladder legs. 81

Physical properties
BaFe 2 S 3 has semiconducting ρ(T), with very low resistivity. 82,83The change of slope in resistivity occurs at about 275 K, 82 where inverse molar magnetic susceptibility has a broad hump. 83This material also exhibits negative magnetoresistive effect of about 10 % at low temperatures.The divergence between ZFC (zero field-cooled) and and FC (field-cooled) magnetic susceptibility below 25 K points out to the spin-glass behaviour, which is confirmed by other measurements. 83Strong intrachain AFM coupling of the ions, together with the additional crystal field splitting due to the neighbouring Fe atoms and direct Fe-Fe interactions cause ground state with S = 0. 83 Takahashi et al. 30 recently measured the resistivity of BaFe 2 S 3 single crystals under various pressures and found the gradual suppression of insulating behaviour with increasing pressure, with metal--insulator transition at about 11 GPa.With further increasing pressure, this material exhibits SC below T c = 14 K.The increased metallicity of the sample at higher pressures is caused by the anisotropic compression of the crystal. 30NPD measurements indicate the stripe-type magnetic order, with magnetic moment 1.2 μ B (at 4 K) per Fe site.These moments form FM units along the rung direction, whereas these units order antiferromagnetically along the lag direction. 30aFe 2 Se 3 single crystal also has semiconducting ρ(T) properties, similar to BaFe 2 S 3 , but without magnetoresistive effect.33 Large diversity of susceptibilities for different field directions indicatesmagnetic anisotropy.29,33 The transition in Available on line at www.shd.org.rs/JSCS/_________________________________________________________________________________________________________________________ (CC) 2017 SCS 976 OPAČIĆ and LAZAREVIĆ magnetic susceptibility at 255 K for all field directions is attributed to the crossover from short-range to long-range AFM order.33 This transition was not observed, 29 since a divergence of ZFC and FC magnetic susceptibilities is attributed to the spin-glass behavior with T f ≈ 50 K.
Resistivity measurements on BaFe 2 Se 2 O single crystals revealed the insulating behaviour.At T a = 240 K, there is anomaly in resistivity, allowing their fitting below T a with the relation ρ = ρ 0 exp{(E a /k B T) α }, α < 1, which means that thermal activation is less effective at low temperatures and the other mechanism is responsible for electron trapping. 80Authors proposed the existence of long range AFM order below 240 K, which is confirmed by the strong peak in differential magnetic susceptibility ∂χ/∂T at T a .Anisotropy in the magnetic susceptibility indicates that the easy axis of magnetization is in the ab-plane.Besides that, a sudden decrease of susceptibility below 115 K, with much less anisotropy, was attributed to the spin-singlet dimers, believed to be formed at low temperatures. 80All iron ions in BaFe 2 Se 2 O are in Fe 2+ state and high spin state, and this compound can be considered as S = 2 spin-ladder system, with the dominant AFM superexchange interaction along the ladder rungs. 32

Raman scattering studies
Raman spectra of BaFe 2 Se 2 O were analysed. 31In the optical part of the spectra 6 (of 6) A g modes and 2 out of 2 B 1g modes were observed and assigned (Fig. 13) whereas the remaining modes (of B 2g and B 3g symmetry) could not be observed by measuring from the (001)-plane of the sample.Three new modes appearing below T N = 240 K are attributed to the crystal structure and/or crystal symmetry change.Analysis of the Raman mode energy and linewidth depend- ence on temperature showed significant hardening and narrowing of A g modes below T N .B 1g modes asymmetry above T N (persisting in the region of short-range magnetic order) is believed to originate from the spin fluctuations. 31esides the optical phonon modes, two broad and asymmetric structures appear in the Raman spectra of BaFe 2 Se 2 O single crystals at higher energies, in c(bb)c̄ polarization only (which coincides with the spin orientations).Therefore, they are assigned as two-magnon continuum modes. 31These structures are shown in Fig. 14.From the ratio T N /T max = 0.53 (where T max denotes temperature where magnetic susceptibility has a maximum), it was concluded that BaFe 2 Se 2 O is a quasi-2D magnetic system.From the onset of the magnetic continuum, which should correspond to 2∆ S (where ∆ S is a spin gap energy), it was estimated ∆ S ≈ ≈ 27 meV.Magnon modes disappear above 623 K, e.g., 2.6 T N 31 in agreement with the other results indicating that the short-range magnetic order in oxychalcogenides persists at least up to 2 T N . 84Phonon properties of BaFe 2 S 3 and BaFe 2 Se 3 were analysed. 81By measuring from the (110)-plane of the BaFe 2 S 3 sample, in parallel polarization configurations 5 (of 5) A g symmetry modes and 5 out of 6 B 1g , the symmetry modes were clearly observed.In crossed polarization configuration B 2g and B 3g modes could appear in the Raman spectra; therefore, the assignation was done with the help of lattice dynamics calculations.Three such modes were observed in phonon spectra.
On the other hand, lower symmetry of BaFe 2 Se 3 single crystals compared to BaFe 2 S 3 , caused more Raman active modes to be observed in the phonon spectra.Indeed, by measuring from the (100)-plane of the sample, 9 (of 11) A g symmetry modes were observed in parallel polarization configuration, whereas in the crossed one three additional modes were assigned as of B 3g symmetry. 81he temperature analysis of phonon energy and linewidth was performed in terms of lattice thermal expansion and phonon anharmonicity for both BaFe 2 S 3 and BaFe 2 Se 3 single crystals.It turned out that the contribution of the phonon--phonon scattering to the Raman mode energy temperature dependence is negligible.The sudden change of slope of energy and linewidth temperature dependence of the A g 4 mode at about 275 K (where the hump in inverse molar magnetic susceptibility and change of slope in resistivity also occur) in BaFe 2 S 3 is attributed to the AFM spin ordering within the ladder lag from the short-range to the long-range state, without spin ordering of the whole crystal, followed by the change in the electronic structure.The energies of the all analyzed modes in BaFe 2 Se 3 sharply increase below T N , which was ascribed to the spin-phonon coupling.This mechanism is also responsible for the deviation from the usual anharmonic behaviour of the phonon linewidth. 81

SUMMARY AND CONCLUSIONS
The results discussed in this review clearly demonstrate that Raman spectroscopy is a very powerful technique for investigating the vibrational properties of iron chalcogenides.Moreover, almost all structural and magnetic transitions leave a clear fingerprint on the vibrational spectra of 11, 122  and spin-ladder iron-based superconductors, reviewed in this article, through the appearance of new phonon modes or a sudden change in the phonon energy and/or linewidth.
Raman spectra of Fe(Te, Se) single crystals measured from the ab-plane consist of two modes, assigned as A 1g and B 1g ones.Magnetic transition in FeTe causes softening and narrowing of the B 1g (Fe) mode.With Se doping of FeTe crystals the A 1g mode hardens and narrows, whereas the B 1g ones softens and broadens, compared to the pure FeTe.Large B 1g mode hardening observed for FeSe is explained as a consequence of the dynamical crossover between different Fe spin states.Electronic nematic fluctuations leave a fingerprint through highly polarized quasielastic response in the Raman spectra of FeSe in the tetragonal phase.
Vibrational spectra of K x Fe 2-y Se 2 single crystals have large number of phonon peaks.Some authors assigned them according only to the I4/m space group, whereas the others assume the existence of I4/mmm and I4/m phases, which is confirmed by the other techniques.Renormalization of the A 1g mode energy at T c in SC K x Fe 2-y Se 2 and the absence of renormalization in non-SC isostructural K x Fe 1.8 Co 0.2 Se 2 indicates that it is induced by the opening of SC gap, confirming that this mode indeed represents the I4/mmm phase vibration.Raman studies also revealed that doping of K x Fe 2-y Se 2 single crystals with different amount of Co and Ni significantly affects their crystal structure.When Ni (Co) content is low, large number of modes points out to the presence of both I4/mmm and I4/m Available on line at www.shd.org.rs/JSCS/_________________________________________________________________________________________________________________________ (CC) 2017 SCS VIBRATIONAL PROPERTIES OF IRON CHALCOGENIDES 979 phases.At high dopant concentrations, as well as for pure K x (Co, Ni) 2-y Se 2 , only two modes, of A 1g and B 1g symmetry, appear in phonon spectra, confirming the lack of ordered vacancies.Spin-dependent electron-phonon coupling and magnetostriction effects leave a clear fingerprint on the vibrational spectra of K x Co 2-y Se 2 , through a strong deviations of the phonon energy and the linewidth temperature dependence from the anharmonic behaviour.
The magnetic ordering manifests itself through the impact on energy, linewidth and lineshape of the observed phonon modes of spin-ladder iron-based systems BaFe 2 S 3 , BaFe 2 Se 3 and BaFe 2 Se 2 O.Besides that, the analysis of the two--magnon continuum modes of BaFe 2 Se 2 O allows the estimation of the spin gap energy and classification of this material as a quasi-2D magnetic system.
Future work could be concentrated on the high pressure Raman scattering studies, as well as on the investigations of possible new materials from this class that will be produced by the doping of the existing ones.The results presented in this paper show that Raman spectroscopy is an invaluable tool which can expand our knowledge of the fundamental properties of iron chalcogenides.

VIBRATIONAL PROPERTIES OF IRON CHALCOGENIDES 959 Fig. 1 .
Fig. 1.Crystal structure of the representative iron-based superconductors.

Fig. 3 .
Fig. 3. Comparison of energy and linewidth temperature dependence for A 1g and B 1g Raman active modes of Fe 1+y Te crystals.Filled circles represent data from Ref. 48, open triangles data from Ref. 50, y = 0.09, filled triangles data from Ref. 50, y = 0.02, and filled squares data from Ref. 52.Solid and dashed lines are calculated spectra using phonon anharmonicity model.(Reprinted from Ref. 52, copyright (2017) with permission from Elsevier).

Fig. 5 .
Fig. 5. Raman spectra of BaFe 2 As 2 and FeSe single crystals.The inset shows temperature dependence of the FeSe Raman spectrum near 130 cm -1 , vertically offset for clarity. 54(Reprinted with permission from Ref. 54, copyright (2016) by the American Physical Society).

Fig. 6 .
Fig. 6.Crystal structure of K x Fe 2-y Se 2 within: a) I4/mmm and b) I4/m unit cells; c) FeSe layer in the (001)-plane of the sample.The solid line represents I4/m, whereas shaded square illustrates I4/mmm unit cell.Angle between principal axes of the two phases is around 26.6°.Parallel: Raman spectra of K x Fe 2-y Se 2 measured at 85 K in various polarization configuration (Θ = ∡(e i ,e s )).28

Fig. 7 .
Fig. 7. Raman spectra of the three superconducting crystals measured at room temperature.Additional modes, appearing below 60 cm -1 in the Tl-and Rb-substituted samples, are denoted by blue arrows.Dotted lines are guides indicating the peak positions. 75(Reprinted with permission from Ref. 75, copyright (2012) by the American Physical Society).

Fig. 11 .
Fig. 11.Temperature dependence of the energy and linewidth (FWHM) for the A 1g and B 1g Raman modes of K x Co 2-y Se 2 single crystal.Solid lines are the theoretical fits which take into account lattice thermal expansion and phonon-phonon scattering for energy and linewidth temperature dependence, respectively.The dotted lines are the extrapolation to 0 K. Shaded area denotes temperature range of the ferromagnetic phase.Inset of B 1g energy: temperature dependence of the B 1g mode frequency, compared with (M(T)/M(0)) 2 curve.Inset of B 1gFWHM: measure of the electron-phonon coupling (1/q) of the B 1g mode as a function of temperature.64

Fig. 13 .
Fig. 13.Left: the (aa) and (bb) polarized Raman spectra of BaFe 2 Se 2 O single crystals measured at room temperature and at 15 K. Vertical bars denote calculated values of the A g Raman active modes.New modes appearing below 240 K are denoted by asterisks.Right: the (ab) polarized Raman spectra of BaFe 2 Se 2 O single crystals measured at various temperatures.Vertical bars denote calculated values of the B 1g symmetry modes.Insets show normal modes of the two B 1g symmetry vibrations.31

Fig. 14 .
Fig. 14.Raman scattering spectra of BaFe 2 Se 2 O single crystals measured at various temperatures between 15 and 300 K in c(bb)c̄ polarization configuration.Only 400-670 cm -1 spectral range is shown.Inset: energy (circles) and linewidth (squares) of the 2∆ S (spin gap)mode as a function of temperature.31

TABLE I .
51perimentally obtained energies of the A 1g and B 1g Raman modes at room temperature (except for FeSe,51for which data are shown at T = 5 K) for some FeCh single crystals

the observed modes. 39 (Reprinted with permission from Ref. 39, copyright (2013) by the American Physical Society).
Preliminary analysis of K x Co 2-y Se 2 single crystals indi-Available on line at www.shd.org.rs/JSCS/ _________________________________________________________________________________________________________________________(CC) 2017 SCS Fe 2-y Se 2 and K 0.8 Fe 1.8 Co 0.2 Se 2 single crystals.Inset: An enlarged view of A 1g temperature dependence in a low temperature region near T c .
Fig. 8. Temperature dependence of A 1g and B 1g mode energy in K x 61 as in pure K x Fe 2-y Se 2 . 28Broad asymmetric structures, appearing in Raman spectra of both series of samples for the intermediate Ni (Co) concentrations, were attributed to the large structural disorder.At high Ni (Co) concentrations, as well as for pure K x Ni 2-y Se 2 67 and K x Co 2-y Se 2 ,