P Adler

A Lebon

V Damljanoviü

C Ulrich

C Bernhard

A V Boris

A Maljuk

C T Lin

B Keimer

Magnetoresistance Effects in SrFeO 3-G : Dependence on Phase Composition and Relation to Magnetic and Charge Order

Keywords: numbers: 75.47.De, 75.50.Ee, 76.80.+y, 78.30.-j

Single crystals of iron(IV) rich oxides SrFeO 3-with controlled oxygen content (0 G have been studied by Mössbauer spectroscopy, magnetometry, magnetotransport measurements, Raman spectroscopy, and infrared ellipsometry in order to relate the large magnetoresistance (MR) effects in this system to phase composition, magnetic and charge order. It is shown that three different types of MR effects occur. In cubic SrFeO 3 (G = 0) a large negative MR of 25% at 9 T is associated with a hitherto unknown 60 K magnetic transition and a subsequent drop in resistivity. The 60 K transition appears in addition to the onset of helical ordering at ~130 K. In crystals with vacancy-ordered tetragonal SrFeO 3-¡ as majority phase (G ~0.15) a coincident charge/antiferromagnetic ordering transition near 70 K gives rise to a negative giant MR effect of 90% at 9 T. A positive MR effect is observed in tetragonal and orthorhombic materials with increased oxygen deficiency (G = 0.19, 0.23) which are insulating at low temperatures. Phase mixtures can result in a complex superposition of these different MR phenomena. The MR effects in SrFeO 3-¡ differ from those in manganites as no ferromagnetic states are involved.

I. INTRODUCTION

The complex electronic phase diagrams of many transition metal (TM) oxide systems, for instance the intensely studied perovskite-type manganites Ln 1-x A x MnO 3 [START_REF]Colossal Magnetoresistance, Charge Ordering and Related Properties of Manganese Oxides[END_REF][START_REF]Colossal Magnetoresitive Oxides[END_REF], reflect a situation where the width of the conduction band, the electron correlation energy, and the strength of the electron-phonon coupling are of comparable magnitude. If two electronic phases are separated by a first-order transition, phase coexistence is often observed over a range of compositions, and the volume fractions can be changed by varying the composition, temperature, pressure, or magnetic field. This situation is encountered in the colossal magnetoresistance (CMR) manganites, where the ferromagnetic metallic state is stabilized by a magnetic field with respect to competing charge ordered antiferromagnetic or paramagnetic insulating states [START_REF] Uehara | [END_REF]4]. As a baseline for a description of the properties of the CMR manganites, it is helpful to consider the electronic structure of the prototype undoped parent compound LaMnO 3 , which contains only Mn 3+ ions with a t 2g 3 e g 1 high spin configuration.

Since the lowest energy optical excitations in LaMnO 3 were assigned to intersite d-d transitions [5], LaMnO 3 can be considered as a Mott-Hubbard type insulator. Both, t 2g and e g electrons are localized, and the t 2g 3 e g 1 electron configuration gives rise to a cooperative Jahn-Teller effect. This is the origin of orbital ordering (T OO ~ 750 K) [6] and of the type-A antiferromagnetic spin structure (T N = 140 K) [7]. Hole doping of LaMnO 3 leads to the formation of Mn 4+ (t 2g 3 ) ions. The double exchange (DE) mechanism, which favors delocalization of the e g electrons if the t 2g spins are ferromagnetically aligned, then stabilizes a ferromagnetic metallic state. Depending on the composition and structural details, however, various charge-ordered antiferromagnetic states have also been observed.

In order to improve our understanding of the physical properties of the manganites, it is interesting to consider iron(IV) based oxides, because the Fe 4+ ion is isoelectronic with the Mn 3+ ion. In contrast to LaMnO 3 the prototype Fe(IV) oxide SrFeO 3 is metallic and exhibits a cubic perovskite structure at all temperatures, without any evidence of a Jahn-Teller effect [8,9]. The different properties of Fe(IV) compared to Mn(III) oxides reflect the strongly enhanced covalency of iron(IV)-oxygen bonding, which is in agreement with the chemical trend that the M 3d orbitals are stabilized from the left to the right in a TM series and with increasing oxidation state for a given M. This is corroborated by band structure calculations of SrFeO 3 [10] as well as by comparative band structure calculations of CaFeO 3 and LaMnO 3 [11]. The larger covalency leads to a larger width of the conduction band which is formed from the V* (Fe 3d -O2p) antibonding e g orbitals. The increased itinerancy of the e g electrons explains the absence of the Jahn-Teller effect in SrFeO 3 and related compounds. Basic electronic structure parameters of SrFeO 3 were derived from the analysis of Fe 2p core level spectra within a cluster configuration interaction model [12]. Within this approach, the strong covalency of the Fe-O bonding results in a negative effective charge transfer energy ', which is the energy difference between the lowest lying states arising from the d 4 and d 5 L multiplets.

This means that the electronic ground state of Fe(IV) oxides is dominated by the d 5 L rather than the ionic d 4 configurations. Here L denotes a hole in the oxygen 2p orbitals.

Overall, the electronic situation in single-valent SrFeO 3 appears to be comparable to that in mixed-valent manganites. In both cases the DE mechanism favors the delocalization of the e g electrons, which are coupled to the localized t 2g 3 subshell. In contrast to the manganites, no doping is required, and the itinerancy of the e g electrons is bandwidth-driven in SrFeO 3 .

However, the charge carriers have a larger O 2p hole character. While it might be expected that the DE mechanism results in a ferromagnetic metallic state for SrFeO 3 , the compound actually undergoes a phase transition from a paramagnetic to a helicoidal magnetic state near 130 K [13,14]. This was originally explained by a competition between antiferromagnetic superexchange and DE interactions. Recently this view has been challenged, and it was shown by model calculations that for negative ' the DE mechanism alone is capable of stabilizing an incommensurate helical spin structure [15]. The metallic state found in SrFeO 3 becomes unstable with respect to a charge disproportionation of Fe 4+ into Fe (4-¡ )+ ("Fe 3+ ") and Fe (4+¡ )+

("Fe 5+ "), if the V bandwidth is somewhat reduced. This situation occurs in the distorted perovskite CaFeO 3 [16], where an intricate interplay between lattice distortions and correlation effects [17] leads to charge ordering (T CO = 290 K) [18] and the opening of a band gap. Remarkably, the helical spin structure (T N = 115 K) is not much influenced by the insulator-metal transition driven by replacing Sr with Ca. This can also be understood as a consequence of the negative ' in these materials [15].

The above considerations show that in iron(IV) based oxides spin-dependent electron delocalization processes as well as electron-lattice interactions are important. This has motivated a search for CMR effects akin to those observed in the manganites. It turned out that a successful route to large MR effects in Fe(IV) materials is the partial substitution of iron by cobalt or nickel, which stabilizes ferromagnetic ordering. MR effects up to -65% at 4

K and 5 T have been achieved in the systems SrFe 1-x Co x O 3-¡ [19,20], Sr 3 Fe 2-x (Co,Ni) x O 7-¡ [21 -25], and Sr 2/3 La 1/3 Fe 1-x Co x O 3-¡ [26]. Recently, Zhao et al. reported a sizable MR effect of up to -15% at 4 K and 9 T even for unsubstituted polycrystalline SrFeO 2.95 [27]. This effect is apparently related to an anomaly in the resistivity data near 55 K, which can be shifted by a magnetic field. The resistivity anomaly in turn appeared to be correlated with an anomaly near 65 K in magnetic susceptibility data and the appearance of paramagnetic Fe (3+¡ )+ sites in the Mössbauer spectra for T . ZKLFK LV EHORZ WKH 1pHO WHPSHUDWXUH LQ WKH 6U)H2 2.95 sample). In the light of earlier neutron diffraction experiments on SrFeO 2.90 [14], it was proposed that a modification of the pitch angle of the helical spin structure or a magnetic-field induced change from the helical to a conical spin structure could be reasons for the observed magnetotransport effects.

In contrast to manganites and the cobalt-or nickel-substituted ferrates, the MR effect in SrFeO 2.95 does not involve a ferromagnetic state. It is therefore of fundamental interest to understand its microscopic origin. Since previous experience with the manganites has shown that the coexistence of different phases can have a key influence on the physical properties [START_REF] Uehara | [END_REF]4], it is essential to consider the exact phase compositions in the investigated samples. ) phases separated by miscibility gaps [28]. Other compositions correspond to phase mixtures. In order to investigate the magnetotransport properties in the system SrFeO 3-¡ in more detail and to establish the relation to magnetic and charge ordering, we have conducted a systematic study of a series of SrFeO 3-¡ single crystals with different oxygen contents (G 6RPH KLJhlights of our work have already been communicated [29]. Here we report a comprehensive set of magnetotransport data, as well as Mössbauer, Raman, and optical reflectivity spectra, which enable us to give a detailed account of the relationship between the phase compositions, the magnetic and charge ordering transitions, and the magnetotransport properties. In particular, it is shown that depending on the phases present different types of magnetoresistance phenomena occur in this system. A large negative MR is observed in cubic SrFeO 3 , which is associated with a transition seen near 55 K in the magnetic as well as in the resistivity data. A giant negative MR related to a combined magnetic/charge ordering transition near 70 K is found for SrFeO 2.85 , a material with the tetragonal phase as the major component. Finally, a large positive MR effect at low temperatures is evident in samples with further increased oxygen deficiency. In the light of our results, we reconsider the data reported by Zhao et al. and argue that the properties of their sample should be interpreted in terms of a mixture of cubic and tetragonal phases.

The paper is structured as follows. In order to support the interpretation of our experimental findings, the most important structural features of the system SrFeO 3-¡ are summarized in Section II. In Section III the experimental details are given. In Section IV Mössbauer, magnetotransport, and optical data are presented. Finally, Section V offers some Concluding Remarks.

II. SUMMARY OF STRUCTURAL DATA

The known phases in the system SrFeO 3-¡ can be described by the general formula Sr n Fe n O 3n-1 with n = 7KHLU FU\VWDO VWUXFWXUHV ZHUH VWXGLHG SUHYLRXVO\ DW URRP temperature by powder neutron diffraction [28]. The n = PHPEHU 6U)H2 [31,32].

Only two iron sites are present in the crystal structure of Sr 4 Fe 4 O 11 [28]. Again, dimers of Fe1O 5 units are formed. These are connected to rows of strongly distorted Fe2O 6 octahedra. The bond distances of the square pyramids are similar to those in Sr 8 Fe 8 O 23 .

Therefore the Fe1 sites again correspond to Fe 4+ , whereas the large Fe-O distances in the Fe2O 6 octahedra are in accord with an assignment as Fe 3+ . This was concluded previously on the basis of bond valence calculations [28] whose validity has, however, been questioned in course of a recent neutron diffraction study on Sr 4 Fe 4 O 11 [33]. Considering a possible Jahn-Teller effect of Fe 4+ it was proposed that the distorted Fe2O 6 octahedra should be associated with the Fe 4+ sites and the square pyramids with the Fe 3+ sites. We discard this possibility as it is in clear contradiction to the known bond distances in perovskite-type Fe 3+ and Fe 4+ oxides (see above). Furthermore, due to strong covalency of iron-oxygen bonding the Jahn-Teller effect of Fe 4+ is usually suppressed.

Finally we mention the brownmillerite-type crystal structure of the pure Fe 3+ phase Sr 2 Fe 2 O 5 (n = 2 space group Icmm [28] or Ibm2 [34]) where alternating layers of tetrahedrally and octahedrally coordinated iron sites occur.

III. EXPERIMENTAL DETAILS

The experiments were performed on high quality SrFeO 3-¡ single crystals synthesized in a four-mirror type floating zone furnace [35]. The oxygen contents were determined to an accuracy of a0.02 by thermogravimetry (TG) in a reducing Ar/H 2 atmosphere (H 2 content 5 at.%). As-grown oxygen-deficient crystals with G = 0.13, 0.15, 0.19 and 0.23 were obtained under different growth conditions, depending upon applied oxygen pressure and growth rate.

Nearly stoichiometric SrFeO 3.00 and slightly oxygen-deficient SrFeO 2.95 were prepared by post-annealing at 400°C under high oxygen pressure of 5 kbar and 700 -800 bar, respectively.

A more strongly oxygen-deficient sample of composition SrFeO 2.69 was obtained by postannealing at 550°C in argon flow. In the following the samples will be labeled according to the oxygen contents determined by TG. An independent check of oxygen stoichiometries as well as an estimate of the phase compositions was derived from Mössbauer spectra (Section IV.A).

The magneto-transport characterization was performed with a PPMS system (Quantum Design). For measurements of the electrical resistivity, U, the crystals were cut and oriented along (100) faces, Cr/Au electrodes were deposited in a four-point contact geometry, and gold leads were glued on the electrodes with silver epoxy. The susceptibility curves were recorded in Field Cooling (FC) and subsequent Field Heating (FH) runs, with a 1T field. The electrical resistivities were measured in ac-mode in Zero Field Cooling (ZFC) and subsequent Zero Field Heating (ZFH), this was followed by FC and FH runs at 9T. The zero-field and in-field runs were compared to obtain the MR. We adopt the following definition:

) 0 ( )) 0 ( ) ( ( U U U H MR
. Isothermal field scans were recorded near the temperature of the anomalies observed in FC and FH runs. For this series of measurements, the sample was first heated to room temperature and subsequently cooled to the required temperature in zero field.

Mössbauer spectra were measured with a standard spectrometer operating with a sinetype drive signal. The source was 57 Co in a Rh matrix. For the Mössbauer investigations, crystals of the different SrFeO 3-compositions were ground, and the resulting powder was diluted with polyethylene in order to ensure a homogeneous distribution of the material in the plexiglass sample container. The container was placed in an Oxford flow cryostat. The spectra normally were evaluated by fitting Lorentzians to the data. Spectra of magnetically ordered phases were evaluated with six-line patterns. Spectra of magnetically ordered SrFeO 3 were evaluated with the Voigt based fitting algorithm of the Mössbauer software package " RECOIL" [36]. The intensity ratios were taken as 3:2:1:1:2:3 (thin absorber approximation).

All spectra are referenced to D-iron.

The Raman spectra were collected with incident light of wavelength 514.5 nm emitted by mixed gas Ar/Kr lasers on two triple-monochromator DILOR spectrometers. The spectrometers were equipped with identical charge coupled device (CCD) detectors cooled with liquid N 2 . The spectra were calibrated at each temperature using the lines of an argon lamp. The samples SrFeO 3.00 and SrFeO 2.85 were studied in macro-Raman mode, while SrFeO 2.69 was studied in micro-Raman mode. Great care was taken to focus on the same point in the whole temperature range. All samples investigated were cut along the <001> directions and they had a mirror-like finish.

The ellipsometric measurements were performed with a home-built ellipsometer in combination with a fast-Fourier-transform interferometer at the infrared beamline of the ANKA synchrotron at Forschungszentrum Karlsruhe, Germany [37].

IV. RESULTS AND DISCUSSION

IV.A Mössbauer spectroscopy

Room temperature spectra

In Fig. 2 room temperature Mössbauer spectra of various SrFeO 3-samples studied in this work are shown. By comparison with literature data [31,32], the spectra can be used to identify the different phases present. The spectrum of the 5 kbar annealed sample essentially consists of a single line with an isomer shift IS which is typical for stoichiometric cubic SrFeO 3 (C phase). On the other hand, the spectrum of SrFeO 2.95 reveals an additional quadrupole doublet with a higher IS. This indicates the presence of the tetragonal (T) phase 2.

SrFeO 3.00

From the absence of any Fe 3+ or Fe 3.5+ signals in the low and room temperature Mössbauer spectra of 5kbar annealed SrFeO 3.00 we had concluded that this sample is stoichiometric (G < 0.02) [29]. In order to clarify the origin of anomalies in the magnetic and magnetotransport data near 55 K (see Ref. [29] and Section IV.B), we have now performed a detailed Mössbauer study of the SrFeO 3.00 sample in the temperature range 10 to 130 K.

Considering the pronounced hysteresis effects in the magnetotransport data, Mössbauer experiments have been performed in the heating as well as in the cooling mode. A selection of spectra is shown in Fig. 3. As expected, the spectra confirm the development of magnetic ordering below 130 K, indicated by six-line hyperfine patterns. Similar to the 10 K spectrum shown in Ref. [29], all spectra at T d 60 K consist only of a single sextet, with isomer shifts IS and magnetic hyperfine fields B hf in good agreement with earlier Mössbauer data of SrFeO 3 [31]. Within the error limits (about 2%) there is no indication of additional Fe sites in these spectra. Up to 60 K no major changes are seen. However, at somewhat higher temperature between 60 and 70 K some intensity near v = 0 mm s -1 starts to emerge (v is the velocity of the Mössbauer drive), and between 70 and 90 K a certain fraction of a paramagnetic signal becomes apparent. Furthermore, above 60 K the outer lines of the magnetic sextet become asymmetric, and the lines broaden progressively up to 125 K. At 130 K, a single line spectrum is seen, which means that the Npel temperature for the present sample lies between 125 and 130 K. This is somewhat lower than the literature value T N = 134 K for cubic SrFeO 3 [9]. At first glance the spectra of the paramagnetic phase consist of a single line. However, detailed inspection of the room temperature spectrum (Fig. 2) indicates a weak shoulder towards higher Doppler velocities.

Considering the Mössbauer spectra of SrFeO 2.87 and SrFeO 2.95 (see below), it appears likely that the occurrence of paramagnetic sites between 70 and 90 K as well as the small asymmetry in the room temperature spectrum indicate the presence of small regions of tetragonal SrFeO 3-even in the 5kbar annealed sample. In fact, the room temperature spectrum (Fig. 2) can be fitted by one Fe 4+ single line and a 4% contribution of Fe 3.5+ sites.

The Mössbauer parameters of the latter sites were taken from a sample with increased oxygen deficiency, where the presence of the T phase is more obvious. Using the common oxidation states +2 and -2 for the Sr and O atoms, respectively, one obtains a sample composition SrFeO 2.99 which is within the error limit ±0.02 for G derived from the TG data. At low temperatures the Fe 3.5+ sites in the tetragonal domains are expected to reveal charge localization (see below). The resulting 2% contribution of magnetically ordered Fe 3+ sites is, however, at the detection limit of the low temperature Mössbauer spectra.

It is apparent that the inner lines of the hyperfine sextets are narrower than the outer ones. This suggests that the line broadening above 60 K reflects a distribution of magnetic hyperfine fields. Accordingly the spectra were evaluated with a Voigt-based fitting algorithm [36]. In order to account for the asymmetry of the line shapes, a B hf distribution with two components was required: a major sharper and a minor broader one. The B hf distributions at selected temperatures are shown in Fig. 4. In the spectra at T t 70 K one Fe 3.5+ quadrupole doublet and one Fe 4+ singlet were added to account for the paramagnetic fraction. This model yields a reliable description of the spectral shapes (see Fig. 3). The area fraction of the magnetically ordered Fe 4+ sites (Fig. 5) decreases between 60 and 90 K, and changes only slightly upon further heating to 125 K. This means that the minority phase undergoes magnetic ordering near 70 K, which is similar to the Npel temperature of tetragonal SrFeO 3-.

The area fraction of the paramagnetic phase at 110 K is ~6% and is composed of 3% Fe 3.5+ and 3% Fe 4+ sites. These values are in reasonable agreement with the area fractions at room temperature. It is noted that the area fractions from spectra measured in the heating mode compare well with those from spectra measured in the cooling mode. Accordingly, there is no evidence of a hysteresis in the Mössbauer data. In indicates the presence of a small amount of oxygen vacancies (G ~ 0.01) which are concentrated in more strongly oxygen-deficient domains with a behavior similar to that of bulk tetragonal SrFeO 3-. These domains are embedded in the majority cubic perovskite matrix. In the light of these results the question arises whether the 55 K transition in the magnetic and magnetotransport data (see [29] and Sect. IV.B) is an intrinsic property of pure cubic SrFeO 3 , or rather related to phase inhomogeneity on a submicroscopic level. The transition in the magnetic and magnetotransport data occurs at somewhat lower temperature than the minority magnetic phase transition in the Mössbauer spectra. In addition there is no evidence for hysteresis effects in the Mössbauer area fractions whereas a quite pronounced hysteresis is observed in the magnetotransport anomaly. These findings suggest that the two transitions are of different origin. This conclusion is also supported by the Mössbauer and magnetotransport data of SrFeO 2.95 , a sample with increased fraction of T phase (see below).

Finally, we point out that the magnetic susceptibility of a SrFeO 3 sample annealed under even higher oxygen pressure is nearly identical to that of the sample annealed under 5 kbar [38]. In particular, the anomaly near 60 K is undiminished while the paramagnetic signals in the Mössbauer spectra between 70 and 130 K are absent. This underscores our conclusion that it is an intrinsic feature of the cubic phase.

SrFeO 2.87

In order to establish the properties of the T phase, we now turn to the Mössbauer spectra of SrFeO 2.87 . The spectra shown in Fig. 7 Considering the low-temperature area fractions and assuming equal Debye-Waller factors for the various Fe sites, this leads to an average iron oxidation state of 3.74 and an oxygen content of 2.87 (G = 0.13), in agreement with the TG data. Above 130 K, SrFeO 2.87 is completely in the paramagnetic state. Following previous work [31,32], the spectra were analyzed in terms of two components only: one Fe 4+ single line, and one average charge Fe 3.5+ quadrupole doublet. The area fraction of the Fe 3.5+ sites decreases from ~55% in the paramagnetic phase to a residual fraction of about 10% in the magnetically ordered phase.

This suggests that the magnetic ordering near 70 K coincides with charge ordering (CO) of most of the Fe 3.5+ into Fe 3+ and Fe 4+ sites. A charge disproportionation of Fe 4+ , as for instance in CaFeO 3 [16], should lead to higher Fe 3+ area fractions and is therefore excluded.

Based on the Mössbauer spectra and previously reported room temperature structural data [28], the following microscopic model for the physical properties of tetragonal Sr 8 Fe 8 O 23 is proposed. The high electrical conductivity in the paramagnetic phase arises from a delocalized electronic system with higher electron density at the Fe2 sites (Fe 3.5+ ) and lower electron density at the Fe1 and Fe3 sites (both formally Fe 4+ ). Although the coordination numbers are different, the two Fe 4+ species cannot be resolved in the Mössbauer spectra of the paramagnetic phase. Near 70 K the Fe2 3.5+ sites undergo a charge ordering transition, which leads to electronically localized Fe 3+ and Fe 4+ sites and to a concomitant development of three-dimensional magnetic order. Sextet F in the spectra can then be attributed to the Fe 4+ sites arising from the CO. Their more localized behavior is in agreement with a more negative IS than that in SrFeO 3 (c.f. with IS of sextet D) [START_REF]Comparison of the IS data of known iron(IV) oxides shows that more localized electronic systems exhibit more negative IS[END_REF]. This view is supported by the nearly equal values of the total Fe 3+ area fraction due to sites A, B and of the area fraction of the Fe 4+ Accordingly there is an excess of Fe 3.5+ species, in agreement with the residual fraction of magnetically ordered Fe 3.5+ sites in the low temperature spectra. The latter sites are obviously not involved in CO and possibly are located at a crystallographically different site in the low temperature crystal structure. The above area fractions in the 110 K spectrum lead to the composition SrFeO 2.85 for the T phase in the present sample. There is no evidence of the orthorhombic phase in the spectra (see below). Finally it is noted that two magnetically distinct Fe 3+ sites are discernible, one of which (indicated by an arrow in Fig. 7) exhibits an unusual temperature dependence of B hf . This behavior could also be related to disorder effects introduced by additional oxygen vacancies. Clearly the chemical, structural, electronic and magnetic behavior of the T phase is very complex, and more studies on crystals with improved phase homogeneity are required.

SrFeO 2.95

The 800 bar oxygen-annealed SrFeO 2.95 crystals are also a phase mixture of C and T phases, but with the C phase as the majority component. This is confirmed by the Mössbauer spectra shown in Fig. 10. At 100 K, for instance, the spectra show the coexistence of paramagnetic sites and the magnetically ordered C phase. From the area ratios, the fractions of C and T phases are estimated as 60% and 40%, respectively. Near 80 K the minority phase begins to develop magnetic order, and the low temperature spectra reveal the various Fe sites present in the charge-ordered T phase. The spectra are well described as a superposition of the spectra of C and T phases. These results also support our interpretation of the Mössbauer spectra of the 5 kbar annealed SrFeO 3 , where the small minority component behaves in a fashion very similar to that of the T phase fraction in SrFeO 2.95 . The temperature evolution of the present SrFeO 2.95 Mössbauer spectra is comparable to that of a ceramic sample of similar composition reported by Zhao et al. [27]. These authors attributed the paramagnetic signal near 80 K to a single Fe (3+ )+ site, and included a single Fe 3+ line in addition to the Fe 4+ sextet in their model of the 4 K spectrum. In the light of the present work, it appears likely that the ceramic sample of Ref. [27] is also a mixture of C and T phases, and that the changes seen in the spectra near 80 K correspond to the magnetic/CO transition of the T phase. However, the signal-to-noise ratio of the Mössbauer spectra in Ref. [27] is not sufficient to resolve the complex low temperature sub-spectrum of the T phase.

SrFeO 2.69 and SrFeO 2.81

The O phase Sr 4 Fe 4 O 11 is characterized by magnetically disordered Fe 4+ sites down to 4 K [31,41]. The latter are indeed evident in the 4 K spectrum of the present SrFeO 2.69 sample (Fig. 11) which reveals an Fe 4+ quadrupole doublet in addition to magnetic hyperfine sextets.

The Fe 4+ ions have been associated with the square pyramidal Fe1O 5 sites in the room temperature crystal structure of Sr 4 Fe 4 O 11 [28]. By contrast, the Fe2 sites with Fe 3+ ions located in chains of vertex-sharing FeO 6 octahedra undergo magnetic ordering near 230 K [42,33]. In the spectra at T d 200 K shown in Fig. 11, they give rise to one Fe 3+ hyperfine sextet with a large quadrupole interaction parameter. At T t 250 K, only a quadrupole doublet with large quadrupole splitting is observed ( sextet with large quadrupole interaction in the 140 K and magnetically disordered Fe 4+ sites in the 12 K Mössbauer spectra (Fig. 12). The essential features of the spectra are well modeled by a superposition of those of the T and O phases. The fraction of the O phase is most reasonably estimated from the 140 K spectrum. As the Fe 3+ and Fe 4+ sites in the O phase occur in the ratio 1:1, its volume fraction is given by twice the area fraction of the magnetically ordered Fe 3+ component and amounts to 24%. The average iron oxidation state is 3.67, which leads to the overall composition SrFeO 2.84 . Subtracting the Fe 4+ fraction of the O phase from the total Fe 4+ content, the composition of the T phase in the sample is derived as SrFeO 2.86 . Again, there is an excess of Fe

IV.B Magnetic susceptibility and ac transport

Magnetic susceptibility

Fig. 13 shows the magnetic susceptibility F of a set of single crystals measured at 1 T in field cooling and heating runs. The temperatures corresponding to anomalies in the F(T)

curves are summarized in Table 3. In the G = 0 sample, a maximum heralds the onset of helical order at 130 K, and an additional pronounced anomaly of the susceptibility is observed at a 60 K (FC data). The latter anomaly shows a thermal hysteresis with a width of 10 K. In the G = 0.05 sample the maximum at 130 K is predominant, but a pronounced shoulder is observed around 75 K. This is followed by a decrease of the susceptibility upon further cooling. The latter feature is a signature of the onset of antiferromagnetic order in the minority tetragonal phase and also displays thermal hysteresis. In agreement with this interpretation, the G = 0.15 sample exhibits a sharp maximum at 70 K with a hysteresis of ~ 3 K width. The weaker shoulder near 130 K is evidence of residual C phase. A noteworthy additional anomaly of the susceptibility is observed at 115 K for the three compositions containing metallic C phase. This feature has no obvious counterpart in the Mössbauer spectra, and its microscopic origin is presently unknown. With a further increase of the oxygen deficit, the 70 K feature is broadened for G = 0.19 and shifted towards lower temperature in the G = 0.23 sample. In addition, the small inflection point in the susceptibility near 230 K and the slight upturn below 50 K are consistent with what is known of the orthorhombic phase [33]. The former feature reflects the antiferromagnetic ordering of the Fe 3+ sites near 230 K, whereas the latter is associated with the Fe 4+ sites which remain magnetically disordered. It is emphasized that the 230 K transition in SrFeO 3-samples corresponds to the well-known magnetic phase transition of the orthorhombic phase. It is not a new and unexpected feature as has been claimed recently [43].

Magnetoresistance

Figures 14 and 15 summarize the magnetoresistance (MR) properties of the SrFeO 3-system.

The temperatures corresponding to anomalies in the MR are also included in Table 3. In agreement with earlier work [9], the temperature dependence of the resistivity of SrFeO 3.00 (Fig. 14a) indicates that the C phase is metallic. A precipitous decrease of the resistivity by a factor of two is observed at 52 K (ZF data). The transition exhibits a hysteresis with a width of 9 K and appears to be related to the 60 K anomaly in the magnetic susceptibility data.

Application of a 9 T magnetic field shifts the transition by a5 K to higher temperature. This induces a large negative MR effect (Fig. 15) in a narrow temperature range around 55 K ('T 1/2 a 8 K, max. MR ~ -25%).

SrFeO 2.95 also exhibits metallic behavior with a resistivity anomaly below 70 K (Fig. 14b), which coincides with the 70 K maximum in the susceptibility of this sample. In contrast to the SrFeO 3.00 data, the resistivity first exhibits an upturn upon cooling below 70 K, followed by a decrease at lower temperature. Application of a 9 T magnetic field reveals that the resistivity anomaly in SrFeO 2.95 actually reflects two phase transitions. The shape of the U(T) curve can be well understood as the superposition of the properties of C and T phases for this composition. This is evident by considering the magnetotransport data of SrFeO 2.85 , where the T phase is the majority component. As opposed to the samples dominated by the C phase, the oxygen-deficient SrFeO 2.85 composition displays a weakly activated, semiconducting behavior upon cooling from room temperature to 70 K, where the resistivity increases by an order of magnitude (Fig. 14c)). The resistivity jump is in agreement with a charge ordering transition near 70 K, as suggested by the Mössbauer spectra of SrFeO 2.87 . The transition is characteristic of the T phase and shifted by a6 K to lower temperature in a magnetic field of 9 T, in contrast to the 52 K transition in cubic SrFeO 3 . The field-induced low temperature shift of the transition gives rise to a giant negative MR (GMR) effect of -90% that peaks sharply at ~69 K in a narrow temperature range ('T 1/2 a3.8K) (Fig. 15). Below 50 K, the small down-turn of the resistivity could be assigned to percolation paths of the metallic minority phase within the insulating matrix.

Returning now to the SrFeO 2.95 magnetotransport data, the small resistivity upturn near 70 K, which is shifted to lower temperature at 9 T, can be assigned to the charge ordering transition in the minority T phase. On the other hand, the overall resistivity decrease, which is shifted to higher temperature at 9 T, reflects the resistivity anomaly in the majority C phase.

These considerations are in full agreement with the Mössbauer data on SrFeO 2.95 . It is noteworthy that at 9 T, in contrast to the zero-field properties, the resistivity decrease in the C phase occurs at higher temperature than the CO transition in the T phase. As the oxygen deficit is further increased, the amount of metallic phase decreases and accordingly the percolation paths vanish. This is exemplified for SrFeO 2.81 , where the weakly activated semiconducting behavior is evidenced down to 70 K, and a resistivity jump of an order of magnitude occurs akin to the one of SrFeO 2.85 . Below 50 K, however, an additional strong upturn in U is noticed, and the sample becomes fully insulating at low temperatures. Finally, the resistivity of the SrFeO 2.77 samples exhibits behavior closely similar to that of SrFeO 2.81 , but the jump of the resistivity shifts slightly to lower temperature and the thermal hysteresis is reduced. This presumably reflects the increasing volume fraction of the orthorhombic phase.

We now address the magnetic field dependence of the resistivity, which exhibits a variety of behaviors as a function temperature, oxygen deficit, and phase mixture.

Representative data are shown in Fig. 16. The samples with the C phase as majority component (G=0.00 and G=0.05) have a large negative MR effect in a quite narrow temperature range (Fig. 15). Within this temperature range, the resistivity is weakly field dependent up to about 8 T, and is abruptly reduced for larger fields. Addition of a minority amount of tetragonal phase lowers the critical field significantly to a5.5 T (Fig. 16a). For G=0.00 and G=0.05, the MR effect is remnant after a subsequent ramp-down of the field, and even when the field is reversed (data not presented here). For the samples containing predominantly the T phase (Fig. 15), a giant negative MR effect is observed. This effect also requires fields around 8 T (Fig. 16b), but it is fully reversible upon reducing the field back to zero, and a symmetric curve is observed when the field is reversed. Finally, a pronounced positive MR effect is apparent in the low temperature insulating phases of SrFeO 2.81 and SrFeO 2.77 . For these compositions, the MR effect is history dependent, e.g. the value of MR measured at a given temperature (T = 10 K) changes between isothermal field scans and temperature scans. From the first method a MR effect of 52% is derived, while for the second a positive MR as large as 256% is measured.

The origin of the main MR effects in the C and T phases appears to be a shift in the thermodynamic balance of two phases with different conductivities, which induces a shift in the critical temperature separating these phases. A similar effect has been observed at the Verwey transition of magnetite [44]. The more complex behavior shown in Fig. 15, as well as the positive MR exhibited by the insulating samples at low temperatures, probably reflect at least in part the field dependence of current paths in a mixture of phases with different conductivities. If this is the case, a full understanding of these effects requires detailed information about the microstructure of these samples, an interesting subject of future work.

We now compare the present magnetotransport data on SrFeO 3-single crystals with the study by Zhao et al. [27] on ceramic samples. One of our crystals had the same composition, SrFeO 2.95 , as the one investigated by Zhao et al. Considering the similar composition and the similar Mössbauer spectra of the two materials (see above) it is likely that the sample of Ref. [27] also contains a mixture of cubic and tetragonal phases. The pronounced U(T) anomaly near 50 K in Ref. [27] and the associated MR effect then reflect the transition of the majority C phase, whereas the magnetic anomaly at a somewhat higher temperature (65 K) and the development of paramagnetic sites in the Mössbauer spectra correspond to the magnetic/CO transition in the minority T phase. In contrast to the present SrFeO 2.95 single crystal, the signature of the CO transition is not seen in the U(T) data of the ceramic sample. However the detailed electronic transport paths are determined by the microstructure of the materials, which may differ in single crystals and ceramics. We emphasize that the pure C phase is metallic both below and above 55 K ruling out that the resistivity anomaly coincides with a metal -insulator transition. Accordingly the low temperature upturn in the resistivity data of Ref. [27] reflects the coexistence of metallic C and insulating T phases rather than a metal-insulator transition in SrFeO 2.95 as was claimed by Zhao et al. [45]. In the present single crystals, large MR effects are only found in the vicinity of the phase transitions in the respective compositions. The low temperature MR effects in ceramic SrFeO 2.95 possibly correspond to grain boundary effects in the polycrystalline material. A further weak resistivity anomaly coupled with a small MR effect was established near 107 K in ceramic SrFeO 2.95 and associated with the magnetic ordering transition. A similar feature near 115 K is also apparent in the present data of SrFeO 3.00 . It is, however, rather related to an additional cusp near 115 K in the magnetic susceptibility (indicated by an arrow in Fig. 13), than to the onset of helical ordering near 130 K. The relation between magnetic and resistivity anomalies is clarified in Fig. 17 where we compare the derivatives dlnF/dT and dlnU/dT for SrFeO 3.00 . It is obvious that the 130 K magnetic transition does not give rise to any anomaly in U(T). Fig. 17 also suggests that the resistivity response related to the 60 K magnetic transition occurs at somewhat lower temperature.

The negative GMR effect near 70 K in mainly tetragonal materials has recently been confirmed for a ceramic sample of SrFeO 3-with G = 0.17 [43]. This material appears to be a mixture of T and O phase, as can be inferred from the presence of a 230 K transition in the magnetic susceptibility data. The onset of the GMR effect is already seen at 6 T, a somewhat lower field than in the present G = 0.15 sample. Finally, we note that a combined magnetic ordering/CO transition giving rise to a similar resistivity jump as in SrFeO 2.85 was reported previously for Sr 2/3 Ln 1/3 FeO 3 [46]. In this system an antiferromagnetic phase transition is coupled to a charge disproportionation of Fe 4+ , which results in Fe 3+ Fe 3+ Fe 5+ CO along the pseudocubic [111] direction [47]. For samples with Ln = La and Pr, a weak MR effect of -2% at 7 T was observed near T N . Somewhat larger MR effects up to -7% were reported at low temperatures [48]. However, that there is no charge disproportionation of Fe 4+ in the chargeordered state of SrFeO 2.85 .

IV.C Raman scattering and far-infrared ellipsometry

In the cubic perovskite SrFeO 3 (space group Pm-3m) no Raman vibrational modes are allowed, but three IR active modes of F 1u symmetry are expected. This is in agreement with the experimental Raman and ellipsometric IR spectra of SrFeO 3.00 depicted in Fig. 18. While the Raman spectra do not show any features attributable to phonons, three IR modes with room temperature frequencies 172, 249, and 559 cm -1 are observed. The temperature independence of the spectra corroborates the absence of any structural phase transitions below room temperature. The phonon modes are superimposed on an electronic background due to a Drude-like charge carrier response, which is strongly enhanced at low temperature. This compares well with the increased electrical conductivity below the 55 K phase transition.

Further evidence for the CO transition in the T phase is obtained from Raman and infrared spectra of SrFeO [33]. This implies that the orthorhombic phase does not undergo a CO instability.

These conclusions are supported by far-infrared ellipsometry data on the G=0.15

sample. It was reported already in our previous work [29] that the optical conductivity suddenly drops upon cooling below ~70 K, and that additional optical modes appear in the same temperature range. Figure 20 provides a synopsis of room temperature and low temperature Raman scattering data in two different polarization geometries as well as farinfrared ellipsometry data on this sample. Note that comparable changes in the optical conductivity have been reported for the CO transition in Sr 2/3 La 1/3 FeO 3 [49]. All data sets exhibit numerous additional phonon modes at low temperatures. Their frequencies are summarized in Table 4. Since the crystal structure of the tetragonal phase that undergoes the CO transition has thus far not been determined, it is impossible to assign the modes. However, it is evident that a number of modes are observed in both Raman polarization geometries and in the ellipsometry data at the same frequencies. This may either reflect the low symmetry of the crystal structure in the CO state, or a symmetry lowering at the boundaries of the constituent T and C phases.

V CONCLUDING REMARKS

Iron(IV) rich oxides reveal a variety of magnetoresistance effects. In the previously studied cobalt or nickel substituted materials, the generation of MR is related to creation of ferromagnetic clusters or regions. The largest MR effects are encountered in compositions with spin-glass like magnetic behavior [22] pointing to competing ferro-and antiferromagnetic interactions. In this respect these materials behave in a similar fashion as other magnetoresistive oxides, for instance certain cobaltites [50]. In contrast, the MR effects in single crystals of SrFeO 3-which are the subject of the present work are apparently different as they do not involve ferromagnetic ordering. We have shown that it is essential to consider the phase composition of the samples in order to establish the physical properties of this system. Actually three different types of MR effects are found. In cubic SrFeO 3 helical magnetic ordering emerges near 130 K which is, however, not associated with any anomalies in the electrical resistivity. In contrast a hitherto unknown magnetic transition near 60 K gives rise to a sharp decrease of the resistivity. The latter is shifted by a magnetic field of 9 T to higher temperature which results in a large MR effect. The detailed nature of the 60 K transition remains to be established, but it obviously neither involves ferromagnetic ordering nor charge reorganization. A coincident charge -magnetic ordering transition is the origin of a resistivity jump by an order of magnitude in materials containing tetragonal oxygendeficient SrFeO 3-(ideal composition Sr 8 Fe 8 O 23 ) as major component. The transition is shifted by a 9 T field to lower temperature which results in a giant negative MR effect of 90%. This is the largest MR effect discovered so far in an iron(IV) based oxide. The magnetic phase transition shows antiferromagnetic characteristics, but the detailed low-temperature spin and crystal structures remain to be clarified. Finally, there is a pronounced positive MR effect in low-temperature insulating SrFeO 3-materials which may either be a property of the pure tetragonal phase or related to the coexistence of tetragonal and orthorhombic phases.

We believe that exploration of the different types of magnetoresistance effects in iron(IV) based oxides is a valuable addition to our understanding of the magnetotransport properties of transition metal oxides and may broaden the concepts for the design of magnetoresistive materials and devices. (lines) was influenced by micro-cracks, these data were normalized around room temperature to IR data extrapolated to zero frequency (see [29]).

  It is known that the structural phase diagram of the SrFeO 3-¡ system encompasses four phases, namely the stoichiometric cubic phase (C, G = 0) as well as the oxygen vacancy ordered tetragonal (T, G = 0.125, Sr 8 Fe 8 O 23 ), orthorhombic (O, G = 0.25, Sr 4 Fe 4 O 11 ), and brownmillerite-type (B, G = 0.5, Sr 2 Fe 2 O 5

Sr 8 Fe 8 O

 88 23 and can be assigned to an average charge Fe3.5+ signal arising from the structurally distorted Fe2 sites. The spectrum of SrFeO 2.87 mainly reflects the features of the T phase and consists of the Fe 3.5+ quadrupole doublet in addition to an Fe 4+ single line. As the lowtemperature spectra reveal also some C phase (see below), the Fe 4+ single line in the spectrum of SrFeO 2.87 is attributed to a superposition of the Fe1 and Fe3 sites of the T phase and Fe 4+ sites of cubic SrFeO 3 . An additional Fe 3+ doublet with a much larger quadrupole splitting in the spectrum of SrFeO 2.81 is a signature of the structurally distorted Fe 3+ (Fe2) sites in the crystal structure of orthorhombic (O) Sr 4 Fe 4 O 11 . Accordingly, SrFeO 2.81 corresponds to a mixture of the T phase as majority and the O phase as minority components. As expected, the sample with composition SrFeO 2 . 69 contains the O phase as its main constituent. This is again apparent from the characteristic Mössbauer spectrum. In addition to the Fe 3+ quadrupole doublet, a second doublet with a smaller quadrupole splitting is apparent. Based on its IS value, it is assigned to the square pyramidal Fe 4+ (Fe1) sites in the crystal structure of the O phase. Two further weak lines in the spectrum of SrFeO 2.69 are the inner components of sextets arising from magnetically ordered Sr 2 Fe 2 O 5 . These additional lines are more readily seen in spectra measured over an extended range of Doppler velocities. Quantitative estimates of oxygen stoichiometries and phase fractions as well as details about magnetic and charge ordering phenomena are obtained from the temperature dependence of the Mössbauer spectra of the various materials, described below. Selected Mössbauer parameters and the sample compositions derived from data are given in Table

Fig. 6

 6 the temperature dependence of the mean values <B hf > for the two components in the hyperfine field distribution is shown. The minor broad component 2 reveals a more pronounced temperature dependence than the major sharper component 1 and accounts for the increasing asymmetry of the spectra. The temperature dependence <B hf >(T) of component 1 was reproduced by the relation <B hf (T)>/<B hf (0)> = (1-T/T N ) with <B hf (0)> = 33.5 T, T N = 126.9 K, E = 0.16. In summary, the detailed Mössbauer study of the 5 kbar annealed sample SrFeO 3.00

  provide evidence of two magnetic phase transitions, in agreement with magnetic susceptibility data of the same sample. The magnetic susceptibility curve of the SrFeO 2.87[START_REF]Colossal Magnetoresitive Oxides[END_REF] crystal is very similar to that of the SrFeO 2.85(2) sample used in magnetotransport and optical experiments (Sections IV.B and IV.C below). The first transition below T N1 ~130 K leads to a single hyperfine sextet D (area fraction ~20%), with isomer shifts IS and a temperature dependence of the magnetic hyperfine field B hf (T) (Fig.9) typical for cubic SrFeO 3 . Near T N2 ~ 70 K, a second magnetic phase transition occurs. The complicated but well-structured low-temperature spectra were modeled by a superposition of five (15 K) or six (>15 K) hyperfine sextets. A typical decomposition is illustrated in Fig.8for 50 K, and the results of the data evaluation are depicted in Fig.9. From B hf (T) it is evident that the magnetic order for all components except D vanishes near 70 K. Thus all sites except D are considered as intrinsic to the T phase. Based on the IS and B hf values, charge states of 3+ , 4+, and 3.5+ are assigned to the sub-spectra (A,B), (D,E,F), and C, respectively.

FIG. 1 (FIG. 2 (FIG. 3 (FIG. 5 (FIG. 6 (FIG. 7 FIG. 8 (FIG. 9 (FIG. 11 (FIG. 12 (FIG. 14 (

 12356789111214 FIG. 1 (Color online) Illustration of the crystal structures of Sr 8 Fe 8 O 23 (top) and Sr 4 Fe 4 O 11 (bottom).

Fig. 15 FIG. 16 (FIG. 17 (FIG. 18 (FIG. 19 (FIG. 20 (

 151617181920 Fig. 15 Temperature dependence of the magnetoresistance MR at 9 Tesla for the five compositions. MR values were calculated according to MR(9T) = (U(9T)-U(0))/U(0) from the isothermal field scans at the temperatures indicated by dots.

  FIG.16

  Fig.17

Fig. 18 100

 18 Fig. 18

  FIG.19

  site F below T N . The sum of the area fractions of the two other Fe 4+ sites D and E is comparable to the Fe 4+ fraction in the paramagnetic phase, but below T N2 they are resolved due to their different B hf . It is suggested that component E corresponds to magnetically ordered square pyramidal Fe 4+ sites in Sr 8 Fe 8 O 23 which are connected only to Fe2 atoms. In the course of the CO involving Fe2, the electrons at Fe1 also become more localized, which again gives rise to a more negative IS than in SrFeO 3 . It is observed that the area fraction of sextet D decreases considerably between 70 and 90 K (see Fig.9). This implies that a certain fraction of about 10 -12% of D in the low temperature spectra is not due to cubic SrFeO 3 , but intrinsic to the T phase. These sites possibly originate from the nearly regular Fe(3)O 6 octahedra.The arguments considered so far rely on ideal stoichiometric Sr 8 Fe 8 O 23 corresponding to SrFeO 2.875 . However, from the Mössbauer spectra it is evident that the present crystals of nominal composition SrFeO 2.87 contain a fraction of ~ 20% Fe 4+ sites arising from cubic SrFeO 3 . This implies that an additional oxygen deficiency must be accommodated in the T phase compared to stoichiometric Sr 8 Fe 8 O 23 . This is confirmed by the analysis of the 110 K spectrum where the C phase contribution is already magnetically ordered. The paramagnetic sub-spectrum that completely reflects the T phase is composed of 59% Fe 3.5+ and 41% Fe 4+ sites. For stoichiometric Sr 8 Fe 8 O 23 one would expect equal fractions of Fe 4+ and Fe 3.5+ sites.

Table 2 )

 2 . The present spectra confirm that in Sr 4 Fe 4 O 11 only the Fe 3+ sublattice is magnetically ordered below T N . The unusual coexistence of magnetically ordered and magnetically disordered sublattices at low temperature in Sr 4 Fe 4 O 11 has been attributred to magnetic frustration[41,28,33].As expected from the oxygen content, the crystals of nominal composition SrFeO 2.69 are not single phase. The spectra at 250 K and at room temperature still reveal two magnetically ordered Fe 3+ sites with somewhat different IS and B hf values. They can be assigned to the octahedral and tetrahedral Fe 3+ sites of the magnetically ordered brownmillerite-type ferrite Sr 2 Fe 2 O 5 . Considering the 250 K spectrum, where the O phase is completely paramagnetic, one estimates that 64% of O phase and 36% of SrFeO 2.50 are present. The average iron oxidation state derived from the data is 3.32, leading to an overall sample composition of SrFeO 2.66 . This estimate is in reasonable agreement with the TG data.Finally, the presence of the O phase as minority component in SrFeO 2.81 crystals (showing low temperature positive MR effects, see below) is confirmed by a magnetic Fe 3+

  3.5+ sites in comparison with stoichiometric Sr 8 Fe 8 O 23 .

  2.85 . Due to symmetry lowering, Raman modes become allowed for the T and O phase even in the absence of CO. In agreement with this expectation, the Raman spectra of the G=0.15 and G=0.31 samples, shown in Fig.19, exhibit several phonon features at room temperature. For SrFeO 2.85 (Fig.19, upper panel), several new vibrational modes appear upon cooling below 70 K, the CO temperature of the T phase already discussed in Sections IV.A and IV.B. As expected on general grounds, this shows that the CO transition is coincident with a structural transition. For the SrFeO 2.69 sample (Fig.19, bottom panel), which does not contain any T phase, no new Raman-active phonons are observed upon cooling to low temperatures. This is in agreement with a recent neutron diffraction study on Sr 4 Fe 4 O 11 , which has shown that the orthorhombic crystal structure is retained down to 1.5 K

Table 1

 1 Iron-oxygen distances for the various members of the Sr n Fe n O 3n-1 series of ferrates.

	Compound	Bond distances (Å)	Valence	Rel.
			assignment	abundance
	SrFeO 3 [28] Sr 8 Fe 8 O 23 [28]	6 x 1.926 Fe1 4 x 1.851, 1 x 1.926 Fe2 2x1.931, 2x1.952, 2 x 2.036	Fe 4+ Fe 4+ Fe 3.5+	1 1:2:1
		Fe3 4 x 1.912, 2 x 1.925	Fe 4+
	Sr 4 Fe 4 O 11 [28]	Fe2 4 x 2.044, 2 x 1.937 Fe1 4 x 1.855, 1 x 1.90	Fe 3+ Fe 4+	1:1
	Sr 2 Fe 2 O 5 [34]	Fe2 2 x 1.916, 1 x 1.819, 1 x 1.980 Fe1 2 x 1.87, 2 x 2.091, 2 x 2.180	Fe 3+ Fe 3+	1:1

Table 4

 4 Comparison of the phonon frequencies in far infrared ellipsometry and Raman scattering for mostly tetragonal SrFeO 2.85 sample at low temperature.

	Raman Scattering	ZZ (cm -1 ) XZ	106 107	140 139	159 160	178 177	194 195	205 204	242 244	258 260	268	293
	Far-infrared ellipsometry (cm -1 ) 114 121 138 160 175 195 213 247 259 267 280 296
	Raman	ZZ (cm -1 )	303	323	355	391	413		481	525	567	616
	Scattering	XZ	304	322 337	354.5	391	415		481	520	571	612
	Far-infrared ellipsometry (cm -1 ) 308			397		427			539 570

Acknowledgment

We thank S. Ahlert, E. Brücher, K. Förderreuther, W. Hölle, Y.-L. Mathis, and F. Schartner for generous technical assistance, and L. Alff for valuable discussions.

1 sample compositions estimated from TG data. 2 Data evaluation with Voigt based fitting algorithm. See text for details. 3 Parameter was not varied. 4 Octahedral (o) and tetrahedral (t) sites from the brownmillerite phase Sr 2 Fe 2 O 5 . 5 Area fraction normalized to 100% O phase.

Table 3 Summary of the temperatures T m and T corresponding to anomalies in the magnetic susceptibility F(T) and zero-field electrical resistivity U(T) curves. The T m and T values were obtained from the derivatives dlnF/dT and dlnU/dT, respectively. The first value corresponds to the cooling mode, the values in parenthesis to the heating mode data.


Majda Lafhel
email: majdalafhel1@gmail.com

Hocine Cherifi
email: hocine.cherifi@u-bourgogne.fr

Benjamin Renoust
email: renoust@ids.osaka-u.ac.jp

Mohammed El Hassouni
email: mohamed.elhassouni@gmail.com

Youssef Mourchid
email: youssefmour@gmail.com

Movie Script Similarity using Multilayer Network Portrait Divergence

Keywords: Multilayer networks, Movies, Network portrait, Network similarity

This paper addresses the question of movie similarity through multilayer graph similarity measures. Recent work has shown how to construct multilayer networks using movie scripts, and how they capture different aspects of the stories. Based on this modeling, we propose to rely on the multilayer structure and compute different similarities, so we may compare movies, not from their visual content, summary, or actors, but actually from their own storyboard. We propose to do so using "portrait divergence", which has been recently introduced to compute graph distances from summarizing graph characteristics. We illustrate our approach on the series of six Star Wars movies.

Introduction

Network models have been increasingly used to support the analysis of stories [START_REF] Labatut | Extraction and analysis of fictional character networks: A survey[END_REF], such as novels and plays [START_REF] Stiller | The small world of shakespeare's plays[END_REF] [START_REF] Waumans | Topology analysis of social networks extracted from literature[END_REF] [START_REF] Markovič | Applying network theory to fables: complexity in slovene belles-lettres for different age groups[END_REF], famous TV series [START_REF] Tan | A character network study of two sci-fi tv series[END_REF], news [START_REF] Renoust | When face-tracking meets social networks: a story of politics in news videos[END_REF] [START_REF] Renoust | Visual analytics of political networks from facetracking of news video[END_REF], and movies [START_REF] Park | Social network analysis in a movie using characternet[END_REF][15] [START_REF] Mourchid | Movienet: a movie multilayer network model using visual and textual semantic cues[END_REF]. However, most of these models only focus on one facet of the movie story. Indeed, usually, they capture interactions between the characters at play [START_REF] Labatut | Extraction and analysis of fictional character networks: A survey[END_REF] to bring out a global picture of the story content. Other works went beyond by introducing other semantic elements such as scenes and dialogues [START_REF] Tan | A character network study of two sci-fi tv series[END_REF]. Nevertheless, they have always captured the information in a single layer network or a bipartite graph. To enrich the representation, we have previously proposed a multilayer network model that captures key elements of the movie story [START_REF] Mourchid | Multilayer network model of movie script[END_REF] [START_REF] Mourchid | Movienet: a movie multilayer network model using visual and textual semantic cues[END_REF]. It encompasses the single network analysis based either on characters or scenes and proposes new topological analysis tools.

Recently, various studies are being conducted to measure the similarity of movie stories [START_REF] Lee | Explainable movie recommendation systems by using storybased similarity[END_REF] [START_REF] Lee | Measuring character-based story similarity by analyzing movie scripts[END_REF] focusing on characters interactions. This work, aims at quantifying similarity between movies by incorporating knowledge extracted from complementary aspects of a story, including character, dialogues, and locations. To do so, rather than relying on a single-layer network, a multilayer network extracted from the movie script is exploited. It combines semantically extracted characters, keywords, and locations, allowing to compute similarity between the corresponding networks. Starting from the previously proposed model [START_REF] Mourchid | Multilayer network model of movie script[END_REF] [START_REF] Mourchid | Movienet: a movie multilayer network model using visual and textual semantic cues[END_REF] the multilayer network is automatically extracted from the scripts of the movies to compare. At this point the similarity issue reduces to compute the similarities between the layers. Plenty of methods have been proposed in the literature for comparing networks [START_REF] Tantardini | Comparing methods for comparing networks[END_REF]. Here, a recent method introduced by Bagrow et al. [START_REF] Bagrow | An information-theoretic, all-scales approach to comparing networks[END_REF] is used. The so-called Network Portrait Divergence is based on the network portrait [START_REF] Bagrow | Portraits of complex networks[END_REF], which characterizes a network by determining its degree distribution at various distances. Experiments performed on the Star Wars series show encouraging results that match up with the perceptual analysis.

The rest of the paper is organized as follows. Section 2, summarizes the multilayer movie script model and its extraction process, together with network portrait and its divergence.. Section 3 starts with introducing the data then results of the evaluation are discussed. Conclusion and discussions are reported in Section 4.

Background

Extracting multilayer networks from movie scripts

The multilayer network model [START_REF] Mourchid | Multilayer network model of movie script[END_REF] considers three types of entities, each forming a unique layer: characters C, keywords K, and locations L, together with their interactions. Intralayer interactions: C -C when two characters share a conversation; K -K when two keywords co-occur in a conversation; L -L when two locations are in successive scenes. Interlayer interactions also exist: C -K when a character pronounces a keyword; C -L when a character is in a location; K -L when a keyword is pronounced in a location.

A movie script is a semi-structured text containing all technical information concerning scenes, dialogues, and settings. It is divided into scenes delimited by scene heading that specify the physical spaces (INT or EXT), location, and the time (DAY or NIGHT).

The first step of processing consists in dividing the script into scenes based on the scenes headings. Fig. 1 illustrates a scene. Locations are extracted from the scene heading. Characters are then extracted as dialogues header (in capital). Finally, keywords are extracted from dialogues by applying Latent Dirichlet Allocation (LDA) [START_REF] Blei | Latent dirichlet allocation[END_REF]. Named Entity Recognition (NER) [START_REF] Nadeau | A survey of named entity recognition and classification[END_REF] is further applied to extract character and location from the keywords.

From Fig. 1, the following links and entities can be extracted: C-C: ANAKIN and SHMI ; K -K: Mom and Annie; L -L: TUSKEN RAIDER HUTT and GEONOSIS, then GEONOSIS and TATOOINE ; C -K: ANAKIN and Mom; C -L: ANAKIN and TUSKEN RAIDER HUTT, then SHMI and TUSKEN RAIDER HUTT ; K -L:Mom and TUSKEN RAIDER HUTT.

Network comparison using portrait and portrait divergence

In 2008, Bagrow introduced Network Portraits [3] to summarize large complex networks. The Network Portrait is a matrix B with B l,k elements such as defined in eq. (1). Given a network G with N nodes, k is a number of nodes such that 0 ≤ k ≤ N , and l is the shortest path length between two nodes, such that 0 ≤ l ≤ d (graph diameter).

More formally:

B l,k ≡ the number of nodes connected with k nodes at distance l

Each row in B represents the probability distribution P (k|l) such that k nodes are reachable at distance l from a randomly chosen node:

P (k|l) = 1 N B l,k B 1,k = N P(k) (2)
B is a signature of G. Bagrow then introduced a distance measure between two networks G and G , the Network Portrait Divergence [START_REF] Bagrow | An information-theoretic, all-scales approach to comparing networks[END_REF] based on this signature.

Let B and B be the portraits associated with G and G respectively. The portrait divergence computes first the probability distribution of nodes based on the matrices B and B , such as in eq. 3, 4. Then, the distance between the probability distributions is computed using the Jensen Shannon divergence D JS , such as in eq. 5.

Let G be a network of node size N . The portrait B is associated with G. Consider two randomly chosen nodes at distance l. The probability distribution P B (k|l) is defined as follows:

P B (k|l) = 1 N B l,k = kB l,k Σ c n 2 c ( 3
)
where n c is the number of nodes inside each connected component c. Accordingly, let G be a network with a total number of nodes N with a portrait B , the probability distribution P B (k|l) is defined as follows:

P B (k|l) = 1 N B l,k = kB lk Σ c n c 2 (4)
where n c is the number of nodes inside each connected component c.

The Network Portrait Divergence between G and G is defined as follows:

D JS (G, G ) = 1 2 (KL(P B ||P * ) + KL(P B ||P * )) (5)
where P * is a combination of P B and P B , such as:

P * = (P B +P B ) 2
, and KL(.||.) is the Kullback-Liebler divergence. The KL divergence within two probability distributions P and P is defined as: (2005). The experiment process proceeds as follows. First, the multilayer network of each episode of the saga are extracted. Their basic topological properties are summarised in Table 1. Then, the corresponding portrait for each layer (character, location, and keyword ) of each multilayer network are computed individually and discussed. Finally, the distance between each pair of same-type layers between all movies are compared using their portrait divergence.

KL(P (k|l)||P (k|l))) = Σ max(d,d ) l=0 Σ N k=0 P log( P (k|l) P (k|l) ) (6

Comparing portraits

Comparing all three layers: A quick look at all three layers: characters in Fig. 2, keywords in Fig. 3, and locations in Fig. 4, clearly shows that each type of layers display a distinct pattern making it recognizable. Character layers display a k between 15 and 30, for a maximum path length between 3 and 5. Keyword layers do not display much larger path length (up to 6) but the number of nodes are much larger. Despite this larger number of nodes, most nodes are distributed in the lower path corner with degree 1 and 3, maybe suggesting a lot of small components. The character and keyword layers both display clear characteristics common to small-world and scale-free networks [START_REF] Bagrow | Portraits of complex networks[END_REF] in their shape such as the elongated form and knot near the center of the portrait. It may be less obvious for the character layer, but one should remember that character graphs are rather small. Location layers diverge the most from small world patterns and seem to greatly vary upon trilogies, while being minimalist in the prequel series. This suggests that locations networks are probably more linear loops in the prequel while they show more complexity in the original trilogy. Comparing character layers: Each character layer portrait is illustrated in Fig. 2. The overall six portraits display a very similar pattern. SW1 (Fig. 2(a)) and SW2 (Fig. 2(b)) -a surprising similarity given that this layer shows a double number of edges as shown in Table 1-together with SW5 (Fig. 2(e)) and SW6 (Fig. 2(f)) make two similar pairs, with SW3 (Figs. 2(c)) and SW4 (Figs. 2(d)) being somewhat intermediary between them. In SW5 and SW6, a lot of action separates the main characters into different groups with parallel actions, while the first series is rather focused on the main character, Anakin. The aspect ratio of the character layer portraits seems to vary upon the different movies. This has been linked to the small world characteristics of the graph that each portrait summarizes [START_REF] Bagrow | Portraits of complex networks[END_REF]. We can notice a progression from SW1 to SW6 suggesting a "smaller" world effect for episodes 5 and 6. Comparing keyword layers: Each keyword layer portrait is reported in Fig. 3. These layers can be well distinguished from the character layers portrait. Nevertheless, they also exhibit similar patterns across episodes. The aspect ratio of the keyword layer portraits also seems to vary upon the different movies, but not as regularly as the character layer. Especially, the first (Fig. 3 (a)) and last (Fig. 3(f)) episodes seem to share a very similar pattern. SW2 (Fig. 3 (b)) and SW3 (Fig. 3 (c)) also display a close pattern with an elongated aspect ratio, while SW4 (Fig. 3 (d)) and SW5 (Fig. 3 (e)) portraits are much shorter. Interestingly, the portrait of this latter one differs in its lowest path length, but all portraits present the "knot" characteristic to scale-free networks. This visual proximity between keyword layers can be expected due to the tendency of language-based graphs to follow Zipf's law [START_REF] Cancho | The small world of human language[END_REF] Comparing location layers: Each location layer portrait is illustrated in Fig. 4. At a glance, one can recognize a pattern very different to the character and keyword layers. The pattern is common to all three episodes of the prequel trilogy (Fig. 4(a-c)). It shows very low maximum path length and degree. This strongly suggest the presence of chain-type topology. As a consequence, the cut of these three movies between locations may be quite linear. Indeed this trilogy mostly follows the actions of Anakin and Obi-wan, very often together. The three episodes of the original trilogy display a more complex structure. The structure is more complex in the first (Fig. 4(d)) of these episodes, then gradually simplify to the last episode (Fig. 4(f)). In SW4, iconic star ship locations are introduced, such as the Millenium Falcon and the Death Star, and the movie cuts a lot scenes between star ships and other locations (this can be confirmed from the number of edges in Table 1). The rhythm is also different in the original trilogy, which often separates its main characters such that actions happen in parallel. Frequent cuts between them generate transitions that are less linear. This trend seems to be less adopted after the fourth episode. Overall comparison: Comparing overall layer divergence suggests that relationships in character layers are very similar along the saga. This confirms the intuition we can have at a glance from the portraits figures. Location layers also show an overall high similarity. The keyword heat-map departs from the others. Indeed, differences are more marked between the keyword layers that exhibit a more patchy structure. This is surprising considering that the visualization of each portrait made one movie to another looks very similar. It is however harder to make sense of why the fifth episode stands out. Finally, the separation between each trilogy appears clearly in the location layer. Note that the pairwise character layer similarity also makes sense considering the movies.

Comparing portrait divergence

Divergence between characters layers: From Fig. 5(a), the prequel trilogy (SW1-3) shows a low divergence between characters. Relationships between characters of SW1 appear more closely related to SW2 (D JS =0.279) than to SW3 (D JS =0.299). That may be due the appearance and disappearance of some key characters. For instance, Shmi dies in SW2. In SW3, Anakin changes side to become Vader, and the clones start to appear. This last episode shows an even lower divergence with the sequel: the clones being instrumental in the original series may help shaping a common structure of relationships. This may also confirm the efforts taken in the third episode of the prequel to link characters with the original series.

In the orginal trilogy, SW5 and SW6 show the lowest divergence (D JS =0.132). Indeed, individual inspection shows that a lot of the links are shared in both episodes. SW4 appears the most diverging with the other movies in the trilogy. This make sense since the movie was made so that it could have been a stand alone movie at first. It shows its closest relationship with SW3 (D JS =0.134), once more underlining the special care taken to connect the prequel to the sequel from the character relationships point of view. SW1 and SW6 show the highest divergence. This is not surprising since at this point the story of the prequel and original trilogies are completely different in their characters and plots.

Divergence between keyword layers: The keyword layers show the highest divergence among the different movies (Fig. 5(b)). In both trilogies, the divergence appears lower for a pair of movies, SW2 and SW3 in the prequel (D JS =0.29), and SW4 and SW5 in the sequel. SW1 shows its lower divergence with SW4 (D JS =0.4) and SW6 (D JS =0.33). It remains difficult to conclude what in the structure of the movies can lead to a similar relationship structure in keywords between those three. We suspect the frequent association of the key terms young and master in these movies to play some important role.

Divergence between location layers: Observing Fig. 5(c), the portrait divergence shows very high similarity within the structure of locations of the first prequel. The original series also shows a low divergence between movies. We observe a noticeable difference between the prequel trilogy and SW4, specifically, between SW3 and SW4 with D JS = 0.585. From SW4, a lot of scenes start taking place in the Millenium Falcon, and death stars, giving a specific rhythm in cuts and locations. Nonetheless, divergence is rather low between the prequel and the last two episodes of the series. Remembering that all information is extracted from the scripts, we may suspect here different influences the movie director may have. Indeed, SW4 was written to possibly be a standalone movie, while the following SW5 and SW6 scripts were written in a short period of span, planned to complete the trilogy. This concerns even more the prequel trilogy which was planned from the beginning to be a unified trilogy.

Discussion and conclusion

In this work, a multilayer network model is used to represent the main elements of a movie script: characters, key elements of the conversations (keywords), and locations of the scenes. Investigations based on the single-layer components of the model are performed to relate the similarity of the 6 Star Wars Saga episodes to the distance between the layers based on portrait divergence.

Preliminary results using portrait and portrait divergence measures are quite encouraging. Indeed, the analysis of the movie networks confirms a good correspondence between characters of the prequel and sequel trilogies; and a difference between locations in the prequel and sequel trilogy. Each of the prequel and sequel trilogies shows a good relationship between characters; and high similarity between locations. Results show similarity between topic relationships (keywords) in the movies SW2 and SW3; and also of SW1 with SW4 and SW6. Otherwise, other episodes appear to be dissimilar, mainly, the relation connecting keywords of SW5 with SW2 and SW3. Although more experiments are needed to fully assess that movie similarities can be discovered by measuring their network distances, this work opens multiple research directions.

Note that the current results are only based on the sole script of each movie. The script of SW4 was written in the late 70's, the two following movies in the 80's and the prequel in the late 90's/2000's. How movies are scripted have definitely changed over this span, and may impact our results. To even go further, we can enrich the model. Previous works have also formulated multimedia cues for movie analysis [START_REF] Mourchid | Movienet: a movie multilayer network model using visual and textual semantic cues[END_REF] including its visual features often important for recommendation systems [START_REF] Zhou | Movie genre classification via scene categorization[END_REF]. We may further enrich the model, using for example sentiment analysis. To further evaluate how the network similarity performs, we wish to further proceed with user evaluation, and script-based topical [START_REF] Bougiatiotis | Content representation and similarity of movies based on topic extraction from subtitles[END_REF] and style [START_REF] Kovacs | Language-style similarity and social networks[END_REF] similarity.

Our processing scheme is currently exploiting layers of the multilayer network as separated single-layer networks. One interesting task would be to compare with distance measures of multilayer networks. Since the Kullback-Liebler divergence is not a metric and does not respect the triangular inequality, although tempting, we have found irrelevant to average divergence over all layers and measure overall similarity between movies. Alternative strategies could be to project the whole multilayer network into a single-layer knowledge graph, but such projection remains unsatisfying. We further need to investigate pure multilayer approaches and include in the comparison the effect of transition layers. We can try embedding-based comparisons [START_REF] Bagavathi | Multi-net: Scalable multilayer network embeddings[END_REF], and investigate proper multilayer metrics such as entanglement [START_REF] Škrlj | Patterns of multiplex layer entanglement across real and synthetic networks[END_REF] or nodes and edge coupling [START_REF] Cozzo | Structure of triadic relations in multiplex networks[END_REF] between movies. This however requires to align named entities between layers and movies, such that they refer to the same entity. This is not straightforward since we have at least two entities with an ambiguous definition which are Anakin/Vader and Amidala/Padme. Finally, we believe this methodology to be useful once incorporated into recommendation systems to increase their efficiency [START_REF] Reddy | Content-based movie recommendation system using genre correlation[END_REF] since we provide a different definition of a genre based on actual elements of the movie content [START_REF] Deldjoo | Movie genome recommender: A novel recommender system based on multimedia content[END_REF].

Fig. 1 :

 1 Fig. 1: Excerpt of Attack of the Clones script describing one scene.

) 3

 3 Experimental evaluationExperiments are performed using the movie scripts of six episodes of the Star Wars saga 5 . It is divided into the sequel (original) and prequel trilogies. The sequel trilogy is the first created by George Lucas. It is composed of Episode IV (SW4): A New Hope (1977), Episode V (SW5): The Empire Strikes Back (1980) and Episode VI (SW6): Return of the Jedi (1983). It is followed by the prequel trilogy composed of Episode I (SW1): The Phantom Menace (1999), Episode II (SW2): Attack of the Clones (2002), and Episode III (SW3): Revenge of the Sith

Fig. 2 :

 2 Fig. 2: Portraits of the characters layer for each movie of the Star Wars saga. (a) SW1, (b) SW2, (c) SW3, (d) SW4, (e) SW5, (f) SW6. The horizontal axis is the node degree k. The vertical axis is the distance l. Colors are the entries of the portrait matrix B lk . The white color indicates B lk = 0.

Fig. 3 :

 3 Fig. 3: Portraits of the keyword layers for each movie of the Star Wars saga. (a) SW1, (b) SW2, (c) SW3, (d) SW4, (e) SW5, (f) SW6. The horizontal axis is the node degree k. The vertical axis is the distance l. Colors are the entries of the portrait matrix B lk . The white color indicates B lk = 0.

  [START_REF] Grabska-Gradzińska | Complex network analysis of literary and scientific texts[END_REF].

Fig. 4 :

 4 Fig. 4: Portraits of the locations layer for each movie of the Star Wars saga. (a) SW1, (b) SW2, (c) SW3, (d) SW4, (e) SW5, (f) SW6. The horizontal axis is the node degree k. The vertical axis is the distance l. Colors are the entries of the portrait matrix B lk . The white color indicates B lk = 0.

Fig. 5

 5 Fig. 5 illustrates the network portraits divergence between each SW movie. Fig. 5(a) shows the divergence between character layers, Fig. 5(b) shows divergence between keyword layers, and Fig. 5(c) shows the divergence between location layers.

Fig. 5 :

 5 Fig. 5: Portrait divergence of the characters, keywords, and locations networks in the 6 episodes of the Star Wars saga. (a) Character layers. (b) Keyword layers. (c) Location layers. Each cell of the heat-map represents the portrait divergence between a couple of episodes.

Table 1 :

 1

		Character Layers	Keyword Layers	Location Layers
	Episode N E	D T	A	N E	D T	A	N E	D T	A
	SW1	61 1090 3 0.53 -0.12 229 4492 4 0.66 -0.01 116 26 2 0	-0.03
	SW2	52 506 3 0.43 -0.14 244 6009 4 0.52 -0.01 118 24 2 0	0.24
	SW3	56 476 4 0.53 -0.008 233 4532 5 0.45 0.003 152 16 2 0	-0.19
	SW4	58 576 4 0.51 -0.11 234 2201 7 0.61 0.11 133 428 6 0.42 0.17
	SW5	45 504 5 0.48 0.15 211 568 6 0.31 0.08 145 132 4 0.12 -0.2
	SW6	44 266 4 0.42 0.34 213 2648 4 0.45 -0.03 84 30 4 0.2 -0.27

Global properties of the character, keyword and location layers for each movie, with: number of nodes (N ), number of edges (E), diameter (D), transitivity (T ), and assortativity (A).

Here is a quick summary of the plot: The saga follows Anakin Skywalker, a young child freed from slavery to become a Jedi and endeavored to save the galaxy. Anakin instructed by the Jedi Masters of the light side, married the senator Padme. Unfortunately, the Sith (Palpatine) submits him to the dark side, rebelling and losing against his Master (Obi-Wan). Anakin is saved by the Sith, now ruling over the galaxy, and transformed to Darth Vader. Padme died while giving birth to twins Luke and Leia. Luke becomes a farmer while Leia becomes a princess. Nineteen years later, Obi-Wan met Luke and taught him the Jedi way, while receiving a distress call from the princess Leia, leading the resistance against Palpatine. Joining smuggler Han Solo in the Millenium Falcon they went to save her, and support the resistance. Luke completes his Jedi training, while Solo gets captured by the Sith, who crushes most of the resistance. Vader tries to turn Luke to the dark side when discovering that Luke is his son. Unsuccessful, Palpatine tries to kill Luke, awaking in Vader his old self. Vader turns back against Palpatine and rescues the galaxy.