Electrodynamics near the Metal-to-Insulator Transition in V3O5

a r X i v :c o n d -m a t /0701742v 1 [c o n d -m a t .s t r -e l ] 30 J a n 2007

Electrodynamics near the Metal-to-Insulator Transition in V 3O 5

L.Baldassarre 1,A.Perucchi 1,E.Arcangeletti 1,D.Nicoletti 1,D.Di Castro 1,P.Postorino 1,V.A.Sidorov 2and S.Lupi 1

1

CNR-INFM COHERENTIA and Dipartimento di Fisica,Universit`a di Roma ”La Sapienza”Rome Italy and

2

Institute for High Pressure Physics Russian Academy of Sciences 142190Troitsk,Moscow Region Russia

(Dated:February 6,2008)

The electrodynamics near the metal-to-insulator transitions (MIT)induced,in V 3O 5single crys-tals,by both temperature (T )and pressure (P )has been studied by infrared spectroscopy.The T -and P -dependence of the optical conductivity may be explained within a polaronic scenario.The insulating phase at ambient T and P corresponds to strongly localized small polarons.Meanwhile the T -induced metallic phase at ambient pressure is related to a liquid of polarons showing inco-herent dc transport,in the P -induced metallic phase at room T strongly localized polarons coexist with partially delocalized ones.The electronic spectral weight is almost recovered,in both the T and P induced metallization processes,on an energy scale of 1eV,thus supporting the key-role of electron-lattice interaction in the V 3O 5metal-to-insulator transition.

PACS numbers:71.30.+h,78.30.-j,62.50.+p

I.INTRODUCTION

The metal-to-insulator transition (MIT)in electronic correlated systems and especially in transition metal ox-ides has received renewed consideration in recent years 1.Such interest has been mainly triggered by the variety of charge ordering (CO)phenomena recently observed in several systems as nickelates and manganites,as well as by the presence of charge and spin stripes in cuprate su-perconductors.The di?culties in achieving a proper un-derstanding of such phenomena basically lie on the prob-lem of treating on the same footing the electron-phonon (e ?ph )and the electron-electron (U )interactions in sys-tems where the electron bandwidth (W )is rather small.Within this context the study of vanadium oxides de-served special attention for both the technological ap-plications and the fundamental theoretical issues they raise 1,2.The di?erent cation valences observed in the se-ries of the binary vanadium oxide compounds result in a wide range of electronic and magnetic properties.Metal-to-insulator transitions with conductivity jumps up to 7orders of magnitude have been observed in some of these systems.Despite the advances in the understand-ing of the complex electronic behavior of vanadium ox-ides,many open questions still remain.The metal-to-insulator transition observed in V 2O 3at 160K is usually considered as a prototype for a MIT induced by Mott-Hubbard interaction 1.On the contrary it is still unclear whether a Mott-Hubbard or a Peierls mechanism domi-nates the occurrence of the MIT in VO 2at 340K (Ref.1).Pressure-induced MIT have been studied,in partic-ular,both in Mott insulators like V 2O 3(Ref.3)and in organic Bechgaard salts 4.In these cases the transitions have been explained in terms of a reduction in the U/W ratio in good agreement with the prediction of the dy-namical mean ?eld theory 5,6within the Mott-Hubbard

T e m p e r a t u r e (K )

Pressure (GPa)

FIG.1:(P ?T )Pictorial phase diagram of V 3O 5as deter-mined in Ref.7.The AF order is found at ambient pres-sure below T N =75K.The blue curve represents the P -dependence of T N (Ref.8).The measurements performed in this paper vs.both T and P have been collected along the black dotted lines shown in ?gure.

model.

V 3O 5,the object of the present paper,belongs to the so-called Magneli phase V n O 2n ?1(n =3-9)9.At high temperatures it is a paramagnet (PM),but it orders an-tiferromagnetically (AF)below T N =75K.Like in VO 2and V 2O 3,a MIT occurs in V 3O 5(T MIT =428K at am-bient pressure).Above T MIT the resistivity (ρ)sharply drops by more than one order of magnitude,but dρ/dT is still negative,thus indicating an activated transport behavior,also in the metallic state 10.The phase transi-tion is accompanied by a structural rearrangement of the lattice,leading to the symmetry change P 2/c →I 2/c ,and to a reduction in the unit cell size of about 0.14

2

%(Ref.10,11).Since T MIT>>T N,the MIT appears to be decoupled from the AF order.Therefore V3O5is a suitable system to study the charge dynamics near a metal-to-insulator transition without any charge localiza-tion induced by magnetic e?ects.

The monoclinic crystal structure of V3O5is made up of oxygen octahedra surrounding the vanadium atoms. These octahedra form two types of alternating one-dimensional chains11,12:one chain(A)is composed by double-octahedra sharing a face,where these double-octahedra are coupled together by sharing edges.The other chain(B)is made up of single corner-sharing octa-hedra.The chains A and B are mutually connected by sharing both octahedral edges or corners.

At high temperature,two di?erent kinds of octahe-dra(V(1)and V(2))have been identi?ed,which split into four below T MIT(V(11),V(12),V(21),V(22))11,12. Hong and?A sbrink suggested in Ref.11that,in the insu-lating phase,the octahedra V(11)host the V4+ions while in the three other kind of octahedra V3+ions are found. The V(1)octahedra can host either V3+or V4+vana-dium ions,with a3.5mixed valence,while in V(2)octa-hedra there are only V3+ions.V(1)octahedra occupy the chains made of double octahedra,while V(2)compose the single octahedra chains.The MIT seems therefore to be driven by charge disproportion and spatial ordering of the V4+and V3+ions10.It has been argued10that the mechanism involved in the transition may be similar to that of the so-called Verwey transition13observed in magnetite(Fe3O4).Scenarios involving the formation of a polaronic Wigner crystal below T MIT,and its melting at high temperatures,have therefore been put forward10. MIT and structural transition appear to be coupled also in the high pressure regime.X-ray di?raction measurements14show a discontinuity in the pressure de-pendence of the lattice constants in the region near6.3 GPa.This discontinuity corresponds to a lattice rear-rangement at P MIT.The application of hydrostatic pres-sure to V3O5leads to a continuous reduction of T MIT,as demonstrated by both resistivity7and X-ray di?raction11 measurements(see Fig.1).The phase transition at room temperature is observed when the applied pressure reaches P MIT～6GPa.The pressure dependence of T N has been determined by ac-calorimetry measurements up to5GPa:T N linearly increases with pressure at a rate dT N/dP=0.82K/GPa(Ref.8).At5GPa T N=79 K,still less than T MIT(6GPa)～300K,suggesting that magnetic and charge order are decoupled also in the high pressure regime.

Infrared spectroscopy is a good tool to probe the dy-namics of the charge carriers and provides important in-formation on the fundamental energy scales involved in the metal-to-insulator transition.In this paper,we will present the?rst complete measurements of the infrared properties of high quality single crystals of V3O5,as a function of both temperature and pressure.The only available data were early measurements10performed at ambient pressure over a limited energy range(not extend-ing into the far infrared)and at two temperatures only. We describe in Section II the experimental set-up used in our experiments.In Sections III and IV we illustrate the temperature-dependent and pressure-dependent data,re-spectively.An interpretation of our results within a po-laronic scenario is given in Section V.

II.EXPERIMENT

High quality single crystals of V3O5were grown by the chemical transport method12,15.The samples were characterized by resistivity measurements as a function of T and P(Ref.7)which provided the(P?T)phase diagram shown in Fig. 1.A metallic behavior may be identi?ed above the critical temperature T MIT(P).The critical temperature decreases with increasing pressure up to9GPa.At higher pressure,no feature due to the MIT appears in the resistivity curves down to4K(Ref.

7).Below the critical temperature T MIT(P),the system is a paramagnetic insulator.An AF order is present at ambient pressure below T N=75K.The crystal structure and its modi?cations with temperature and pressure have been determined by X-ray di?raction11,14,16.

A single crystal was polished to obtain a clean,mirror-like surface.Near-normal-incidence re?ectivity R(ω)was measured with a Michelson interferometer between50 and20000cm?1and,through a Kramers-Kronig(KK) analysis,the complex conductivity(σ(ω)=σ1(ω)+ iσ2(ω))was obtained.Measurements were carried out at several temperatures between10and573K,thus al-lowing to probe both the AF and the paramagnetic PM insulating phase and to assess the properties of the metal-lic state.

A diamond anvil cell(DAC)equipped with high-quality IIa diamonds was used to perform pressure de-pendent measurements.A hole of about150μm diameter was drilled in a stainless steel gasket.A small piece(～30x30μm2)was cut from the sample and placed in the gasket hole on top of a pre-sintered pellet of KBr,used as hydrostatic medium.Great care was taken in placing the sample in order to create a clean sample-diamond(S?D) interface.The pressure was measured in situ,using the standard ruby?uorescence technique17.Re?ectivity data in the mid-and near-infrared region were collected with a microscope coupled to an interferometer.The micro-scope was equipped with a15x Cassegrain objective.As a reference we used the re?ection from a gold-coated Si wafer,placed between the diamonds.To obtain reliable data in such a critical experiment,the high brilliance of infrared synchrotron radiation was needed.High pressure measurements were therefore performed at the infrared beamline SISSI of the ELETTRA storage ring18.Since the intensity re?ected by the sample I S(ω)and that re-?ected by the reference I Au(ω)are not measured at the same time,one must take into account the variation of the spectral intensity of synchrotron radiation induced by the decreasing electron beam current.Therefore we

3

also measured,as an internal correction,the intensity re-?ected at each pressure by the upper diamond face I D .At the end of the entire pressure run,the gold reference was measured in the DAC with the same procedure 19

(i.e.we measured I Au (ω)and I ′

D (ω)respectively).The re?ectivity at each pressure was then obtained by:

R S ?D (ω)=I S (ω)

I Au (ω)

.(1)

III.

TEMPERATURE-DEPENDENT

REFLECTIVITY

The optical re?ectivity R(ω)is plotted between 50and 20000cm ?1in a linear scale in Fig.2,while the low-frequency behavior of the re?ectivity can be better visu-alized in the inset of Fig.2where a logarithmic scale is used.In the 10-373K temperature range,the re?ectiv-ity is nearly constant at R (ω)?0.6for ω<250cm ?1.Several evident phonon lines are present between 200÷800cm ?1.At 423K R (ω)increases to ～0.7.For tem-peratures higher than T MIT ,R (ω)continously increases,with R (ω)→1for ω→0,indicating a metallic-like be-havior.The intensity of the narrow phonon lines is also strongly reduced in the high temperature phase.Across the transition a change in the slope of the re?ectivity is also observed in the near-infrared range (7000÷15000cm ?1).

R e f l e c t i v i t y

Frequency (cm -1

)

FIG.2:Full-scale temperature dependence of R (ω),and its far-infrared behavior (inset).

The re?ectivity range has been extended towards both low and high frequency with suitable extrapolations to perform KK transformations.At low temperature (i.e.

in the insulating phase)a constant extrapolation has been

used below 50cm ?1,as suggested by the shape of R (ω).In the metallic phase (T >T MIT )the Hagen-Rubens for-mula was employed.Since no temperature dependence is found above 15000cm ?1,the same standard 1/ω4high-frequency extrapolation is used both for the insu-lating and the metallic phase.20To check the reliability of our KK analysis a low-frequency extrapolation based on Drude-Lorenz ?t of the re?ectivity was also used with no signi?cant changes in the resulting σ(ω).

Frequency (cm -1

)

FIG.3:Real part of the optical conductivity σ1(ω)at var-ious temperatures.Diamonds are σdc data from resistivity measurements of Ref.10.In the inset the MIR peak fre-quency (ωMIR )and its half-width half-maximum (ΓMIR ),as a function of temperature are shown.Those values have been obtained by a Drude-Lorenz ?t of the optical conductivity (see text).

The real part of the conductivity is shown up to 8000cm ?1in Fig.3.In the insulating phase,σ1(ω)presents a broad,temperature-dependent high frequency mid-infrared (MIR)band and several phonon peaks.On the low-frequency side of the MIR band a gap-like feature is present,corresponding to a negligible conductivity at low frequency.Between 10K and 300K the MIR band continuously shifts towards low frequency (see Fig.3).No major changes in the spectra are observed on cross-ing T N (=75K),thus indicating that the main variation in the low-energy electrodynamics is determined by the MIT and not by the AF order.The MIR band shows a de?nite and clear trend upon increasing the tempera-ture from 300K to T MIT =428K:the peak frequency ωMIR strongly softens with increasing temperature and narrows.Across the transition,the MIR band rapidly moves towards 1000cm ?1and a non-zero dc conductiv-ity is achieved.It is worth to notice that good agreement is found between the extrapolation to zero frequency of our optical data in the metallic phase and the dc con-ductivity (diamonds in Fig.3)obtained by resistivity

4

measurements on similar samples 10.

The presence in the metallic phase of a low-frequency MIR band,without any clear evidence of a Drude term,suggests to explain the low-energy dynamics through an incoherent transport mechanism.Indeed the optical con-ductivity of V 3O 5presents two di?erent absorption scales in the observed temperature range (10÷573K).The highest one (HF-MIR)develops mainly above 3000cm ?1and is peculiar to the insulating phase,while the low-est one (LF-MIR),around 1000cm ?1,is typical of the metallic phase.With increasing T ,before and across the transition,the higher energy scale develops in the lower one.This may be easily seen in the T -dependence of the MIR peak frequency as shown in the inset of Fig.3.Here one may observe a small reduction of the peak frequency between 10and 300K,whereas around 420K it drops to about 1000cm ?1.Moreover,the half-width-half-maximum of the MIR,ΓMIR ,slightly reduces (see inset of Fig.3),while the ratio ΓMIR /ωMIR remains nearly constant as T ≤T MIT .In the metallic phase ωMIR saturates slightly over 1000cm ?1,meanwhile its ΓMIR strongly increases,possibly indicating that a more disordered phase is generated at T >T MIT .ωMIR and ΓMIR have been determined at all temperatures by a ?t based on a single Lorentzian oscillator,where an over-damped Drude term was added only in the metallic phase to take into account the non-zero dc conductivity.We emphasize that neither ωMIR nor ΓMIR depend on ?t details.

S W (ω)

Frequency (cm -1

)

FIG.4:Spectral Weight as a function of frequency at given temperatures.In the inset both the T -dependence of the phonon-subtracted SW at 800cm ?1and the dc conductiv-ity (from Ref.10)are shown.

The main temperature-dependent changes of the opti-cal conductivity occur below 8000cm ?1,as it is pointed

out by the behavior of the spectral weight (SW ),de?ned as the e?ective number of carriers per formula unit par-ticipating in optical transitions:

SW =m

πe 2 ω

0σ1(ω′)dω′.(2)Here m is the bare electron mass,m ?the e?ective mass and V cell is the volume per formula unit.Indeed,the SW presents a strong T -dependence below 5000cm ?1(see Fig.4),whereas it is recovered above 8000cm ?1.Moreover,the transport properties across the MIT are mainly determined by a strong redistribution of SW at low-frequency.Indeed the phonon-subtracted SW at 800cm ?1shows an abrupt discontinuity around T MIT ,closely following the dc conductivity behavior (see inset of Fig.4).A similar behavior of the SW has been found in Fe 3O 4(Ref.21),where the charge-ordered ground state seems to be related to a polaronic localization and ordering.Instead,in materials where electronic corre-lations play a more important role,as for istance VO 2(Ref.22)and V 2O 3(Ref.23),the SW is recovered at much higher frequencies.This behavior of SW ,as well as the optical response that follows the structural transition,may imply that charge localization in V 3O 5is mainly induced by a strong electron-lattice interaction.

IV.

PRESSURE-DEPENDENT MID-INFRARED

REFLECTIVITY

Re?ectivity curves at the sample-diamond interface (R S ?D (ω))at room T for ?ve di?erent pressures up to 10GPa are plotted in the upper panel of Fig.5in the frequency range 1300÷8000cm ?1.The small size of the sample did not allow us to measure R (ω)at lower frequencies.The 1700÷2300cm ?1range is not shown because of the high multiphonon absorptions of the di-amond.As a comparison for these curves,we produced a re?ectivity curve at the sample-diamond interface at 0GPa.This re?ectivity is obtained from the curve at T =300K reported in Fig.2.The complex refraction index ?n ,obtained with KK analysis from the re?ectivity,was employed in the formula 20:

R (ω)=

?n ?n d

5

(ω) (103

??1

c m -1

)

Frequency (cm -1

)

R FIG.5:Upper panel:re?ectivity curves measured at the sample-diamond interface are shown at room T for selected pressures and compared to the ambient pressure (black line)sample-diamond re?ectivity (see text).Thin continuous lines are ?tting curves obtained by a Drude-Lorentz model (see text):only two of them are shown for clarity.In the inset,the quantity ?R/R is shown at 1600cm ?1.The dashed line is a phenomenological sigmoid ?t to data.Lower panel:Optical conductivity curves obtained by the ?tting parameters,com-pared with the ambient P ?T conductivity.Diamond symbols are σdc data from resistivity measurements of Ref.7.Thin dashed lines are the HF-and the LF-MIR components of the ?t for P =9.8GPa data.In the inset both the total spectral weight and that of the MIR components is shown.

increasing the pressure,the re?ectivity increases its ab-solute value and a dip shows up around 3000cm ?1and gets more de?ned in the high pressure regime.

We show in the inset of the upper panel of Fig.5the quantity

?R

R (P =0.5GPa)

,

(4)

evaluated at 1600cm ?1.The dashed line is a phenomeno-logical sigmoid ?t to the data.The ?t has been used to estimate,directly from re?ectivity,the pressure P MIT at which a clear discontinuity appears.We found P MIT =6.0GPa in very good agreement with the pressure (as de-

termined by resistivity measurements)at which the room temperature metallization takes place.7?R/R has been evaluated also at other frequencies,with similar results.In order to evaluate the pressure dependence of the low-energy charge excitations of V 3O 5,the optical con-ductivity has been obtained by ?tting the re?ectivity curves with a Drude-Lorentz model 25.As a starting point we took the parameters corresponding to the room-temperature ?t of the optical conductivity.Two ?ts (at 0.5and 9.8GPa)are reported as an example in Fig.5.Those ?ts are consistent with a two-absorption-band sce-nario:a band at high frequency that presents a similar energy scale as the HF-MIR band observed in the low-T insulating phase,and a low-frequency one,consistent with the energy scale of the LF-MIR band of the high-T metallic phase.The optical conductivity curves calcu-lated from the ?t parameters are shown in the lower plot of Fig. 5.At variance with the temperature-dependent data,in which the MIR band shifts towards low energy,the pressure-dependent curves show the coexistence of two MIR bands and a transfer of SW between them.In the inset of the lower panel of Fig.5the behavior of the SW of the bands as a function of P is shown.While the SW of the HF-MIR band decreases,the one of the LF-MIR band increases.The sum of those par-tial SW (also shown)is instead almost constant.One may argue that a Drude term may be used instead of the ?nite-low-frequency contribution.However,any rea-sonable Drude-Lorentz ?t that can be performed on the re?ectivity would imply a high value of σdc ,not consis-tent with resistivity data 7(see diamond symbols in the lower panel of Fig.5).Moreover,due to the activated behavior of the resistivity as a function of pressure (at least at room temperature)one can assume that there is no term in the optical conductivity due to coherent transport,i.e.,no Drude term is expected to show up in the low-frequency region.

V.DISCUSSION

A polaronic scenario may explain the behavior of the optical conductivity here measured as a function of both T and P in V 3O 5.In the insulating phase hole carriers are con?ned within the V(11)octahedra (related to V 4+ions),namely the smallest and most distorted ones 12.The localized hole with the surrounding distorted octa-hedron,therefore represents a small polaron.Di?raction suggests that those small polarons spatially order at low T (at least at short or intermediate range).It has also been suggested that this ordering may be described in terms of a polaronic Wigner crystal 10.In this scenario the HF-MIR band corresponds to the photo-induced hop-ping process of carriers between the V(11)octahedron and the other less distorted V 3+centered octahedra.The peak energy of this band is an estimate of the localization energy of polarons in the ordered Wigner crystal.At low T ,the three V 3+octahedra show di?erent distortions

thus determining a distribution of localization energies and an intrinsic bandwidth of the HF-MIR.By increas-ing T and approaching the MIT,the weak softening of that band is probably induced by the activation of ther-mal defects in the lattice and indicates a rise of the disor-der in the crystal26.Moreover the slight decrease of the ΓHF?MIR,on increasing T,indicates,in agreement with di?raction data,a progressive reduction in the distor-tion among the three di?erent V3+octahedra.For T≤T MIT,the ratioΓMIR/ωMIR is nearly constant(see inset of Fig.3),probably indicating that a single energy scale determines the pre-melting and the melting transition of the polaronic crystal.The high-T state,due to fast charge exchange at least among V(1)lattice sites,results in poor metallic conductivity.Holes present,therefore, a highly di?usive motion,corresponding to the absence of a Drude peak in the optical conductivity(see Fig.3). On the other hand,optical transitions between V(1)and V(2)octahedra(presenting a smaller di?erence in distor-tion than those,in the insulating phase,among V(11) and V(12),V(21)and V(22)),generate,in the metallic phase,an absorption at?nite frequency(LF-MIR)with a maximum around1000cm?1(see Fig.3and its inset). This phase,in agreement with the very largeΓMIR of the LF-MIR(see inset of Fig.3),can be,therefore,described in terms of disordered small polarons.

The pressure-induced MIT shows instead no variation in the peak frequency of the HF-MIR band.Approach-ing the MIT,as pressure is increased,a lower scale in the polaronic excitation spectra,with a characteristic energy corresponding to the LF-MIR band,is induced in the sys-tem.Therefore the main e?ect of pressure is the transfer of spectral weight towards low-frequency,as it happens in the T-induced MIT.However,the coexistence of the LF-and HF-MIR bands in the spectra suggests that a di?erent microscopic mechanism(with respect to the T-dependent MIT)is inducing the P-driven charge delo-calization.Considering the anisotropy in the compress-ibility extracted from X-ray measurements14,the coex-istence of two MIR bands can be understood as follows. Since,on increasing P,one lattice parameter(b)reduces more than the other two(a,c),the compression of the layers containing only V3+is larger than that of those composed of both V3+and V4+ions.Moreover,this im-plies that the distortion di?erences between the tri-and tetra-valent octahedra are not removed along certain lat-tice directions,not modifying the hopping energy,thus explaining the presence of the HF-MIR.However,in the other lattice directions the oxygen octahedra rearrange and reduce their distortion,thus inducing a lower energy scale in the polaronic excitation spectra(LF-MIR band) and incoherent dc transport.

VI.CONCLUSIONS

In conclusion,we studied by IR spectroscopy the metal-to-insulator transitions,driven by both tempera-ture and pressure,in V3O5single crystals.The temper-ature and pressure dependence of the optical conductiv-ity are explained within a polaronic scenario,in which the localization of the charge carriers partially decreases crossing the MIT.Indeed,the T-dependence of the op-tical conductivity shows a progressive reduction of the polaron localization-energy,thus inducing,at high T,a liquid of small polarons.In the P-driven MIT,instead, a reduction of the localization energy occurs only along some lattice directions,showing a coexistence of strongly localized and partially delocalized polarons.The di?er-ences in P-or T-dependent optical data suggest that the two metal-to-insulator transitions are based on di?erent microscopic mechanisms corresponding to a di?erent re-arrangement of the oxygen octahedra in temperature and pressure.However,since the SW is almost recovered at around1eV and the lattice rearrangement is contextual to the MIT in both cases,this supports the key-role of electron-lattice interaction in the processes of carriers de-localization in V3O5material.

Acknowledgments

We thank V.A.Sidorov and A.Waskowska for supply-ing us single crystals of V3O5synthesized by S.?A sbrink. P.Calvani and S.Fratini for useful discussions.

1M.Imada e t al.,Rev.Mod.Phys.70,1039(1998).

2N.F.Mott,Rev.Mod,Phys.40,677(1968).

3P.Limelette,A.Georges,D.Jerome,P.Wzietek,P.Met-calf,and J.M.Honig,Science302,89(2003).

4N.Drichko,M.Dressel,C.A.Kuntscher,A.Pashkin,A. Greco,J.Merino and J.Schlueter,Phys.Rev.B74,235121 (2006)

5A.Georges,G.Kotliar,W.Krauth,and M.J.Rozenberg, Rev.Mod.Phys.68,13(1996).

6G.Kotliar,S.Y.Savrasov,K.Haule,V.S.Oudovenko,O. Parcollet,and C.A.Marianetti,Rev.Mod.Phys.78,865 (2006).

7V.A.Sidorov,A.Waskowska and D.Badurski,Solid State Commun.125,359(2003).

8V.A.Sidorov,unpublished.

9U.Schwingenschl¨o gl and V.Eyert,Ann.Phys.13,475 (2004).

10F.A.Chudnovskii,E.I.Terukov,D.I.Khomskii,Solid State Commun.25,573(1978).

11S.-H.Hong and S.?A sbrink,Acta Crystallogr.B38,713 (1982).

12S.?A sbrink,Acta Crystallogr.B36,1332(1980).

13E.J.W.Verwey,Nature144,327(1939).

14S.?A sbrink and M.Malinowski,J.Appl.Cryst.20,195

(1987).

15K.Nagasawa,Y.Bando and T.Takada,J.Cryst.Growth 17,143(1972).

16S.?A sbrink,Nature279,624(1979).

17H.K.Mao,J.Xu,and P.M.Bell,J.Geophys.Res.91,4673 (1986).

18S.Lupi,A.Nucara,A.Perucchi,M.Ortolani,P.Calvani, L.Quaroni,M.Kiskinova,to be published in JOSA B. 19A.Sacchetti,E.Arcangeletti,A.Perucchi,L.Baldassarre, P.Postorino,S.Lupi,N.Ru,I.R.Fisher and L.Degiorgi, Phys.Rev.Lett.98,026401(2007).

20F.Wooten,in”Optical Properties of Solids”,(Academic Press,NewYork,1972)and M.Dressel and G.Gr¨u ner,in ”Electrodynamics of Solids”,(Cambridge University Press, 2002).21L.V.Gasparov,D.B.Tanner,D.B.Romero,H.Berger,G.

Margaritondo and L.Forr`o,Phys.Rev.B62,7939(2000). 22M.M.Qazilbash,K.S.Burch,D.Whisler,D.Schreken-hamer,B.G.Chae,H.T.Kim,and D.N.Basov,Phys.

Rev.B74,205118(2006).

23M.J.Rozenberg,G.Kotliar,H.Kajueter,G.A.Thomas,

D.H.Rapkine,J.M.Honig and P.Metcalf,Phys.Rev.

Lett.75,105(1995).

24P.Dore,A.Nucara,D.Cannav`o,G.De Marzi,P.Calvani,

A.Marcelli,R.S.Sussmann,A.J.Whitehead,C.N.Dodge,

A.J.Krehan,and H.J.Peters,Appl.Opt.37,5731(1998). 25A conventional KK analysis cannot be performed due to the reduced spectral range(limited to the MIR).

26S.Ciuchi and F.De Pasquale,cond-mat/9812393