The study of the electrical properties of the layered compound CuFeTe2 shows that there are three well differentiated conduction regimes depending on the temperature. Below TSDW ~ 300 K the formation of a Spin Density Wave (SDW) state has been reported, in the frame of a metal to non metal transition. Below 100 K (~ TSDW/3) the behavior of the electrical resistance as a function of temperature and magnetic field is attributable to the still present not condensed electrons (quasi particles) in the SDW state. At low temperatures (1.8 - 20K), low current (< 1 mA) and magnetic eld (0<H <6 Tesla), the effects of weak localization and electronic interactions in two dimensions appear. At intermediate temperatures (20 < T < 100 K) a hopping conductivity behavior is observed

Broto, J. M.

González Gómez, Jesús Antonio

González-Jiménez, F.

Rakotob, H.

Rivas-Mendoza, A.

English

UCrea

14REVISTA CUBANA DE FÍSICA, Vol. 28, No. 1 (Agosto 2011)COORDENADASINTRODUCTIONe systems of reduced dimensionality are the focus of attention of many studies in physics of the condensed matter. e electrons in these systems are conned to geometries that force them to strongly interact with each other, giving rise to a rich variety of behaviors and phase transitions. e free electron gas instability allows, at low tem-peratures, the appearance of states like superconductivity, or Charge Density Waves (CDW) or Spin Density Waves (SDW).e SDW state, proposed by A. W. Overhausser in 1962[1], has been broadly studied in two prototypic families of materials, Cr and their alloys[2,3] and  Bechgaard salts[4]. It has also been put in evidence that two dichalcogenide compounds, CuFeSe2 (quasi-1D system, TSDW = 71 K)[5] and CuFeTe2 (quasi-2D system, TSDW = 300 K )[5], present a SDW state. More recently thermodynamic and transport measurements in the layered compound Fe-oxypnictide, LaFeAsO, show a structural phase transition at Ts = 155K, which has been associated with the formation of a SDW state[6].e SDW state in CuFeTe2 is supported by previous magnetic susceptibility, electrical resistance and Mössbauer spectroscopy measurements[5,7,8] in a sample prepared by the Bridgman vertical growth technique. A magnetic transition is observed at 308 K, with a Pauli paramagnetism behavior above this temperature. e ther-mal evolution of the Mössbauer spectra between TSDW and TSDW/3 reect the presence of the condensed state (a magnetically split wide distribution of hyperne elds) and the normal state (a non magne-tic contribution). A spectrum at low applied magnetic elds in the Pauli paramagnetic zone suggests the absence of localized magnetic moments on iron, conrming that the magnetic order observed is of itinerant origin. ere is a metal to non metal transition, at TSDW = 300 K, indicating the opening of a gap at the Fermi level. I-V measu-rements indicate a non linear electrical conductivity, which suggests the coexistence of two conduction channels, one associated with the normal electrons (ohmic conductivity) and the other one associated with the SDW state (non ohmic conductivity). is behavior is a con-sequence of the depinning and sliding of the SDW condensate[4].e compound CuFeTe2 crystallizes in a tetragonal structure with unit cell parameters of a = 3.934 Å and c=6.078 Å (space group P4/nmm, No. 129)[9], formed by conductive planes of Cu and Fe cations and planes of Te anions, perpendicular to the crystallogra-phic c-axis. e layered structure is shown in gure 1. e anions are arranged in a tetragonal deformed fcc sublattice. Each Cu or Fe atom is surrounded by four Te atoms in tetrahedral coordination. Two adjacent planes of Te atoms are separated by Van der Waals gaps (gure 1) that allow the cleavage in directions perpendicular to Recibido el 9/12/10.  Aprobado en versión final el 10/2/11. ORIGINAL PAPERWEAK LOCALIZATION AND ELECTRON-ELECTRON INTERACTION IN THE LAYERED COMPOUND CuFeTe2A. Rivas-Mendozaa†, F. González-Jiménezb, J. M. Brotoc, H. Rakotob and J. Gonzálezda) Departamento de Física, Universidad de Carabobo, Valencia, Venezuela. aerivas1@uc.edu.ve†b) Laboratorio de Magnetismo, Dpto. de Física, Ciencias, UCV, Caracas, Venezuela. c) Laboratoire National de Champs Magnétiques Intenses, University of Toulouse, UPS, INSA, CNRS-UPR 3228, 143 Av. de Rangueil, F-31400 Toulouse, France.d) Departamento de Física, Ciencias, ULA, Mérida, Venezuela†  autor para la correspondenciaEl estudio de las propiedades eléctricas del compuesto lami-nar CuFeTe2 indica que hay tres regímenes de conducción bien diferenciados dependientes de la temperatura. Por de-bajo de TSDW ~ 300 K se ha reportado la formación de un estado de Ondas de Densidad de Espín (SDW), en el marco de  una transición metal no metal. Por debajo de 100 K (~ TSDW/3) el comportamiento de la resistencia eléctrica como una función de la temperatura y el campo magnético se atri-buye a los electrones no condensados (cuasi partículas) en el estado SDW. A bajas temperaturas (1.8 - 20K), baja corriente (< 1 mA) y campo magnético (0 <H <6 Tesla), los efectos de localización débil e interacciones electrónicas aparecen. A temperaturas intermedias (20 < T < 100 K) se observa un comportamiento de conductividad hopping. The study of the electrical properties of the layered compound CuFeTe2 shows that there are three well differentiated con-duction regimes depending on the temperature. Below TSDW ~ 300 K the formation of a Spin Density Wave (SDW) state has been reported, in the frame of a metal to  non metal tran-sition. Below 100 K (~ TSDW/3) the behavior of the electrical resistance as a function of temperature and magnetic eld is attributable to the still present not condensed electrons (quasi particles) in the SDW state. At low temperatures (1.8 - 20K), low current (< 1 mA) and magnetic eld (0<H <6 Tesla), the effects of weak localization and electronic interactions in two dimensions appear. At intermediate temperatures (20 < T < 100 K) a hopping conductivity behavior is observed.Palabras Clave. Localization effects 72.15.Rn, Hopping transport 72.20.Ee, Weak localization 73.20.Fz, Spin-density waves REVISTA CUBANA DE FÍSICA, Vol. 28, No. 1 (Agosto 2011)ARTÍCULOS ORIGINALES15REVISTA CUBANA DE FÍSICA, Vol. 28, No. 1 (Agosto 2011)COORDENADASthe c-axis. e overlap of 3d Cu and Fe orbitals in the cation planes is expected (minimum separation between cations is 2.81 Å). Such atomic metallic planes can be considered as conducting sheets of, say, 2 Å thickness.e electrical transport properties of CuFeTe2 were initially stu-died by Vaipolin et al.[10] by means of resistivity measurements as a function of temperature. Between 4.2 and 500 K, ρ(T) decrea-ses two orders of magnitude, wich a thermal variation given by x T)(TcT= (T) /exp 0  with x ~ 1 below 200 K. F. N. Abdullaev et al.11 have investigated the temperature de-pendences of the electrical resistivity of CuFeTe2 semiconduc-tor single crystals, parallel and perpendicular to the plane of the crystal layers, in the temperature range 5-300 K. e temperatu-re dependence of the electrical resistivity presents two regions associated with di"erent mechanisms of electrical conduction, thermally excited impurity charge carriers in the allowed ener-gy band and hopping between localized states lying in a narrow energy band near the Fermi level.Figure 1. Crystalline structure of the CuFeTe2 compound. Unit cell (left) and crystal (right).In this work we present a detailed study of the compound Cu-FeTe2 at low temperatures and high magnetic elds. In particu-lar, we have measured the resistance as a function of the tem-perature along the conducting planes, as well as, the transverse magnetoresistance down to 1.8 K and up to 6 Tesla. e results suggest that the conduction in this system is determined by the e"ects of weak localization and electronic interactions in two dimensions.2 EXPERIMENTAL TECHNIQUESWe have carried out a study of the electrical conduction on a new sample of CuFeTe2 prepared by the standard melting and annealing technique of a stoichiometric mixture of each of the constituent elements. e layered sample obtained is of high quality, as it has been observed in the optical microscope, as well as, by x-ray di"raction. A monocrystalline sheet with a brilliant surface has been obtained by cleavage.e measurements of the resistance as a function of temperatu-re, between 1.8 and 290 K, and the magnetoresistance, in pulsed high magnetic elds up to 6 Tesla, were made in direct current (dc) using the standard four probe method. e sample selected for the study was approximately 0.35 mm thickness, cleaved (in the plane a-b) directly from the original ingot. e electric con-tacts were made using gold wires of 25 µm and silver paint. Due to the layered structure of the compound, the electric contacts were placed on the edge of the sample. is allows a better current dis-tribution in many conducting planes. e sample was covered with vaseline to avoid the oxygen contamination, known to take place between the Var der Waals gaps, which cause their deterio-ration and the appearance of jumps in the resistance. e results are reproduced very well in the di"erent thermal cycles and in high magnetic elds, indicating the stability of the sample.RESULTS AND DISCUSIONResistance vs temperature. Figure 2 shows the resistance as a function of temperature in log-log scale, between 1.8 and 290 K, for a current of 1 mA dc (ohmic regime). In the whole measu-rements interval a non metallic type behavior is appreciated, with a variation in R(T) of one order of magnitude. ere exist three well di"erentiated conduction regimes: low, intermediate and high temperatures. Above 20 K a smooth change in the re-sistance takes place, say oTR=R(T) , that can be attributed to hopping conductivity assisted by phonons. is dependence in temperature has been observed in CuFeTe2 by Vaipolin et al.[9] and F. N. Abdullaev et al.[10]e analysis of the R(T) curve between 20 and 100 K by means of the logarithmic derivative technique T)d(R)d( ln/ln , allow us to determine the value of the parameter β= -0.48 ± 0.06 (see insert of gure 2). On the other hand, the zero value of the slope in this gure indicates that thermal activation doesn't exist in this temperature range. Above 100 K the conduction in CuFeTe2 is associated to the thermal evolution of the con-densate fraction in the SDW regime[7], which decreases up to the non metal to metal transition (TSDW), already observed in other samples of this system[7].In the linear regime the condensate (the SDW) does’nt contri-bute to the conductivity. e SDW is pinned to the lattice by impurities, defects and imperfections, and only the non con-densed electrons participate in the conduction. At low tempe-ratures it is expected that only a small fraction of the conduc-tion electrons is responsible for the behavior of the resistance in CuFeTe2. e Mösbauer spectroscopy allowed us to observe simultaneously the fraction of condensed electrons (the mag-netic SDW contribution to the spectra) and in the other hand the non condensed fraction (the non magnetic quadrupole do-ublet). e results indicate that almost 10% of the conduction electrons remain uncondensed at 4.2 K7.Magnetoresistance. e magnetoresistance was measured at 1.8, 4.2 and 20 K, in pulsed magnetic elds perpendicular to the sheets (conductive planes). A dc current of 5 mA was applied parallel to the sheets. e results indicate a negative magnetoresistance in the whole range of magnetic eld.e negative behavior of the magnetoresistance can be as-sociated to the e"ects of weak localization in disordered 2D systems. In systems with CDW and SDW this behavior has REVISTA CUBANA DE FÍSICA, Vol. 28, No. 1 (Agosto 2011)ARTÍCULOS ORIGINALES16REVISTA CUBANA DE FÍSICA, Vol. 28, No. 1 (Agosto 2011)COORDENADASbeen observed, which is an indication of the disorder existing in those compounds.To estimate the values of the sheet magnetoresistance, Rs, we look the sample as a parallelepipede of ≈ 2x1x0.35 mm3. If the sample is assumed to be formed by 0.35mm/6.087x10-7mm = 5.76x105 sheets in parallel, with, say, d=2x10-7 mm metallic width (cations planes) per sheet and per unit cell (cell para-meter c=6.087x10-7 mm), leading to a metallic e"ective thic-kness tef=5.76x 105x2x10-7 mm=1.152x10-1 mm, which gives a resistivity ρ=2.57x 10-2 Ω. cm and a sheet resistance Rs=ρ /d=1.29 MΩ at 1.8 K.Figure 2. Resistance as a function of temperature in CuFeTe2.According to the weak localization model in two dimensions[12,13], the magnetic eld dependence of the magnetoresistance is given by  !"##$%&&'())*+,&&'())*+ssH+HHfHHfe =R!R222222 23212 h (1)  where α is a parameter of the order of 1.e characteristic elds Hφ and H2 are dened as si +H=H 2H    y  - .sso HH=H ,342          (2)  and represent the di"erent scattering mechanisms of the elec-trons, that is, inelastic (i), spin (s) and spin-orbit (so). e function f2 is dened as h+h+"=(h)f ln/1212 #$%&'(                                     (3)  here Ψ is the digamma function.e perturbation theory calculations up to rst order show that the corrections to the conductivity, of the localization and electronic interactions, are additive. ere is a correction term due to the electron-electron interactions which for 2D systems was calculated by P. A. Lee and T. W. Ramakrishnan[12] and is given by &&'())*+TkHg#geF=!R!RBB2ss22222 h                                  (4)  where F is the Coulomb screening factor, that can be calculated only in the free electron model. Taking the electronic density ~ 5x1020/cm3 for  CuFeTe2, the value F=0.363 is obtained.e function g2 is given by the integral expression - . ////// ,&'()*+,0 $he$d$dd$=hg$1ln12                          (5)  where  TkHg#=h BB / .  With the values of Rs as a function of the magnetic eld for each temperature, and the value of F, the contribution of the electro-nic interactions was calculated and it was subtracted from the experimental data. e curves of the resulting magnetoresistan-ce (due to the e!ects of weak localization) are shown in gure 3 (circles). e solid lines correspond to the tting by means of equation 1. In the weak localization regime, when increasing temperature and magnetic eld, the inelastic mean free-path li decrease and the electron becomes less located, and the resistivi-ty of the system decrease.e tting parameters are α, Hφ and H2. e best tting is achieved with H2 = 0. We find pi aT=H=H   (see the in-sert in gure 3), with a = 0.726 and p = 1.2. !is means that there are not contributions to the electron scattering by mag-netic impurities (Hs=0) or spin-orbit coupling (Hso=0) and that the important mechanism is the inelastic scattering. !e para-meter values of the magnetoresistance are shown in Table I.Table IFitted parameters of the transverse magnetoresistance of the layered compound CuFeTe2T(K) Rs (Ω) α Hφ (Tesla) LTh (Å)1.8 1.29x106 0.65 1.429 1074.2 947520 0.82 3.869 6520 354240 1.16 23.803 26!e e"ects of weak localization in two dimensions appear if the thickness d of the metallic sheets  is much smaller than the !ouless length L , which is related to the characteristic eld Hi by the expression[12]24 ThieLHh1                                                     (6) !e values of L  are indicated in the table 1. We can see that L  >> d (d = 2Å according to the layered structure shown in gure 1), therefore it is reasonable to consider the CuFeTe2 as an almost-2D system in relation to the electronic localization phenomena.REVISTA CUBANA DE FÍSICA, Vol. 28, No. 1 (Agosto 2011)ARTÍCULOS ORIGINALES17REVISTA CUBANA DE FÍSICA, Vol. 28, No. 1 (Agosto 2011)COORDENADAS!e Tp behavior of Hi has been observed in many disordered systems, such AuxSi1-x/Si (with p=2) and Cu/Si[13] multila-yers, as well as in metallic thin lms of Cu[14], Ag or Ag-Pd. Another case is the organic conductor (DMtTSF)2BF4, isomor-phous to the Bechgaard salts (SDW systems), in which the-re were found e"ects of weak localization with Hi ∝ T (p ~ 1)[15]. In CuFeTe2 we found p = 1.2. !e value of p depends on the inelastic scattering mechanism at low temperatures. For the electron-phonon interaction p = 5, while for the s-d electron-electron interaction, p = 2. However, in metals with nesting in the Fermi surface a linear T scattering has been found[16], this could be the case of CuFeTe2, in agreement with the SDW state.Figura 3. Transverse magnetoresistance of the CuFeTe2. Insert: caracte-ristic eld Hφ as a function of temperature.CONCLUSIONS!e study of the electronic conduction at low temperature (down to 1.8 K), low current and high pulsed magnetic elds, performed for the rst time on the layered compound CuFeTe2, indicates the presence of weak localization in the cation pla-nes of the almost-2D structure, being the interactions between conduction electrons the fundamental mechanism of inelastic scattering. Between 20 and 100 K the conduction is of hopping type assisted by phonons, without thermal activation of the ca-rriers. Above 100 K the behavior of the resistance is attributed to the decrease of the fraction of electrons condensed in the SDW state.ACKNOWLEDGEMENTS!is work has been supported by the PCP program "Nanosys-tems and nanomeasurements" of the FONACIT (Venezuela) and the French government. Also partially supported by the "Alma Mater" program of the CNU-OPSU, Venezuela. !e measurements were carried out in the Laboratoire National des Champs Magnétiques Intenses in Toulouse, France.[1] A. W. Overhausser, “Spin Density Waves in an Electron Gas”, Phys. Rev. 128, 1437–1452 (1962).[2] E. Fawcett, “Spin-density-wave antiferromagnetism in chromium”, Rev. Mod. Phys. 60, 209–283 (1988).[3] E. Fawcett, H. L. Alberts, V. Yu. Galkin, D. R. Noakes  and Y. V. Yakhmi, “Spin-density-wave antiferromagnetism in chromium alloys”, Rev. Mod. Phys. 66, 25–127 (1994).[4] G. Grüner, “!e Dynamics of Spin-density Waves”, Rev. Mod.  Phys, 66, No. 1, 1-24 (1994)[5] F. González-Jimenez, E. Jaimes, A.  Rivas, L. D'Onofrio, J. González and M. Quintero, “New spin-density waves systems: Cu and Fe selenides and tellurides”, Physica B 259-261, 987-989 (1999).[6] C. De la Cruz et al, “Magnetic order close to superconductivity in the iron-based layered LaO1-xFxFeAs systems”, Nature 453, 899-902 (2008).[7] A. Rivas, “Ondas de Densidad de Espín en el Compuesto Casi-2D CuFeTe2: Evidencia Directa de la Coexistencia de los Estados Normal y Condensado”, Tesis Doctoral, Universidad Central de Venezuela, Caracas, Venezuela (2005).[8] A. Rivas, F. González-Jiménez, E. Jaimes, L. D'Onofrio, J. González and M. Quintero “SDW in the 2D Compound CuFeTe2”, Hyperne Interac-tions 134, 115-122 (2001).[9] A. A. Vaipolin, V. D. Prochukhan, Yu V. Rud and V. E. Skoriukin, Izv. Akad. Nauk. SSSR Ncorg. Mater. 20, 578 (1984).[10] A. A. Vaipolin, S. A. Kijaev, L. V. Kradinova, A. M. Polubotko, V. V. Po-pov, V. D. Prochukhan, Yu V. Rud and V. E. Skoriukin, “Investigation of the gapless state in CuFeTe2”, J. Phys: Condens. Matter. 4, 8035-8038 (1982).[11] F. N. Abdullaev, T. G. Kerimova, G. D. Sultanov, and N. A. Abdullaev, “Conductivity anisotropy and localization of charge carriers in CuFeTe2 single crystals with a layered structure”, Phys. Solid State 48, No. 10, 1848-1852 (2006).[12] P. A. Lee and T. V. Ramakrishnan, “Disordered electronic systems”, Rev. Mod. Phys. 57, 287-337 (1985).[13] A. Audouard, A. Kazoun, J. M. Broto, G. Marchal and A. Fert, “Tem-perature and magnetic eld dependence of the two-dimensional conduc-tivity in AuxSi1-x/Si and Cu/Si multilayers”, Phys. Rev. B 42, 2728-2734 (1990).[14] C. van Haesendonck, L. van den Dries, Y. Bruynseraede and G. Deuts-cher, “Localization and negative magnetoresistance in thin copper lms”, Phys. Rev. B 25, 5090-5096 (1982).[15] J. P. Ulmet, L. Bachere and S. Askenazy, “Negative magnetoresistance in some dimethyltrimethylene-tetraselenafulvalenium salts: A signature of weak-localization e"ects”, Phys. Rev. B 38, 7782-7788 (1988).[16] A. Virosztek and J. Ruvalds, “Nested-Fermi-liquid theory”, Phys. Rev. B 42, 4064-4072 (1990).REVISTA CUBANA DE FÍSICA, Vol. 28, No. 1 (Agosto 2011)ARTÍCULOS ORIGINALES

Weak localization and electron-electron interaction in the layered compound CuFeTe2

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Weak localization and electron-electron interaction in the layered compound CuFeTe2

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