Pairing of oxygen holes into heavy bipolarons in the paramagnetic phase and
their magnetic pair-breaking in the ferromagnetic phase [the so-called
current-carrier density collapse (CCDC)] has accounted for the first-order
ferromagnetic phase transition, colossal magnetoresistance (CMR), isotope
effect, and pseudogap in doped manganites. Here we propose an explanation of
the phase coexistence and describe the magnetization and resistivity of
manganites near the ferromagnetic transition in the framework of CCDC. The
present quantitative description of resistivity is obtained without any fitting
parameters by using the experimental resistivities far away from the transition
and the experimental magnetization, and essentially model independent.Comment: 10 pages, 3 figure

Alexandrov, A. S.

Bratkovsky, A. M.

Kabanov, V. V.

Physical Review Letters

English

arXiv

Pairing of oxygen holes into heavy bipolarons in the paramagnetic phase and their magnetic pair breaking in the ferromagnetic phase (the so-called current-carrier density collapse) has accounted for the first-order ferromagnetic-phase transition, colossal magnetoresistance, isotope effect, and pseudogap in doped manganites. Here we propose an explanation of the phase coexistence and describe the magnetization and resistivity of manganites near the ferromagnetic transition in the framework of the current-carrier density collapse. The present quantitative description of resistivity is obtained without any fitting parameters, by using the experimental resistivities far away from the transition and the experimental magnetization, and is essentially model-independent

A.S. Alexandrov (7170284)

A.M. Bratkovsky (7170647)

V.V. Kabanov (7170560)

Loughborough University Institutional Repository

PRL 96, 117003 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending24 MARCH 2006Phase Coexistence and Resistivity near the Ferromagnetic Transition of ManganitesA. S. Alexandrov,1 A. M. Bratkovsky,2 and V. V. Kabanov31Department of Physics, Loughborough University, Loughborough LE11 3TU, United Kingdom2Hewlett-Packard Laboratories, 1501 Page Mill Road, 1L, Palo Alto, California 94304, USA3Josef Stefan Institute, 1001 Ljubljana, Slovenia(Received 31 January 2006; published 23 March 2006)0031-9007=Pairing of oxygen holes into heavy bipolarons in the paramagnetic phase and their magnetic pairbreaking in the ferromagnetic phase (the so-called current-carrier density collapse) has accounted for thefirst-order ferromagnetic-phase transition, colossal magnetoresistance, isotope effect, and pseudogap indoped manganites. Here we propose an explanation of the phase coexistence and describe the magne-tization and resistivity of manganites near the ferromagnetic transition in the framework of the current-carrier density collapse. The present quantitative description of resistivity is obtained without any fittingparameters, by using the experimental resistivities far away from the transition and the experimentalmagnetization, and is essentially model-independent.DOI: 10.1103/PhysRevLett.96.117003 PACS numbers: 75.10.b, 72.15.Jf, 75.47.mFerromagnetic oxides, in particular manganese perov-skites, show very large magnetoresistance near the ferro-magnetic transition. The effect observed in these materialswas termed ‘‘colossal’’ magnetoresistance (CMR) to dis-tinguish it from the giant magnetoresistance in metallicmagnetic multilayers. The discovery raised expectations ofa new generation of magnetic devices and is a focus ofextensive research aimed at describing the effect. Signific-ant progress has been made in understanding the propertiesof CMR manganites, but many questions remain. Theferromagnetic metal-insulator transition in manganiteshas long been thought to be a consequence of the so-calleddouble-exchange mechanism (DEX), which results in avarying bandwidth of electrons in the Mn3 d shell as afunction of temperature [1]. More recently, it has beennoticed [2] that the effective spin interaction cannot aloneaccount for CMR within the double-exchange model. Infact, there is strong experimental evidence for exception-ally strong electron-phonon interactions in doped mangan-ites from the giant isotope effect [3], the Arrheniusbehavior of the drift and Hall mobilities [4] in the para-magnetic phase above the Curie temperature TC, and otherexperiments. In view of this, Ref. [2] and some subsequenttheoretical studies have combined DEX with the Jahn-Teller e-ph interaction with d states, arriving at the con-clusion that the low-temperature ferromagnetic phase is aspin-polarized metal, while the paramagnetic high-temperature phase is a polaronic insulator.However, some low-temperature optical [5], electron-energy-loss (EELS) [6], photoemission [7], and thermo-electric [8] measurements showed that the ferromagneticphase of manganites is not a conventional metal. In par-ticular, broad incoherent spectral features and a pseudogapin the excitation spectrum were observed. EELS confirmedthat manganites were, in fact, charge-transfer doped insu-lators having p holes as current carriers rather thandMn3 electrons. Photoemission and x-ray absorption06=96(11)=117003(4)$23.00 11700spectroscopies of La1xSrxMnO3 also showed that theitinerant holes doped into LaMnO3 have oxygen p char-acter. Further, CMR has been observed in the ferromag-netic pyrochlore manganite Tl2Mn2O7 [9], which hasneither the mixed valence for DEX magnetic interactionnor the Jahn-Teller cations such as Mn3.These and other observations [10], in particular the factthat some samples of ferromagnetic manganites manifestan insulatinglike optical conductivity at all temperatures[11], clearly rule out DEX as the mechanism of CMR. Theearlier of the above observations [3–6,9] led to a noveltheory of ferromagnetic-paramagnetic phase transition andCMR, based on the so-called current-carrier density col-lapse (CCDC) [12], confirmed by later observations. In theCCDC model, the p holes are bound into heavy bipolaronsabove the Curie temperature TC due to the Fro¨hlichelectron-phonon interaction, which is written in the real-space representation asHe-ph Xnn0";#fn0 ncyncnn0 ; (1)where n0 is the ion displacement operator, and the form ofelectron-phonon interaction is specified via the force func-tion [13] fn0 n. The latter is defined as the force withwhich an electron in state jni interacts with the ion degreeof freedom n0 .The resistivity peak and CMR are the result of themagnetic pair breaking below TC (Fig. 1) caused by thep-d spin-exchange interaction Jpd, described asHpd  2N1Xn;mJpdS^zmcyn"cn"  cyn#cn#: (2)Here S^zm is the z component of Mn3 spin on site m, cn"and cn# annihilate a p"; # hole on the oxygen site n, withspin up and down, respectively, and N is the total numberof unit cells.3-1 © 2006 The American Physical SocietycJSσE E∆/2−∆/2BP (bound pairs)PPPP0T<Tc T>TFIG. 1 (color online). Bipolaron model of CMR: Pairs (BP) arelocalized on impurity levels in the paramagnetic phase, wherethe only current carriers are single thermally excited polarons. Ifthe exchange interaction JS between p-hole polarons andordered manganese spins exceeds the pair binding energy ,the pairs break at T < TC because the spin-up polaron subbandsinks abruptly below the bipolaron level. The ferromagnetic stateis a polaronic conductor.PRL 96, 117003 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending24 MARCH 2006Different from cuprates, on-site or more extended inter-site oxygen bipolarons are much heavier in manganitesbecause the e-ph Fro¨hlich interaction [Eq. (1)] is stronger[14] and the band structure is less anisotropic. They arereadily localized by disorder, so it is mainly thermallyexcited single polarons that conduct in the paramagneticphase. Upon temperature lowering, single polarons polar-ize manganese spins at TC via the exchange interaction Jpd,and the spin polarization of manganese ions breaks thebipolaronic singlets, creating a spin-polarized polaronicconductor.The CCDC model has explained CMR in the experi-mental range of external magnetic fields [12,15]. Morerecently, the theory has been further confirmed experi-mentally. In particular, the oxygen isotope effect hasbeen observed in the low-temperature resistivity ofLa0:75Ca0:25MnO3 and Nd0:7Sr0:3MnO3 and explained byCCDC with polaronic carriers in the ferromagnetic phase[16]. The current-carrier density collapse has been directlyobserved using the Hall data in La0:67Ca0:33MnO3 andLa0:67Sr0:33MnO3 [17], and the first-order phase transitionat TC, predicted by the theory [12], has been firmly estab-lished in the specific heat measurements [18]. Importantly,the character of the magnetic phase transition in Tl2Mn2O7pyrochlores has also been determined to be of the firstorder [19] and attributed to the tendency of small polaronsto phase separation at finite carrier density. Indeed, recentMonte Carlo simulations [20] of lattice polarons withanisotropic e-ph interactions and the realistic long-rangeCoulomb repulsion show diverse mesoscopic textures inthe adiabatic limit, where spatially disordered pairs (i.e.,bipolarons) dominate at finite doping.11700On the other hand, resistivity and the magnetization ofsome La0:7Ca0:3Mn1TiO3 samples showed a moregradual (second-order-like) transition [21]. Also, the coex-istence of ferromagnetic and paramagnetic phases near theCurie temperature observed in tunneling [22] and otherexperiments has not yet been addressed in the frameworkof CCDC. Here we show that diagonal disorder, which isinevitable with doping in those solid-state solutions, ex-plains both the phase coexistence and the resistivity ormagnetization behavior near the transition.The mean-field equations [12] describing p-hole po-laron atomic density n, polaron m, and manganese reduced magnetizations and the chemical potential  kBT lny are readily generalized, taking into account arandom distribution of the bipolaron binding energy  =2Jpd across the sample,ni  6y coshi=t; mi  ni tanhi=t;i  B2mi=2t; y2  x ni18 exp2i=t;(3)where t  kBT=Jpd is the reduced temperature, BS is theBrillouin function, x is the number of holes at zero tem-perature in p-orbital states, which are threefold degenerate.The subscript i means different parts of the sample withdifferent i and, hence [12], with different Curie tempera-tures TCi, owing to disorder.While averaging these simple equations over a randomdistribution of i is rather cumbersome, one can apply asimplified approach using the fact that the phase transi-tion in a homogeneous system is of the first order in awide range of  [12]. Taking i  TCi  T andni xTCiT2xpexp=2kBTTTCi andaveraging both quantities with the Gaussian distributionof random TCis around the experimental TC, we obtain anaveraged manganese magnetizationT  12erfcT  TC; (4)where  is the average bipolaron binding energy, y  1for y > 0 and zero for y < 0, and erfcz  2=1=2 	R1z dy expy2. The CCDC with disorder [Eq. (4)] fitsnicely the experimental magnetizations [21] near the tran-sition with physically reasonable  of the order of 10 K,depending on doping (Fig. 2). Hence, we believe that therandom distribution of transition temperatures with thewidth  across the sample caused by the randomness ofthe bipolaron binding energy is responsible for the phasecoexistence near the transition as seen in the tunnelingexperiments [22]. We note that some drop of magnetizationat low temperatures as seen in Fig. 2 might be caused bydomain walls [23].Resistivity of inhomogeneous two-phase systems hasto be calculated numerically. Nevertheless, the compre-hensive numerical simulations are consistent with asimple analytical expression for the resistivity of the binary3-2FIG. 3 (color online). The CCDC model [Eq. (5), lines] de-scribes the experimental resistivity near the ferromagnetic tran-sition in La0:7Ca0:3Mn2TiO3 (squares [21]), if the phasecoexistence caused by disorder is taken into account. No fittingparameters are used in Eq. (5) but the experimental resistivitywell below and well above the transition and the experimentalmagnetization.150 200 250 3000123456δ=0.03 0.01 0.00Magnetization (emu/g)Temperature (K)FIG. 2 (color online). Experimental magnetizations inLa0:7Ca0:3Mn2TiO3 (symbols [21]) compared withEq. (4) (lines) with   8 K, TC  278 K for   0:00;  8 K, TC  264 K for   0:01; and   18 K, TC  224 K for  0:03.PRL 96, 117003 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending24 MARCH 2006mixture  11 2 ; (5)which is valid in a wide range of the ratios 1=2 [24].Here 1;2 is the resistivity of each phase, respectively, and is the volume fraction of the second phase. The expres-sion Eq. (5) is a homogeneous function of 1;2 satisfyingthe duality relation. Scaling arguments [25] proved that theexpression is exact near a percolation threshold in twodimensions. Numerical analysis [24] has shown thatEq. (5) describes the effective resistivity of 2D randomsystems even far away from the percolation threshold, ifthe resistivity ratio 1=2 is not extremely large (&20).The same expression is also asymptotically correct for any3D system, if j1 1=2j  1, and for specific 3D latticestructures [26], if 1=2  1. Of course, there is no uni-versal formula for any material with randomly distributedphases. Generally, one could write f  1 f1 f2, where fx is a model function (for a comprehen-sive list of mixture formulas, see Refs. [27,28]).Equation (5) corresponds to the average of ln in isotropicmixtures providing a qualitatively reasonable and numeri-cally accurate description of the effective resistivity inmany physically important cases (see below).In the framework of CCDC, the resistivity of the para-magnetic phase is 1T  fT exp=2kBT and the re-sistivity of the ferromagnetic phase is 2T  T,where fT and T are polynomial functions of tem-perature depending on the scattering mechanisms. Wellbelow the transition, T can be parametrized as T 0  aT2, and fT  bT well above the transition, wherethe temperature-independent parameters 0, a, =2, and bare taken directly from the experiment [21]. The micro-11700scopic origin of 0, a, b, and alternative parametrizationformulas have been discussed, e.g., in Refs. [21,29] and arenot an issue here. The volume fraction  of the ferromag-netic phase is simply the relative magnetization in ourmodel   T, also available from the experiment[21]. As a result, Eq. (5) provides the quantitative descrip-tion of T in the transition region without any fittingparameters by using the experimental resistivities far awayfrom the transition and the experimental magnetization[21], as shown in Fig. 3. On the other hand, fitting theferromagnetic-phase resistivity with a magnetic scattering(m4:5T4:5) leads to an unrealistic doping-dependent coeffi-cient m4:5 that is changing with doping by more than5 orders of magnitude (see the table in Ref. [21]). Notethat, if one were using an estimate  / 1=n, where n is theaverage single-polaron density, one would obtain1T / erfcT  TC 2=x1=2e=2kBT erfcTC  T: (6)This expression can also fit the experimental curves butwith a value of TC, which turns out to be smaller than thatin the magnetization [Eq. (4)] by several tens of degreesKelvin [30]. The latter expression corresponds to a linearexpansion of Eq. (5) in powers of 1 1=2. It is easy tosee why Eq. (5), when compared with Eq. (6), resolves theproblem of different TCs in the magnetization and resis-tivity, thus providing a parameter-free description of ex-perimental T. If we take 1  2, the resistivity at themagnetic transition (i.e., for     1=2),  21=2pcalculated with Eq. (5) turns out larger thanthe resistivity   22 calculated with the perturbationexpression Eq. (6). It is important that the present descrip-3-3PRL 96, 117003 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending24 MARCH 2006tion of resistivity does not depend on a particular model buton the assumption that the ferromagnetic transition is of thefirst order. The CCDC [12] has provided a basis for thisassumption in terms of the microscopic model.In summary, we have shown that the conventional DEXmodel, proposed half a century ago and generalized morerecently to include the electron-phonon interaction, is inconflict with a number of recent experiments. Among theseexperiments are the site-selective spectroscopies, whichhave shown unambiguously that oxygen p holes are thecurrent carriers rather than d electrons in ferromagneticmanganites. Also, some samples of ferromagnetic man-ganites manifest an insulatinglike optical conductivity atall temperatures, contradicting the DEX notion that theirferromagnetic phase is metallic. On the other hand, thepairing of oxygen holes into heavy bipolarons in the para-magnetic phase and their magnetic breakup in the ferro-magnetic phase has explained the colossal magneto-resistance, the isotope effects, and the pseudogaps ob-served in doped manganites. It also explains the CMR insystems where DEX simply cannot exist, such as manga-nese pyrochlores [9]. The CCDC theory of CMR pre-dicts the first-order phase transition and allows the presentsimple explanation of the coexistence of high- and low-resistive phases. It explains the temperature dependenciesof the magnetization and the resistivity near the transitionas the result of the unavoidable disorder and transportthrough the two-phase mixture in doped manganites.This work was supported by EPSRC (U.K.) (GrantsNo. EP/D035589/1 and No. EP/C518365/1).[1] C. Zener, Phys. Rev. 82, 403 (1951).[2] A. J. Millis, P. B. Littlewood, and B. I. Shraiman, Phys.Rev. Lett. 74, 5144 (1995).[3] G. M. Zhao, K. Conder, H. Keller, and K. A. Mu¨ller,Nature (London) 381, 676 (1996).[4] M. Jaime, H. T. Hardner, M. B. Salamon, M. Rubinstein,P. Dorsey, and D. Emin, Phys. Rev. Lett. 78, 951 (1997).[5] Y. Okimoto, T. Katsufuji, T. Ishikawa, T. Arima, andY. Tokura, Phys. Rev. B 55, 4206 (1997); K. H. Kim,J. H. Jung, and T. W. Noh, Phys. Rev. Lett. 81, 1517(1998); T. Ishikawa, T. Kimura, T. Katsufuji, andY. Tokura, Phys. Rev. B 57, R8079 (1998).[6] H. L. Ju, H.-C. Sohn, and K. M. Krishnan, Phys. Rev. Lett.79, 3230 (1997).[7] D. S. Dessau, T. Saitoh, C.-H. Park, Z.-X. Shen, Y. Mori-tomo, and Y. Tokura, Int. J. Mod. Phys. B 12, 3389 (1998);Y. D. Chuang, A. D. Gromko, D. S. Dessau, T. Kimura,and Y. Tokura, Science 292, 1509 (2001).11700[8] J.-S. Zhou, J. B. Goodenough, A. Asamitsu, and Y. Tokura,Phys. Rev. Lett. 79, 3234 (1997).[9] M. A. Subramanian, B. H. Toby, A. P. Ramirez, W. J.Marshall, A. W. Sleight, and G. H. Kwei, Science 273,81 (1996).[10] G. M. Zhao, Phys. Rev. B 62, 11 639 (2000); G. M. Zhao,Y. S. Wang, D. J. Kang, W. Prellier, M. Rajeswari,H. Keller, T. Venkatesan, C. W. Chu, and R. L. Greene,Phys. Rev. B 62, R11 949 (2000).[11] A. Nucara, A. Perucchi, P. Calvani, T. Aselage, andD. Emin, Phys. Rev. B 68, 174432 (2003).[12] A. S. Alexandrov and A. M. Bratkovsky, Phys. Rev. Lett.82, 141 (1999); J. Phys. Condens. Matter 11, 1989 (1999).[13] A. S. Alexandrov, Theory of Superconductivity: FromWeak to Strong Coupling (Institute of Physics, Bristol,2003).[14] A. S. Alexandrov and A. M. Bratkovsky, Phys. Rev. Lett.84, 2043 (2000); J. Phys. Condens. Matter 11, L531(1999).[15] L. M. Wang, H. C. Yang, and H. E. Horng, Phys. Rev. B64, 224423 (2001).[16] A. S. Alexandrov, G. M. Zhao, H. Keller, B. Lorenz,Y. S. Wang, and C. W. Chu, Phys. Rev. B 64, 140404(R)(2001).[17] W. Westerburg, F. Martin, P. J. M. van Bentum, J. A. A. J.Perenboom, and G. Jakob, Eur. Phys. J. B 14, 509 (2000).[18] J. E. Gordon, C. Marcenat, J. P. Franck, I. Isaac, G. W.Zhang, R. Lortz, C. Meingast, F. Bouquet, R. A. Fisher,and N. E. Phillips, Phys. Rev. B 65, 024441 (2002).[19] P. Velasco, J. Mira, F. Guinea, J. Rivas, M. J. Martinez-Lope, J. A. Alonso, and J. L. Martinez, Phys. Rev. B 66,104412 (2002).[20] T. Mertelj, V. V. Kabanov, and D. Mihailovic, Phys. Rev.Lett. 94, 147003 (2005).[21] X. M. Liu, H. Zhu, and Y. H. Zhang, Phys. Rev. B 65,024412 (2002).[22] M. Uehara, S. Mori, C. H. Chen, and S. W. Cheong, Nature(London) 399, 560 (1999).[23] See, for example, A. Senchuk, H. P. Kunkel, R. M.Roshko, C. Viddal, Li Wei, G. Williams, and X. Z.Zhou, Eur. Phys. J. B 37, 285 (2004).[24] V. V. Kabanov, K. Zagar, and D. Mihailovic, Zh. Eksp.Teor. Fiz. 127, 809 (2005) [JETP 100, 715 (2005)].[25] A. L. Efros and B. I. Shklovskii, Phys. Status Solidi B 76,475 (1976).[26] J. B. Keller, J. Math. Phys. (N.Y.) 28, 2516 (1987).[27] G. W. Milton, The Theory of Composites (CambridgeUniversity Press, Cambridge, England, 2002).[28] F. G. Shin, W. L. Tsui, and Y. Y. Yeung, J. Mater. Sci. Lett.8, 1383 (1989).[29] Guo-meng Zhao, V. Smolyaninova, W. Prellier, andH. Keller, Phys. Rev. Lett. 84, 6086 (2000).[30] A. S. Alexandrov, cond-mat/0506706.3-4

Phase coexistence and resistivity near the ferromagnetic transition of manganites

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Phase coexistence and resistivity near the ferromagnetic transition of manganites

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