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High-frequency magnetoimpedance of double perovskite La 1.2 Sr 1.8 Mn 2 O 7 : Secondary transitions at high temperatures P. V. Patanjali, P. Theule, Z. Zhai, N. Hakim, and S. Sridhar* Department of Physics, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115 R. Suryanarayanan, M. Apostu, G. Dhalenne, and A. Revcolevschi Laboratoire de Chimie des Solides, UA 446, Universite ´ Paris Sud, 91405 Orsay, France ~Received 9 October 1998! Radio frequency magnetoimpedance measurements reveal a pronounced anomaly at 260 K besides the main metal-insulator transition at 125 K in the double-perovskite material La 1.2 Sr 1.8 Mn 2 O 7 . This feature is not seen clearly in static resistivity and magnetization measurements. We suggest that this anomaly represents short- range magnetic correlations enhanced at radio frequencies, with the easy axis along the c axis. @S0163-1829~99!08437-4# The observation of colossal magnetoresistance ~CMR! in perovskite manganites La 1 2x A x MnO 3 ( A 5Sr,Ca) (113) has triggered further research into related systems. 1–4 The CMR in these materials is normally observed at temperatures close to the ferromagnetic-to-paramagnetic transition associ- ated with a metal-insulator ~MI! transition. Following the double-exchange mechanism of Zener, 5 based upon the strong on-site ~Hund’s rule! coupling between the charge carriers ( e g -like state! and the local spins ( t 2 g -like state!, several models 6–10 have been proposed to account for these properties, but many of the observed features cannot be ac- counted by the double-exchange interaction alone. These well-studied 113 compounds can be considered as the n 5members of the Ruddlesden-Popper ~RP! series (La 1 2x Sr x ) n 11 Mn n O 3 n 11 which can be described as inter- growths between La 1 2x Sr x MnO 3 perovskite blocks and rock salt-type layers ~La,Sr!O. In order to examine further the relation between CMR, magnetic, and MI transitions, attention has been focused on other materials with reduced dimension n. 11–14 In particular, for the n 52 member of the RP series (La 1 2x Sr x ) n 11 Mn 2 O 7 ~327!, the material is antiferromagnetic for x 50 , while in the region 0.2<x <0.4 the material is ferromagnetic and exhibits a MI transition at T c . The maximum T c 5125 K obtained in this series is for x 50.4. Moritomo et al. 15 have reported a high value of the CMR in x 50.4 composition at tempera- tures near and far away from T c . Most of the experiments that probe the manganites are static in nature and have limited capabilities in elucidating the basic mechanisms involved. Recent dynamic measure- ments like electron paramagnetic resonance 16 ~EPR! and and ferromagnetic resonance 17 ~FMR! have provided micro- scopic evidence for the formation of Jahn-Teller polarons and spin-wave resonance, respectively, in the manganites. In La 1 2x Sr x MnO 3 , Srikanth et al. 18 have very recently ob- served additional new features in the rf impedance measure- ments, which are not clearly visible in the dc resistivity and magnetization measurements. These results show that the dy- namic rf measurements reveal new transitions, and in addi- tion also give information on the collective response of spin and charge dynamics. In this paper we describe the tempera- ture and field dependence of the radio frequency dynamic response of the double perovskite La 1.2 Sr 1.8 Mn 2 O 7 . We fo- cus on a pronounced anomaly around 260 K observed in many samples and suggest that this anomaly represents mag- netic correlations, perhaps two dimensional ~2D! in nature, with a single energy and temperature scale. Single crystals ~5 cm long and 0.5 cm diameter! of La 1.2 Sr 1.8 Mn 2 O 7 were grown from the melt by the floating- zone method using a mirror furnace. 19 Powder x-ray diffrac- tion ~XRD! analysis resulted in the lattice parameters a 53.86460.002 Å and c 520.13060.006 Å, in close agree- ment with those previously reported. 15 The polycrystalline material was synthesized by the conventional solid-state sin- tering technique. No extra phases were detected by XRD and the lattice parameters were found to be identical to those determined in the case of the single crystals. Three single crystals labeled SC1, SC2, and SC3, and a polycyrstalline sample labeled PC were studied. The rf measurements were carried out using an ultrastable tunnel diode oscillator. The sample is placed in a coil which forms the inductive part of the LC resonant circuit. In this technique, a change in the effective reactance X of the sample, caused by varying the temperature T, magnetic field H, or angle u ~between crystalographic axis and H ), leads to a change in the inductance of the coil which in turn results in a shift of the resonant frequency of the oscillator. The quan- tity that is measured is the change in the resonant frequency, df ( T ) 5@ f ( T ) 2 f 0 ( T ) # 2@ f ( T 5270) 2 f 0 ( T 5270) # , where f 0 ( T ) is the empty coil frequency. From the elementary con- sideration of ac impedance and Maxwell’s equations for magnetic, conducting materials, it can be shown that df 52G ( dX ) } 2d ( m r ) 1/2 . Here, dX ( T , H , u ) 5X ( T , H , u ) 2X ( T 5270,H 50,u 50) is the change in reactance, G the geometric factor, and r ( T , H ) and m ( T , H ) are the resistivity and permeability of the magnetic material, respectively. The change in the reactance is calculated using the above rela- tion. The stability of the circuit is very high, typically, 1 Hz in 4 MHz and the operating frequency is in the range 2–4 MHz PHYSICAL REVIEW B 1 OCTOBER 1999-I VOLUME 60, NUMBER 13 PRB 60 0163-1829/99/60~13!/9268~4!/$15.00 9268 ©1999 The American Physical Society

: Secondary transitions at high temperatures

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PHYSICAL REVIEW B 1 OCTOBER 1999-IVOLUME 60, NUMBER 13

High-frequency magnetoimpedance of double perovskite La1.2Sr1.8Mn2O7:Secondary transitions at high temperatures

P. V. Patanjali, P. Theule, Z. Zhai, N. Hakim, and S. Sridhar*Department of Physics, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115

R. Suryanarayanan, M. Apostu, G. Dhalenne, and A. RevcolevschiLaboratoire de Chimie des Solides, UA 446, Universite´ Paris–Sud, 91405 Orsay, France

~Received 9 October 1998!

Radio frequency magnetoimpedance measurements reveal a pronounced anomaly at 260 K besides the mainmetal-insulator transition at 125 K in the double-perovskite material La1.2Sr1.8Mn2O7. This feature is not seenclearly in static resistivity and magnetization measurements. We suggest that this anomaly represents short-range magnetic correlations enhanced at radio frequencies, with the easy axis along thec axis.@S0163-1829~99!08437-4#

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The observation of colossal magnetoresistance~CMR!in perovskite manganites La12xAxMnO3 (A5Sr,Ca) (113)has triggered further research into related systems.1–4 TheCMR in these materials is normally observed at temperatuclose to the ferromagnetic-to-paramagnetic transition assated with a metal-insulator~MI ! transition. Following thedouble-exchange mechanism of Zener,5 based upon thestrong on-site~Hund’s rule! coupling between the chargcarriers (eg-like state! and the local spins (t2g-like state!,several models6–10 have been proposed to account for theproperties, but many of the observed features cannot becounted by the double-exchange interaction alone. Thwell-studied 113 compounds can be considered as thn5` members of the Ruddlesden-Popper~RP! series(La12xSrx)n11MnnO3n11 which can be described as integrowths between La12xSrxMnO3 perovskite blocks and rocksalt-type layers~La,Sr!O.

In order to examine further the relation between CMmagnetic, and MI transitions, attention has been focusedother materials with reduced dimensionn.11–14 In particular,for then52 member of the RP series (La12xSrx)n11Mn2O7~327!, the material is antiferromagnetic forx50, while in theregion 0.2<x<0.4 the material is ferromagnetic and exhiba MI transition atTc . The maximumTc5125 K obtained inthis series is forx50.4. Moritomoet al.15 have reported ahigh value of the CMR inx50.4 composition at temperatures near and far away fromTc .

Most of the experiments that probe the manganitesstatic in nature and have limited capabilities in elucidatthe basic mechanisms involved. Recent dynamic measments like electron paramagnetic resonance16 ~EPR! and andferromagnetic resonance17 ~FMR! have provided micro-scopic evidence for the formation of Jahn-Teller polaroand spin-wave resonance, respectively, in the manganiteLa12xSrxMnO3, Srikanth et al.18 have very recently ob-served additional new features in the rf impedance measments, which are not clearly visible in the dc resistivity amagnetization measurements. These results show that thnamic rf measurements reveal new transitions, and in ation also give information on the collective response of s

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and charge dynamics. In this paper we describe the tempture and field dependence of the radio frequency dynaresponse of the double perovskite La1.2Sr1.8Mn2O7. We fo-cus on a pronounced anomaly around 260 K observedmany samples and suggest that this anomaly representsnetic correlations, perhaps two dimensional~2D! in nature,with a single energy and temperature scale.

Single crystals~5 cm long and 0.5 cm diameter! ofLa1.2Sr1.8Mn2O7 were grown from the melt by the floatingzone method using a mirror furnace.19 Powder x-ray diffrac-tion ~XRD! analysis resulted in the lattice parametersa53.86460.002 Å andc520.13060.006 Å, in close agreement with those previously reported.15 The polycrystallinematerial was synthesized by the conventional solid-statetering technique. No extra phases were detected by XRDthe lattice parameters were found to be identical to thdetermined in the case of the single crystals. Three sincrystals labeled SC1, SC2, and SC3, and a polycyrstalsample labeled PC were studied.

The rf measurements were carried out using an ultrasttunnel diode oscillator. The sample is placed in a coil whforms the inductive part of theLC resonant circuit. In thistechnique, a change in the effective reactanceX of thesample, caused by varying the temperatureT, magnetic fieldH, or angleu ~between crystalographic axis andH), leads toa change in the inductance of the coil which in turn resultsa shift of the resonant frequency of the oscillator. The qutity that is measured is the change in the resonant frequed f(T)5@ f (T)2 f 0(T)#2@ f (T5270)2 f 0(T5270)#, wheref 0(T) is the empty coil frequency. From the elementary cosideration of ac impedance and Maxwell’s equationsmagnetic, conducting materials, it can be shown td f52G(dX)}2d(mr)1/2. Here, dX(T,H,u)5X(T,H,u)2X(T5270,H50,u50) is the change in reactance,G thegeometric factor, andr(T,H) andm(T,H) are the resistivityand permeability of the magnetic material, respectively. Tchange in the reactance is calculated using the abovetion.

The stability of the circuit is very high, typically, 1 Hz in4 MHz and the operating frequency is in the range 2–4 M

9268 ©1999 The American Physical Society

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depending on the coil and sample used. The inductivewith the sample is inserted into a helium flow cryostat acoupled through a rigid coaxial cable to enable a temperavariation between 4.2 and 300 K. In all the measurementsrf field is perpendicular to thec axis of the crystal. For field-dependent measurements, a dc magnetic field~up to 6 kOe!was applied by placing the sample coil-cryostat assembetween the pole pieces of an electromagnet.

The magnetization and CMR of the crystal have beenscribed elsewhere.20 Briefly, a sharp ferromagnetic to paramagnetic and~MI ! transition is observed around 125 K,the temperature dependence of the magnetization,M (T), andresistivity, r(T), measurements, respectively. However,strong deviation from the Curie-Weiss law was notedaboveT.200 K. Interestingly, in the case of sample SCwhile a very small change in slope is observed at aroundK in the M (T), no such anomaly is observed in the dcr(T)in bothab-plane (rab) andc-axis (rc) directions~inset, Fig.2!. From the field dependence of magnetizationM (H) at 5 Kit is found that the easy axis of magnetization lies in theabplane which is in agreement with reported results.21,22 Themagnetic moment atH55 T was found to be 3.5mB /Mnatom which is in close agreement with the theoretical val3.6mB /Mn atom, ensuring the almost 100% spin polarizatiof the conduction electrons due to a large Hund’s-rule cpling energy.24

Figure 1 shows the shift in the radio frequency reactadX as the temperature is varied between 300 and 70 K,single crystals SC1, SC2, and SC3. As can be seen fromfigure all the three single crystals show a sharp main tration at Tc5125 K. Results for the polycrystal sample P~not shown! were similar but the transition atTc was broad-ened. In the case of sample SC1, interestingly, a very strjump, representative of a secondary transition, is observea temperature 260 K, which we callT* . It is worth notingthat the shift at this temperature is almost 35% of the shifTc and has similar characteristics as that of the transitioTc5125 K. Such a transition is not seen in the staticresistivity and is only observed as a very small changeslope in the magnetization measurements. Samples SSC3, and PC also show similar but weaker transitions arothe same temperature. While the first transition at 125 K

FIG. 1. Temperature dependence of radio frequency reactfor single crystals SC1, SC2, and SC3.

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the well-known MI transition@which is also observed in thedc M (T) andr(T) measurements#, the origin of the transi-tion at T* 5260 K is quite intriguing and worth studying.

In the magnetization measurements, very weak featuare observed in the vicinity ofT* , but are nowhere as pronounced as in Fig. 1. In the literature similar weak featuhave been reported in double perovskite but have not badequately addressed.15,22,23In the present ac measurementhe features are striking and unavoidable. In this paperfocus on this anomaly—a subsequent paper will discussdetails of the field and temperature dependence of the rfsponse over the entire temperature range. It is importandwell on these unusual transitions as they may hold a kean understanding of the basic mechanism involved inCMR materials.

It was earlier demonstrated from a transmission electmicroscopy ~TEM! analysis that intergrowths could bpresent in these materials.25,22 The intergrowths are missingor extra layers of SrO between MnO6 octahedra, which couldform higher order (n.2) phases of RP series. The unit ceof 327 may be written as SrO(La12xSrxMnO3)2, where it isclear that MnO6 octahedra are separated from each otheran insulating SrO layer. If the second transition is thoughbe due to the impurity 113 phase which forms due tomissing of SrO layers, then this phase is likely toLa0.6Sr0.4MnO3. The corresponding transition temperaturethis phase is well above 300 K.26 Second, any phase transtion in the MnO3 sytem is, generally, associated with a larCMR at the transition. From ther(T) it can be inferred thata large change in magnetoresistance is not observed aT*even though as noted previously the overall magnetoretance is substantial. Hence, the transition atT* that we ob-serve is not due to La0.6Sr0.4MnO3 but due to some othemechanism. The transition atT* could not be due to anyother impurity phases since experimental XRD~Ref. 20! andelectron diffraction27 studies show that the sample is frefrom impurity phases. Therefore, one can rule out the ingrowths or impurities playing any role in inducing this trasition.

In Fig. 2 we present the effect of external field in theab

plane (Huuab) and along thec axis (Huuc). As can be seenfrom the figure, in the case ofHuuab the change indX at theMI transition ~at 125 K! decreases when compared to tsame in the absence of field and, interestingly, the transiat T* is almost smeared out. However, in the case ofHuucthe change indX at the MI transition increases and the trasition at T* disappears as in the case ofHuuab. Since theeasy axis of the magnetization is in theab plane, the de-crease or increase indX, in the case ofHuuab/Huuc, can beunderstood in terms of the decrease or increase in magzation, respectively. If theT* is due to an impurity phase~which ought to have an easy axis in certain direction!, as isexpected from the intergrowth mechanism, thedX at thistemperature should have opposite responses forHuuab andHuuc configurations, as in the case of the MI transition. Tpresent response, unequivocally, suggests that the transat T* is not due to impurity phases or intergrowths. It instesuggests some kind of ordering with a weak exchange inaction which gets destroyed in the presence of modemagnetic fields.

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Recently, Moritomoet al.15 have observed a transitioaround 275 K inx50.4 compositions. However, no case hbeen made to explain it. In the case ofx50.3 compositions,Kimura et al.21 observed a striking secondary MI transitioin theab plane (MIab) resistivity, in addition to the usual Mtransition around 100 K. They did not observe such a sondary MI transition in thec-axis resistivity measurementsThe result was ascribed to the 2D ferromagnetic correlatiwithin the MnO2 bilayers leading to a MIab transition at 275K. The 3D spin ordering across the nonmagnetic insulat~La,Sr!O layers was suggested to be taking place at theTc .However, in the present crystal but for the magnitude chain the resistivitiesrab and rc , no further difference is ob-served~inset, Fig. 2!. In both the cases in the temperaturangeTc,T,T* the sample shows insulating behavior.

The CMR, defined as2@r(H)2r(0)#/r(0), is almost100% forTc,T,150 K and exceeds 10% in the entire temperature range. This CMR behavior is in sharp contrast wthat of the La12xAxMnO3 perovskite, where it is present onlbelow and close toTc .1–4 The enhanced CMR in the presecompound could be due to an anisotropic exchange intetion. The intralayer exchange interaction can be understin terms of double exchange. BelowTc the interlayer cou-pling is established which contributes to the 3D magneordering. The very large CMR observed in the vicinityTc , both below and above, is due to the alignment of thet2gspins in the presence of an applied magnetic field whreduces the scattering of the carriers by the local spins.fact that a large CMR is observed even aboveTc indicatesthat some kind of spin correlation is maintained in thisgion. There could be many competing interactions and ording aboveTc such as antiferromagnetic superexchange, etron lattice ~the Jahn-Teller effect!, and charge orderingFrom an inelastic neutron scattering study it was earlier

FIG. 2. Temperature dependence of rf reactance in the presof a magnetic field,H50.6 T, for sample SC1.dX at Tc increaseswhen the field is parallel to thec axis contrary to the behavior whethe field is parallel to theab plane. The inset shows the temperatudependence of resistivity in theab plane and along thec axis, bothin the presence and absence of field.

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ferred, in the case ofx50.4 double perovskite, that the spinin the neighboring layers are strongly canted28 and that thereexists in-plane antiferromagnetic~AF! correlations aboveTc

which lead to insulating behavior.29 In the present crystalsalso from the inelastic neutron scattering study30 it has beenobserved that there is a coexistence of antiferromagneand ferromagnetism aboveTc . Such a competition betweeferromagnetic double exchange and antiferromagnetic suexchange has frequently been observed in the mangawhich show a large negative CMR at temperatures aboveTc

because of the field suppression of the AF fluctuations.31

However, a careful analysis of the present results ox50.4 compositions indicates that the transition atT* is notdue to antiferromagnetic correlations but, probably, dueweak ferromagnetic correlations. The results show thatmain transition atTc and the secondary transition atT* aresimilar in nature.

In Fig. 3 the change in reactance,dX, in the presence of a0.3 T magnetic field, as a function of the angle between

field and c axis of the crystal at various temperatures,shown. The response at 10 K can be considered purely mnetic since the field has no effect onr at this temperature~inset, Fig. 2!. It can be seen that the overall response shoa reduction in permeability with an increase in the anfrom 0° to 90°. Since the easy axis of the 327 phase is inab plane, this reduction inm is expected. However, at lowangles one can see an increase in permeability whichidentify as the response due to the secondary phase.worth noting that the minima are separated by exactly 9Therefore, it is not improper to conclude that the easy axisthe secondary phase is along thec axis. This result coupledwith the dX(T) provides strong evidence that the transitiat T* is ferromagnetic in nature and is independent offerromagnetic transition atTc . AboveTc (T5188, 280, and301 K! it can be seen that a much reduced response~changein m) persists. The reason for this small change is the e

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FIG. 3. Angular variation of rf reactance,dX vs u ~angle be-tween the dc field andc axis of the crystal!, in the presence of a 0.3T field at various temperatures for sample SC1. The variationsmall u is shown in the inset for clarity. The minimum at 0°associated with the secondary transition atT* while the minimumat 90° is associated with ferromagnetic ordering belowTc .

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PRB 60 9271BRIEF REPORTS

tence of ferromagnetic fluctuations aboveTc which is evi-denced by the ferromagnetic hysteresis loop even at 29520

The aforementioned field-dependent anisotropy~Fig. 3! andtemperature-dependent~Figs. 1 and 2! measurements clearlsuggest two kinds of ferromagnetic correlations occurrintrinsically.

It is very interesting to note that the neutron diffractiostudy by Mitchell et al.32 shows a clear change in slopd(a,b axis)/dT at 260 K in thea,b-axis vs temperature plotHowever, they do not observe any change ind(c axis)/dT at260 K. Together, these two points clearly indicate thatT* is most probably associated with spin-lattice coupliand the associated ferromagnetic correlations lie in theabplane. Local lattice or Jahn-Teller distortions of the peroskite unit cells could lead to spin-lattice coupling. The copling of the double exchange to the lattice degrees of frdom in manganites is theroreticallly studied by Milliset al.10

and Roderet al.33 in terms of magnetoelastic polarons. Thdeviation from linearity in the temperature dependence oflattice parameters of La0.6Y0.07Ca0.3MnO3 ~Ref. 34! andLa0.65Ca0.35MnO3 ~Ref. 35! was, earlier, interpreted in termof a transition from large to small polarons. In the prescase, the suggested 2D nature of the secondary trans

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The present secondary transition is very important inderstanding the microscopic picture of the manganites. Sintrinsic spin-lattice coupling can be sensitive to impuritiin the crystal, which may be the reason for not observingT*clearly in samples SC2 and SC3. It is worth mentioning tsimilar high-frequency studies on very-high-quality singcrystals of perovskite YBa2Cu3O7 high-temperature superconductors gave rise to many novel features36,37 which arenot observed in general. In conclusion we have presentedtemperature and field dependence of a dynamic radioquency permeability study of the double perovskLa1.2Sr1.8Mn2O7. These results indicate a secondary trantion at 260 K similar to the main MI transition at 125 K. Thanomalous secondary transition could be due to ferromnetic correlations which are independent of the ferromnetic ordering atTc , which affect the dynamic permeabilitbut are weakly coupled to charge transport.

We thank J.B. Sokoloff for useful comments. The workNortheastern was supported by Grant Nos. NSF-9711and NSF-9623720. This joint collaboration was supportedU.S.-France NSF-CNRS Grant No. NSF-INT-9726801.

ci.,

*Electronic address: [email protected]. von Helmoltet al., Phys. Rev. Lett.71, 2331~1993!.2S. Jinet al., Science264, 413 ~1994!.3C. N. R. Raoet al., Chem. Mater.8, 8421~1996!.4A. P. Ramirez, J. Phys.: Condens. Matter9, 8171~1997!.5C. Zener, Phys. Rev.82, 403 ~1951!.6P. W. Anderson and H. Hasegawa, Phys. Rev.100, 675 ~1955!.7P.-G. de Gennes, Phys. Rev.118, 141 ~1960!.8K. Kubo and N. Ohata, J. Phys. Soc. Jpn.33, 21 ~1972!.9N. Furukawa, J. Phys. Soc. Jpn.63, 3214~1994!.

10A. J. Millis et al., Phys. Rev. Lett.74, 5144 ~1995!; 77, 175~1996!; Phys. Rev. B54, 5389~1996!; 54, 5405~1996!.

11R. Maheshet al., J. Solid State Chem.122, 448 ~1996!.12P. D. Battleet al., J. Phys.: Condens. Matter8, L427 ~1996!.13P. Laffezet al., J. Appl. Phys.80, 5850~1996!.14H. Asanoet al., Appl. Phys. Lett.70, 2303~1997!.15Y. Moritomo et al., Nature~London! 380, 141 ~1996!.16A. Shengelayaet al., Phys. Rev. Lett.77, 5296~1996!.17S. E. Loflandet al., Phys. Rev. B52, 15 058~1995!.18H. Srikanthet al., in Science and Technology of Magnetic O

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No. 494~Materials Research Society, Pittsburgh, 1998!, p. 311.19A. Revcolevschi and R. Collongues, C. R. Seances Acad. S

Ser. C266, 1767~1969!.20W. Prellieret al., Physica B259-261, 833 ~1999!.21T. Kimura et al., Science274, 1698~1996!.22S. D. Baderet al., J. Appl. Phys.83, 6385~1998!.23Despina Loucaet al., Phys. Rev. Lett.80, 3811~1998!.24Y. Okimoto et al. Phys. Rev. Lett.75, 109 ~1995!.25R. Seshadriet al., Chem. Mater.9, 1778~1997!.26H. Kawanoet al., Phys. Rev. B53, R14 709~1996!.27M. Dechampset al. ~unpublished!.28R. Osbornet al., Phys. Rev. Lett.81, 3964~1998!.29T. G. Perringet al., Phys. Rev. Lett.78, 3197~1997!.30T. Chatterjiet al. ~unpublished!.31H. Kuwaharaet al., Science272, 80 ~1996!.32J. F. Mitchellet al., Phys. Rev. B55, 63 ~1996!.33H. Roderet al., Phys. Rev. Lett.76, 1356~1996!.34M. R. Ibarraet al., Phys. Rev. Lett.75, 3541~1995!.35P. Daiet al., Phys. Rev. B54, R3694~1996!.36H. Srikanthet al., Phys. Rev. B55, R14 733~1997!.37Z. Zhai et al., Physica C282-287, 1601~1997!.