Colossal Magnetoresistance Without Mn3+/Mn4+ Double Exchange in the Stoichiometric Pyrochlore Tl2Mn2O7

Structural analysis from powder neutron and single-crystal x-ray diffraction data for a sample of the Tl2Mn2O7 pyrochlore, which exhibits colossal magnetoresistance (CMR), shows no deviations from ideal stoichiometry. This analysis gives an Mn-O distance of 1.90 angstroms, which is significantly shorter than the Mn-O distances (1.94 to 2.00 angstroms) observed in phases based on LaMnO3 perovskites that exhibit CMR. Both results in Tl2Mn2O7 indicate oxidation states very close to Tl3+2Mn4+2O7. Thus, Tl2Mn2O7 has neither mixed valence for a double-exchange magnetic interaction nor a Jahn-Teller cation such as Mn3+, both of which were thought to have an important function in CMR materials. An alternate mechanism for CMR in Tl2Mn2O7 based on magnetic ordering driven by superexchange and strong spin-fluctuation scattering above the Curie temperature is proposed here.

tures. Perhaps the best known example of this is EuO95Gdo.05Se with a critical temperature (To) 20 K (5). Here, CMR is not driven by the same interatomic DE mechanism as are the manganese oxides but rather by an intra-atomic version of the process. We present evidence here for a different mechanism that leads to CMR in Tl2Mn2O7 at high temperatures.
The La1 .A2+MnO3 materials showing CMR have a perovskite structure. Recently, comparable CMR has been found for Tl2Mn2O7 (6), which has a pyrochlore structure (7) (Fig. 1). Because Tl2Mn2O7 also contains Mn as the magnetic constituent, it was thought that this compound would also contain significant amounts of the Jahn-Teller cation Mn3+ and that it was again Mn3+/Mn4+ DE that gave rise to ferromagnetism. Mixed valence could result from oxygen deficiency (6); in fact, the lattice constant of Tl2Mn2O7 is greater than expected when compared to that in the isostructural compounds, where Tl is Q completely replaced by a rare earth ion. The larger lattice constant could result from the formulation Tl2Mn42i Mn3+O7 x because Mn3+ is significantly larger than Mn4+ and oxygen deficiency is well established in many compounds with the pyrochlore structure (7). However, our structural analysis on Tl2Mn2O7 indicates negligible oxygen deficiency and an Mn-O distance inconsistent with a mixture of Mn3+ and Mn4+. Thus, the accepted theoretical description for CMR in the perovskites is unlikely to be applicable in these systems. We report results of neutron powder and single-crystal x-ray diffraction (XRD) measurements and transport data for Tl2Mn2O7 that provide the structure, oxygen stoichiometry, and magnetic moment in this material. These results show that the pyrochlores represent a distinct class of CMR materials, with magnetic ordering driven by superexchange rather than by DE. Appropriate quantities of high-purity T1203 and MnO2 were mixed together in an agate mortar and sealed in a gold capsule. The capsule was heated to 850°C for 30 min at a pressure of 58 kbar in a tetrahedral anvil press and was then rapidly cooled to room temperature before the pressure was released (8). The powder XRD pattern for Tl2Mn2O7 showed that all observed peaks could be indexed with a cubic cell with a = 9.890 + 0.001 A and space group Fd3m. The resistivity as a function of temperature, p(T) (9), for the Tl2Mn2O7 samples used in this study ( Fig. 2A) (Fig. 2B), slightly less than that expected for Mn4+ (3 -B) and consistent with results from a recent study (6). This correspondence between a sharp resistance drop and the development of an FM moment is also seen in the perovskites and is the hallmark of CMR compounds. Neutron powder diffraction data were collected at 298 and 50 K (10). In the single-crystal XRD experiments, a full sphere of reflections were collected at 296 K on an Enraf-Nonius CAD-4 diffractometer (MoKox radiation) from a wedge-shaped crystal of approximately 0.04 mm by 0.03 mm by 0.04 mm. The structural refinements from both neutron powder and x-ray single crystal diffraction data (11) gave similar lattice and positional parameters (Table 1) and hence similar bond distances and angles ( Table 2).
The structure of T12Mn2O7 ( Fig. 1) is based on a network of corner-sharing MnO6 octahedra, just as in the case of perovskite CaMnO3. However, the manner of linking octahedra leads to Mn-C-Mn angles in the range close to 1800 in the perovskite structure (for La1 XCaXMnO3, this angle is -1600) but near 134°in the pyrochlore structure. The site symmetry at the Mn site in the pyrochlore structure is 3. Thus, whereas all of the Mn-C distances are equal, the C-Mn-C angles are not constrained to be 900. The MnO, octahedron is distorted and is actually a trigonal antiprism, as it is in all compounds with the pyrochlore structure. This distortion is, however, not a Jahn-Teller type distortion, where opposite bonds lengthen or shorten relative to others (12). The A2M207 pyrochlore structure may be viewed as two interpenetrating networks: one with the formula MO"! and the other with the formula A20'. Because the MO3 network forms the backbone of the pyrochlore structure, va-cancies can occur only on the A and O0 sites (7). For this reason, our structural analysis of Tl2Mn207 focused on both TI and OC vacancies.
The refinement of occupation parameters in Tl2Mn207 confirms the ideal stoichiometry within our experimental accuracy (13). Conservative estimates are that there could be no more than 1% of the TI sites vacant or 3.5% of O' sites vacant. This conclusion is further supported by the refined Mn-C distance of 1.90 A. This is the Mn-C distance expected on the basis of the ionic radii sum of Mn4+ and 02- (14). A considerably longer distance would be expected if there were large amounts of Mn3+ substituting for Mn4+ in T12Mn207. Thus, in the LaI_xA2+MnC3 perovskites with mixed Mn3+/Mn4+ valence, the Mn-C distances range from 1.94 to 2.00 A. Structural analysis of insulating Er2Mn207 and Y2Mn207 pyrochlores showed ideal stoichiometries with Mn-C distances of 1.91 A in cases where the Mn valence must be 4+ (12). The Mn-C distance in Tl2Mn2C7 may be slightly less than that in rare earth pyrochlores (Table 3). If some mixed valence exists in Tl2Mn207, it is more likely to be Mn5+/Mn4+ than Mn3+/Mn4+. This mixing could occur in stoichiometric Tl2Mn2C7 if the TI 6s band overlaps the Mn 3d band.
Despite the small Mn-C distance in Tl2Mn2C7, the lattice constant of this compound is unexpectedly large when compared to that in the analogous rare earth pyrochlores; the same anomaly is found for Tl2Ru207 and Tl2Ir2C7 (Fig. 3). For the A2Mn2C7, A2RU207, and A2Ir207 pyrochlores, semiconducting properties are observed when A is a rare earth element, but metallic properties are observed when A is Tl (12,15). However, for A2Pt2C7 pyrochlores, semiconducting properties are observed even for Tl2Pt207, which has a normal lattice constant. The metallic conductivity and the anomalous lattice constants for T12Ru207 and T12Ir2C7 can be ex- Table 2. Selected bond distances and angles for T12Mn2O7 from neutron powder (T = 50 and 298 K) and x-ray single-crystal (296 K) diffraction measurements.  neutron powder (T = 50 and 298 K) and single-crystal x-ray (296 K) diffraction measurements. Numbers in parentheses after the refined parameters represent 1 v in the last digits. The lattice parameter is denoted by a, and the atomic position of Oll is denoted as a fractional coordinate by x.
The thermal factors are given in units of 1000 A2. The values of Ueqv from single-crystal x-ray refinements are taken as one-third of the trace of the refined unconstrained thermal factor tensor. The refinement of site occupancies is discussed in (13). Atomic positions are as follows: TI 16d(1/2,1/2,1/2); Mn 16c(0,0,0); C' 8b ( creases. Although Tl2 + is not a normal oxidation state of TI, this is inconsequential if the electron associated with TI reduction is actually delocalized in a TI 6s band. Hall effect data on Tl2Mn2O7 indicate a small number of high-mobility n-type carriers (6). This would not be expected from an Mn 3d band but could result from a small number of carriers in the Tl 6s band. These carriers could be produced by T13 +xTl2+Mn4+xMn5+O or by Tl2yyTl 2 7Mn4 The value of x or y would need to be only -0.005 to explain the Hall data, and neither of these values would be inconsistent with our measured stoichiometry.
Cooling Tl2Mn2O7 to 50 K leads to a 30% increase in the relative intensity of the (111) reflection in the neutron diffraction pattern (16). Thus, a refinement of the magnetic contribution was possible, which gave a magnetic moment of 2.5 ± 0.2 PB per Mn. This value is in good agreement with the value of 2.74 PB from our magnetization measurements as well as with the value of 2.59 P-B from the earlier measurement on a sample containing a small amount of impurity (6). The orientation of the magnetic vector with respect to the lattice cannot be determined from powder neutron diffraction data (17).
The FM pyrochlore compound T12Mn2O7 bears more than superficial similarity to the CMR manganese oxide perovskite compounds. Both compounds are oxides, and both have strong local moment magnetism arising from octahedrally coordinated Mn. Both exhibit dramatic decreases in the resistivity associated with the transition from the high-temperature paramagnetic state to the low-temperature FM state and the associated CMR. Because of these observed similarities between macroscopic and microscopic properties, one might argue that the underlying mechanism for the FM transition is the same in both cases: namely, one driven by DE among heterovalent Mn neighbors. However, our results underscore the differences between the two compound families, and these differences strongly suggest that a fundamentally different mechanism drives CMR in the pyrochlore system.
On a microscopic level, we see no evidence for significant doping in the pyrochlore Mn-O sublattice (18). First, such doping is necessary to produce the mixed valence responsible for DE in the perovskites; CMR occurs over the range of 20 to 45% of hole concentrations (with respect to Mn), obtained by doping with an alkaline earth on the rare earth site (19). Second, there is no evidence for Jahn-Teller distortions among the Mn-O octahedra, which is consistent with the stoichiometry of the compound and the approximately homovalent Mn population thus implied. Third, the above-mentioned tendency for TI to form 6s conduction bands is unlike the perovskite case, where the rare earth levels are inactive electronically. From a macroscopic perspective, the saturation moment of 2.74 PB is below the value expected for Mn4+, which is consistent with an absence of Mn3+ and the weakly covalent character among the Mn valence electrons. Finally, the resistivity of T12Mn2O7 in the paramagnetic state is metal-like (dp/dT > 0), which is unlike the perovskites, where polycrystalline samples typically exhibit hoppingtype conductivity (dp/dT < 0).
Compounds with a pyrochlore structure cannot exhibit simple antiferromagnetism because the tetrahedral arrangement of metal cations gives rise to classic frustration. In addition, FM exchange interactions between metal cations become significant in the d3 situation as the metal-O-metal bond angle bends appreciably away from 1800 (20). For perovskites, there is no frustration, metal-Ometal angles are near 1800, and FM insulators are rare. Indeed, the end members of the CMR perovskites, LaMnO3 and CaMnO3, are both anti-FM superexchange insulators. Coexisting with this superexchange interaction in T12Mn2O7 is a TI-based conduction band.
In a stoichiometric compound, overlap of the Ti 6s band with the Mn 3d band would lead to valence mixing in the Mn sublattice-hence, the possibility of DE between Mn4+/Mn5+ pairs. We believe, however, that TI 6s-Mn 3d overlap is insufficient to produce DE involving Mn4+/Mns+ given (i) the apparently very small number of carriers in the TI 6s band, (ii) the unstable nature of the Mn5+ ion, (iii) a resulting hopping-transfer integral much reduced from that seen in the Mn3+/Mn4+ perovskites, and (iv) a density of such pairs well below the percolation limit for nearest neighbor hopping in the pyrochlore structure.
We propose that the origin of CMR in T12Mn207 is fundamentally different from that of the perovskites. Instead of a single mechanism (DE) driving both the conduction and the magnetic ordering processes, as in the perovskites, there are two processes in the pyrochlore compound. The magnetic ordering seems to be driven by superexchange, as in other FM pyrochlore insulators. The conduction band, however, most likely involves a large admixture of Ti-based valence states. The interdependence of p and M results from unusually large, incoherent scattering from spin fluctuations accompanying FM ordering in a relaxation-time approximation (21).
Given such interdependence, CMR results from the field-dependence of Tc, dTc/ dH > 0, which is similar to that in the perovskite compounds. This realization of a new route to CMR permits the engineering of new materials for eventual use in magnetic reading applications. quantum interference device (SQUID) magnetometer between 5 and 300 K and for magnetic fields up to 4 T. The resistivity (p) was measured by a standard in-line, four-probe technique and a commercial ac resistance bridge (operating at 16 Hz) at temperatures between 5 and 300 K and at magnetic fields up to 8 T. 10. Data were collected at 298 and 50 K with a Cu(220) monochromator (wavelength X = 1.5543 A) and a Cu(31 1) monochromator (X = 1.5396 A), respectively, on the 32-detector BT-1 diffractometer at the National Institute of Standards and Technology's research reactor. A figure containing the 50 K data with a fitted profile from Rietveld refinement is available at http://www.sciencemag.org/science/ feature/beyond/#subramanian. The neutron sample was a pellet weighing 185 mg, which was loaded into a vanadium tube and positioned in the center of the neutron beam. For the 298 K neutron data set, aluminum in the sample mount was incompletely shielded.  (1). For a homogeneous sample, BEC is sometimes called "condensation in momentum space" (2) because it does not lead to a spatial separation between the condensate and the normal component. However, in any inhomogeneous potential-for example, in atom traps or even in Earth's gravitational field-the condensate and the normal fraction of a Bose gas are spatially separated (2,3). So far, BEC has only been seen in momentum space: the condensate fraction of liquid helium was determined by neutron scattering (4), the condensation of excitons was deduced from the observed energy distribution of the excitonic particles (5), and BEC in dilute atomic gases was detected by observation of the velocity distribution of freely expanding Bose condensates (6, 7). We report the direct and nondestructive observation of the spatially localized condensate in a gas of magnetically trapped sodium atoms. Bose condensates of dilute atomic gases are a new form of quantum matter. The pioneering work toward BEC in atomic gases was done with spin-polarized hydrogen with the use of magnetic trapping and evaporative cooling (8). In work at JILA (9) and the Massachusetts Institute of Technology (10), these techniques were successfully combined with laser cooling (11), which resulted in the observation of BEC in rubidium in June (6) and in sodium in September of 1995 (7). Lithium has also been Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. cooled to the quantum degenerate regime (12). Since these developments, there has been a flurry of both theoretical and experimental activity (13).
In atom traps, the condensation phenomenon results in the formation of a dense core of atoms in the ground state of the system surrounded by the normal component-analogous to droplet formation in a saturated vapor. Our earlier attempts to observe the Bose condensate directly by absorption imaging failed because of the high optical density of the atom cloud near the critical temperature. For typical parameters of our experiment, the peak optical density Do for resonant light was about 300, corresponding to a transmission coefficient of e-300. Thus, the probe light was completely absorbed, even in the wings of the spatial distribution, preventing direct imaging of the condensate. Detuning of the light, which reduced the absorption, revealed major image distortions caused by dispersive effects: the condensate acted as a lens and strongly deflected the light. However, by using the so-called "dark-ground" imaging technique (14), we were able to use the dispersively scattered light to clearly image the condensate.
Dispersive imaging has significant advantages over absorption methods for the imaging of small and dense clouds (Do >> 1). To obtain a good absorption signal, one would like to detune the probe light until the off-resonant optical density D is close to unity; D is given by D = DO/A2, where the detuning A from the resonant frequency w is A = 2(wwo)/r, with F being the natural linewidth. The maximum phase shift 5 of the transmitted wave is 8 = DO/2A, and thus for D -1, the phase shift is 8 -\DL1/2. Such a large phase shift is caused by lenslike refraction, which bends