Main

As shown in Fig. 1a, the colossal magnetoresistive (CMR) oxide La2−2xSr1+2xMn2O7 (x=0.36,0.38) shows a metal–insulator transition at a TC just below 130 K, at which point the system also switches from being a ferromagnet (low temperature T) to a paramagnet (high T)3. We carried out angle-resolved photoemission spectroscopy (ARPES) experiments on cleaved single crystals of these materials, with an experimental arrangement as described elsewhere 4. ARPES is an ideal experimental probe of the electronic structure because it gives the momentum-resolved single-particle excitation spectrum. As discussed in ref. 4, the x=0.36,0.38 compounds studied here do not contain the low-energy pseudogap of the x=0.4 samples5,6,7,8 (see the Methods section for more details on this, the possible issue of surface sensitivity of ARPES and of possible intergrowths at the surface). The much larger metallic spectral weight of these non-pseudogapped compounds also allows us to study the electronic behaviour in greater detail. Although we find only minimal differences between the x=0.36 and x=0.38 compounds, all ARPES spectra shown here are from x=0.38 samples.

Figure 1: Overview of features of La1.24Sr1.76Mn2O7 (x=0.38).
figure 1

a, Resistivity versus temperature for a similarly doped (x=0.36) sample, showing a transition between a ferromagnetic metal (FM) and a paramagnetic insulator (PI). Courtesy of K. Gray, Argonne National Laboratory. b, Low-temperature (20 K) ARPES data over a large energy scale taken along the blue cut near the zone boundary, as shown in the inset.

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Figure 1b shows a large-energy-scale experimental picture of a low-temperature dEquationSource math mrow msub mid mrow msup mix mn2 mo- msup miy mn2 symmetry band taken along the blue cut near the zone boundary, as shown in the inset. We are able to get clean data by isolating the various bilayer-split bands using different photon energies, as described in ref. 4. In particular, in this paper we show only data from the antibonding bilayer-split band, which has Fermi crossings at kx=±0.17π/a,ky=0.9π/a, corresponding to the solid Fermi surface of the inset of Fig. 1b. The energy-distribution curves (EDCs) at the Fermi wavevector kF (indicated by the red line in Fig. 1b) taken at a series of temperatures are shown in Fig. 2a. Figure 2b shows the identical spectra and identical scaling, but offset vertically for clarity. All spectra have been normalized only to the incident photon flux.

Figure 2: EDCs as a function of temperature at kF (red line of Fig. 1b), indicating metallic spectral weight above TC.
figure 2

a,b, The same data set scaled by the incident flux and taken while warming. c, EDCs from a different sample taken in the high-temperature range. Clear breaks are seen in the spectral intensity near EF for all but the highest temperature, indicating finite metallic spectral weight and a T* just above 285 K (see Fig. 3 for details of the T* determination).

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At low temperature, the EDCs clearly show a peak–dip–hump structure, where the peak and the hump would nominally be considered the coherent part (quasiparticle) and ‘incoherent’ part of the single-particle spectrum respectively, as has been discussed for the spectra of the high-TC cuprate superconductors9,10,11. One sees that the near-EF spectral weight diminishes with increasing temperature, whereas the high-binding-energy (>700 meV) part is less affected by temperature. As will be discussed in future publications, other portions of the Brillouin zone pick up the ‘lost’ weight from these spectra. Contrary to the general picture of the metal–insulator transition, in which a gap develops in the single-particle spectrum when an electronic system becomes insulating1, the EDCs here still show a sharp Fermi cutoff, indicating metallic behaviour, at temperatures at which the macroscopic d.c. conductivity is characteristic of insulation (see, for example, the spectra at 135, 150 and 180 K). To our knowledge, this unusual behaviour, a metallic Fermi edge in a globally insulating system, has not been previously observed on the insulating side of a metal–insulator transition. The opposite, in which a metallic system shows a lack of a Fermi cutoff, is on the other hand expected in exotic low-dimensional systems such as the Luttinger liquids12, and has probably been observed13. The other situation most likely to show a metallic Fermi edge in a globally insulating system is that of an Anderson-localized system beyond the mobility edge. However, in such systems a Coulomb gap is expected to remove the metallic weight near the Fermi energy14. Our data could be consistent with such a scenario only if the Coulomb gap were extremely small—of the order of a few millielectronvolts or less. Moreover, such a picture would not naturally explain the metallic spectral weight dependence on temperature, to be discussed in more detail later.

On a different sample we have carried out higher-temperature scans, looking for a possible temperature scale at which the metallic spectral weight disappears. These data are shown in Fig. 2c and show a clear discontinuity in the slope near the Fermi energy for all but the 285 K data, indicating a finite metallic spectral weight. This effect is emphasized by an extrapolation of the spectral weight using a simple linear fit to the data between −0.3 and −0.05 eV, as shown by the dashed lines in Fig. 2c. On raising the sample temperature we see that the intercept of these dashed lines with the horizontal axis decreases towards zero (EF) monotonically (Fig. 3). This plot shows that the intercepts should reach zero near 300 K, which should roughly be the temperature where the first bits of metallic weight become apparent. We call this temperature T*. Technical factors including sample ageing and excessive manipulator drift preclude us from making the full range of measurements on a single cleave. We therefore used different samples to study the electronic excitations in different temperature regimes.

Figure 3: Determination of T*pla.
figure 3

The blue-shaded area shows the zero-intensity intercepts in Fig. 2c as a function of temperature. These intercepts go to zero near 300 K (grey shaded area), which we label as T*. Error bars include uncertainties about the appropriate energy range of Fig. 2c over which to do the linear fits.

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Figure 4a shows the electronic dispersion of the near-Fermi states as a function of temperature obtained from an analysis of momentum-distribution curves (MDCs). These data indicate that the main properties of the metal, such as kF, the Fermi velocity vF, the electron–phonon coupling parameter λ and the effective mass m*, do not change significantly as a function of temperature, even as TC is traversed. This is unexpected behaviour for a metal–insulator transition, in which these parameters would vary dramatically with temperature, and probably even diverge1.

Figure 4: Properties of the metallic portion of the sample.
figure 4

a, Electronic dispersion showing a similar kF, vF and λ as a function of temperature. b,c, Metallic EDCs or M-EDCs obtained by subtracting the 180 K EDC from all lower-temperature data: b shows the raw scaling whereas c scales each spectrum to have a similar maximum intensity. d, MDC widths (green triangles) and integrated M-EDC spectral weights (blue squares) as a function of temperature. The error bars come from the numerical fits of the MDC widths to a lorentzian lineshape.

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Our data can be understood by invoking a model of disconnected local ferromagnetic metallic regimes above TC up to approximately the temperature T*. This suggestion is consistent with earlier studies, which have found significant ferromagnetic signals far above TC (refs 15–18), because metallicity and ferromagnetism should have a connection in these systems via the double-exchange interaction. In general, the metallic regions may be either phase separated (and possibly static) domains19,20, or they may be dynamic fluctuations of the ferromagnetic metallic state, which in a two-dimensional system may persist to quite high temperatures15,16,17,18. We will discuss these two possibilities later. Here we show that we can study the metallic portions further by our ability to approximately deconvolve the spectrum into the components that arise from the metal and non-metal portions. We do this by subtracting the 180 K EDC from all other EDCs, as shown in Fig. 2b, to create ‘metallic EDCs’ or M-EDCs, as shown in Fig. 4b. It should be pointed out that the slight variation of spectra from sample to sample, which has been commonly observed in ARPES, imperils the practice of subtracting data of one sample from those of another. Therefore, we do not use the higher-temperature data of Fig. 2c to carry out the subtraction, as these are from a different sample. Figure 4c shows the same M-EDCs but scaled to all have the same amplitude. Within the noise, all the M-EDCs have similar lineshapes with coherent peaks near EF and an incoherent background at high binding energy, though the M-EDC coherent peak (or low-energy MDC peak) becomes broader with increasing temperature (Fig. 4d). The integrated spectral weight of the M-EDCs varies smoothly as a function of temperature, with no clear break at TC (Fig. 4d). This, as well as the approximate temperature independence of the M-EDC lineshape, indicates that the electrons in the metallic regions have similar properties above and below TC, and that temperature has surprisingly little effect on the behaviour or interactions of electrons in the metallic regions. This is consistent with the approximate independence of vF, λ and m* in the metallic regions shown in Fig. 4a. The experimentally determined MDC width of the electrons at the Fermi energy (green triangles of Fig. 4d) does increase with increasing temperature. The inverse of this quantity, the mean free path of the electrons, thus decreases with increasing temperature, consistent with a decreased size of metallic regions or increased scattering events at higher temperatures.

Although many aspects of our data are consistent with either the phase-separation or the magnetic-fluctuation picture, certain aspects of them can address the question of whether the metallic regions above TC are phase separated out from a more insulating environment19,20, or whether they are just fluctuations from a lower-temperature ordered environment, which is otherwise homogeneous17,18. In particular, the smooth dependence of the spectral weight of the metallic regions as a function of temperature across TC (blue squares of Fig. 4d) is more consistent with phase separation, as we would expect a clear drop in the metallic weight near TC if the metallic portions were just fluctuations of the ordered lower-temperature environment. At other doping levels (for example x=0.4), experiments do observe a sharp drop in the metallic weight at TC to zero or almost zero8, and so these samples may be more consistent with the fluctuation physics.

Within the picture of phase separation, we imagine that the metallic islands arise at a temperature T* near room temperature, which may also be related to the temperature scale at which polaronic correlations freeze21. As the temperature is lowered the size and proportion of metallic portions grows until a critical ratio of metallic to insulating portions is reached. At this point electrons can percolate from one metallic region to another, bringing about the macroscopic metallic19 and ferromagnetic states, as well as being consistent with the ‘colossal’ decrease in resistivity with an applied magnetic field. In certain models this behaviour is expected from a competition between different phases, for example between the ferromagnetic metal phase and the charge-ordered antiferromagnetic insulating phase19,22,23, though in contrast to ref. 19 the materials used here are far away from the charge-ordered doping level. Theoretical arguments predict both the phase separation and the existence of a higher-temperature scale T* (ref. 24), with ideas similar to the Griffiths singularity 25, in which T* would be the critical temperature of the associated clean system in the absence of disorder, and which have recently been discussed in the context of manganite physics24,26. We are now undertaking a more thorough study of the full Fermi surface to test this percolation model quantitatively.

A T* scale is one of the key properties of the high TC superconductors, and has for years been the subject of intense controversy2. In these compounds, disorder also seems to be relevant, especially in the underdoped regime where the T* scale exists. In this case it signals the emergence of the pseudogap, which may be the precursor to the long-range superconducting order that forms at TC (ref. 27)—a clear analogy to the manganites, where T* signals the emergence of the metallic domains, which become long range at TC. Also similar to the cuprates, it seems that the T* temperature scales may not be universal to all doping levels of the manganites. Pinning these details down and then understanding their implications will certainly be an area of intense study in the near future.

It is becoming increasingly clear that some of the most dramatic responses in modern materials occur in systems in which multiple phases or orders with similar energy scales compete with each other22,23,24,28. It is then natural that in at least some of these systems spatial heterogeneities will occur, and small perturbations can cause drastic macroscopic alterations to the physical properties or even new types of ‘emergent’ behaviour. The key is finding out which aspects of the inhomogeneity are intrinsic and what their role is in determining the key physical properties of the system.

Methods

The difference between x=0.38 and x=0.4 samples

It should be pointed out that there is a remarkable difference between the ARPES spectra of La2−2xSr1+2xMn2O7 (x=0.38) and La2−2xSr1+2xMn2O7 (x=0.40) samples, even though many macroscopic properties are similar. Quasiparticles have been found near the zone boundary at the doping levels of x=0.36 and 0.38 in La2−2xSr1+2xMn2O7, although there exists a large energy pseudogap in x=0.40 samples (refs 4–8). Temperature-dependent studies have also been carried out on x=0.4 samples and have not shown any evidence for metallic spectral weight above TC (refs 6–8). Similar to high-TC cuprates, physical properties show strong variations with doping in manganites. The cause of the difference between La2−2xSr1+2xMn2O7 (x=0.38) and La2−2xSr1+2xMn2O7 (x=0.40) samples is not understood yet, though it could have to do with the increased lattice anomalies for the 0.4 samples29, the onset of spin canting between ferromagnetic layers, which starts at the doping level of 0.4 (ref. 30), or even something extrinsic such as a surface issue.

The issue of surface sensitivity

Because of the shallow probing depth of the ARPES experiment (∼5–10 Å), we cannot completely rule out the potential that a surface phase whose properties do not follow those of the bulk gives rise to some of the phenomena reported here. For ARPES on the layered manganites we are relatively well off because the samples cleave readily between the La,Sr–O bilayers, which are ionically (not covalently) bonded. High-quality low-energy electron diffraction pictures without any evidence of surface reconstruction are obtained from these surfaces. The doping level at the surfaces, as obtained from the Fermi surface volume, also seems to be correct for these samples—for example the EquationSource math mrow msub mid mrow msup mix mn2 mo− msup miy mn2 bonding-band Fermi surface nesting vector of 0.27×(2π/a) for the x=0.38 samples used in this study4 exactly matches that obtained from neutron scattering measurements21. The nesting vector of 0.4 samples is slightly larger, at 0.3×(2π/a) (ref. 6), and also matches the results of scattering measurements31.

The issue of intergrowths

One should consider whether it might be possible for the metallic spectral weight far above TC to have originated from small regions of intergrowth of a higher TC sample left near the surface after cleaving. Here we discuss why this is inconsistent with our data. Such intergrowths should not arise from a layered manganite, as the maximum temperature at which bulk metallic behaviour is found among all known layered manganites is ∼160 K. A small amount of (non-layered) perovskite-like intergrowth with a TC=300 K could exist at a cleaved surface, though it would not show the bilayer splitting because the perovskite samples have only one MnO2 plane per unit cell. Both our high- and low-temperature data show this bilayer band splitting (this paper presents only the data from the antibonding component), which is a direct consequence of there being two MnO2 planes per unit cell. In addition to being able to vary the intensity of the bilayer split bands (relative and overall) by taking advantage of the photoemission matrix elements, we can follow the dispersion in E and k of each of the bilayer bands, including tracking them all the way to EF. Therefore, we know the origin of the metallic weight as explicitly originating from these bilayer split bands, and therefore from the bilayer manganite.