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The filled skutterudite CeOs_{4}As_{12}: A hybridization gap semiconductor

Contributed by M. B. Maple, September 9, 2008 (received for review June 27, 2008)
Abstract
Xray diffraction, electrical resistivity, magnetization, specific heat, and thermoelectric power measurements are presented for single crystals of the new filled skutterudite compound CeOs_{4}As_{12}, which reveal phenomena that are associated with felectronconduction electron hybridization. Valence fluctuations or Kondo behavior dominates the physics down to T ∼ 135 K. The correlated electron behavior is manifested at low temperatures as a hybridization gapinsulating state. The small energy gap Δ_{1}/k_{B} ∼ 73 K, taken from fits to electrical resistivity data, correlates with the evolution of a weakly magnetic or nonmagnetic ground state, which is evident in the magnetization data below a coherence temperature T_{coh} ∼ 45 K. Additionally, the lowtemperature electronic specific heat coefficient is small, γ ∼ 19 mJ/mol K^{2}. Some results for the nonmagnetic analogue compound LaOs_{4}As_{12} are also presented for comparison purposes.
The ternary transition metal pnictides with the chemical formula MT_{4}X_{12} (M = alkali metal, alkaline earth, lanthanide, actinide; T = Fe, Ru, Os; X = P, As, Sb), which crystallize in the filled skutterudite structure (space group Im 3̄), exhibit a wide variety of strongly correlated electron phenomena (1–4). Many of these phenomena depend on hybridization between the rare earth or actinide felectron states and the conduction electron states, which, in some filled skutterudite systems, leads to the emergence of semiconducting behavior. This trend is evident in the cerium transition metal phosphide and antimonide filled skutterudite systems, most of which are semiconductors where the gap size is correlated with the lattice constant (5–7). Although these systems have been studied in detail, the arsenide analogues have received considerably less attention, probably because of materials difficulties inherent to their synthesis. In this article, we present measurements of electrical resistivity ρ, magnetization M, specific heat C, and thermoelectric power S which show that CeOs_{4}As_{12} has a nonmagnetic or weakly magnetic semiconducting ground state with an energy gap Δ in the range 45 K ≤ Δ/k_{B} ≤ 73 K and a small electronic specific heat coefficient γ ∼ 19 mJ/mol K^{2}. Thus, we suggest that CeOs_{4}As_{12} may be a member of the class of compounds, commonly referred to as hybridization gap semiconductors or, in more modern terms, Kondo insulators. In these materials the localized felectron states hybridize with the conduction electron states to produce a small gap (∼1–10 meV) in the electronic density of states. Depending on the electron concentration, the Fermi level can be found within the gap, yielding semiconducting behavior, or outside the gap, giving metallic heavy fermion behavior. For a more complete discussion of the topic, we refer the reader to several excellent reviews (8,9). For comparison purposes, we also report results for the weakly magnetic analogue material LaOs_{4}As_{12}.
Experimental Details
Single crystals of CeOs_{4}As_{12} and LaOs_{4}As_{12} were grown from elements with purities ≥99.9% by a molten metal flux method at high temperatures and pressures, as reported elsewhere (10). After removing the majority of the flux by distillation, CeOs_{4}As_{12} single crystals with dimensions up to ∼0.7 mm and LaOs_{4}As_{12} single crystals with dimensions up to ∼0.3 mm were collected and cleaned in acid to remove any impurity phases from the surfaces of the crystals. The crystal structure of CeOs_{4}As_{12} was determined by Xray diffraction on a crystal with dimensions of 0.28 × 0.25 × 0.23 mm. A total of 5757 reflections (454 unique, Rint = 0.1205) were recorded and the structure was resolved by the full matrix leastsquares method by using the SHELX97 program (11,12). A similar measurement was made for the LaOs_{4}As_{12} crystals.
Electrical resistivity ρ(T) measurements for temperatures T = 65 mK to 300 K and magnetic fields H = 09 T were performed on the CeOs_{4}As_{12} crystals in a fourwire configuration by using a conventional ^{4}He cryostat and a ^{3}He–^{4}He dilution refrigerator. Magnetization M(T) measurements for T = 1.9300 K and H = 05.5 T were conducted by using a Quantum Design Magnetic Properties Measurement System on mosaics of both CeOs_{4}As_{12} (m = 154.2 mg) and LaOs_{4}As_{12} (m = 138.9 mg) crystals, which were mounted on a small Delrin disc with Duco cement. Specific heat C(T) measurements for T = 650 mK to 18 K and H = 0 and 5 T were made by using a standard heatpulse technique on a collection of 116 single crystals (m = 65 mg) of CeOs_{4}As_{12} that were attached to a sapphire platform with a small amount of Apiezon N grease in a ^{3}He semiadiabatic calorimeter. Thermoelectric power S(T) measurements for T = 0.5350 K for CeOs_{4}As_{12} single crystals was determined by a method described elsewhere (13).
Results
Singlecrystal structural refinement shows that the unit cells of CeOs_{4}As_{12} and LaOs_{4}As_{12} have the LaFe_{4}P_{12}type structure Im3̄ space group) with two formula units per unit cell, and room temperature lattice constants a = 8.519(2) Å and a = 8.542(1) Å, respectively, in reasonable agreement with earlier measurements of a = 8.5249(3) Å and a = 8.5296 Å for CeOs_{4}As_{12} and a = 8.5437(2) Å for LaOs_{4}As_{12} (6,14). Other crystal structure parameters for these compounds are summarized in Table 1. The displacement parameter D represents the average displacement of an atom vibrating around its lattice position and is equal to its meansquare displacement along the Cartesian axes. The displacement parameters determined for CeOs_{4}As_{12} and LaOs_{4}As_{12} are typical of the lanthanidefilled skutterudites (15,16). Table 1 also indicates that the Ce sites in CeOs_{4}As_{12} may not be fully occupied, as is often the case for filled skutterudite materials. By comparison with other lanthanidefilled skutterudite arsenides, the lattice constant of CeOs_{4}As_{12} is reduced from the expected lanthanide contraction value, indicating that the Ce^{3+} 4f electron states are strongly hybridized with the conduction electron states of the surrounding Os and Asions.
Electrical resistivity data for a typical CeOs_{4}As_{12} singlecrystal specimen for T = 65 mK to 300 K and H = 0 and a polycrystalline LaOs_{4}As_{12} reference specimen (17) are shown in Fig. 1. For H = 0 T, ρ(T) for CeOs_{4}As_{12} decreases weakly with T from a value near 1 mΩcm at 300 K to 0.5 mΩcm at 135 K, below which ρ(T) increases continuously to low T. An extremely broad hump centered around ∼15 K is superimposed on the increasing ρ(T), which saturates below 300 mK toward a constant value near 100 mΩcm. Above 135 K, ρ(T) for CeOs_{4}As_{12} is similar to that of polycrystalline LaOs_{4}As_{12}. However, below 135 K, LaOs_{4}As_{12} continues to exhibit metallic behavior, wherein ρ(T) saturates near 0.1 mΩcm before undergoing an abrupt drop at the superconducting transition near 3.2 K. With the application of a magnetic field (Fig. 1 Left Inset), ρ(T) for CeOs_{4}As_{12} increases for 3 K ≤ T ≤ 300 K by a small and nearly temperatureindependent amount and the broad hump moves toward lower T. Below ∼3 K, ρ(T) for CeOs_{4}As_{12} is drastically affected by H, where the residual resistivity, ρ_{0}, is reduced by more than a factor of 10 with H = 5 T. For fields >5 T, the relative effect of increasing magnetic field on ρ(T) is less pronounced, as ρ_{0} saturates near 6 mΩcm. Finally, it should be noted that the residual resistivity for H = 9 T is slightly larger than that for H = 7 T.
DC magnetization data, χ(T) = M(T)/H, collected in a small constant field H = 0.5 kOe, are shown in Fig. 2 for CeOs_{4}As_{12} and LaOs_{4}As_{12}. For CeOs_{4}As_{12}, χ(T) shows a weak and unusual T dependence. Below 300 K, χ(T) decreases with decreasing T, suggesting a maximum >300 K. Below a first minimum at T ∼ 135 K, χ(T) increases with decreasing T down to T_{χ,0} ∼ 45 K, where it again decreases with decreasing T down to ∼20 K. Near 20 K, χ(T) show a second minimum, below which a weak upturn persists down to 1.9 K with a small feature between 2 and 4 K. The minimum in χ(T) near 135 K roughly corresponds to the temperature where ρ(T) begins to increase with decreasing T. The low T upturn in χ(T) is weakly suppressed in field, as reflected in the lowtemperature M vs. H isotherms (not shown), which have weak negative curvature, and only begin to show a tendency toward saturation above ∼30 kOe. No hysteretic behavior is observed. Similar measurements for LaOs_{4}As_{12} at T = 1.9 K reveal that the low T magnetic isotherm is linear in field up to 55 kOe. The magnetic susceptibility of LaOs_{4}As_{12} is of comparable magnitude to that of CeOs_{4}As_{12}, and shows a weak increase with decreasing T down to the superconducting transition temperature T_{c} ∼ 3.2 K, as is typical for many Labased compounds for which χ(T) often has a weak temperature dependence (18).
Displayed in Fig. 3 are specific heat divided by temperature C(T)/T vs. T^{2} data for T = 650 mK to 18 K in magnetic fields H = 0 and 5 T. For 650 mK < T < 7 K, C(T)/T is described by the expression, where γ is the electronic specific heat coefficient and β ∝ θ_{D}^{−3} describes the lattice contribution. Fits of Eq. 1 to the zero field C(T)/T data show that γ(H = 0) ∼ 19 mJ/mol K^{2} and θ_{D}(H = 0) ∼ 264 K. In contrast to ρ(T), the application of a 5 T magnetic field has only a modest affect on C(T)/T, for which γ remains constant while θ_{D} increases to ∼287 K. It should also be noted that a small deviation from the linear behavior is seen at T^{2} ∼ 40 K^{2} (T ∼ 6 K), as shown in Fig. 3 Inset.
The thermoelectric power S(T) data for CeOs_{4}As_{12} and LaOs_{4}As_{12} are shown in Fig. 4. Near 300 K, S(T) for CeOs_{4}As_{12} is positive and one order of magnitude larger than that for metallic LaOs_{4}As_{12}, which is shown here for reference and studied in greater detail elsewhere (18). From room T, the thermoelectric power for CeOs_{4}As_{12} increases with decreasing T to a maximum value S_{MAX} = 83 μV/K at T_{MAX} = 135 K, close to the T where semiconducting behavior is first observed in the ρ(T) data. The S(T) data then decrease with decreasing T down to a minimum S_{min} = 31 μV/K at T_{min} = 12 K, close to the maximum of the broad hump in ρ(T). Additionally, there is a broad peak superimposed on the decreasing S(T) for T = 12–60 K. Below 12 K, the S(T) data go through a second maximum S_{max} = 46 μV/K at T_{max} = 2 K and finally continue to decrease down to 0.5 K, but remain positive.
Discussion
When viewed globally, measurements of Xray diffraction, ρ(T), M(T), C(T)/T, and S(T) indicate that strong felectronconduction electron hybridization dominates the physics of CeOs_{4}As_{12}, yielding a variety of types of behavior that can be roughly divided into high (T ≥ 135 K) and low (T ≤ 135 K) temperature regions. For T > 135 K, the unusual behavior is most pronounced in the χ(T) data, which deviate from the typical Curie–Weiss T dependence expected for Ce^{3+} ions and instead decrease with decreasing T to a broad minimum near 135 K ≤ T ≤ 150 K. Although it is difficult to definitively determine the origin of this T dependence, possible mechanisms include valence fluctuations and Kondo behavior. In the valence fluctuation picture, which was introduced to account for the nonmagnetic behavior of α  Ce (19), SmS in its collapsed “gold” phase (20), and SmB_{6} (21), the 4f electron shell of each Ce ion temporally fluctuates between the configurations 4f^{1} (Ce^{3+}) and 4f^{0} (Ce^{4+}) at a frequency ω ≈ k_{B}T_{vf}/␣, where T_{vf} separates magnetic behavior at high temperatures T ≫ T_{vf} and nonmagnetic behavior at low temperatures T ≪ T_{vf}. In this phenomenological model, the decrease in χ(T) with decreasing T can be accounted for in terms of an increase in the Ce ion valence v(T) with decreasing T toward 4+, corresponding to a decrease in the average 4f electron shell occupation number n_{4f}(T) toward zero. At T = 0 K, χ(T) should be approximately, since μ_{eff}(4f^{0}) = 0. In this model, the value of T_{sf} can be estimated from the Curie–Weiss behavior of χ(T) for T ≫ T_{sf} where it plays the role of the Curie–Weiss temperature, and n_{4f1}(0) can be inferred from χ(0). Because the Curie–Weiss behavior would be well above room T for this case, it is not possible to estimate T_{sf} and n_{4f1}(T). The behavior of n_{4f1}(0) can also be deduced from measurements of the lattice constant a as a function of T, by Xray diffraction or thermal expansion measurements. The increase in valence with decreasing T is reminiscent of the γ–α transition in elemental Ce, in which the valence undergoes a transition toward 4+ with decreasing T that is discontinuous (first order) for pressures P < P_{c}, where P_{c} is the critical point, and continuous (second order) for P > P_{c}. According to this picture, it would appear that the critical point for CeOs_{4}As_{12} is at a negative pressure and the valence is increasing with decreasing T. A great deal of effort has been expended to develop a microscopic picture of the intermediate valence state, and the reader is referred to two of many review articles on the subject (22,23).
In contrast to the intermediate valence picture, it is possible that the Ce ions remain in the 3+ state at all T, and the Ce^{3+} magnetic moments are screened by the conduction electron spins below a characteristic temperature T_{K}. This scenario is commonly called the Kondo picture (24), and may be appropriate for CeOs_{4}As_{12} if T_{K} > 300 K, leading to Curie–Weiss behavior for T > T_{K} and the observed χ(T) behavior for 135 K < T < T_{K}. A rough approximation of T_{K} can be made by using the expression, where μ_{eff} = 2.54 μ_{B} is the Hund's rule value for Ce^{3+} ions and χ_{0} ∼ 1.2 × 10^{−3}cm^{3}/mol is the saturated value of χ(T) at T ∼ 135 K, representing the magnetic susceptibility of a screened Kondo ion singlet (25). By using this rough expression, T_{K} is found to be near 670 K, supporting the notion of a high Kondo temperature. Moreover, if the Kondo interpretation with a high T_{K} is correct, the decrease of ρ(T) with decreasing T may reflect the onset of Kondo coherence at T > 300 K, in addition to the freezing out of phonons. Finally, it is worth noting that the χ(T) data for LaOs_{4}As_{12} indicate that spin fluctuations associated with the transition metal atoms do not account for the unusual χ(T) behavior seen for CeOs_{4}As_{12}.
The affects of felectronconduction electron hybridization become even more pronounced at T < 135 K, where ρ(T) evolves into a gapped semiconducting state that persists to the lowest T measured. The increase in ρ(T) is not well described by a simple Arrhenius function, as would be expected for a semiconductor with a single energy gap. Instead, the following phenomenological expression (26), where A_{1} = 2.7 (mΩcm)^{−1}, Δ_{1}/k_{B} = 73 K, A_{2} = 0.44 (mΩcm)^{−1}, Δ_{2}/k_{B} = 16 K, A_{3} = 0.18 (mΩcm)^{−1} and Δ_{3}/k_{B} = 2.51 K, describes the data for 1 K ≤ T ≤ 135 K, as shown in the Fig. 1 Right Inset. A possible interpretation of this fit is that the large gap Δ_{1} describes the intrinsic energy gap for CeOs_{4}As_{12}, whereas Δ_{2} and Δ_{3} describe impurity donor or acceptor states in the gap (Kondo holes) (27–29), or, possibly, a pseudogap. In this situation, it is naively expected that the application of a magnetic field will act to close the energy gaps (Δ_{1}, Δ_{2}, Δ_{3}) through the Zeeman interaction, where Δ_{n}(H = 0) are the zero field gaps, g_{J} = 6/7 is the Landé g factor for Ce^{3+} ions, J_{z} = 5/2 is the z component of the total angular momentum for Ce_{3+} ions, and μ_{B} is the Bohr magneton. According to this expression, it is expected that a field H = Δ_{n}(H = 0)/g_{J}J_{z}μ_{B} ∼ 1.74 T is sufficient to close the low T gap. This behavior is qualitatively shown in Fig. 1 Left Inset where the low T resistivity is reduced by nearly 70% for H = 1.5 T.
Concurrent with the emergence of the semiconducting behavior, χ(T) increases slowly down to T_{χ,0} ∼ 45 K, where it goes through a maximum and then continues to decrease with decreasing T. Therefore, there is an apparent correlation between the intrinsic energy gap value Δ_{1} ∼ 73 K taken from fits to ρ(T) and the broad maximum in χ(T) centered around T_{χ,0} ∼ 45 K. If T_{χ,0} is taken to indicate the onset of a coherent nonmagnetic ground state where T_{χ,0} ∼ T_{coh} ∼ Δ_{1}/k_{B}, then the likely description of the ground state is the well known many body hybridization gap picture, where the magnetic moments of the Ce^{3+} felectron lattice are screened by conduction electron spins via an antiferromagnetic exchange interaction.
In the context of this model, the weak upturn in χ(T) for T < 20 K is unexpected. For this reason, it is necessary to consider whether it is intrinsic or extrinsic to CeOs_{4}As_{12}. As shown in Fig. 2 Inset, various functions describe the T dependence of the upturn below ∼10 K, including both power law and logarithmic functions of the forms, and where a = 1.96 × 10^{−3} cm^{3}K^{m}/mol and m = 0.16, or b = 1.92 × 10^{−3} cm^{3}/mol, and c = 0.25 × 10^{−3} cm^{3}/mol, respectively. These weak power law and logarithmic divergences in T of physical properties are often associated with materials that exhibit nonFermi liquid behavior because of the proximity of a quantum critical point (30–32). On the other hand, it is also possible that the upturn is the result of paramagnetic impurities, as is often found for hybridization gap semiconductors (9,33). To address this possibility, the low T upturn in χ(T) was fitted using a Curie–Weiss function of the form, where χ_{0} = 1.13 × 10^{−3} cm^{3}/mol, C_{imp}(T) = 3.12 × 10^{−3} cm^{3}K/mol, and Θ = −3 K. Although it is not possible, by means of this measurement, to quantitatively determine the origin of such an impurity contribution, a rough estimate of the impurity concentration can be made by assuming that it is due to paramagnetic impurity ions, such as rare earth ions like Ce^{3+} or Gd^{3+}, which give impurity concentrations near 0.4% and 0.04%, respectively. Finally, to elucidate the significance of an impurity contribution of this type, the hypothetical intrinsic susceptibility χ_{int}(T) = χ(T) − χ_{imp}(T) is shown in Fig. 2. The resulting χ_{int}(T) remains nearly identical to χ(T) down to ∼100 K, where the affect of χ_{imp}(T) becomes apparent. Near 55 K, χ_{int}(T) goes through a weak maximum and then saturates toward a value near 1.1 × 10^{−3} cm^{3}/mol with decreasing T, consistent with the onset of Kondo coherence leading to a weakly magnetic or nonmagnetic ground state.
Additionally, the behavior of C(T)/T at low T supports the hybridization gap interpretation, for which the low T electronic specific heat coefficient γ = C/T is expected to be zero in the fully gapped scenario, or small and finite if a low concentration of donor or acceptor levels are present or if there is a pseudogap (34). Similar results were seen for the archetypal hybridization gap semiconductor Ce_{3}Bi_{4}Pt_{3}, for which γ ∼ 3.3 mJ/(mol Ce K^{2}). For hybridization gap semiconductors, this value is expected to be sample dependent and to correlate with the number of impurities in the system (9,35). Similar sample dependence has been observed in both ρ(T) and C(T)/T measurements for CeOs_{4}As_{12} specimens. Moreover, a comparison with other systems where large effective masses are seen as the result of many body enhancements can be made by computing an effective Wilson–Sommerfeld ratio R_{W} = (π^{2}k_{B}^{2}/3μ_{eff}^{2})(χ/γ). The values χ, χ_{int}, and γ are taken at 1.9 K to probe the lowtemperature state. Also, the Hund's rule effective magnetic moment μ_{eff} = 2.54 μ_{B} for Ce^{3+} ions is used. From these values, R_{W} is calculated to be ∼1.04 and ∼0.67, for the χ and χ_{int} cases. As expected, these values are similar to those found in felectron materials where the low T transport and thermodynamic properties are due to conduction electrons with or without enhanced masses.
The T dependence of the thermoelectric power provides further insight into the hybridization gap picture. Because S(T) remains positive over the entire T range, it appears that charge carriers excited from the top of the valence band to the conduction band dominate the transport behavior for all T. However, a single energy gap and charge carrier picture does not adequately describe the T dependence of the data. Instead, there are several unusual features, which include, (i) T_{MAX} = 135 K, which corresponds to the high T transition in ρ(T) from semimetallic to metallic behavior, (ii) T_{min} = 12 K, which is close to the low T portion of the extremely broad hump superimposed on ρ(T), and (iii) T_{max} = 2 K, which is close to Δ_{3}/k_{B}. Thus, there is a close correspondence between the deviations from a single energy gap picture between S(T) and ρ(T), although the deviations are more pronounced in S(T), because electrons and holes make contributions of opposite sign to the total S(T). To further characterize S(T), it is useful to consider the expression (36), which describes intrinsic effects in S(T) for a gapped system, such as activation of electrons from the lower band to the higher one, which creates both hole and electron charge carriers. For this expression, the coefficients P(μ_{n}, μ_{p}) = (μ_{n} − μ_{p})/(μ_{n} + μ_{p}) and Q = −(k_{B}/e)[(a/2k_{B}) − 2] − (3/4) ln(m_{n}/m_{p}), are defined by the electron mobility μ_{n}, hole mobility μ_{p}, the temperature coefficient a of Δ vs. T, the electron effective mass m_{n}, and the hole effective mass m_{p}. Because the quantity Q(a, m_{n}, m_{p}) is expected to be weakly T dependent, this expression is a useful tool for identifying energy gap behavior, as was the case for the semiconductor Th_{3}As_{4} (37). However, as shown in Fig. 4 Left Inset, there is only one T range, 6.5 K ≤ T ≤ 15 K, where this type of behavior is observed. A linear fit to S(T) in this T range yields Δ/k_{B} = 2.2 K, which is of the order of Δ_{3}/k_{B} found by fits to ρ(T). To further characterize S(T), it is also of interest to consider dS/dT vs. log T (not shown), which was used previously to analyze the compound Ce_{x}Y_{1−x}Cu_{2.05}Si_{2}(38), where a change in the slope was interpreted as evidence for a change of dominant electronic transport mechanism. For CeOs_{4}As_{12}, inspection of dS/dT vs. log T yields a characteristic temperature T* = 32 K.
Behnia et al. (39) have argued that, in the zero temperature limit, the thermoelectric power should obey the relation, where N_{A} is Avogadro's number, e is the electron charge, and the constant N_{A}e = 9.65 × 10^{4} C mol^{−1} is the Faraday number. The dimensionless quantity q corresponds to the density of carriers per formula unit for the case of a freeelectron gas with an energyindependent relaxation time. Taking the values S/T = 17.5 V/K^{2} and γ = 19 mJ/mol K^{2} at T = 0.5 K and 0.65 K, respectively, the quantity q = 89 is calculated. This value is nearly two orders of magnitude larger than that seen for most of the correlated electron metals analyzed by Behnia et al., but is similar to that found for the Kondo insulator CeNiSn (q = 107), for which the Hall carrier density was found to be 0.01/f.u. at 5 K (39). Thus, the q determined for CeOs_{4}As_{12} is consistent with a related hybridization gap insulator and may be indicative of a lowcharge carrier density in CeOs_{4}As_{12} at low T.
Summary
The compound CeOs_{4}As_{12} is considered in the context of a simple picture where valence fluctuations or Kondo behavior dominates the physics down to T ∼ 135 K. The correlated electron behavior is manifested at low temperatures as a hybridization gapinsulating state, or in modern terminology, as a Kondo insulating state. The size of the energy gap Δ_{1}/k_{B} ∼ 73 K, is deduced from fits to electrical resistivity data and the evolution of a weakly magnetic or nonmagnetic ground state, which is evident in the magnetization data below a coherence temperature T_{coh} ∼ 45 K. Additionally, the lowtemperature electronic specific heat coefficient is small, γ ∼ 19 mJ/mol K^{2}, as is expected for hybridization gap insulators. The thermoelectric power and electrical resistivity data also indicate that either impurity states in the energy gap or the presence of a pseudogap strongly perturbs the physical behavior away from that of an ideal hybridization gap insulator.
Acknowledgments
This work was supported by Department of Energy Grant DE FG0204ER46105 and National Science Foundation Grant NSF DMR0802478 and by Polish Ministry of Science and Higher Education Grant NN 202 4129 33.
Footnotes
 ^{1}To whom correspondence should be addressed. Email: mbmaple{at}ucsd.edu

Author contributions: R.E.B., P.C.H., T.A.S., M.B.M., R.W., T.C., A.P., and Z.H. designed research, performed research, analyzed data, and wrote the paper.

The authors declare no conflict of interest.
 © 2008 by The National Academy of Sciences of the USA
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