Thermal-expansion properties

First, the present NTE of Ca 2 RuO 4 is compared with NTE that are presently known. Figure 1 shows linear thermal expansion ΔL(T)/L of Ca 2 RuO 4 and Ca 2 Ru 1−x M x O 4 (M: Mn, Fe and Cu) in this study. The vertical (cylindrical, z) and horizontal (radial, r) expansions of the Ca 2 RuO 4 sintered pellets are identical. Therefore, it is isotropic and volumetric NTE (inset of Fig. 1, see ‘Methods’ section for conditions of linear thermal-expansion measurements). Parameters related to NTE for recently discovered giant NTE materials are presented in Table 1. The largest ΔV/V related to NTE reported until now is 3.2% for MnCo 0.98 Cr 0.02 Ge (ref. 11). Data of ΔL/L for this alloy are presented for comparison in Fig. 1. Data for Pu23 and YMn 2 (ref. 24) are also included in Table 1 for comparison. These reference materials exhibit large volume contraction on heating at the phase transition, but they exhibit abrupt volume changes. Therefore, these materials are not categorized as NTE materials. Extreme volume contraction on heating of Pu is 5.4% in successive δ→δ′→ɛ phase transitions23. ΔV/V reaches 6.7% at most for the present Ca 2 RuO 4 . Such a large total volume change produces gigantic NTE of α=−115 × 10−6K−1 at T=135−345 K. The present Ca 2 RuO 4 possesses greater volume contraction on heating at ambient pressure than all the listed materials. Moreover, it exhibits giant NTE over a wide T range, including room temperature.

Figure 1: Linear thermal expansion ΔL/Lof reduced layered ruthenates. The data were collected on a warming process using a laser-interference dilatometer (the y values are presented in Table 2). Reference temperature: 500 K. The reduced Ca 2 RuO 3.74 exhibits giant negative thermal expansion (NTE) of α=−115 × 10−6 K−1 (α: coefficient of linear thermal expansion) over 200 K interval below 345 K. The vertical (z) and horizontal (r) expansions measured using a thermomechanical analyzer were found to be identical (inset). Therefore, this NTE is volumetric. The total volume change ΔV/V related to NTE reaches 6.7% at most. Substituting the transition-metal elements for Ru reduces the total volume change, but increases the onset of NTE. Particularly, the Fe-doped ruthenate exhibits temperature-linear behaviour below 500 K, which is favourable for practical applications. For comparison, data of MnCo 0.98 Cr 0.02 Ge11 are also shown. Full size image

Table 1 Parameters related to negative thermal expansion for recently discovered giant negative thermal-expansion materials. Full size table

Earlier studies have revealed that Ca 2 RuO 4 undergoes a Mott MI phase transition from a high-T metallic to a low-T insulating state at T MI of ∼360 K (refs 15, 16, 17). At this transition, the crystal structure also changes from the high-T L phase with a longer c axis to the low-T S phase with a shorter c axis while preserving the orthorhombic crystal structure of the Pbca symmetry. Some earlier studies have also found the appearance of NTE in Ca 2 RuO 4 because the unit-cell volume v of the S phase is greater than that of the L phase. Detailed structural analysis17 has revealed volume contraction ΔV/V of ∼1% during heating from 100 to 400 K. Qi et al.20 reported successive phase transitions with ΔV/V of completely 0.9% of volume contraction on heating for Ca 2 Ru 0.933 Cr 0.067 O 4 and NTE of α=−10 × 10−6 K−1 at T=120−400 K (ΔV/V of ∼0.8%) for Ca 2 Ru 0.90 Mn 0.10 O 4 (ref. 21). The total volume change of the present Ca 2 RuO 4 , ΔV/V=6.7%, is much greater than those previous results.

Partial replacement of Ru by other elements alters the thermal-expansion properties of Ca 2 RuO 4 such as the operating-temperature window ΔT, negative slope α, and the total volume change ΔV/V. We investigated the effects of three dopants, Mn, Fe and Cu (Fig. 1). The dopants Mn, Fe and Cu increase the onset of NTE, T onset , although they decrease the respective total volume changes: T onset =470 K and ΔV/V=3.1% for Ca 2 Ru 0.90 Mn 0.10 O 4 (Mn0.10), T onset =500 K or higher and ΔV/V=2.8% for Ca 2 Ru 0.92 Fe 0.08 O 4 (Fe0.08), and T onset =430 K and ΔV/V=4.4% for Ca 2 Ru 0.90 Cu 0.10 O 4 (Cu0.10). Particularly, the Fe-doped ruthenate exhibits T-linear expansion in almost the entire range of T below 500 K, which is favourable for practical applications. Thermal expansion exhibits almost T-linear behaviour, even near the lowest temperature (95 K) used for the present dilatometry measurements. Therefore, NTE apparently continues down to the lower temperature. In that case, the total volume change ΔV/V might become greater than the present estimate of 2.8% (T=95–500 K).

Effects of oxygen deficiency

We can examine the differences between the present materials showing giant NTE and previous materials. Figure 2 shows linear thermal expansion ΔL(T)/L of reduced (#1), oxidized (#2), and re-reduced (#3) Ca 2 RuO 4 in the present experiments (see ‘Methods’ section for sample preparation conditions). The giant NTE of the reduced sample is suppressed dramatically by high-pressure oxidizing procedures. When this oxidized sample is reduced again, the giant NTE is recovered. The results presented above imply that differences in oxygen contents produce a striking difference in thermal-expansion properties. Evaluations of the oxygen contents by thermogravimetric analysis are y=−0.26(1), 0.03(1) and −0.31(1), respectively, for the reduced, oxidized and re-reduced samples in the notation of Ca 2 RuO 4+y . Reports of an earlier study described that y fell within the range of −0.01(1) to +0.07(1)15. The present reduced ruthenates are regarded as having larger amounts of oxygen deficiency than the previous ones. Hereinafter, we use Ca 2 Ru 1−x M x O 4+y notation as the present materials. The y values are presented in Table 2.

Figure 2: Linear thermal expansion ΔL/L of Ca 2 RuO 4+y . The data were collected on a warming process using a laser-interference dilatometer. Reference temperature: 500 K. The hysteresis loop was observed in ΔL/L measurements using a thermomechanical analyzer for #1 (inset). The giant negative thermal expansion (NTE) of #1 is suppressed by the oxidizing procedure, but is fully recovered by the re-reducing procedure. Inset shows temperature dependence of resistivity ρ(T) for #1 and #2. The abrupt jump in ρ(T) at 345 K for #1 corresponds to the Mott metal-to-insulator transition, which coincides with the onset of NTE. Full size image

Table 2 Crystallographic parameters of layered ruthenates obtained from Le Bail analysis of the X-ray diffraction data at 295 K. Full size table

High-temperature L to low-temperature S phase transition

The giant NTE of Ca 2 RuO 3.74 seems to be triggered by the transition from the high-T metallic L phase to the low-T insulating S phase. The inset of Fig. 2 presents the temperature dependence of resistivity ρ(T) for the reduced and oxidized Ca 2 RuO 4+y . The resistivity of the reduced sample indicates that the system undergoes the MI transition at T MI =345 K. The onset of NTE is almost identical to this MI transition. In contrast, resistivity of the oxidized sample shows no abrupt change that can be interpreted as prolonged high-T L phase down to lower temperatures. Corresponding to this MI transition, the anomaly appears in the magnetic susceptibility χ(T) (Supplementary Fig. 2). χ(T) is hysteretic (∼10 K). It therefore supports the first-order nature of this phase transition. Such hysteretic behaviour is confirmed also in the linear thermal expansion. The hysteresis loop was observed in dilatometry measurements (inset of Fig. 2). The onset of NTE is 340 and 355 K on cooling and warming processes, respectively. This loop behaviour is partly attributable to the first-order phase transition. The loop behaviour is reproducible through several successive measurements.

Structural characterization of Ca 2 Ru 1−x M x O 4+y

Giant NTE can be considered in terms of its crystal structure. The XRD profiles were refined using Le Bail method by RIETAN-FP25 (Supplementary Figs 3 and 4). The structural parameters such as the lattice constants (a, b and c) and the unit-cell volume (v) determined by the present refinements are presented in Table 2 and Figs 3 and 4. Although some differential peaks still exist for the statistics problem of data, the whole pattern fittings are accomplished fairly well, indicating that the peak positions are adequately refined and hence the obtained lattice parameters are reliable. The 111 peak (2θ∼24 deg.) is a single peak for both the L and S phases. The width of this peak is as narrow as those of other diffraction peaks such as the 002 peak (2θ∼14 deg.). In addition, the 200 and 020 peaks are split in both the L and S phases (insets of Supplementary Fig. 4). These two features support that the present crystals belong to orthorhombic symmetry. Through careful investigation of the extinction rule of k≠2n for 0kl, l≠2n for h0l and h≠2n for hk0, we conclude that the space group of the present crystals is Pbca for both the L and S phases. Note that the 200 and 020 peaks are still split in the high-T L phase, although the peak positions are quite close. The difference between the a axis and b axis parameters is significantly large compared with the standard deviations of the present analysis. These features indicate that, despite discontinuous change in lattice parameters, the space group is not changed across the transition. Because the difference between the a axis and b axis parameters is small, some ambiguity persists as to whether a>b or a<b for the L phase in the present analysis. Following a detailed neutron diffraction study17, we assumed the former.

Figure 3: Temperature dependence of the lattice parameters. (a) Ca 2 RuO 3.74 , (b) Ca 2 RuO 4.03 and (c) Ca 2 Ru 0.92 Fe 0.08 O 3.82 . These values are estimated based on Le Bail analysis of the XRD data. For Ca 2 RuO 3.74 , the c axis decreases abruptly below T MI =345 K. The S phase is characterized by highly anisotropic thermal expansion. The a and b axes increase, although the c axis decreases concomitantly with decreasing temperature. The present results confirmed that the negative thermal expansion appears in the S phase. Full size image

Figure 4: Volumetric thermal expansion of Ca 2 Ru 1−x M x O 4+y . (a) Ca 2 RuO 3.74 , (b) Ca 2 RuO 4.03 and (c) Ca 2 Ru 0.92 Fe 0.08 O 3.82 . Results estimated from crystallographic (Δv/v) measurements are compared with the dilatometry (3ΔL/L) results. Reference temperature: 500 K. The discrepancy is conspicuous when the dilatometric negative thermal expansion becomes large. Full size image