Effects of thermal and non-thermal structural phase transitions on the reflectance of metavalent bonding PbGeTe

Phase change materials (PCMs), which are widely used in optical recording devices, such as DVDs or Blu-ray disks,¹ exhibit significant property differences between their highly reflective crystalline and less reflective amorphous phases. Currently, a nanosecond (ns) pulse laser is used to control both phases through thermal melting (amorphization) and crystallization processes. According to many past reports, the above-mentioned phase dependence of properties of PCMs originates from “resonant bonding” in the crystalline phase.^2–4 Resonant bonding was first pointed out by Lucovsky and White⁵ to explain the physical properties of V or IV–VI group compound materials. Resonant bonding has been known to consist of the long-range linear alignment of p-orbitals, and it largely enhances the dielectric functions of the crystalline phase, especially in visible-light regions.^2–4 This results in the crystalline phase of resonant bonded materials becoming metal-like (highly reflective). In the amorphous phase, due to its random atomic structure, resonant bonding cannot be constituted, resulting in its optical property becoming insulator-like (less reflective).

It should be noted here that the term “resonant bonding” used to describe the properties of PCMs has recently become controversial. Wuttig et al. have discussed the differences in properties between IV–VI compounds and organic compounds such as benzene and graphite.^6,7 In their works, they propose “metavalent bonding” as the term for the bonding in the former. In the present work, following their suggestion, we term the characteristic bonding in the crystalline phase of PCMs metavalent bonding, and materials with metavalent bonding metavalent solids.

It is known that metavalent bonding deteriorates under external perturbations such as electron excitation or lattice oscillations, resulting in a decrease in reflectivity. Thus, the reflectivity can be seen as an indicator with regard to the stability of the metavalent bonding. Regarding the influence of lattice oscillations, we have previously reported that the optical properties of the metavalent solid PbTe, which has a cubic rocksalt structure, largely depend on the sample temperature.⁸ It became more transparent and less reflective with temperature increase. We attributed this effect to the deterioration of the metavalent bonding due to the disturbance of the aforementioned long-range p-orbital alignment by enhanced thermal atomic vibrations at higher temperatures. That is, the metavalent bonding and the optical properties of metavalent solids would sensitively respond to the dynamic changes of lattice systems. However, the effect of static changes such as lattice symmetry or polymorphic changes is still unclear.

Recently, substances that exhibit polymorphic phase transitions with property changes have attracted attention as new PCMs.⁹ Unlike the amorphization process, polymorphic phase transition does not require the melting process and atomic diffusion, which is advantageous in terms of energy consumption and processing time. Manganese monotelluride (MnTe) was demonstrated to be capable of showing the reversible polymorphic phase transition between its highly reflective α and less reflective β′ phases, which can realize the PCMs with higher energy efficiency and phase change speed than conventional Ge₂Sb₂Te₅ (GST).⁹ In metavalent solids, polymorphic transitions are also expected to change their optical properties, since such a structural change can disarrange the p-orbital alignment that forms the metavalent bonding.

As for inducing a phase transition, a femtosecond (fs) laser rather than an ns laser would be the most suitable light source. Fs laser is known to be capable of inducing the nonthermal polymorphic phase transition between different crystal structures. Most studies have reported the transition that increases the symmetry of the substances.^10–12 In the research field of PCMs, the ultrafast amorphization process induced by irradiation of fs laser has attracted the attention of researchers.^13–15 Depending on the intensity of the fs laser, it may also be possible to induce polymorphic transition for metavalent solids.

In this context, Pb_1−xGe_xTe (PGT) is a good candidate to study the effect of the polymorphic phase transition on the metavalent bonding and optical property changes. Similar to PbTe, PGT has a cubic rocksalt structure at room temperature (RT). However, it undergoes a cubic–rhombohedral phase transition with a decrease in sample temperature. The transition temperature depends on the concentration of Ge and that of Pb_0.9Ge_0.1Te has been reported to be around 200 K.¹⁶ Since the optical properties of metavalent solids are largely affected even by thermal atomic vibrations, the study of property changes accompanied by the polymorphic transition would be important to reveal the characteristics of metavalent bonding. Since the metavalent bonding would be formed most properly in the rocksalt structure, changes in optical properties would be expected during phase transition, if the structural change has an impact on the metavalent bonding. Furthermore, if the change in optical property is sufficiently large, the polymorphic phase transition of metavalent solids can be applied to a new type of PCMs. In the current study, we investigated the effect of structural change on metavalent bonding, by considering the reflectivity of the sample as an indicator of its stability. The static optical properties of PGT were measured by temperature-controlled spectroscopic ellipsometry, while the dynamic optical properties were measured by ultrafast optical spectroscopy (UOS).

The polycrystalline bulk PGT samples for optical measurements with different compositions [Pb_0.93Ge_0.07Te (PGT7) and Pb_0.8Ge_0.2Te (PGT20)] were prepared by the melting method: for each sample, high-purity Pb, Ge, and Te shots with stoichiometric ratios were sealed into quartz tubes under high vacuum (around 10⁻⁵ Torr). These raw materials were heated at 1000 °C for 24 h and well mixed by shaking the quartz tube. The quartz tube was slowly cooled to 600 K at the rate of 2 K/min, followed by quenching with ice water. The prepared ingot was cut into a disk with a radius of 10 mm and a thickness of 2 mm. The surface of the sample was mechanically polished until a mirror surface was obtained so that the light spot during optical measurement was not distorted after reflection. Since the polishing process was performed under atmospheric conditions, the sample surface is likely covered by a thin oxide layer. The literature reports that the surface of PbTe is covered mainly by PbTeO₃.^17,18 Since its direct bandgap energies are around 4.0 eV¹⁹ and its thickness is reportedly very thin,²⁰ we can conclude that the oxide layer does not have a significant effect on the optical measurement for the infrared to visible range where we mainly focus on in the current work. The crystal structure of the PGT sample was measured by x-ray diffraction (XRD) method. All samples have cubic rocksalt structures at RT. The structural change with the temperature of Pb_0.9Ge_0.1Te (PGT10) was measured by low-temperature XRD. According to the literature, the phase transition temperatures (T_c) for PGT7, PGT10, and PGT20 are around 170, 200, and 300 K, respectively.¹⁶ The compositions of the samples were confirmed by using SEM-EDS. The sample compositions were slightly Te-rich, but almost matched the nominal composition. The results obtained by SEM-EDS showed Pb:Ge:Te = 0.90:0.66:1.034, 0.88:0.09:1.03, and 0.76:0.22:1.03 for PGT7, PGT10, and PGT20, respectively. The elemental mapping images by SEM-EDS are available in the supplementary material.

The static optical properties of the prepared PGT samples were determined by spectroscopic ellipsometry (SE-2000, Semilab). The measurements were performed between RT and 133 K. From the determined complex refractive index n (or complex dielectric function ε), we calculated the temperature dependence of the reflectivity (R) of samples. In this article, the static optical properties of PGT7 are mainly presented. The results for PGT20 are provided in the supplementary material.

Since the PGT samples measured in this study were bulk samples, UOS was performed by measuring the change in R. A combination of commercial Ti:sapphire laser (Spectra-Physics, Tsunami) and regenerative amplifier (Spectra-Physics, Spitfire) was used as the light source to generate 100 fs pulses with a repetition rate of 1 kHz. By using a beam splitter, the fundamental 800 nm pulses were split into pump and probe pulses. The repetition rate of pump pulses was reduced from 1 kHz to 500 Hz using an optical chopper. Thus, the sample was irradiated by the laser at a time interval of 2 ms. However, the probe pulses were focused onto the sapphire single crystal before being irradiated onto the sample to generate a supercontinuum with energies ranging from 1.0 to 2.60 eV. The detailed setup for UOS measurement has been presented in the previous work.⁸ In the present UOS measurement, samples were mounted on a temperature-controllable thermo-cryostat with a vacuum of 10⁻⁴ Pa. The measurement was performed basically at 78 K. The bandgap of PGT is reported to be around 0.3 eV,²¹ and the fundamental 800 nm pump light can sufficiently excite the electron system of the sample.

For the PGT10 sample, we conducted low-temperature XRD measurement to estimate the critical temperature for the rhombohedral–cubic phase transition. In Fig. 1(a), we present the XRD results obtained over the temperature range from 80 to 280 K. Figures 1(b) and 1(c) show enlarged views of the peaks corresponding to 220 and 420 reflections from the cubic phase (denoted below as 220_C and 420_C), where peak splitting is expected to occur due to the rhombohedral structural phase transition. Even when the sample temperature was decreased to 80 K, no clear peak splitting indicative of a transition to the rhombohedral phase was observed. However, the peaks for the 220_C and 420_C reflections became asymmetric at lower temperatures. This asymmetry is believed to result from the cubic-to-rhombohedral phase transition, causing slight splitting below the resolution limit of our measurement apparatus. To clarify the critical temperature of this phase transition, we calculated the integral breadth (B) of the 220_C peak at each temperature. B is defined as ∫(I(θ) − I_BG(θ))dθ/[I(θ) − I_BG (θ)]_max. Here, I(θ), I_BG(θ), and [I(θ) − I_BG (θ)]_max represent the intensity at θ, the background intensity at θ, and the peak height, respectively. The temperature dependence of B is shown in the inset of Fig. 1(a). Above and below approximately 200 K, B exhibits different temperature dependencies during cooling. The increasing trend of B below 200 K can be attributed to the peak-splitting effect of the phase transition described above. Conversely, the change in B in the temperature range from 280 to 200 K can result from thermal effect or non-uniform strain. Grains subjected to non-uniform strain exhibit a distribution in areal spacings and a larger peak width. In polycrystalline specimens, grains restrain their neighboring grains during thermal expansion, causing non-uniform strain. As the temperature rises, non-uniform strain increases, leading to an increase in peak width. These results confirm that the phase transition temperature of PGT10 is approximately 200 K, which is close to the literature value.¹⁶ 

Next, we show the static optical properties of PGT alloys. Figure 2(a) shows the complex dielectric function ε of PGT7, determined by spectroscopic ellipsometry at RT, where ε₁ and ε₂ indicate the real and imaginary parts of ε, respectively. This figure also shows R of PGT7 at normal incidence for the infinite thickness, calculated by using the formula: R = [(n − 1)²+ k²]/[(n + 1)²+ k²], where n and k represent the real and imaginary parts of the refractive index of PGT7, respectively. The broad peaks of ε₂ are located around 1–1.7 eV, being in contrast to that of PbTe,^8,22 which has two distinct peaks at 1.2 and 2.2 eV. This difference in ε between PbTe and PGT may reflect the changes in band structure with the addition of Ge. Figure 2(b) presents R at T of PGT7 normalized by R at 133 K [namely, R(T)/R(133 K)]. It should be noted that, according to the literature, PGT7 has a rhombohedral structure at 133 K.¹⁶ The results show that R of PGT tends to decrease with an increase in temperature, especially at the peak position of R in Fig. 2(a). A similar behavior in response to temperature changes has been observed in PbTe,⁸ suggesting that enhanced thermal atomic vibrations also degrade the metavalent bonding in PGT. (For reference, the values of dielectric functions measured at different temperatures are shown in Fig. S4 in the supplementary material.) Figure 2(c) shows the changes in the peak values (at 1.2 and 2.4 eV) in R as a function of sample temperature; see also Fig. S4 in the supplementary material for details. For both energies, R decreases essentially in proportion to the increase in temperature. However, the slope of R with temperature changes around 170 K. According to the literature,^16,21,23 this temperature corresponds to the rhombohedral–cubic transition temperature of PGT7, and similar behavior was not observed for PGT20 (see Fig. S4 in the supplementary material). Given the reported phase transition temperature, a certain bending point in R would be closely related to the cubic phase transition PGT7. The slope of R with temperature below T_c is larger than that above T_c. Therefore, if the phase transition has not occurred, R above 200 K could be lower than the observed values. This indicates that the phase transition to the cubic phase results in an increase in R, likely due to the enhanced metavalent bonding in the cubic structure.⁷ However, the change in R caused by the cubic phase transition is as small as 0.1%. Thus, even if the rhombohedral phase and the cubic phase can be maintained at the same temperature (e.g., at RT) as the conventional GeSbTe materials, where the crystalline and amorphous phases coexist at the same temperature, such a small difference in their reflectance would be unsuitable for PCMs. The small reflectivity change accompanied by the phase transition is potentially due to the small distortion (or deviation) from cubic crystal structure. The reported rhombohedral angle (tilt from cubic crystal axis) of Pb_0.75Ge_0.25Te is 0.23°, which is significantly smaller than that of GeTe (1.067°).²⁴ Thus, it will likely be difficult to realize PCMs that utilize polymorphic phase transitions of metavalent solids unless materials tailored to have a large rhombohedral angle are developed. Here, we noted that the R of PGT20 at 1.2 eV increased with heating, while R at 2.4 eV decreased. This difference between them may be due to the competition of the temperature-dependent rhombohedral angle and thermal atomic vibration. This is discussed in the supplementary material in more detail.

Figure 3(a) shows the UOS results at various time delays (Δt) after excitation with a fluence (F) of 0.93 mJ cm⁻², performed at 78 K. At this F, it was estimated that the sample temperature after photoexcitation does not exceed the phase transition temperature (see Fig. S6 in the supplementary material). The decrease in R just after excitation across a broad energy range after excitation is likely attributable to the photoinduced degradation of the metavalent bonding, as observed in many metavalent solids.^8,15,25,26 The change in R after pump is significant at around 1.2 and 2.4 eV, which corresponds to the energies where the change in R due to temperature was also significant in Fig. 2(b). Here, the more intense and time-dependent change in R around 1.2 eV after photoexcitation may suggest that electronic excitations induced by photons around 1.2 eV correspond to transitions between states more closely associated with metavalent bonding. The R change spectrum becomes almost unchanged after 10 ps over all energies up to 200 ps. Given that the thermalization time after photoexcitation was around 12 ps measured for PbTe,⁸ the R change in PGT7 after such a time is likely due to the effect of the temperature increase by laser irradiation. Figure 3(b) shows the change in R as a function of Δt, probed at 1.77 eV (700 nm) light, measured at different sample temperatures. At 78 K, the R changes exhibit short-lived oscillations following a sharp decrease and subsequent increase immediately after excitation. The oscillations in the R change were most prominently observed by 1.77 eV probe energy. Since 78 K is less than the T_c of PGT7, this oscillation comes from the coherent optical phonon induced by fs-laser irradiation. Although the oscillation lasted for less than one complete cycle, the frequency was estimated to be about 0.8 THz based on the time interval between the peak and trough of the oscillations (shown by arrows). This frequency is consistent with the reported frequency of 0.7 THz determined at 7 K in the literature.^23,27 However, the oscillation was not observed at 228 K; this is because PGT7 was already transformed into the cubic phase at about 170 K on the way to a temperature increase. Since the rocksalt cubic phase does not have any Raman active mode, any coherent oscillation cannot be observed in the R change.

In Figs. 4(a) and 4(b), we present the R change induced by various F, probed at 1.77 eV of PGT7 and PGT20, respectively. The magnitude of the R change becomes more significant with increasing F. We note that the coherent phonon oscillation disappears and is replaced by a plateau-like structure at the threshold fluence (F_th) of 1.38 and 3.68 mJ cm⁻² for PGT7 and PGT20, respectively. In previous literature, a similar reflectivity change of PGT7 was observed,²⁷ but the authors interpreted this behavior as an oscillation damping due to the electron–phonon interaction, in that the oscillation becomes gradual with increased F. However, a more pronounced plateau observed in the result for PGT20 cannot be explained by damped oscillation, since the oscillation disappeared suddenly at a clear threshold fluence. Therefore, it is considered that the disappearance of the coherent phonon oscillation is due to the cubic phase transition of PGT alloys, rather than damping by the electron–phonon interaction (especially for PGT20). The coherent phonons generated in the rhombohedral phase attempt to modulate the reflectivity, but this modulation can be hindered by the transition to the cubic phase which has no Raman active modes. The plateau-like structure is likely a remnant of the hindered coherent phonon oscillation. These results indicate that the photoinduced phase transition of PGT alloys occurs transiently within less than 1 ps after excitation. This short-time domain suggests that this transient phase transition in PGT alloys occurs via a nonthermal process resulting from the excitation of the electronic system. The increase in F_th with Ge concentration arises from the greater stability of the rhombohedral phase with higher Ge concentrations.

In Fig. 4(c), we present the changes in R at 15 ps after the excitation of PGT7 and PGT20. At this elapsed time, it is considered that the photoexcited sample has reached a thermally equilibrated state in terms of energy transfer from the electronic to lattice systems. The threshold fluences of the phase transition for PGT7 and PGT20 (F_{th_7} and F_{th_20}) are indicated by the vertical dashed lines. We estimated the maximum temperatures after excitation with the threshold fluences by using the specific heat of PbTe,²⁸ which are around 440 and 750 K for PGT7 and PGT20, respectively, under adiabatic conditions, where the dissipation of heat and electrons is ignored. Although the actual temperatures are lower than these estimates, the temperatures of the samples after photoexcitation could exceed the T_c of each sample. The magnitude of R decreased across all time and probe-energy ranges, without any clear discontinuity or flexure despite the cubic phase transition. This is likely due to the decrease in R induced by temperature increase, which obscures the effect of phase transition in R, since its effect is small as presented in Fig. 2(c).

In this study, we investigated the effect of a structural phase transition on reflectivity by focusing on the optical properties of PGT alloys. Using spectroscopic ellipsometry, we determined the dielectric functions of PGT alloys at various temperatures and confirmed that the reflectivity of the samples essentially decreases with temperature in the visible range. It was shown that the reflectivity of metavalent solids eventually decreases due to the temperature increase even though it was supposed to be enhanced owing to the rhombohedral-to-cubic phase transition. Using ultrafast optical spectroscopy, we observed coherent phonon oscillations associated with the rhombohedral structure in the reflectivity change. As the excitation fluence increased, these oscillations disappeared at threshold fluences that depend on the Ge composition in PGT alloys. This indicates that the nonthermal rhombohedral–cubic phase transition occurs transiently in an ultrashort time range of less than 1 ps after excitation. The optical properties of the present PGT alloys cannot be substantially controlled by tuning the strength of the metavalent bonding via the phase transition, which makes it difficult to apply them as PCMs. In this work, it is clearly shown that the significantly large optical change requires a marked change of bonding nature (e.g., from metavalent bonding to covalent bonding) of the two crystals, even though there is a crystal structural change caused by the phase transition, that is, just because a structural phase transition occurs does not ensure that the material can be a PCM. If we utilize the characteristics of metavalent bonding to PCMs, the drastic structural change would be necessary in terms of the degradation of metavalent bonding by using an external strain or substrate constraint.

See the supplementary material for the room-temperature XRD results of PGT alloys with different composition (Fig. S1); elemental mapping image for each sample by SEM-EDS (Fig. S2); the Ψ and Δ of PGT7 and PGT20 observed various temperatures by spectroscopic ellipsometry (Fig. S3); the dielectric functions of PGT7 and PGT20 at various temperatures [Figs. S4(a) and S4(b)]; the reflectivity spectra of PGT7 and PGT20 at various temperatures [Figs. S4(c) and S4(d)]; the temperature dependence of reflectivity of PGT20 [Figs. S4(e) and S4(f)]; the ultrafast reflectivity change of PGT20 induced by photoexcitation [Figs. S5(a) and S5(b)]; and the ultrafast reflectivity change of PGT7 at 133 K observed to evaluate the sample temperature after laser irradiation [Figs. S6(a) and S6(b)].

This work was supported by the Japan Society of the Promotion of Science (JSPS) KAKENHI under Grant Nos. 21K14400, 21H05009, and 23K17808.

The authors have no conflicts to disclose.

Hiroshi Tanimura: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Yohei Kaise: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Visualization (equal). Takumi Nakajima: Data curation (equal); Visualization (equal). Yuji Sutou: Conceptualization (equal); Funding acquisition (equal); Writing – review & editing (equal). Tetsu Ichitsubo: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.