# Pressure dependence of the metal-semiconductor transition of K 2Pt(CN)4Br0.3.3 H2O

W. H-G Müller, Denis Jerome

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W. H-G Müller, Denis Jerome. Pressure dependence of the metal-semiconductor transition of K 2Pt(CN)4Br0.3.3 H2O. Journal de Physique Lettres, 1974, 35, pp.103 - 105. 10.1051/jphyslet:01974003507-8010300. hal-05129640

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Classification
*Physics Abstracts*
8.220 — 8.150

# PRESSURE DEPENDENCE OF THE METAL-SEMICONDUCTOR TRANSITION
OF K₂Pt(CN)₄Br₀.₃·3 H₂O

W. H.-G. MÜLLER (*) and D. JÉROME

Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France (**)

(Reçu le 8 avril 1974)

**Résumé.** — Des mesures de conductivité ont été effectuées sous pression sur

K₂Pt(CN)₄Br₀.₃·3 H₂O

entre la température ambiante et 60 K. La forte variation sous pression est d'autant plus nette que la température est basse. Les résultats sont discutés à l'aide du modèle d'une transition d'un métal unidimensionnel (1-D) vers un semiconducteur dont la température de transition décroît sous pression. On obtient une variation de la température de Peierls en champ moyen

$$ \frac{d \ln T_p^{\text{mt}}}{dP} = -0,035 \ 2 \text{kbar}^{-1}. $$

**Abstract.** — Conductivity measurements under pressure of K₂Pt(CN)₄Br₀.₃·3 H₂O between room temperature and 60 K are reported. The strong pressure dependence at room temperature increases very rapidly with decreasing temperature. The results are discussed in terms of a transition from a one dimensional (1-D) metal to a semiconductor whose transition temperature decreases with increasing pressure. A coefficient $\frac{d \ln T_p^{\text{mt}}}{dP} = -0.035 \ 2 \text{kbar}^{-1}$ is measured for the mean-field Peierls temperature.

The mixed-valence platinum compound

K₂Pt(CN)₄Br₀.₃·3 H₂O,

(KCP) is one of the most interesting one dimensional quasimetallic systems. Crystal structure [1], conductivity anisotropy as a function of temperature [2] and optical behavior [3] are well known. Recent X-Ray diffuse scattering [4] and neutron diffraction [5] experiments have pointed out the existence in the temperature range 300 K – 110 K of a fluctuating Peierls distortion on every 1-D strand. They also hint at a very interesting 3-D ordering [6] at a temperature of about 110 K as a consequence of the establishment of a coupling between different chains. Moreover, in such a one-dimensional system fluctuations have to be taken into account [7]. N. M. R. measurements [8] show the importance of the critical fluctuations, which dominate in a very wide temperature range due to the very pronounced one dimensional character of this material.

Previous measurements of the pressure dependence of the conductivity [9] and the optical properties [10]

show a big influence in this material. Moreover, previous pressure investigations of the metal-semiconductor transition in the one-dimensional system (TTF) (TCNQ) emphasize a shift of this transition with pressure [11, 12] and have motivated the pressure investigation of KCP at low temperature reported in this note. A helium-gas pressure setup was used. Helium as pressure-transmitting medium gives a perfectly hydrostatic pressure down to the freezing point of the fluid and has moreover the advantage of being completely inert, an aspect which is especially important for the organic compounds and also for KCP which is known to be soluble in a large number of organic solvents currently used as pressure transmitting media. The crystals have the typical size of 6 mm × 0.8 mm × 0.8 mm. Care was taken to avoid a loss of crystal water (preservation under controlled humidity, fast cooling down to the freezing point after mounting). The contact arrangements are similar to those reported by Zeller *et al.* [13]; the contacts were made with aquadag, but gold paint was also used.

The conductivity parallel and perpendicular to the strands was measured with a lock-in technique (30 Hz). The values at room temperature are

$$ \sigma_{\parallel} = 10 - 10^3 (\Omega \cdot \text{cm})^{-1} $$

<footnote>(*) On leave from: University of Karlsruhe, Physikalisches Institut, Germany.</footnote>

<footnote>(**) Laboratoire associé au C. N. R. S.</footnote>
and $\sigma_{\perp} = (2.4 \pm 0.3) 10^{-3} (\Omega \cdot cm)^{-1}$, in good agreement with literature values [14]. These were found on different crystals. The contact arrangement of Montgomery [15] gives the same values, but was not used, because the crystals are too short to give reasonable variations under pressure. $\sigma_{\parallel}$ differs from sample to sample and the results are not very reproducible. However the results for $\sigma_{\perp}$ are very reproducible even after several runs in pressure and temperature. First we report results for the pressure dependence of the conductivity perpendicular to the strands.

Figure 1 gives the pressure dependence of the resistivity for three temperatures. At room temperature an

<figure><img src="image_2.png" /><figcaption>FIG. 1. — Relative transverse resistivity of KCP versus pressure at various temperatures.</figcaption></figure>

exponential decrease of the resistivity is observed, indicating a law $R(P) = R(0) \exp(-aP)$ with $a = 0.115 \text{ kbar}^{-1}$. At 9 kbar the conductivity is enhanced by a factor 2.8 in good agreement with the data of Interrante et al. [9].

A reasonable explanation of this large increase under pressure can be found, regarding the change of the inter chain distance [9]. A decrease of this distance leads to an increase of the uniformity distributed hopping probability between the strands.

To discuss the pressure effect on the conductivity $\sigma_{\parallel}$ one has to distinguish between samples with low conductivity ($\sigma_{\parallel} = 10-100 (\Omega \cdot cm)^{-1}$) and samples with high conductivity ($\sigma_{\parallel} = 10^2-10^3 (\Omega \cdot cm)^{-1}$). In the first case there is no drastic difference in the pressure dependence of $\sigma_{\parallel}$ and $\sigma_{\perp}$. The measured quantity $\sigma_{\parallel}$ is in this case not the intrinsic conductivity along a strand but a composite conductivity, where the intrinsic conductivity is multiplied by a tunneling factor expressing the quantum jump at the carriers through the interruptions between two adjacent strands. The pressure dependence of the intrinsic conductivity

is provided by the pressure variation of the Fermi energy and the electron-phonon coupling constant. An estimation of the two effects gives for both an exponential law and the same order of magnitude. So it is not clear which effect is the important one.

The pressure variation of $\sigma_{\parallel}$ for samples with high conductivity is not reproducible; increases as well as decreases are observed for samples with

$$\sigma_{\parallel} \sim 10^3 (\Omega \cdot cm)^{-1}.$$

After several runs the conductivity becomes usually smaller. An explanation of these results can be found assuming that the high conductivity is given by long, perfect chains. These chains are very sensitive to new interstrand defects which are caused by the pressure and responsible for the irreproducible results.

It was noticed in the ambient-pressure conductivity report of Bernasconi et al. [14] that the $\ln \sigma_{\parallel}$ or $\ln \sigma_{\perp}$ versus $1/T$ curves are nearly parallel at low temperature. Therefore one can deduce that the electronic process governing the conductivity is the same for both directions. This assumes that in the Peierls distorted state the variation of the Peierls gap with temperature will dominate the temperature dependence of the conductivity in all directions.

Below 150 K the pressure effect increases very rapidly. At 63 K, 9 kbar gives an enhancement by a factor of 40. This supports the assumption that the pressure has a strong influence on the semiconductor transition. In figure 2 $\ln \sigma$ is given as function of $1/T$ for three pressures. At 9 kbar the conductivity remains constant between 300 K and 200 K and the decrease is smaller. At the low temperature side this plot gives almost a constant slope. Neglecting the temperature

<figure><img src="image_3.png" /><figcaption>FIG. 2. Transverse conductivity versus $1/T$ for 0.3 and 9 kbar.</figcaption></figure>
dependence of the mobility an apparent gap $2\Delta(T)$ can be derived at every temperature according to a law

$$ \frac{\Delta(T)}{kT} = \ln\left(\frac{2\sigma_0}{\sigma(T)} - 1\right) $$

where $\sigma_0$ is the saturation value of $\sigma_\perp$ for $T \to \infty$.

Figure 3 gives the temperature dependence of this apparent gap; the parameter is the pressure. All

<figure><img src="image_4.png" /><figcaption>FIG. 3. — Temperature dependence of the apparent energy gap of KCP determined from the conductivity measurements of figure 2. Dotted lines represent extrapolations of the data actually measured.</figcaption></figure>

curves tend to saturate at the low temperature side; at zero pressure the result agrees with the apparent gap reported by Zeller [2]. The pressure has two effects: it shifts the curves towards lower temperature and reduces the low temperature value of the gap.

Rice and Strässler [16] have shown that the mean-field theory provides the BCS-like relation

$$ \frac{2 \Delta(0)}{kT_p^{mf}} = 3.5 \qquad (1) $$

between the Peierls gap $\Delta(T=0)$ and the mean-field transition temperature.

The low-temperature results for the apparent gap (Fig. 2) together with eq. (1) lead to a mean-field Peierls temperature of 350 K at ambient pressure, in fairly good agreement with the results of neutron and X-Ray diffuse scattering experiments as well as NMR measurements [5, 8, 9]. It is probably clear that the apparent gap measured by conductivity approaches at low temperature the value of $2\Delta(0)$ entering eq. (1). Lee et al. have pointed out the importance of the critical fluctuations in a Peierls transition. Therefore the effective transition temperature to a static semiconductor with static long range order is actually much lower than the mean-field Peierls temperature. It is now currently believed to be $T_{3d} \approx 110$ K [17] at ambient pressure, corresponding to a ratio $T_p^{mf}/T_{3d} = 3.17$.

The most significant result of our data is the fact that pressure induces a very important change of the temperature scale, given by $T_p^{mf}$. A change of the gap under 9 kbar by 30 meV indicates a shift of $T_p^{mf}$ by 95 K down in temperature and accordingly a shift of the actual metal-semiconductor transition by 30 K. It should be possible to see such a large effect with high-pressure NMR measurements which are under investigation in our laboratory, as well as in neutron diffraction experiments under hydrostatic pressure at low temperature which are planned at the high-flux reactor of the Laue-Langevin Institut.

**Acknowledgments.** — It is a pleasure to thank Dr. Barisic, Dr. H. Launois and Prof. H. Nagasawa for helpful discussions. The crystals were prepared and kindly supplied by Dr. H. Launois. We also thank G. Malfait for his skilful technical assistance.

## References

[1] KROGMANN, K., HAUSEN, H. D., Z. Anorg. Allg. Chem. 358 (1968) 67.

[2] For a recent review on KCP see ZELLER, H. R. in Festkörper-probleme, edited by H. J. Queiser (Pergamon, New York) 13 (1973) 31.

[3] KUSE, D., ZELLER, H. R., Phys. Rev. Lett. 27 (1971) 1060; GESERICH, H. P., HAUSEN, H. D., KROGMANN, K., STAMPFL, P., Phys. Stat. Sol. a 10 (1972) 537.

[4] COMES, R., LAMBERT, M., LAUNOIS, H., ZELLER, H. R., Phys. Rev. B 8 (1973) 571.

[5] RENKER, B., PINTSCHOVIUS, L., GLASER, W., RIETSCHEL, H., BRUESCH, P., KUSE, D., RICE, M. J., Phys. Rev. Lett. 30 (1973) 1144.

[6] COMES, R., LAMBERT, M., ZELLER, H. R., Phys. Stat. Sol. (b) 58 (1973) 587; BARISIC, S., Phys. Rev. B 5 (1972) 932 and Phys. Rev. B 5 (1972) 941.

[7] LEE, P. A., RICE, T. M., ANDERSON, P. W., Phys. Rev. Lett. 31 (1973) 462.

[8] NIEDOBA, H., LAUNOIS, H., BRINKMANN, D., KELLER, H. J. preprint March 1974; NIEDOBA, H., LAUNOIS, H., BRINKMANN, D., BRUGGER, R. and ZELLER, H. R., Phys. Stat. Sol. b 58 (1973) 309.

[9] INTERRANTE, L. V., BUNDY, F. P., Solid State Commun. 11 (1972) 1641.

[10] KUSE, D., Solid State Commun. 13 (1973) 885.

[11] CHU, C. W., HARPER, J. M. E., GEBALLE, T. H., GREENE, R. L., Phys. Rev. Lett. 31 (1973) 1491.

[12] JÉROME, D., MULLER, W., Weger, M., J. Physique Lettres 35 (1974) L-77.

[13] ZELLER, H. R., BECK, A., J. Phys. Chem. Sol. 35 (1974) 77.

[14] BERNASCONI, J., KUSE, D., RICE, M. J., ZELLER, H. R., J. Phys. C 5 (1972) L 127.

[15] MONTGOMERY, H. C., J. Appl. Phys. 42 (1971) 2971.

[16] RICE, M. J., STRASSLER, S., Solid State Commun. 13 (1973) 1931.