Suppression of the energy gap in SmB6 under pressure

The electr'ical resistance R of SmB6 as a function of temperature T and pressure P has been measured in the range 1 K ~ T ~300 K and 0 ~ P & 220 kbar. The behavior of R ( T) changes continuously from that of a narrow gap semiconductor to that of a metal in the range of 0 ~ P & 70 kbar. The dependence of R on T and P can be analyzed phenomenologically within the context of a thermal activation model with an activation energy that decreases linearly with pressure from — 33 K at zero pressure to zero at — 70 kbar. The data resemble those of SmS and SmSe under pressure and suggest a general behavior of R (T, P) for intermediate-valence Sm compounds.

The intermediate-valence (IV) compound SmB6 has attracted the attention of both experimentalists and theoreticians alike because of its striking physical properties, some of which are indicative of a poor metal, and others which are characteristic of a semiconductor with a small energy gap of several meV. ' A number of theoretical models have been advanced to account for the unusual physical properties of Sm86 such as the dfhybridization ga-p model proposed by Mott, and the disordered Wigner lattice model of Kasuya et al. 9 The first evidence for semiconducting behavior of Sm86 was provided by the temperature dependence of the electrical resistivity. The resistivity increases with decreasing temperature in a thermally activated manner and then, below 3 K, saturates to a value that can be as large as 104 times the room-temperature value. ' " " NMR, ' electron tunneling, "'" ' far-infrared absorption, ' ' and lowtemperature specific-heat' measurements are all consistent with the existence of a small energy gap of several meV.
Recently, x-ray diffraction measurements on SmB6 under pressure were carried out by King, LaPlaca, Penney, and Fisk' in a diamond anvil cell at room temperature.
The results indicate that the valence of the Sm ions changes from 2.8 at zero pressure to 2.9 at 60 kbar, the highest pressure attained in the experiment. A transition to a fully trivalent state at higher pressure could conceivably occur and should lead to magnetic order since trivalent Sm is a Kramer's ion.
In this paper, we report the results of measurements of the pressure dependence of R(T) of SmB6 up to -220 kbar. The experiment was undertaken in order to (I) determine how the energy gap varies with pressure, (2) search for evidence of phase transitions (e.g. , crystallographic, valence, insulator-metal, magnetic) under pressure, and (3) compare the pressure dependences of R ( T) of SmB6 and A Bridgman anvil technique was employed in attaining quasihydrostatic pressures P & 160 kbar at UCSD and P & 220 kbar at KFA, Julich. The SmB6 powder and a Pb manometer were sandwiched between two steatite disks and contained within a pyrophyllite gasket, although in the case of sample 1, the Pb manometer was omitted. Pressures relevant to sample 1 were estimated from the applied press load during pressurization using a previously established calibration which was based on the T, vs P behavior of Pb.
A Pb manometer was included in the pressure cell in the experiments on sample 2. The higher-pressure measurements at KFA, Julich were also calibrated via Pb manometers assuming a linear relationship for T, (Pb) vs P between the Fb (I-II) transformation fixed point at 130 kbar and the GaP transformation fixed point at 220 kbar. Fig. 1

Shown in
The data of Fig. 1 are also displayed as logR vs logT and logR vs T ' in Figs. 2 and 3, respectively. A second set of experiments on sample 2 revealed the same general behavior displayed by curve E of Fig. 1 at the same applied press force, although the low-pressure value R (1 K)/R (300 K) = 10 indicated that sample 2 was not as pure as sample 1. Samples 3 and 4 were measured up to pressures of -190 kbar and -216 kbar, respectively.
The R ( T) curves for both samples showed the same evolution with pressure from semiconducting to metallic character exhibited by samples 1 and 2.
The R ( T) data of sample 4 are displayed in Fig. 4. Between 125 and 216 kbar, the transition towards more metallic behavior with pressure is apparent from the disappearance of the maximum in R ( T) above 125 kbar and the relative steepening of the R(T) curves for 50 & T &300 K.
The R ( T) data depicted by curve A were taken at 21 kbar before the excursion up to 216 kbar, while the R ( T) data represented by curve B were taken at 21 kbar upon reload- curred by the SmB6 sample after it had been subjected to an inhomogeneous pressure of 216 kbar. The logR vs T ' data (Arrhenius plots) at the lower pressures shown in Fig'. 3 are consistent with conduction by thermal activation of electrons across an energy gap. Therefore we have analyzed the data phenomenologically with an activation law R = Roexp(bE/kT), where b E is the activation energy. This equation describes the 18-kbar data (curve A of Fig. 3) with b.E =27 K in the temperature ranges 6 -14 and 140 -300 K. It is interesting to note that thermally activated behavior of R ( T) with the same activation energy AEbelow -20 and above -50 K has been observed in single-crystal specimens of SmB6 at ambient pressure with values of AE between 28 and 41 K. '  curves changes from semiconducting to metallic near -70 kbar for SmB6, it occurs near -20 kbar for SmS  and -100 kbar for SmSe. ' Moreover, the overall shapes of the R( T) curves of Sm86 above -70 kbar, gold SmS above -20 kbar, and SmSe above -100 kbar are surprisingly similar to one another and to those of many metallic IV compounds whose R vs T curves exhibit strong negative curvature and saturation in the neighborhood of or below room temperature. ' An interesting feature in the R ( T) curve of Sm86 is the maximum that disappears above -125 kbar. A corresponding maximum in the R(T) data of SmS vanishes completely by -108 kbar. ' Recent electron tunneling experiments have revealed the appearance of a small energy gap -1.7 meV at 4.2 K for SmS above the pressure at which the "black" phase transforms into the gold phase. '7 Thus the energy gap for gold SmS is comparable to the energy gap of Sm86.
The fact that SmB6, SmS, and SmSe all display similar pressure-induced transitions from a narrow gap semiconductor to a metal suggests that this may be a general behavior of IV Sm compounds with an underlying common mechanism that remains to be elucidated. Finally, the IV compound TmSe has also been found to exhibit a small energy gap -2-3 meV as well as an insulator-metal transition near 32 kbar, although this case is complicated by the occurrence of several types of magnetic order. '

ACKNOWLEDGMENTS
The research at UCSD and Los Alamos National Laboratory was carried out under the auspices of the U.S. Department of Energy under Contract No. DE-AT03-76ER70227 at UCSD.