Research Express@NCKU - Articles Digest

ransport and optical measurements are common techniques for the study of semiconducting materials. For a narrow gap semiconductor such as the present case of CoSb₃, these macroscopic measurements usually fail to yield reliable results if impurity phases and/or defects appear in the sample. Hence, a full understanding of the physical properties of the material requires a detailed analysis at the microscopic level. The nuclear magnetic resonance (NMR) measurement is such a tool which is not sensitive to those extrinsic effects because it employs the hyperfine interactions between probed nuclei and electrons to investigate the microscopic magnetic and electronic properties of materials. In this investigation, we thus probe the electronic characteristics of CoSb₃ by means of NMR techniques. This material has been of great interest due to its unusual electronic properties and promising potential for thermoelectric applications. Measurements extending up to 450 K allow us to examine the nature of the energy gap in this compound. Our NMR results support the assignment of CoSb₃ as a narrow gap semiconductor, with a band gap of about 40 meV. We further demonstrate that the observed exotic features are mainly governed by the thermally excited s-character carriers across the band edges.

NMR measurements were performed in a constant field of 7.0665 T with two home-built probes employed for the low-temperature and high-temperature experiments, respectively. The powdered specimen was put in a Teflon vial that showed no observable ⁵⁹Co NMR signal. Since the ⁵⁹Co NMR resonance is extremely quadrupolar broadened, the wide-line satellite spectrum was mapped out by integrating spin echo signal of various excitations. Due to electric quadrupole coupling, the ⁵⁹Co NMR spectrum I = 7/2 consists of seven transition lines, as illustrated in Fig. 1. For the powder sample, these lines exhibit as a typical powder pattern, with distinctive edge structures corresponding to the quadrupole parameter. Since the first order quadrupole shift is the main effect shaping the satellite lines, the quadrupole frequency, ν_Q = 1.18 ± 0.02 MHz, was determined directly from these lines. The synthetic profile which matches well with the experimental powder pattern, was plotted as a solid curve in Fig. 1.

Fig. 1. Fully resolved ⁵⁹Co NMR powder pattern for CoSb₃. The synthetic curve, shown as a solid line, has been shifted down for clarity.

Room-temperature central transition line shape for CoSb₃ is displayed in Fig. 2. The spectrum splits into two peaks because of the simultaneous presence of anisotropic Knight shift and second-order quadrupole interactions. For a polycrystalline sample, shape function fitting for the case of combined quadrupole and anisotropic shift interactions was performed and the result matches well with the experimental ⁵⁹Co NMR spectrum, drawn as a dashed curve in Fig. 2. This fit can provide the accurate isotropic Knight shift K_iso = -0.0154 %, indicated as an arrow in Fig. 2. It is important to note that the feature of the line shape remains unchanged with temperature, signifying no magnetic moment associated with the Co sites, being consistent with the diamagnetic character for CoSb₃.

Fig. 2. ⁵⁹Co central transition NMR spectrum for CoSb₃ measured at room temperature. The isotropic Knight shift is indicated by an arrow. The simulated curve, dawn as a dashed line, has been shifted down for clarity.

To further probe the semiconducting behavior, we measured the temperature-dependent ⁵⁹Co isotropic Knight shift up to 450 K, with the result plotted in Fig. 3. The Knight shift here was referred to the ⁵⁹Co resonance frequency of one molar aqueous K₃Co(CN)₆. The observation is a combination of two terms: K_iso = K_o + K(T). The first part is a temperature-independent shift while the later is a shift to higher frequencies as rising temperature. The temperature-dependent shift is easily understood in terms of semiconducting characteristics for CoSb₃, with the increase in Knight shift due to an increase in the number of carriers because of thermal excitation across an energy gap E_g. Using an effective-mass approximation for the band edges of CoSb₃ with Fermi energy located at midgap, the temperature-dependent shift can be written as K(T) = A₁T^1/2exp(-E_g/2k_BT). The coefficient A₁ is associated with the effective mass of carriers as well as their concentrations. Each carrier density varies with temperature according to T^3/2exp(-E_g/2k_BT). The solid curve in Fig. 3 represents a fit to the above relation, yielding K_o = -0.042 %, A₁ = 3.17×10^-5 K^-1/2, and E_g = 39 meV. The tiny negative K_o can be related to the diamagnetic shift, a typical character for an insulating material. Note that the prefactor A₁ is positive for CoSb₃, which cannot be associated with the negative electron hyperfine coupling for the core-polarization mechanism. With this respect, we conclude that the thermally excited carriers in the present case of CoSb₃ are mainly s-like, with positive s-hyperfine constant responsible for the observed positive shift with temperature.

Fig. 3. Temperature dependence of the isotropic ⁵⁹Co Knight shift for CoSb₃. The solid curve represents a fit to the semiconducting behavior with E_g = 39 meV.

Temperature dependence of the spin-lattice relaxation rate 1/T₁ was measured using the inversion recovery method. In the inset of Fig. 4, it clearly demonstrates that 1/T₁ rises rapidly, with an activated temperature dependence. By analogy to the Knight shift, the relaxation rate is expressed by 1/T₁ = A₂T²exp(-E_g/2k_BT), where A₂ is a constant depending upon the same factors as A₁. The fit gives good agreement with the data, shown as a solid curve in a semilogarithmic plot of Fig. 4. The result of the least-squares fit yields A₂ = 1.39×10^-5 sec^-1 K^-2 and E_g = 39 meV

Fig. 4. Semilogarithmic plot of ⁵⁹Co spin-lattice relaxation rate for CoSb₃. Solid curve: fit to the semiconducting character with E_g = 40 meV. The inset shows thermally activated behavior in the spin-lattice relaxation rate.

The extracted E_g values from the Knight shift and T₁ measurements appear to be very close, indicating that the thermally excited carriers are essentially from the same band edges. Also the value of 40 meV agrees well with the theoretical calculation of about 50 meV. For an intrinsic semiconductor, the Korringa relation can be written as follows: K²(T) T₁T = Cexp(-E_g/k_BT), where the pre-exponential factor C = A₁ ²/A₂ has been determined to be 7.2×10^-5 sec K from the experimental values of A₁ and A₂. In pure semiconductors, the constant C can be simply estimated in terms of Here γ_n and γ_e are gyromagnetic ratios for ⁵⁹Co nuclei and conduction electrons in CoSb₃, and m^*_h and m^*_e represent effective masses for holes and electrons, respectively. Taking γ_e/2 = 1.41×10⁷ Hz/G (using the average g factor of 10.1 determined from the Shubnikov-de Hass oscillation measurement in CoSb₃), γ_n/2 = 1.0102×10³ Hz/G, and the experimental value of C = 7.2×10^-5 sec K, we can thus obtain the ratio of m^*_h/m^*_e = 0.24. The ratio less than unity points out that the mass of hole carriers is considerably lighter than that of electrons. This result indicates that the transport properties of CoSb₃ are dominated by holes, in agreement with the fact that CoSb₃ is a p-type material as revealed from Seebeck coefficient and Hall effect measurements. Based on the above analysis, it reinforces the conclusion that CoSb₃ is essentially a narrow-gap semiconductor with thermally excited s-character carriers responsible for the exotic behavior in the present Knight shift as well as the relaxation rate.

In summary, the microscopically electronic properties of CoSb₃ have been studied by means of ⁵⁹Co NMR. The observed temperature-dependent isotropic Knight shift and spin-lattice relaxation rate can be easily understood in terms of a simple semiconducting scenario for CoSb₃, with a small band gap of about 40 meV. The deduced value has been found to be quite similar to those via band-structure calculations. We further indicate that the thermally excited s-character carriers are responsible for the observed exotic features.