Magnetic field effects on transport properties of PtSn${}_4$

The anisotropic physical properties of single crystals of orthorhombic PtSn${}_4$ are reported for magnetic fields up to 140 kOe, applied parallel and perpendicular to the crystallographic b axis. The magnetic susceptibility has an approximately temperature-independent behavior and reveals an anisotropy between the ac plane and b axis. Clear de Haas-van Alphen oscillations in fields as low as 5 kOe and at temperatures as high as 30 K were detected in magnetization isotherms. The thermoelectric power and resistivity of PtSn${}_4$ show the strong temperature and magnetic field dependencies. A change of the thermoelectric power at $H=140$ kOe is observed as high as $\simeq$50 $\mu$V/K. Single crystals of PtSn${}_4$ exhibit very large transverse magnetoresistance of $\simeq$$5\times {10}^5$% for the ac plane and of $\simeq$$1.4\times {10}^5$% for the b axis resistivity at 1.8 K and 140 kOe, as well as pronounced Shubnikov de Haas oscillations. The magnetoresistance of PtSn${}_4$ appears to obey Kohler's rule in the temperature and field range measured. The Hall resistivity shows a linear temperature dependence at high temperatures followed by a sign reversal around 25 K which is consistent with thermoelectric power measurements. The observed quantum oscillations and band structure calculations indicate that PtSn${}_4$ has three-dimensional Fermi surfaces.

Figure 1

(a) Crystal structure of PtSn${}_4$, along the b axis showing Sn-Pt-Sn layers. (b) Photo of a representative single crystal over a millimeter grid. The b axis is perpendicular to the plate.

Figure 2

Observed and calculated x-ray powder patterns of PtSn${}_4$. The open circles represent the observed data points and the solid line represents the calculated pattern. Representative ($hkl$) values are indicated.

Figure 3

Temperature dependence of the specific heat $C_P$ of PtSn${}_4$ in $H=0$ (open circle) and 140 kOe (solid line). (Inset) $C_p/T$ vs $T^2$ plot. Horizontal arrow in the upper right corner indicates the classical limit of the Dulong-Petit law.

Figure 4

(a) Temperature-dependent $M\left(T\right)/H$ of PtSn${}_4$ for H $\parallel$ b, H $\perp$ bI, and H $\perp$ bII. (Inset) Low-temperature $M\left(T\right)/H$ for H $\parallel$ b. (b) Magnetization isotherms of PtSn${}_4$ for H $\parallel$ b, H $\perp$ bI, and H $\perp$ bII at 1.8 K.

Figure 5

Zero-field electrical resistivity of PtSn${}_4$ for three samples. The current I was applied parallel to the plane of longer axis (I $\perp$ bI) and shorter axis (I $\perp$ bII). Inset shows the low-temperature resistivity. For details see text.

Figure 6

Resistivity measurements as a function of temperature and field on PtSn${}_4$ single crystals. Temperature-dependent resistivity for (a) an applied field along the ac plane (H $\perp$ b) and (b) along the b axis (H $\parallel$ b). Insets (a) and (b) are as follows: $\rho \left(T\right)$ vs log($T$) plot. Magnetic field-dependent resistivity $\Delta \rho /\rho \left(0\right)$ for (c) H $\perp$ b and (d) H $\parallel$ b at $T=1.8$, 3, 5, 7, 10, 15, 20, 25, 30, 50, 100, 200, and 300 K (top to bottom). Insets (c) and (d) are as follows: $\Delta \rho /\rho \left(0\right)$ at $T=100$, 200, and 300 K. The electrical current was applied in the ac plane (I $\perp$ b) for all measurements.

Figure 7

(a) Hall resistivity (${\rho }_H$) of PtSn${}_4$ measured at $T=100$, 150, 200, 250, 300, and 50 K (top to bottom) and $T=1.8$, 5, 10, 15, 20, and 25 K (bottom to top). (b) Hall coefficient, $R_H={\rho }_H/H$, of PtSn${}_4$ at $H=50$, 100, and 140 kOe. Solid lines are obtained from the temperature dependence of ${\rho }_H$ and solid symbols are taken from the field dependence of ${\rho }_H$. Inset shows $R_H$ at low temperatures. The electrical current was applied in the ac plane (I $\perp$ b) and the magnetic field was applied along the b axis (H $\parallel$ b) for all measurements.

Figure 8

(a) Temperature-dependent thermoelectric power (TEP, $S$) of PtSn${}_4$ at $H=0$, 70, and 140 kOe. Inset shows zero-field TEP. (b) Magnetic field dependence of the TEP of PtSn${}_4$ at $T=2.4$ K, showing quantum oscillation for $H>$ 20 kOe. Inset shows the TEP at $T=2.4$, 5, and 15 K. The magnetic field was applied along the b axis (H $\parallel$ b) and the temperature difference across the sample was generated in the ac plane ($\Delta T$ $\perp$ b) for all measurements.

Figure 9

(a) Electrical resistivity and (b) Hall resistivity as a function of field at 1.8 and 300 K for H $\parallel$ b. Solid lines are fits to the data using two-band model (see text for details). (c) Electron (squares) and hole (circles) concentrations as a function of temperature, as determined from a two-band model fit to electrical resistivity and Hall resistivity. (d) Ratio (${\mu }_e/{\mu }_h$) between the hole and electron mobility as a function of temperature, as determined from the two-band model fit. Lines in (c) and (d) are guides to the eye.

Figure 10

Hall coefficient ($R_H$, left axis), TEP [$S\left(T\right)/T$, right axis], and resistivity [$d\rho \left(T\right)/dT$, inset] of PtSn${}_4$ as a function of temperature. Vertical arrows indicate the sign reversal temperature corresponding to $R_H=0$ and $S\left(T\right)/T=0$.

Figure 11

A Kohler plot for PtSn${}_4$ using $\Delta \rho /\rho \left(0\right)=F[H/\rho \left(0\right)]\simeq H^{1.8}$. Inset shows a Kohler plot at high temperatures for H $\perp$ b.

Figure 12

(a) Magnetization isotherms of PtSn${}_4$ at $T=1.8$ K for three different orientations, plotted as a function of $1/H$. Inset shows a magnetization isotherm at 20 K for H $\parallel$ b. (b) FFT spectra of dHvA data for three different orientations. (c) Resistivity of PtSn${}_4$ at 1.8, 5, and 10 K for H $\parallel$ b. (d) FFT spectra of SdH data at $T=1.8$ K. Inset shows the FFT spectra in the high frequency region. (e) TEP of PtSn${}_4$ at $T=2.4$ K for H $\parallel$ b. Inset shows the TEP in the high field region. (f) FFT spectra of TEP data at $T=2.4$ K. Inset shows the FFT spectra in the high frequency region.

Figure 13

FFT spectra of the dHvA, SdH, and TEP data. Vertical arrows are guides to the eye.

Figure 14

Temperature dependence of the dHvA and SdH amplitudes. Solid lines represent the fit to the Lifshitz-Kosevich formula.

Figure 15

The theoretically calculated Fermi surface of PtSn${}_4$.