Magnetotransport in single-crystal half-Heusler compounds

We present the results of electrical resistivity and Hall effect measurements on single crystals of HfNiSn, TiPtSn, and TiNiSn. Semiconducting behavior is observed in each case, involving the transport of a small number of highly compensated carriers. Magnetization measurements suggest that impurities and site disorder create both localized magnetic moments and extended paramagnetic states, with the susceptibility of the latter increasing strongly with reduced temperature. The magnetoresistance is sublinear or linear in fields ranging from $0.01–9\mathrm{T}$ at the lowest temperatures. As the temperature increases, the normal quadratic magnetoresistance is regained, initially at low fields, and at the highest temperatures extending over the complete range of fields. The origin of the vanishingly small field scale implied by these measurements remains unknown, presenting a challenge to existing classical and quantum mechanical theories of magnetoresistance.

Figure 1

Electron backscattering images of as cast polycrystalline HfNiSn (a), and after annealing for $720\mathrm{h}$ at $1000°\mathrm{C}$ (b), and for $72\mathrm{h}$ at $1300°\mathrm{C}$ (c). The white lines in each panel indicate a length of $100\text{microns}$.

Figure 2

The temperature dependent resistivity $\rho$ for as cast polycrystalline HfNiSn (filled circles), annealed polycrystalline HfNiSn (open circles: $720\mathrm{h}$ at $1000°\mathrm{C}$; open squares: $72\mathrm{h}$ at $1300°\mathrm{C}$), and for a single crystal of HfNiSn (filled squares). Note that the resistivity of the HfNiSn single crystal has been divided by 25 for comparison to the polycrystalline samples.

Figure 3

(a) Temperature dependent resistivities of single crystal TiPtSn (filled circles), TiNiSn (stars), and HfNiSn (filled diamonds). (b) Activation plots for the same data. Dashed lines are activation fits over the indicated temperature ranges.

Figure 4

(a) Hall constants $R_H$ and (b) the corresponding single band electron concentrations $n$ for TiNiSn and TiPtSn single crystals. Solid lines indicate upper limit for $R_H$ and lower limit for $n$ for single crystal HfNiSn.

Figure 5

(a) Magnetization $M\left(H\right)$ of a HfNiSn polycrystal annealed at $1000°\mathrm{C}$ for $720\mathrm{h}$, and a TiNiSn single crystal (b). Note the large diamagnetic magnetization in (b), and the relatively much smaller diamagnetic contribution in (a), evident only in the $2\mathrm{K}M\left(H\right)$ curve above $3\mathrm{T}$.

Figure 6

Temperature dependence of the magnetization $M$ divided by a $1.5\mathrm{T}$ measuring field $H$ for polycrystalline HfNiSn, both as cast and annealed for $720\mathrm{h}$ at $1000°\mathrm{C}$, and for a single crystal of TiNiSn.

Figure 7

Magnetization sweeps, corrected for a linear diamagnetic susceptibility, collapse onto scaling curves as a function of $g{\mu }_{B}H∕k_{B}T$, for both polycrystalline HfNiSn (annealed at $1000°\mathrm{C}$ for $720\mathrm{h}$) and single crystal TiNiSn. The solid lines are $J=1∕2$ Brillouin functions.

Figure 8

(a) The temperature dependence of the diamagnetic susceptibility ${\chi }_0$ for annealed samples of polycrystalline HfNiSn (filled circles and open squares) and single crystal TiNiSn (open circles) Solid lines are power law fits, demonstrated in a double logarithmic plot in (b). The slopes of the power law fits to $\mid {\chi }_0\mid$ are 1.0 for one HfNiSn (filled circles) and TiNiSn, and 1.8 for the other HfNiSn polycrystalline sample (open squares).

Figure 9

The magnetoresistances of single crystals of HfNiSn [HfNiSn(3)], TiPtSn, and TiNiSn at $2\mathrm{K}$. For comparison, data are shown for polycrystalline samples of HfNiSn, both as-cast [HfNiSn(1)] and annealed for $720\mathrm{h}$ at $1000°\mathrm{C}$ [HfNiSn(2)]. The TiNiSn, TiPtSn, and polycrystalline HfNiSn data have all been offset for comparison.

Figure 10

The magnetoresistance $\mathrm{\Delta }\rho ∕\rho$ for single crystal HfNiSn at different fixed temperatures. The inset shows the same data for an expanded range of low fields. The 2 and $4\mathrm{K}$ data in the inset have been offset vertically for comparison.

Figure 11

The magnetoresistance of a single crystal of HfNiSn plotted as a function of the field squared at different temperatures. Vertical arrows indicate the highest field $H*$ at which quadratic field dependences are observed, and the dashed lines are linear fits to the data having $H⩽H*$.

Figure 12

$H*\left(T\right)$ defines a crossover from quadratic magnetoresistances at low fields to linear or sublinear magnetoresistance at high fields. $H*$ varies substantially among the different samples: Single crystal HfNiSn (filled circles), two different annealed polycrystalline HfNiSn samples (open circles, filled squares), and the corresponding two different as cast polycrystalline HfNiSn (filled diamonds, open squares), and single crystals of TiNiSn (filled triangles) and TiPtSn (open triangles).