Superlinear Temperature-Dependent Resistivity and Structural Phase Transition in BaNi$_2$P$_4$

Abstract

The mechanism of anomalous superlinear temperature-dependent resistivity, $ρ(T)$, in the metallic unconventional clathrate BaNi$_2$P$_4$ was studied by examining its evolution with artificial disorder induced by low-temperature ($\sim$ 20 K) 2.5 MeV electron irradiation. We find a dominant effect of the tetragonal-orthorhombic transition at $T_s$ ($ \sim$373 to 378 K, depending on heat cycle rate and direction) on $ρ(T)$, with standard metallic $T-$linear resistivity above the transition and anomalous behavior in the orthorhombic phase below. The transition is accompanied by the formation of structural domains and a notable (about 4~K) hysteresis in the magnetization and resistivity measurements, clearly showing its first order character. Matthiessen rule is obeyed both above and below the transition, suggesting negligible changes in the electronic structure. This conclusion is supported by the smooth evolution of the Hall effect through the transition. The Hall number is in good agreement with band structure calculations both above and below the transition. The transition temperature is notably suppressed with electron irradiation. Raman scattering at temperatures above room temperature find softening of local Ba vibration mode in the orthorhombic phase on approaching the transition. $^{31}P$ NMR line splits in the orthorhombic phase, suggesting a partial shift of the Ba atom from the central position in the cage. We suggest that local Ba rattling leads to enhanced residual contribution to resistivity in the high temperature tetragonal phase, the decay of which is responsible for the anomalous temperature-dependent resistivity in the orthorhombic phase.

Figures (15)

• Figure 1: Universal scaling of electrical resistivity of conventional metals with the Debye temperature Bardeen1940. The plot presents electrical resistivity data for silver, copper and aluminum using normalized resistivity, $\rho/\rho(\Theta_D$), and temperature, $T/\Theta_D$, scales. The right triangles show resistivity data for clathrate BaCu$_2$P$_4$, following generic metallic behavior. Red curve shows the data for BaNi$_2$P$_4$ strongly deviating from the normal metallic temperature dependence.
• Figure 2: Polarized optics image of the orthorhombic domains in the crystal of BaNi$_2$P$_4$ at room temperature (left panel). Domains are seen as bright stripes crossing through the terraces on sample surface. On warming to the temperatures ($\sim$450 K) higher that structural transition temperature(376 K), the domains disappear leaving terraces unaffected (right panel).
• Figure 3: Temperature-dependent magnetic susceptibility of BaNi$_2$P$_4$$\Delta M/ \Delta H$= ($M_1$-$M_2$)/ ($H_1$- $H_2$), where $H_1$ = 70 kOe, $H_2$ = 25 kOe (left scale, see first for more details). Main panel shows zoom of the transition region measured on heating (cyan) and cooling (blue) in magnetization measurements revealing notable hysteresis. High temperature data were taken both on warming and on cooling using 1 K/min heating/cooling rate. Red and orange lines are from resistivity measured on warming and cooling using the same protocol (right scale). Inset shows the magnetization data over the whole temperature range, including the low temperature data reported in Ref. first.
• Figure 4: Top panel. Variation of the temperature-dependent resistivity, $\rho (T)$, of BaNi$_2$P$_4$ with controlled disorder. Black symbols represent the data in pristine state, red solid dots are after 3.1 C/cm$^2$. When the temperature of irradiated sample rises above 300 K, sample annealing starts (open red diamonds). The resistivity transients to a new value depending on the highest temperature reached. The $\rho(T)$ after 400 K annealing is stable (open blue up-triangles). The black dotted line is linear fit through the $\rho(T)$ above the structural transition in the pristine state. Both linear behavior of resistivity and extrapolation to positive temperatures are in line with expectations for a good metal, see Fig. \ref{['fig:DebyeTemp']}. Nearly parallel shift with respect to the pristine sample is observed after annealing. The bottom right inset in the top panel shows zoom of the temperature-dependent resistivity derivative in the transition area with stars highlighting the $T_s$ position (reproduced in the main panel) and its shift in response to disorder. The left top inset in the top panel shows a comparison between the resistivity behavior of BaNi$_2$P$_4$ (black open circles) and BaCu$_2$P$_4$ (green solid circles). Bottom left panel shows defects creation cross-sections for Ba (top black curve), Ni (red curve) and P (blue curve) in BaNi$_2$P$_4$ as function of electron energy assuming the displacement energy threshold, $E_d=25~\mathrm{eV}$. Bottom right panel shows variation of the structural transition temperature with resistivity of the sample immediately above the transition, used as a proxy for sample disorder level.
• Figure 5: Temperature-dependent Hall effect measured in two samples of BaNi$_2$P$_4$ (red solid circles and black solid up-triangles), no change of the Hall constant on crossing $T_s$ (vertical dashed line) beyond approximately 10% uncertainty of the Hall effect measurements. Thicker and thinner gray lines show Hall effect in the tetragonal and orthorhombic phases from the calculated band structure assuming constant scattering rate. The effect of the transition at $T_s$ is negligible and well below error bars of the measurements. Right inset shows comparisons of the temperature dependent resistivity of BaNi$_2$P$_4$ (red curve), of the anomalous charge density wave material TaSe$_2$ (black curve) (from Ref.Naito1982) and of ferromagnetic LaCrGe$_3$ (green symbols, after LaCrGe3), using normalized resistivity, $\rho/\rho(T^*)$ and temperature $T/T^*$ scales. Despite close resemblance of the resistivity curves for BaNi$_2$P$_4$ and TaSe$_2$, the two compounds find quite different temperature dependent Hall effect (shown for TaSe$_2$ in the left inset).