Critical behavior of the metallic triangular-lattice Heisenberg antiferromagnet ${\text{PdCrO}}_2$

We report physical properties of the conductive magnet ${\text{PdCrO}}_2$ consisting of a layered structure with a triangular lattice of ${\text{Cr}}^{3+}$ ions $\left(S=3/2\right)$. We confirmed an antiferromagnetic transition at $T_{\text{N}}=37.5\text{K}$ by means of specific heat, electrical resistivity, magnetic susceptibility, and neutron-scattering measurements. The critical behavior in the specific heat persists in an unusually wide temperature range above $T_{\text{N}}$. This fact implies that spin correlations develop even at a much higher temperature than $T_N$. The observed sublinear temperature dependence of the resistivity above $T_{\text{N}}$ is also attributed to the short-range correlations among the frustrated spins. While the critical exponent for the magnetization agrees reasonably with the prediction of the relevant model, that for the specific heat evaluated in the wide temperature range differs substantially from the prediction.

Figure 1

(Color online) Crystal structure of ${\text{PdCrO}}_2$. This structure consists of alternating stacks of a triangular lattice of palladium and a triangular lattice of edge-shared ${\text{CrO}}_6$ octahedra. These drawings were produced using the software VESTA (Ref. 20).

Figure 2

(Color online) Temperature dependence of (a) the specific heat, (b) electrical resistivity, and (c) magnetic susceptibility of ${\text{PdCrO}}_2$. The antiferromagnetic transition gives rise to anomalies at $T_{\text{N}}=37.5\text{K}$ in all these quantities. The solid line in (a) represents the specific heat of the isostructural but nonmagnetic compound, ${\text{PdCoO}}_2$ (Ref. 25). The insets in (b) and (c) indicate the temperature derivatives of the resistivity and susceptibility. They exhibit a clear peak at $T_{\text{N}}$. Figure 2c includes results of both zero-field-cooling and field-cooling measurements of the magnetic susceptibility at 0.1 T.

Figure 3

(Color online) Temperature dependence of the magnetic specific heat of ${\text{PdCrO}}_2$. These data were obtained by subtracting the contribution of phonons and conduction electrons. The phononic contribution was estimated from the specific heat of isostructural but nonmagnetic ${\text{PdCoO}}_2$. The solid line is a fit to the data $\sim T^{2.0\pm 0.1}$ indicating a realization of the 2D-magnon excitation in an antiferromagnetically spin-ordered state. In the inset the temperature dependence of the magnetic specific heat divided by temperature $C_{\text{mag}}/T$ is shown. A sharp peak clearly indicates the transition at $T_{\text{N}}=37.5\text{K}$.

Figure 4

(Color online) Critical behavior of the magnetic specific heat. The temperature range in which the critical behavior is observed extends up to around $T/T_{\text{N}}-1=0.6$ (around 60 K). The critical exponents ${\alpha }^{\pm }$ are estimated as ${\alpha }^{+}=0.13\pm 0.02$ above $T_{\text{N}}$ and as ${\alpha }^{-}=0$ below $T_{\text{N}}$.

Figure 5

(Color online) Powder neutron-diffraction patterns obtained at 0.8, 10, 15, 20, and 45 K in zero field with the counting time of 60 s for each data point. The peak positions are indexed. The observed magnetic Bragg peaks are clearly broader than the instrument resolution. The diffuse scattering feature centered around $\theta \sim 32°$ remains visible above $T_{\text{N}}$. An impurity peak was detected at $2\theta =53°$ (see text).

Figure 6

(Color online) Temperature dependence of the peak intensity of the powder neutron diffraction at several $q$ positions. The counting time is 90 s except for $\mathit{q}=\left(\frac{1}{3},\frac{1}{3},4\right)$ for which it is 180 s. The dotted line indicates the background, $I_{\mathit{q}}^B=920\text{counts}/90\text{s}$. The curves represent the results of the fitting between 15 and 35 K with Eq. (3) for the peaks at $\mathit{q}=\left(\frac{1}{3},\frac{1}{3},0\right)$, $\left(\frac{1}{3},\frac{1}{3},1\right)$, and $\left(\frac{1}{3},\frac{1}{3},\frac{3}{2}\right)$. The resulting critical exponent lies within the value $\beta =0.18\pm 0.03$.