Degenerate ground state in the classical pyrochlore antiferromagnet ${\mathrm{Na}}_3\mathrm{Mn}{\left({\mathrm{CO}}_3\right)}_2\mathrm{Cl}$

In an ideal classical pyrochlore antiferromagnet without perturbations, an infinite degeneracy in a ground state leads to the absence of magnetic order and a spin-glass transition. Here we present ${\mathrm{Na}}_3\mathrm{Mn}{\left({\mathrm{CO}}_3\right)}_2\mathrm{Cl}$ as a new candidate compound where classical spins are coupled antiferromagnetically on the pyrochlore lattice and report its structural and magnetic properties. The temperature dependences of the magnetic susceptibility and heat capacity and the magnetization curve are consistent with those of an $S=5/2$ pyrochlore lattice antiferromagnet with nearest-neighbor interactions of 2 K. Neither an apparent signature of a spin-glass transition nor magnetic order is detected in magnetization and heat capacity measurements or powder neutron diffraction experiments. On the other hand, antiferromagnetic short-range order of the nearest neighbors is evidenced by the $Q$ dependence of the diffuse scattering which develops around $0.85{\AA }^{-1}$. A high degeneracy near the ground state in ${\mathrm{Na}}_3\mathrm{Mn}{\left({\mathrm{CO}}_3\right)}_2\mathrm{Cl}$ is supported by the magnetic entropy, estimated as almost $4\mathrm{J}{\mathrm{K}}^{-2}{\mathrm{mol}}^{-1}$ at 0.5 K.

Figure 1

Crystal structure of ${\mathrm{Na}}_3\mathrm{Mn}{\left({\mathrm{CO}}_3\right)}_2\mathrm{Cl}$. Mn, C, O, Na, and Cl atoms are represented by red, black, blue, dark yellow, and green ellipsoids, reflecting the atomic displacement parameters of each atom. (a) Arrangement of ${\mathrm{MnO}}_6$ octahedra in a unit cell. ${\mathrm{MnO}}_6$ octahedra are connected by carbonate ions, forming a pyrochlore network of Mn atoms. One of the tetrahedrons forming the pyrochlore lattice is indicated by dashed white lines. Na and Cl atoms are omitted for clarity. (b) Local structures around Mn and Cl atoms. The VESTA program is used for visualization [38].

Figure 2

Powder neutron diffraction pattern at 1.5 and 200 K collected by ECHIDNA together with Rietveld analysis. Total neutron counts are normalized by $1.5\times {10}^6$ ncu. Observed and calculated intensities and the difference between the intensities are shown by red points, black curves, and blue curves, respectively. Reflection positions for ${\mathrm{Na}}_3\mathrm{Mn}{\left({\mathrm{CO}}_3\right)}_2\mathrm{Cl}$ and ${\mathrm{MnCO}}_3$ expected at a wavelength of 2.4395 Å are indicated by the upper and lower vertical lines, respectively. Reflections from Al cryostats are removed from the figure.

Figure 3

(a) Temperature dependence of the magnetic susceptibility measured at 1 T (red curve) and 0.1 T (orange curve) with zero-field cooling. The blue curve indicates the inverse magnetic susceptibility. Dashed and dotted curves represent a fit to the [4, 4] Padé approximant for a high-temperature series expansion of a pyrochlore lattice [47] and a Curie-Weiss fit, respectively. (b) Magnetic susceptibility down to 0.6 K measured by the low-temperature probe after cooling in a field of 5 T that is then decreased to 0.1 T. (c) The ac susceptibility below 10 K.

Figure 4

Magnetization curves (top) and field derivative (bottom) measured at 0.5 K (red curve), 1.6 K (green curve), 3.0 K (blue curve), and 4.2 K (black curve). Curves measured at higher temperatures are shifted for clarity. Arrows indicate the time sequence of the magnetization process around a hysteresis loop.

Figure 5

(a) Temperature dependence of the heat capacity at 0 T. The solid black curve indicates the fit including both phonon and magnetic contributions, while the solid blue curve represents the phonon contribution estimated from the fit (see text for details). (b) Magnetic heat capacity at 0 T (filled circles) compared with that at 7 T (open squares). (c) Magnetic heat capacity divided by the temperature $C_{\mathrm{mag}}/T$ at 0 T. Inset: Enlarged view below 2 K. The dashed black line corresponds to the extension of $C_{\mathrm{mag}}/T$ below 0.5 K just for the estimation of the magnetic entropy. (d) Magnetic entropy determined from integrating $C_{\mathrm{mag}}/T$. The dashed black line in the inset in Fig. 5 leads to the estimate indicated by filled red circles. Dashed red curves are obtained by shifting the estimated entropy above so that they match the solid black curve, which indicates the magnetic entropy expected for a pyrochlore lattice with $J=2.0\mathrm{K}$. The error bar for the solid black curve corresponds to an entropy difference of 0.2 K in $J$.

Figure 6

(a) Neutron powder diffraction patterns measured at 0.05 K (red points) and 2 K (blue points) compared with simulated patterns (black points). Total neutron counts are normalized by $6.0\times {10}^5$ ncu. Vertical black lines indicate the positions of nuclear reflections. The lower panel indicates the intensity difference between the data at 0.05 K and those at 2 K. (b) Intensity difference between the data at 0.05 K and those at 2 K as a function of $Q$. Data points are binned to improve the statistics.

Figure 7

$Q$ dependence of the intensity measured at 1.5, 10, 50, and 200 K. Data points are binned to improve the statistics. Total counts are normalized by $1.5\times {10}^6$ ncu. Solid and dashed curves represent the fit for a pyrochlore antiferromagnet with NN interactions $\left(J=2\mathrm{K}\right)$ and that for a pyrochlore antiferromagnet with NN and NNN interactions $\left(J=2\mathrm{K},J^{\prime }=-0.4\mathrm{K}\right)$, respectively.