Magnetic ground state of the frustrated honeycomb lattice antiferromagnet Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$)

Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$), in which the Mn${}^{4+}$ ions carry $S=3/2$, is the first honeycomb lattice system that shows no long-range magnetic ordering. We investigated the magnetic ground state of this compound by measuring magnetic susceptibility and μSR with a pure powder sample synthesized under an improved reaction condition. It was found that the system underwent a spin glass transition at 6 K in a zero magnetic field. A comparison of the temperature dependence of the magnetic susceptibility with the results of a Monte Carlo simulation suggests the importance of intra-bilayer coupling and further neighbor interactions beyond those of second neighbors.

Figure 1

The Mn-O network in a honeycomb layer (a) and the crystal structure of Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$) (b). Solid, dotted, and double lines show the position of the nearest ($J_1$), the next-nearest neighbor ($J_2$), and the opposite site ($J_3$) interactions. The face-to-face ($J_{\mathrm{c}}$) and the diagonal ($J_{\mathrm{c}}$′) intra-bilayer interactions are also indicated.

Figure 2

SXRD pattern of Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$) and the Rietveld refinement profile. The observed (dot), calculated (line), and difference (bottom line) patterns are shown. Bragg reflections are indicated by tick marks. Inset shows comparison of the SXRD patterns of the previous and present samples.

Figure 3

(a) Temperature dependence of the magnetic susceptibility of Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$) in zero field cooling and field cooling conditions. (b) Total specific heat divided by temperature of a solidified Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$) pellet. Insets show magnification of the data between 2 K and 12 K.

Figure 4

Temperature dependence of the in-phase (χ′) and the out-of-phase (χ′′) components of the AC susceptibility at 1 Hz.

Figure 5

μSR time spectra at 120 K in longitudinal magnetic fields up to 0.01 T. The solid curves represent the result of a fitting analysis by using the dynamic Kubo-Toyabe function.

Figure 6

μSR time spectra in a longitudinal field of 0.01 T at various temperatures between 2 to 50 K.

Figure 7

Temperature dependence of the initial asymmetry ($A_0$), relaxation rate (λ), and the power (β) in a longitudinal field of 0.01 T.

Figure 8

Comparison of the calculated and the experimental susceptibility of Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$). (a) $J_2/J_1$ dependence with $J_1=30.7$ K and $J_{\mathrm{c}}/J_1=0.0$ and (b) the results assuming various combinations of $J_2/J_1$, $J_{\mathrm{c}}/J_1$, and $J_1$. (c) Magnified view of (b).