Magnetic properties of the $S$=$\frac{5}{2}$ anisotropic triangular chain compound ${\mathrm{Bi}}_3{\mathrm{FeMo}}_2{\mathrm{O}}_{12}$

Competing magnetic interactions in low-dimensional quantum magnets can lead to the exotic ground state with fractionalized excitations. Herein, we present our results on an $S=\frac{5}{2}$ quasi-one-dimensional spin system ${\mathrm{Bi}}_3{\mathrm{FeMo}}_2{\mathrm{O}}_{12}$. The structure of ${\mathrm{Bi}}_3{\mathrm{FeMo}}_2{\mathrm{O}}_{12}$ consists of very well separated, infinite zigzag $S=\frac{5}{2}$ spin chains. The observation of a broad maximum around 10 K in the magnetic susceptibility $\chi \left(T\right)$ suggests the presence of short-range spin correlations. $\chi \left(T\right)$ data do not fit the $S=\frac{5}{2}$ uniform spin chain model due to the presence of second-nearest-neighbor coupling ($J_2$) along with the first-nearest-neighbor coupling ($J_1$) of the zigzag chain. The electronic structure calculations infer that the value of $J_1$ is comparable with $J_2$ ($J_2/J_1\approx 1.1$) with a negligible interchain interaction ($J^{\prime }/J\approx 0.01$) implying that ${\mathrm{Bi}}_3{\mathrm{FeMo}}_2{\mathrm{O}}_{12}$ is a highly frustrated triangular chain system. The absence of magnetic long-range ordering down to 0.2 K is seen in the heat-capacity data, despite a relatively large antiferromagnetic Curie-Weiss temperature ${\theta }_{CW}\approx –40$ K. The magnetic heat capacity follows nearly a linear behavior at low temperatures indicating that the $S=\frac{5}{2}$ anisotropic triangular chain exhibits the gapless excitations.

Figure 1

(a) Unit cell of ${\mathrm{Bi}}_3{\mathrm{FeMo}}_2{\mathrm{O}}_{12}$ [15]. (b) ${\mathrm{FeO}}_4$ tetrahedral units form the zigzag chain running along the $c$ axis. The first-NN Fe-Fe distance is 3.8 Å (with exchange coupling $J_1$) and second-NN Fe-Fe distance is 5.3 Å (with exchange coupling $J_2$).

Figure 2

Rietveld refinement of neutron diffraction (ND) data measured at different temperatures 50, 20, and 6 K are shown in (a), (b), and (c), respectively. Red circles represent the measured data ($I_{\mathrm{obs}}$), the black line represents the calculated diffraction pattern ($I_{\mathrm{cal}}$), the blue line represents the difference ($I_{\mathrm{obs}}-I_{\mathrm{cal}}$), and the green vertical lines represent the Bragg positions. (d) The ND intensities of 6 and 20 K after subtracting the ND intensities at 50 K.

Figure 3

(a) Temperature-dependent magnetic susceptibility from 2 to 300 K. The inset of (a) shows the ZFC and FC magnetic susceptibility data under 100 Oe field. (b) Magnetic isotherm measured at $T$ = 2 K with variation of field 160 kOe. The inset shows the comparison of experimental data with $S=\frac{5}{2}$ uniform spin chain simulation for $J/k_B\approx -1$ K.

Figure 4

Temperature-dependent heat-capacity $C_p\left(T\right)$ data of ${\mathrm{Bi}}_3{\mathrm{FeMo}}_2{\mathrm{O}}_{12}$ and ${\mathrm{Bi}}_3{\mathrm{GaMo}}_2{\mathrm{O}}_{12}$ with lattice part of the heat-capacity data (red) extracted from Debye fit. The observed lattice contribution of the nonmagnetic analog is extremely small at low temperatures, compared to the heat capacity of ${\mathrm{Bi}}_3{\mathrm{FeMo}}_2{\mathrm{O}}_{12}$. Inset shows the magnetic heat capacity $C_m$ (left) and normalized magnetic entropy $\mathrm{\Delta }{S}_m$ ( right) vs $T$.

Figure 5

$C_m/T$ vs $T$ plot. Inset shows $C_m/T$ vs $T^2$ with the comparison of linear and exponential curves.

Figure 6

Total and orbital-decomposed density of states (DOS) for the lowest energy magnetic state obtained using LSDA $+U$ with $U=3\mathrm{eV}$. Fermi energy is set to zero.