Quantum phase near the saturation field in the $S=\frac{1}{2}$ frustrated spin ladder

We present low-temperature specific heat and magnetization measurements of the $S$ = 1/2 organic spin ladder 3-I-V [3-(3-iodophenyl)-1,5-diphenylverdazyl]. $Abinitio$ molecular orbital calculations indicate the existence of an intraladder diagonal interaction $J_{\mathrm{diag}}$ and three types of interladder interactions. The ferromagnetic $J_{\mathrm{diag}}$ induces frustration in the spin ladder, which has an essential contribution to the ground state. The obtained phase diagram exhibits a low-field three-dimensional order and a nontrivial phase near the saturation field. The absence of successive phase transition with decreasing temperature and the anomalous behavior of the magnetization curve near the saturation field suggest that these two phases are longitudinal spin-density-wave and spin-multipolar orders, respectively.

Figure 1

(a) The molecular structure of 3-I-V and (b) its spin-density distribution. Purple and green shapes correspond to positive and negative spin densities, respectively. The isodensity surface corresponds to a cutoff value of 0.001 e ${\mathrm{bohr}}^{-3}.$ (c) Crystal structure around the molecule labeled ${\mathrm{M}}_0.$ Molecular pairs associated with the magnetic interactions (d) $J_{\mathrm{diag}}$, (e) $J_1$, (f) $J_2$, and (g) $J_3$.

Figure 2

(a) Frustrated spin ladder formed by $J_{\mathrm{leg}},J_{\mathrm{rung}}$ and the additional $J_{\mathrm{diag}}$ for 3-I-V. (b, c) The 3D lattices connected by the interladder interactions $J_1,J_2$, and $J_3$ viewed along (b) the leg and (c) the rung directions for 3-I-V. The shadowed plane in each figure shows one of the interladder triangular units, causing frustration.

Figure 3

Temperature dependence of (a) magnetic susceptibility $\chi$ and (b) total specific heat $C$ in the low-temperature regions at various magnetic fields. The inset shows magnetic field dependence of $C$ at 0.2 K. For clarity, $\chi$ for 3.5, 4.0, 4.5, and 5.0 T and $C$ for 1.0, 2.0, 3.0, 4.0, and 5.0 T have been shifted up by 0.003, 0.005, 0.009, and 0.015 emu/mol and 1.0, 2.0, 4.0, 6.0, and 7.5 J/mol K, respectively.

Figure 4

Magnetic field vs temperature phase diagram showing the 3D order phase and nontrivial phase near the saturation field. The circles, triangles, and squares indicate the phase boundaries determined from the specific heat, the magnetic susceptibility, and the magnetization curve, respectively.

Figure 5

(a) Magnetization curves at various temperatures. The inset shows those for 0.5 and 4.2 K with the calculated results shown by the solid lines. (b) Field derivative of the magnetization curve. The inset shows an expansion near the saturation field. The broken lines and arrows indicate the linear extrapolations and their intersection points, respectively. For clarity, the values of the vertical axes have been shifted arbitrarily.