Field-Induced Tomonaga-Luttinger Liquid Phase of a Two-Leg Spin-1/2 Ladder with Strong Leg Interactions

We study the magnetic-field-induced quantum phase transition from a gapped quantum phase that has no magnetic long-range order into a gapless phase in the spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY). At temperatures below about 1 K, the specific heat in the gapless phase attains an asymptotic linear temperature dependence, characteristic of a Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat measurements in both phases are in good agreement with theoretical calculations, demonstrating that DIMPY is the first model material for an $S=1/2$ two-leg spin ladder in the strong-leg regime.

Figure 1

Dispersion measured by INS in DIMPY at $T=1.5\mathrm{K}$ as a function of $h$, $k$, and $l$. Lines in (a) and (b) indicate the gap energy. Lines in (c) are from PCUT calculations for an AFH two-leg spin ladder for different values of $x=J_{\mathrm{leg}}/J_{\mathrm{rung}}$.

Figure 2

(a) Background-subtracted constant-$\mathit{q}$ scan in DIMPY at the magnetic zone center (0.5,0,0.9) at $T=1.5\mathrm{K}$ for magnetic fields $H=0$, 5, 8, and 13.5 T. (b) Background-subtracted constant $\hslash \omega =0.7\mathrm{meV}$ scans along the ($h$,0,$1.7-1.44h$) direction at $T=1.5\mathrm{K}$ and $H=0$ and 5 T. The dotted line is a guide for the eye. In both frames, solid lines are fits to a dynamic spin correlation function with the approximate spin-gap dispersion relation [21], convolved with instrumental resolution, and dashed lines indicate zero.

Figure 3

Magnetic specific heat $C_m$ of DIMPY as a function of temperature $T$ for (a) $H<H_c$ and (b) $H>H_c$. In the latter region, the data have been plotted as $C_m/T$ after subtracting the nuclear-quadrupole contribution (see Ref. 27). $v_F$ is extracted from data between 0.3 K and the upper limit of the $T$-linear region, indicated by an arrow. Inset (1) Semilog plot of the $H<H_c$ data against $1/T$. Lines are fits to Eq. (1). Inset (2) Field dependence of the spin gap obtained from the data.

Figure 4

Field dependence of the Fermi velocity $v_F$ scaled with $J_{\mathrm{leg}}$. Filled symbols are DMRG results for $x=2.0$ and 2.5. Open symbols are from specific heat, scaled with $J_{\mathrm{leg}}=1.56\mathrm{meV}$ ($x=2.0$) and $J_{\mathrm{leg}}=1.95\mathrm{meV}$ ($x=2.5$), where $J_{\mathrm{leg}}$ for each $x$ has been found from calculated $\Delta /J_{\mathrm{rung}}$ (see the inset) and the spin gap $\Delta =0.32\mathrm{meV}$. For $x$ from 2.0 to 2.5, scaled experimental data lie in the shaded region.