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Register a new userModeling the spin-Peierls transition of spin-$1/2$ chains with correlated states: $J_1-J_2$ model, CuGeO$_3$ and TTF-CuS$_4$C$_4$(CF$_3$)$_4$
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The spin-Peierls transition at $T_{SP}$ of spin-$1/2$ chains with isotropic exchange interactions has previously been modeled as correlated for $T > T_{SP}$ and mean field for $T < T_{SP}$. We use correlated states throughout in the $J_1-J_2$ model with antiferromagnetic exchange $J_1$ and $J_2 = alpha J_1$ between first and second neighbors, respectively, and variable frustration $0 leq alpha leq 0.50$. The thermodynamic limit is reached at high $T$ by exact diagonalization of short chains and at low $T$ by density matrix renormalization group calculations of progressively longer chains. In contrast to mean field results, correlated states of 1D models with linear spin-phonon coupling and a harmonic adiabatic lattice provide an internally consistent description in which the parameter $T_{SP}$ yields both the stiffness and the lattice dimerization $delta(T)$. The relation between $T_{SP}$ and $Delta(delta,alpha)$, the $T = 0$ gap induced by dimerization, depends strongly on $alpha$ and deviates from the BCS gap relation that holds in uncorrelated spin chains. Correlated states account quantitatively for the magnetic susceptibility of TTF-CuS$_4$C$_4$(CF$_3$)$_4$ crystals ($J_1 = 79$ K, $alpha = 0$, $T_{SP} = 12$ K) and CuGeO$_3$ crystals ($J_1 = 160$ K, $alpha = 0.35$, $T_{SP} = 14$ K). The same parameters describe the specific heat anomaly of CuGeO$_3$ and inelastic neutron scattering. Modeling the spin-Peierls transition with correlated states exploits the fact that $delta(0)$ limits the range of spin correlations at $T = 0$ while $T > 0$ limits the range at $delta= 0$.
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The spin-Peierls transition is modeled in the dimer phase of the spin-$1/2$ chain with exchanges $J_1$, $J_2 = alpha J_1$ between first and second neighbors. The degenerate ground state generates an energy cusp that qualitatively changes the dimerization $delta(T)$ compared to Peierls systems with nondegenerate ground states. The parameters $J_1 = 160$ K, $alpha = 0.35$ plus a lattice stiffness account for the magnetic susceptibility of CuGeO$_3$, its specific heat anomaly, and the $T$ dependence of the lowest gap.
K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ is a highly one-dimensional spin-1/2 inequilateral diamond-chain antiferromagnet. Spinon continuum and spin-singlet dimer excitations are observed in the inelastic neutron scattering spectra, which is in excellent agreement with a theoretical prediction: a dimer-monomer composite structure, where the dimer is caused by strong antiferromagnetic (AFM) coupling and the monomer forms an almost isolated quantum AFM chain controlling low-energy excitations. Moreover, muon spin rotation/relaxation spectroscopy shows no long-range ordering down to 90~mK, which is roughly three orders of magnitude lower than the exchange interaction of the quantum AFM chain. K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$ is, thus, regarded as a compound that exhibits a Tomonaga-Luttinger spin liquid behavior at low temperatures close to the ground state.
The site-diluted compound (Yb$_{1-x}$Lu$_x$)$_4$As$_3$ is a scarce realization of the linear Heisenberg antiferromagnet partitioned into finite-size segments and is an ideal model compound for studying field-dependent effects of quenched disorder in the one-dimensional antiferromagnets. It differentiates from the systems studied so far in two aspects - the type of randomness and the nature of the energy gap in the pure sample. We have measured the specific heat of single-crystal (Yb$_{1-x}$Lu$_x$)$_4$As$_3$ in magnetic fields up to 19.5 T. The contribution $C_{perp}$ arising from the magnetic subsystem in an applied magnetic field perpendicular to the chains is determined. Compared to pure Yb$_4$As$_3$, for which $C_{perp}$ indicates a gap opening, for diluted systems a non-exponential decay is found at low temperatures which is consistent with the thermodynamic scaling of the specific heat established for a Bose-glass phase.
We report results of magnetization and $^{31}$P NMR measurements under high pressure up to 6.4~GPa on RbMoOPO$_4$Cl, which is a frustrated square-lattice antiferromagnet with competing nearest-neighbor and next-nearest-neighbor interactions. Anomalies in the pressure dependences of the NMR shift and the transferred hyperfine coupling constants indicate a structural phase transition at 2.6~GPa, which is likely to break mirror symmetry and triggers significant change of the exchange interactions. In fact, the NMR spectra in magnetically ordered states reveal a change from the columnar antiferromagnetic (CAF) order below 3.3~GPa to the N{e}el antiferromagnetic (NAF) order above 3.9~GPa. The spin lattice relaxation rate $1/T_1$ also indicates a change of dominant magnetic fluctuations from CAF-type to NAF-type with pressure. Although the NMR spectra in the intermediate pressure region between 3.3 and 3.9 GPa show coexistence of the CAF and NAF phases, a certain component of $1/T_1$ shows paramagnetic behavior with persistent spin fluctuations, leaving possibility for a quantum disordered phase. The easy-plane anisotropy of spin fluctuations with unusual nonmonotonic temperature dependence at ambient pressure gets reversed to the Ising anisotropy at high pressures. This unexpected anisotropic behavior for a spin 1/2 system may be ascribed to the strong spin-orbit coupling of Mo-4$d$ electrons.
In this joint experimental and theoretical work magnetic properties of the Cu$^{2+}$ mineral szenicsite Cu$_3$(MoO$_4$)(OH)$_4$ are investigated. This compound features isolated triple chains in its crystal structure, where the central chain involves an edge-sharing geometry of the CuO$_4$ plaquettes, while the two side chains feature a corner-sharing zig-zag geometry. The magnetism of the side chains can be described in terms of antiferromagnetic dimers with a coupling larger than 200 K. The central chain was found to be a realization of the frustrated antiferromagnetic $J_1$-$J_2$ chain model with $J_1simeq 68$ K and a sizable second-neighbor coupling $J_2$. The central and side chains are nearly decoupled owing to interchain frustration. Therefore, the low-temperature behavior of szenicsite should be entirely determined by the physics of the central frustrated $J_1$-$J_2$ chain. Our heat-capacity measurements reveal an accumulation of entropy at low temperatures and suggest a proximity of the system to the Majumdar-Ghosh point of the antiferromagnetic $J_1$-$J_2$ spin chain, $J_2/J_1=0.5$.
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