Magnetic responses of randomly depleted spin ladders

Abstract

The magnetic responses of a spin-1/2 ladder doped with non-magnetic impurities are studied combining both analytical and numerical methods. The regime where frustration induces incommensurability is taken into account. Several improvements are made on the results of the seminal work by A. Furusaki, J. Phys. Soc. Jpn., 65, 2385 (1996)], and deviations from the Brillouin magnetization curve due to interactions are also analyzed. We first discuss the magnetic profile around a single impurity and the effective interactions between impurities within the bond-operator mean-field theory. The results are compared to density-matrix renormalization group calculations. In particular, these quantities are shown to be sensitive to the transition to the incommensurate regime. We then focus on the behavior of the zero-field susceptibility through an effective Curie constant. At zero-temperature, we give doping-dependent corrections to the results of Sigrist and Furusaki on general bipartite lattices, and compute exactly the distribution of ladder clusters due to chain breaking effects. Solving the effective model with exact diagonalization and quantum Monte-Carlo gives the temperature dependence of the Curie constant. Its high-temperature limit is understood within a random dimer model, while the low-temperature tail is compatible with a real-space renormalization group scenario. Interestingly, solving the full microscopic model does not show a plateau corresponding to the saturation of the impurities in isotropic ladders. The second magnetic response which is analyzed is the magnetic curve. Below fields of the order of the spin gap, the magnetization process is controlled by the physics of interacting impurity spins. The random dimer model is shown to capture the bulk of the curve, accounting for the deviation from a Brillouin behavior due to interactions. The effective model calculations agree rather well with density-matrix renormalization group calculations at zero temperature, and with quantum Monte-Carlo at finite temperature. In all, the effect of incommensurability does not display a strong qualitative effect on both the magnetic susceptibility and the magnetic curve. Consequences for experiments on the BiCu2PO6 compound and other spin-gapped materials are briefly mentioned.

Magnetic dimers and trimers in the disorderedS=32spin systemBaTi1/2Mn1/

“…Few examples of spin gap systems have been exhibited in the case of S = 3/2, among which RCrGeO 5 (R = Y or 154 Sm) have been recently confirmed as such by an investigation using inelastic neutron scattering [12]. Furthermore, in BaTi 1/2 Mn 1/2 O 3 the occupation of one of the transition-metal sites is suggested to be disordered [8], making the system also attractive due to the possibility of investigating the role of disorder in the physics of spin-gap systems [13,14]. In addition, the structure allows the formation of magnetic trimers arXiv:1206.3813v5 [cond-mat.str-el] 5 Jun 2015 which, for an antiferromagnetic exchange, will present a degenarate ground state, connecting the physics of spin gap and frustrated systems.…”

Emergent Interacting Spin Islands in a Depleted Strong-Leg Heisenberg Ladder

“…While deviations from the Brillouin function are small at low impurity concentrations, they become up to 45% at z = 0.06. Qualitatively, this is explained by the mean impurity distance L x (z) = (1 − z)/(2z − z 2 ) [26] which is as large as 50 unit cells for z = 0.01 but becomes comparable to the correlation length ξ ≈ 6.3 [24] at z = 0.06. The probability of finding close and strongly interacting islands thus rapidly increases with impurity concentration.…”

“…Following Ref. [26], we calculate the susceptibility and magnetization with Quantum Monte Carlo (QMC) simulations of ladder systems with L = 500 rungs, N = 2Lz randomly placed nonmagnetic sites and averaged over 300 random impurity configurations [27]. The numeric results (dashed lines in Fig.…”

Disorder-Induced Revival of the Bose-Einstein Condensation inNi(Cl1−xBrxDupont1, Capponi2, Laflorencie3 2017Phys. Rev. Lett.Self Cite145280View full textAdd to dashboardCite

“…In order to mimic the exponentially suppressed effective couplings combined with the random distribution of the distances between impurities in the original S = 1 problem, we follow Refs. [41,46] and generate random hoppings from the broad distribution P (t) ∼ t −1+1/δ , with t ≤ 2.2 K along the chains, and t ≤ 0.2 K in the transverse directions, δ being a phenomenological disorder parameter.…”

“…Using the above parameters, the localization length was determined to be very short [28], in units of lattice spacings ξ 0.48 along the chain and ξ ⊥ 0.17 in the transverse directions. Despite its random distribution in real space, this set of localized two-level systems is expected to experience an effective unfrustrated pair-wise coupling, exponentially suppressed with the distance [41][42][43][44][45][46], and their density is controlled by a chemical potential, proportional to the external field µ = gµ B (H − H * ). From such considerations, a minimal toy-model with hard-core bosons (HCB) would read:…”