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arXiv:2001.07970 · Physical review. B./Physical review. B

Magnetization plateaus of spin- 12 system on a 5/7 skewed ladder

Dayasindhu Dey, Sambunath Das, Manoranjan Kumar, S. Ramasesha

Published May 5, 2020• 13 citations
arXivHTMLPDF

Abstract

Magnetization plateaus are some of the most striking manifestations of frustration in low-dimensional spin systems. We present numerical studies of magnetization plateaus in the fascinating spin-1/2 skewed ladder system obtained by alternately fusing five- and seven-membered rings. This system exhibits three significant plateaus at $m=1/4$, 1/2, and 3/4, consistent with the Oshikawa-Yamanaka-Affleck condition. Our numerical as well as perturbative analysis shows that the ground state can be approximated by three weakly coupled singlet dimers and two free spins, in the absence of a magnetic field. With increasing applied magnetic field, the dimers progressively become triplets with large energy gaps to excited states, giving rise to stable magnetization plateaus. Finite-temperature studies show that $m=1/4$ and 1/2 plateaus are robust and survive thermal fluctuations while the $m=3/4$ plateau shrinks rapidly due to thermal noise. The cusps at the ends of a plateau follow the algebraic square-root dependence on $B$.

DOI
10.1103/physrevb.101.195110

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Magnetization plateaus are some of the most striking manifestations of frustration in low-dimensional spin systems. We present numerical studies of magnetization plateaus in the fascinating spin-1/2 skewed ladder system obtained by alternately fusing five- and seven-membered rings. This system exhibits three significant plateaus at m=1/4m=1/4m=1/4, 1/2, and 3/4, consistent with the Oshikawa-Yamanaka-Affleck condition. Our numerical as well as perturbative analysis shows that the ground state can be approximated by three weakly coupled singlet dimers and two free spins, in the absence of a magnetic field. With increasing applied magnetic field, the dimers progressively become triplets with large energy gaps to excited states, giving rise to stable magnetization plateaus. Finite-temperature studies show that m=1/4m=1/4m=1/4 and 1/2 plateaus are robust and survive thermal fluctuations while the m=3/4m=3/4m=3/4 plateau shrinks rapidly due to thermal noise. The cusps at the ends of a plateau follow the algebraic square-root dependence on BBB.
In this brief review, we introduce a new spin ladder system called skewed spin ladders and discuss the exotic quantum phases of this system. The spin ladders studied are the 5/7, 3/4 and 3/5 systems corresponding to alternately fused 5 and 7 membered rings; 3 and 4 membered rings; and 3 and 5 membered rings. These ladders show completely different behaviour as the Hamiltonian model parameter is changed. When the Hamiltonian parameter is increased the 5/7 ladder switches from an initial singlet ground state to progressively higher spin ground state and then to a reentrant singlet state before finally settling to the highest spin ground state whose spin equals the number of unit cells in the system. The 3/4 ladder goes from a singlet ground state to a high spin ground state with each unit cell contributing spin 1 to the state, as the model parameter is increased. The 3/5 ladder shows a singlet ground state for small parameters and high spin ground state for intermediate values of the parameter and for still higher parameters, a reentrant singlet ground state. They can also show interesting magnetization plateaus as illustrated by studies on a specific spin ladder.
We study the T=0T=0T=0 magnetization of frustrated two-leg spin ladders with arbitrary value of the spin SSS. In the strong-rung limit, we use degenerate perturbation theory to prove that frustration leads to magnetization plateaus at fractional values of the magnetization for all spins SSS and to determine the critical ratios of parallel to diagonal inter-rung couplings for the appearance of these plateaus. These ratios depend both on the plateau and on the spin. To confirm these results and to investigate the properties of these ladders away from the strong-coupling limit, we have performed extensive density-matrix renormalization-group calculations for $S\ensuremath{\le}2$. For large enough inter-rung couplings, all plateaus simply disappear, leading to a magnetization curve typical of integer-spin chains in a magnetic field. The intermediate region turns out to be surprisingly rich however, with, upon increasing the inter-rung couplings, the development of magnetization jumps and, in some cases, the appearance of one or more phase transitions inside a given plateau.
The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/21/21/2 ladder, and a two-legged spin-1/21/21/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ\mathrm{XXZ}XXZ spin-1/21/21/2 chain in a magnetic field; the second-order terms give corrections to the XXZ\mathrm{XXZ}XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.
The quantum phase transitions induced by a magnetic field are theoretically studied in a frustrated two-leg spin ladder. Using the density-matrix renormalization-group method, we find some magnetic phase transitions and plateaus in two different cases of strong and weak rung couplings. With the strong rung coupling, the three magnetization plateaus are found at 1/3, 1/2, and 2/3 due to the frustration. Those can be understood in terms of a quasispinon reconstructed from the singlet and the triplets of spins on a rung. The plateau at 1/2 corresponds to the valence bond solid of the quasispinons, while the plateaus at 1/3 and 2/3 can be associated with the array of quasispinons such as the soliton lattice. This is different from the usual Bose-Einstein-condensation picture of triplons. Our results will be useful in understanding magnetization curves in BiCu2PO6{\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}BiCu2​PO6​.
The magnetic phase diagram of a plaquette dimerized and frustrated antiferromagnetic ladder system is studied by using a combination of numerical and analytical techniques. For the strongly frustrated regime, series expansions and bond operator techniques are employed to analyze zero magnetic field, whereas low-energy effective models are used to study the complete magnetization process. The interplay between frustration and dimerization gives rise to a rich plateau structure that is captured by effective models and corroborated by numerical density matrix renormalization group simulations, in particular, the emergence of intermediate plateaus at M=14M=\frac{1}{4}M=41​ and 34\frac{3}{4}43​ of saturation in the magnetization curve is clarified.
The quantum phases in a spin-1 skewed ladder system formed by alternately fusing five- and seven-membered rings are studied numerically using the exact diagonalization technique up to 16 spins and using the density matrix renormalization group method for larger system sizes. The ladder has a fixed isotropic antiferromagnetic (AF) exchange interaction (J2=1{J}_{2}=1J2​=1) between the nearest-neighbor spins along the legs and a varying isotropic AF exchange interaction (J1{J}_{1}J1​) along the rungs. As a function of J1{J}_{1}J1​, the system shows many interesting ground states (gs) which vary from different types of nonmagnetic and ferrimagnetic gs. The study of various gs properties such as spin gap, spin-spin correlations, spin density, and bond order reveal that the system has four distinct phases, namely, the AF phase at small J1{J}_{1}J1​; the ferrimagnetic phase with gs spin SG=n{S}_{G}=nSG​=n for 1.44<J1<4.741.44<{J}_{1}<4.741.44<J1​<4.74 and with SG=2n{S}_{G}=2nSG​=2n for J1>5.63{J}_{1}>5.63J1​>5.63, where nnn is the number of unit cells; and a reentrant nonmagnetic phase at 4.74<J1<5.444.74<{J}_{1}<5.444.74<J1​<5.44. The system also shows the presence of spin current at specific J1{J}_{1}J1​ values due to simultaneous breaking of both reflection and spin parity symmetries.