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arXiv:2409.19512 · Physical review. B./Physical review. B

Magnetic anisotropy effect on stabilizing magnetization plateaus of kagome strip chain Heisenberg antiferromagnets

Chiara Bruzzi, Jian‐Xin Zhu, Yixuan Huang

Published Jul 2, 2025• 0 citations

Abstract

We investigate the anisotropic effect of magnetization plateaus in the antiferromagnetic Heisenberg model on a kagome strip chain. The kagome strip chain Heisenberg model, composed of a hexagonal net of triangles forming five-site unit cells, exhibits four magnetization plateaus in the presence of an applied magnetic field. Using numerical density matrix renormalization group method, we find that the magnetization plateaus are stable against anisotropic interactions in the same direction of the applied magnetic field, but the plateaus become much smaller with anisotropic interactions in other directions. We further show the anisotropic effect of the magnon excitations of the 0.6 plateau state using linear spin wave theory. The magnon bandwidth remains small when tuning the anisotropic interactions along the field where the magnetization plateau is stable, while the band becomes more dispersive with anisotropic interactions perpendicular to the field. In addition, upon tuning down the interaction strength for the two lower legs below a critical value, the Hamiltonian of the kagome strip chain is dominated by two separate spin chains. This can be used to determine the effective lattice structure in materials with strong distortions. Our results enhance the theoretical understanding of the anisotropic effect and the nature of magnetization plateaus in kagome strip chain materials, which can contribute to the design and manipulation of kagome materials with tailored properties.

DOI: 10.1103/s99g-bf7t

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We investigate the anisotropic effect of magnetization plateaus in the antiferromagnetic Heisenberg model on a kagome strip chain. The kagome strip chain Heisenberg model, composed of a hexagonal net of triangles forming five-site unit cells, exhibits four magnetization plateaus in the presence of an applied magnetic field. Using numerical density matrix renormalization group method, we find that the magnetization plateaus are stable against anisotropic interactions in the same direction of the applied magnetic field, but the plateaus become much smaller with anisotropic interactions in other directions. We further show the anisotropic effect of the magnon excitations of the 0.6 plateau state using linear spin wave theory. The magnon bandwidth remains small when tuning the anisotropic interactions along the field where the magnetization plateau is stable, while the band becomes more dispersive with anisotropic interactions perpendicular to the field. In addition, upon tuning down the interaction strength for the two lower legs below a critical value, the Hamiltonian of the kagome strip chain is dominated by two separate spin chains. This can be used to determine the effective lattice structure in materials with strong distortions. Our results enhance the theoretical understanding of the anisotropic effect and the nature of magnetization plateaus in kagome strip chain materials, which can contribute to the design and manipulation of kagome materials with tailored properties.

The spin-

\frac{1}{2}

Heisenberg model on a kagome lattice is a typical frustrated quantum spin system. The basic structure of a kagome lattice is also present in the kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-

\frac{1}{2}

Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions using the density-matrix renormalization-group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking translational and/or reflection symmetry spontaneously. The structures are classified by an array of five-site unit cells with specific bond-spin correlations. In a case with a nontrivial plateau, namely a 3/10 plateau, we find long-period magnetic structure with a period of four unit cells.

We clarify the existence of several magnetization plateaus for the kagome

S=\frac{1}{2}

antiferromagnetic Heisenberg model in a magnetic field. Using approximate or exact localized magnon eigenstates, we are able to describe in a similar manner the plateau states that occur for magnetization per site

m=\frac{1}{3}

,

\frac{5}{9}

, and

\frac{7}{9}

of the saturation value. These results are confirmed using large-scale exact diagonalization on lattices up to 63 sites.

Theory of the

1/9

Magnetization Plateau of the Spin-

1/2

Kagome Heisenberg Antiferromagnet

We investigate the

1/9

magnetization plateau of the spin-

1/2

kagome Heisenberg antiferromagnet using infinite projected entangled-pair states and identify a spin-density-wave state with a

27

-site unit cell and a lower variational energy than previous approaches. In contrast to higher-magnetization plateaus, which are well described by localized magnons on nonoverlapping hexagons and preserve a sixfold rotational symmetry, the

1/9

plateau only keeps a threefold rotational symmmetry and consists of a tiling by three types of

9

-site clusters related by

\pm2π/3

rotations. These conclusions are supported by a complementary cluster mean-field theory which correctly preserves the symmetry of the higher plateaus but leads to the same spontaneous symmetry breaking for the

1/9

plateau with a qualitatively similar pattern of nine different local magnetizations.

We study the ground state of the

S=\frac{1}{2}

Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group method with the sine-square deformation. We obtain magnetization plateaus at

M/{M}_{\mathrm{sat}}=0,\frac{1}{4},\frac{3}{8},\frac{1}{2}

, and

\frac{3}{4}

, where

{M}_{\mathrm{sat}}

is the saturated magnetization. The obtained

\frac{3}{4}

plateau state is consistent with the exact result, and the

\frac{1}{2}

plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the

\frac{1}{3}

plateau of the kagome lattice. Different four-spin loop structures are obtained in the

\frac{1}{4}

and

\frac{3}{8}

plateaus but no corresponding states exist in the kagome lattice. The

\frac{3}{8}

plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\ifmmode\times\else\texttimes\fi{}2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.

We investigate the spin-1 kagome-lattice Heisenberg antiferromagnet using large-scale Lanczos diagonalization and the finite-temperature Lanczos method. The zero-temperature magnetization process exhibits plateaus at m = 0 , 1 / 3 , 7 / 9 , and 8 / 9 , where m is the normalized magnetization. The m = 0 plateau is identified as a trimer valence-bond-crystal state, while the high-field plateaus at m = 7 / 9 and 8 / 9 are identified as magnon crystals. In particular, the m = 8 / 9 plateau corresponds to the exact localized-magnon crystal state. A smoothed zero-temperature magnetization curve constructed using the Gaussian-kernel smoothing method indicates magnetization jumps at the lower-field edge of the m = 1 / 3 plateau and at the upper-field edges of the m = 7 / 9 and 8 / 9 plateaus. At finite temperatures, the specific heat exhibits a double-peak structure with peaks around T / J ≃ 0.1 and T / J ≃ 1.1 , and the low-temperature peak may be related to trimer valence-bond-crystal ordering. The finite-temperature magnetization curves show that the m = 1 / 3 plateau remains visible at low temperatures, whereas the high-field plateaus are rapidly smeared out by thermal effects. These results provide benchmark data for thermodynamic and high-field magnetization measurements in candidate spin-1 kagome-lattice materials.

By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J

^{\prime}

quantum Heisenberg chains with spin

S=1/2

, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when

J

is antiferromagnetic and

J^{\prime}

is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when

% J^{\prime}/J

passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when

J

is ferromagnetic and

J^{\prime}

is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J $ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.