Multiple magnetization plateaus and magnetic structures in theS=12Heisenberg model on the checkerboard lattice

Abstract

We study the ground state of S = 1/2 Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group (DMRG) method with the sine-square deformation. We obtain magnetization plateaus at M/Msat =0, 1/4, 3/8, 1/2, and 3/4 where Msat is the saturated magnetization. The obtained 3/4 plateau state is consistent with the exact result, and the 1/2 plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the 1/3 plateau of the kagome lattice. Different four-spin loop structures are obtained in the 1/4 and 3/8 plateaus but no corresponding states exist in the kagome lattice. The 3/8 plateau has a unique magnetic structure of three types of four-spin local quantum states in a 4 √ 2 × 2 √ 2 magnetic unit cell with a 16-fold degeneracy.Frustrated quantum spin systems exhibit unusual quantum phenomena such as the formations of valence bond solid (VBS), spin-nematic, and quantum spin liquid (QSL) as a result of competing quantum fluctuations [1,2]. Application of an external magnetic field complicates the situation further with the increase in uniaxial anisotropy, and it sometimes leads to a phase transition to a stable quantum state with a jump or cusp in the magnetization curve at zero temperature. Recently observed 1/3 magnetization plateau in the triangular lattice of S = 1/2 quantum spins [3-5] is a typical example, in which up-up-down spin structure emerges with a finite excitation gap [6][7][8][9]. Similar 1/2 plateau is obtained in the J 1 -J 2 square lattice [9-11] and novel multiple magnetization plateaus are realized in the Shastry-Sutherland lattice [12][13][14][15]. In the kagome lattice, 0, 1/9, 1/3, 5/9, and 7/9 plateaus are predicted by the DMRG method with the sine-square deformation [16].The checkerboard lattice shown in Fig. 1 is another example of frustrated system and referred to as twodimensional pyrochlore lattice. Its classical ground state at zero magnetic field is obtained when the magnetic moments of four spins connected by diagonal interactions are canceled as shown in Fig. 2. This means the presence of a macroscopic degeneracy in the ground state as in the cases of the kagome lattice and the J 1 -J 2 square lattice at J 2 /J 1 = 0.5. In contrast, S = 1/2 quantum spins on the checkerboard lattice have stable quantum ground state as in the kagome lattice [16][17][18] and Shastry-Sutherland lattice [12][13][14][15]. Indeed previous studies on the checkerboard lattice indicate that the ground state is a plaquette valence-bond crystal (PVBC) with a large spin singlettriplet gap, ∆ st ≈ 0.6J [19,20] and the 3/4 plateau is realized just before the saturation magnetic field [21] as in the case of the 7/9 plateau in the kagome lattice [22].Although the ideal checkerboard lattice with only one exchange energy J has not been synthesized, similar model substances are present [23,24]. The checkerboard lattice is obtained by replacing the position of anions and cations in the CuO 2 -plane structure. When the nearest-neig...

Numerical study of magnetization plateaus in the spin- 12 Heisenberg antiferromagnet on the checkerboard lattice

“…Similar results for the bond pattern and the local magnetizations have been obtained in Ref. 25 using DMRG as well but with modified boundary conditions to minimize finite-size effects, at the cost of having to fix the magnetic field and not the total magnetization (grand-canonical approach). Both studies agree on the existence and nature of the plateaux phases at m=0, 1/4, 1/2 and 3/4.…”

Translation constraints on quantum phases with twisted boundary conditions

“…Taking advantage of the flux insertion argument, we discussed the groundstate degeneracy on magnetization plateaus of the S = 1/2 checkerboard Heisenberg antiferromagnet. While we explained the numerically found degeneracy on some plateaus at M/M sat = 0, 1/2, 3/8 [18,19], we could not on the plateaus at M/M sat = 1/4 and 3/4. We concluded in Sec.…”

“…Actually, the finitesize clusters used in Refs. [18] and [19] are incompatible with the tilted Klein-bottle boundary conditions because they are not the square defined in Eq. (16).…”

“…In addition, such an argument is attracting in its potential application to magnetization plateaus [16,17]. In fact, it was recently shown that the checkerboard Heisenberg antiferromagnet hosts numerous magnetization plateaus [18,19].…”

Magnetization jump in one dimensional J − Q 2 model with anisotropic exchange

“…One is the magnetization plateau, which usually accompanies with the spin excitation gap and has been found in many systems, such as the frustrated spin systems [3,4], and quasi-periodic systems with nontrivial topological property [5,6]. The other is the magnetization jump, which exhibits discontinuity in the magnetization density.The magnetization jump was first proposed by Néel [7] in the system with the Ising-like anisotropic exchange interaction, and then also investigated in various of lattice spin systems in different dimensions [8][9][10][11][12][13][14][15][16][17][18][19]. Most of these model systems involve anisotropy or frustration.…”