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Bulletin of the American Physical Society

Random Bonds Effects in the Spin-$\frac{1}{2}$ Heisenberg Antifferomagnet on the Square Lattice

Nicolas Laflorencie, Stefan Weßel, Andreas Martin Läuchli, Heiko Rieger

Published Mar 23, 2005• 0 citations
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Bond Randomness Effect in Frustrated Quantum Antiferromagnets

Masari Watanabe

In frustrated magnets, the experimental realization of a quantum disordered ground state (QDGS), especially quantum spin liquid (QSL) ground state, is a central topic in condensed matter physics.Several promising candidates were reported, and a number of QSL-like behavior, such as excitation continuum, Tlinear specific heat, and so on, were observed.However, whether the QSL-like behavior is owing to the synergy between spin frustration and quantum fluctuation or bond randomness effects has not been clarified yet.Several theoretical studies have demonstrated that the synergy effect between the magnetic frustration and the bond randomness suppresses magnetic ordering and induces a QSL-like state.This QSL-like state was proposed to be a random-singlet (RS) state, where not only nearest-neighbor spins but also distant spins form singlet pairs with random coupling energy.Since thermodynamic properties of RS and QSL are predicted to be similar to each other, it is important to elucidate the microscopic nature of randomness-induced QDGSs.However, its experimental verifications are still insufficient due to a lack of model materials.In this work, I synthesized polycrystalline samples of SrLaCuSbO 6 (SLCSO) and SrLaCuNbO 6 (SLCNO) by a solid-state reaction.Magnetic Cu 2+ ions with S = 1/2 Heisenberg spins form a square lattice with nearest-neighbor (J 1 ) and next-nearest-neighbor (J 2 ) exchange interaction.Thus, SLCSO and SLCNO were magnetically described as quasi-two-dimensional S = 1/2 J 1 -J 2 square lattice Heisenberg antiferromagnet (SLHAF).The temperature dependence of the magnetic susceptibilities of both compounds shows a broad maximum characteristic of an S = 1/2 SLHAF.However, both compounds undergo magnetic phase transitions at T N = 13.6 and 15.7 K for SLCSO and SLCNO, respectively, due to weak inter-layer interactions.Neutron powder diffraction measurements reveal contrasting spin structures in both compounds.The spin structures of SLCSO and SLCNO below T N are Néel antiferromagnetic and collinear antiferromagnetic, respectively.This result demonstrates that the nearest-neighbor interaction is dominant in SLCSO, whereas the next-nearest-neighbor interaction is dominant in SLCNO.The magnitude of the ordered moment was evaluated at 3.5 K to be m = 0.39(3) µ B for SLCSO and 0.37(1) µ B for SLCNO, which are significantly reduced from 1µ B expected in the classical spin case.The shrink of the ordered magnetic moment was caused by not only magnetic frustration effects but also bond randomness effects arising from the site disorder of Sr 2+ and La 3+ ions.Next, I synthesized the mixed system SrLaCuSb 1-x Nb x O 6 with 0.1 ≤ x ≤

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Effect of Bond Randomness on Two-Dimensional Spin-Gapped Heisenberg Antiferromagnet

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Phase diagram of the dodecahedron spin model on square lattice with diluted bonds

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Abstract We study the effect of bond dilution of a dodecahedron spin model on ferromagnetic square lattice. The dodecahedron spin constitutes a discrete (polyhedral) counterpart of the continuous Heisenberg spin. Previous work found that, in the absence of dilution, the ferromagnetic dodecahedron system exhibits a finite temperature phase transition. We use Monte Carlo simulation with Wolff cluster algorithm to monitor how phase transitions are impacted by the bond dilution. We simulate the model with various bond concentrations and investigate the resulting phase diagram and critical behavior.

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Novel constructive method for the quantum dimer model in spin-1/2 Heisenberg antiferromagnets with frustration on a diamond-like-decorated square lattice

Yuhei Hirose, Akihide Oguchi, Masafumi Tamura +1 more

We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice. The diamond-like-decorated square lattice is a lattice in which the bonds in a square lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the diagonal bond strength to that of the other four edges controls the frustration strength. For 0.974 < λ < 2, the present system has a nontrivial macroscopic degeneracy, which is called the macroscopically degenerated tetramer-dimer (MDTD) states. The MDTD states are identical to the Hilbert space of the Rokhsar–Kivelson (RK) quantum dimer model (QDM). By introducing further neighbor couplings in the MDTD states, we calculate the second-order effective Hamiltonian, which is exactly the same as the square-lattice QDM with a finite hopping amplitude t and dimer-dimer interaction v. Furthermore, we calculate v/|t| as a function of the ratio λ in the Heisenberg model and examine which phases of the square-lattice QDM appear in our obtained states. Our obtained QDM has a region where λ exhibits a finite hopping amplitude (|t| > 0) and repulsive interaction between dimers (v > 0). This suggests the possibility of realizing the resonating valence bond (RVB) state because the RVB state is obtained at v = |t|, which is known as the RK point.

arXiv:1809.08558•AIP Advances•Sep 10, 2018•4 citations
Random Bonds Effects in the Spin-12\frac{1}{2}21​ Heisenberg Antifferomagnet on the Square Lattice
In frustrated magnets, the experimental realization of a quantum disordered ground state (QDGS), especially quantum spin liquid (QSL) ground state, is a central topic in condensed matter physics.Several promising candidates were reported, and a number of QSL-like behavior, such as excitation continuum, Tlinear specific heat, and so on, were observed.However, whether the QSL-like behavior is owing to the synergy between spin frustration and quantum fluctuation or bond randomness effects has not been clarified yet.Several theoretical studies have demonstrated that the synergy effect between the magnetic frustration and the bond randomness suppresses magnetic ordering and induces a QSL-like state.This QSL-like state was proposed to be a random-singlet (RS) state, where not only nearest-neighbor spins but also distant spins form singlet pairs with random coupling energy.Since thermodynamic properties of RS and QSL are predicted to be similar to each other, it is important to elucidate the microscopic nature of randomness-induced QDGSs.However, its experimental verifications are still insufficient due to a lack of model materials.In this work, I synthesized polycrystalline samples of SrLaCuSbO 6 (SLCSO) and SrLaCuNbO 6 (SLCNO) by a solid-state reaction.Magnetic Cu 2+ ions with S = 1/2 Heisenberg spins form a square lattice with nearest-neighbor (J 1 ) and next-nearest-neighbor (J 2 ) exchange interaction.Thus, SLCSO and SLCNO were magnetically described as quasi-two-dimensional S = 1/2 J 1 -J 2 square lattice Heisenberg antiferromagnet (SLHAF).The temperature dependence of the magnetic susceptibilities of both compounds shows a broad maximum characteristic of an S = 1/2 SLHAF.However, both compounds undergo magnetic phase transitions at T N = 13.6 and 15.7 K for SLCSO and SLCNO, respectively, due to weak inter-layer interactions.Neutron powder diffraction measurements reveal contrasting spin structures in both compounds.The spin structures of SLCSO and SLCNO below T N are Néel antiferromagnetic and collinear antiferromagnetic, respectively.This result demonstrates that the nearest-neighbor interaction is dominant in SLCSO, whereas the next-nearest-neighbor interaction is dominant in SLCNO.The magnitude of the ordered moment was evaluated at 3.5 K to be m = 0.39(3) µ B for SLCSO and 0.37(1) µ B for SLCNO, which are significantly reduced from 1µ B expected in the classical spin case.The shrink of the ordered magnetic moment was caused by not only magnetic frustration effects but also bond randomness effects arising from the site disorder of Sr 2+ and La 3+ ions.Next, I synthesized the mixed system SrLaCuSb 1-x Nb x O 6 with 0.1 ≤ x ≤
Abstract We study the effect of bond dilution of a dodecahedron spin model on ferromagnetic square lattice. The dodecahedron spin constitutes a discrete (polyhedral) counterpart of the continuous Heisenberg spin. Previous work found that, in the absence of dilution, the ferromagnetic dodecahedron system exhibits a finite temperature phase transition. We use Monte Carlo simulation with Wolff cluster algorithm to monitor how phase transitions are impacted by the bond dilution. We simulate the model with various bond concentrations and investigate the resulting phase diagram and critical behavior.
We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice. The diamond-like-decorated square lattice is a lattice in which the bonds in a square lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the diagonal bond strength to that of the other four edges controls the frustration strength. For 0.974 < λ < 2, the present system has a nontrivial macroscopic degeneracy, which is called the macroscopically degenerated tetramer-dimer (MDTD) states. The MDTD states are identical to the Hilbert space of the Rokhsar–Kivelson (RK) quantum dimer model (QDM). By introducing further neighbor couplings in the MDTD states, we calculate the second-order effective Hamiltonian, which is exactly the same as the square-lattice QDM with a finite hopping amplitude t and dimer-dimer interaction v. Furthermore, we calculate v/|t| as a function of the ratio λ in the Heisenberg model and examine which phases of the square-lattice QDM appear in our obtained states. Our obtained QDM has a region where λ exhibits a finite hopping amplitude (|t| > 0) and repulsive interaction between dimers (v > 0). This suggests the possibility of realizing the resonating valence bond (RVB) state because the RVB state is obtained at v = |t|, which is known as the RK point.