Spin-lattice model of Magneto-electric Transitions in RbCoBr$_3$

Nakamura, Tota; Nishiwaki, Yoichi

doi:10.48550/arxiv.0803.1710

2008

DOI: 10.48550/arxiv.0803.1710

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Spin-lattice model of Magneto-electric Transitions in RbCoBr$_3$

Tota Nakamura,

Yoichi Nishiwaki

Abstract: Extensive Monte Carlo simulations are performed to analyze a recent neutron diffraction experiment on a distorted triangular lattice compound RbCoBr3. We consider a spin-lattice model, where both spin and lattice are Ising variables. This model explains well successive magnetic and dielectric transitions observed in the experiment. The exchange interaction parameters and the spin-lattice coupling are estimated. It is found that the spin-lattice coupling is important to explain the slow growth of a ferrimagneti… Show more

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“…The algorithm was successfully applied to the theoretical analysis on the magneto-electric transitions in RbCoBr 3 . [19] The numerical results quantitatively agree with the experimental results. The estimates of the interaction parameters and proposals of new experiments were made possible.…”

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Efficient Monte Carlo Algorithm in Quasi-One-Dimensional Ising Spin Systems

Nakamura

2008

Phys. Rev. Lett.

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We have developed an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with highly anisotropic exchange interactions. Both correlation time and real CPU time are reduced drastically. The algorithm is demonstrated in the layered triangular-lattice antiferromagnetic Ising model. We have obtained the relation between the transition temperature and the exchange interaction parameters, which modifies the result of the chain-mean-field theory. The application of the Monte Carlo (MC) method to the condensed-matter physics has been successful bridging between the experimental study and the theoretical study.[1] The simulational results are now quantitatively compared with the experimental results. We may estimate various physical parameters, predict unknown properties, and propose new experiments on real materials. However, we encounter a difficulty when we apply the MC method to the frustrated systems. The MC dynamics slows down, and it becomes very hard to reach the equilibrium states. Since frustration has been recognized to play an important role in novel effects of many materials, [2] we somehow have to overcome this difficulty to study new properties, new concepts and new function of such materials.In this Letter we consider the quasi-one-dimensional (Q1D) frustrated spin systems. The magnetic exchange interaction of this system is highly anisotropic. The interaction along the c axis is much stronger than those within the ab plane: |J c | ≫ |J ab |. The experimental realizations of this model are the ABX 3 -type compounds. [3,4,5,6,7] The lattice structure is the stacked triangular lattice with the antiferromagnetic exchange interactions. There are two reasons for the slow MC dynamics in this system. One is frustration, and the other is the long correlation length along the c axis. The single-spin-flip algorithm cannot change the states of these correlated clusters. Koseki and Matsubara [8,9,10] proposed the clusterheat-bath method, which accelerates the MC dynamics in Q1D Ising spin systems. When we update a spin state, the transfer matrix is multiplied along the c axis. This matrix operation takes a long CPU time. The possible size of simulation has been restricted to the system with |J c /J ab | = 10, 36 × 36 × 360 spins, and 2 × 10 6 MC steps. [11] Considering that the ratio |J c /J ab | in real compounds is in the order of 100, we need to develop another algorithm that improves the simulation efficiency.We notice that the similar slow-dynamic situation occurs in the quantum Monte Carlo (QMC) simulation.[12] The d-dimensional quantum system is mapped to the (d + 1)-dimensional classical system, on which the simulation is performed. The additional dimension is called the Trotter direction, and its length is called the Trotter number. The (d + 1)-dimensional classical system becomes equivalent to the original d-dimensional quantum system when the Tro...

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Efficient Monte Carlo Algorithm in Quasi-One-Dimensional Ising Spin Systems

Nakamura

2008

Phys. Rev. Lett.

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Spin-lattice model of Magneto-electric Transitions in RbCoBr$_3$

Cited by 1 publication

References 28 publications

Efficient Monte Carlo Algorithm in Quasi-One-Dimensional Ising Spin Systems

Efficient Monte Carlo Algorithm in Quasi-One-Dimensional Ising Spin Systems

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