Author: Tateki Obori

We investigate the ground state properties of ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ based on numerical calculations of the recently proposed ab initio Hamiltonian represented by Kitaev and extended Heisenberg interactions. To overcome the limitation posed by small tractable system sizes in the exact diagonalization study employed in a previous study [Y. Yamaji et al., Phys. Rev. Lett. 113, 107201 (2014)], we apply a two-dimensional density matrix renormalization group and an infinite-size tensor-network method. By calculating at much larger system sizes, we critically test the validity of the exact diagonalization results. The results consistently indicate that the ground state of ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ is a magnetically ordered state with zigzag configuration in agreement with experimental observations and the previous diagonalization study. Applications of the two independent methods in addition to the exact diagonalization study further uncover a consistent and rich phase diagram near the zigzag phase beyond the accessibility of the exact diagonalization. For example, in the parameter space away from the ab initio value of ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ controlled by the trigonal distortion, we find three phases: (i) an ordered phase with the magnetic moment aligned mutually in 120 degrees orientation on every third hexagon, (ii) a magnetically ordered phase with a 16-site unit cell, and (iii) an ordered phase with presumably incommensurate periodicity of the moment. It suggests that potentially rich magnetic structures may appear in $A_2{\mathrm{IrO}}_3$ compounds for $A$ other than Na. The present results also serve to establish the accuracy of the first-principles approach in reproducing the available experimental results thereby further contributing to finding a route to realize the Kitaev spin liquid.

             

(by Naoki Kawashima)

[Reference]

[1] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).

[2] Y. Yamaji, Y. Nomura, M. Kurita, R. Arita, and M. Imada, Phys. Rev. Lett. 113, 107201 (2014).

[3] Tsuyoshi Okubo, Kazuya Shinjo, Youhei Yamaji, Naoki Kawashima, Shigetoshi Sota, Takami Tohyama, and Masatoshi Imada, Phys. Rev. B 96, 054434 (2017)

Motivated by the recent experiment on kagome-lattice antiferromagnets, we study the zero-field ordering behavior of the antiferromagnetic classical Heisenberg model on a uniaxially distorted kagome lattice by Monte Carlo simulations. A first-order transition, which has no counterpart in the corresponding undistorted model, takes place at a very low temperature. The origin of the transition is ascribed to a cooperative proliferation of topological excitations inherent to the model.

    

(by Tsuyoshi Okubo)

Reference

[1] P. Mendels and F. Bert, J. Phys. Soc. Jpn. 79, 011001 (2010), Z. Hiroi, et al, J. Phys.:Conf. Ser. 320, 012003 (2011), Y. Okamoto, J. Phys. Soc. Jpn. 78, 033701 (2009).

[2] H. Masuda, T. Okubo, and H. Kawamura, Phys. Rev. Lett 109, 057201 (2012).

Two-dimensional Heisenberg dipolar lattices are investigated by Monte Carlo simulations. Simulations are performed on triangular, square, honeycomb, and kagome ́ lattices. Lattice-dependent magnetic structures and critical phenomena are observed. Although it is believed that two-dimensional Heisenberg dipolar lattices belong to the same universality class of two-dimensional XY dipolar lattices, results from the Monte Carlo simulations show considerable deviations in the critical exponent between the Heisenberg and XY models of triangular and square lattices. The Heisenberg dipolar honeycomb lattice exhibits unusual magnetic ordering in the form of arrays of vortices. Using finite-size scaling techniques, it is shown that the unusual order undergoes the Kosterlitz–Thouless transition. On the kagome ́ lattice, geometric frustration produces a peculiar ferromagnetic ordered state that is macroscopically degenerate. The degeneracy is expected to explain the missing magnetic entropy in ferromagnetic kagome ́, pyrochlore, and spinel substances.

(by Yusuke Tomita)

Reference

[1] K. Fukui and S. Todo: “Order-N cluster Monte Carlo method for spin systems with long-range interactions”, J. Comput. Phys. 228 (2009) 2629.

[2] Yusuke Tomita: “Monte Carlo Study of Two-Dimensional Heisenberg Dipolar Lattices”, J. Phys. Soc. Jpn 78 (2009) 114004.