Order-by-disorder and magnetic field response in the Heisenberg-Kitaev model on a hyperhoneycomb lattice

Abstract

We study the finite temperature phase diagram of the Heisenberg-Kitaev model on a three dimensional hyperhoneycomb lattice. Using semiclassical analysis and classical Monte-Carlo simulations, we investigate quantum and thermal order-by-disorder, as well as the magnetic ordering temperature. We find the parameter regime where quantum and thermal fluctuations favor different magnetic orders, which leads to an additional finite temperature phase transition within the ordered phase. This transition, however, occurs at a relatively low temperature and the entropic effects may dominate most of the finite temperature region below the ordering temperature. In addition, we explore the magnetization process in the presence of a magnetic field and discover spin-flop transitions which are sensitive to the applied-field direction. We discuss implications of our results for future experiments on a hyperhoneycomb lattice system such as the recently discovered β-Li2IrO3.

Symmetry demanded topological nodal-line materials

“…A tight-binding model reveals the Fermi surface to be a highly anisotropic torus shape and is expected to show quantized Hall conductivity when applying magnetic field along the torus direction [101]. Various antiferromagnetic (AFM) orders are reported in the hyperhoneycomb lattice [116][117][118], some of which can destroy the nodal loop [111]. Including SOC in these systems, regardless of magnetism, evolves them into strong TIs [101,111].…”

Weyl and Nodal Ring Magnons in Three-Dimensional Honeycomb Lattices

“…Naturally, there are also 3D honeycomb lattices [3][4][5][6][7][8][9][10][11][12][13][14], and their exotic properties have been explored, such as nodal line semimetal in body-centered orthorhombic C 16 [3], loop-nodal semimetal [7,9] and topological insulator [7] in the hyperhoneycomb lattice, nodal ring [14,15] and Weyl [14] spinons of interacting spin systems in the hyperhoneycomb and stripyhoneycomb lattices, and loop Fermi surface in other similar systems [16][17][18][19][20][21][22]. Based on these studies, Ezawa [23] proposed a wide class of 3D honeycomb lattices constructed by two building blocks.…”

Loop-Nodal and Point-Nodal Semimetals in Three-Dimensional Honeycomb Lattices

“…A series of three-dimensional (3D) honeycomb lattices named harmonic honeycomb lattices 10 have also been proposed. They attracts much attention [11][12][13][14][15][16][17][18] recently. It has been argued 11,13 that the hyperhoneycomb lattice is a loop-nodal semimetal where the Fermi surface forms a loop (which we call a Fermi loop).…”