%0 Journal Article %1 PhysRevB.109.075104 %A Francini, Niccoló %A Janssen, Lukas %D 2024 %I American Physical Society %J Phys. Rev. B %K b %N 7 %P 075104 %R 10.1103/PhysRevB.109.075104 %T Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to Na$_2$Co$_2$TeO$_6$ %U https://link.aps.org/doi/10.1103/PhysRevB.109.075104 %V 109 %X The honeycomb magnet $Na_2Co_2TeO_6$ has recently been argued to realize an approximate hidden SU(2) symmetry that can be understood by means of a duality transformation. Using large-scale classical Monte Carlo simulations, we study the finite-temperature phase diagram of the pertinent Heisenberg-Kitaev-$\ensuremath\Gamma\ensuremath-\ensuremath\Gamma^'$ model near the hidden-SU(2)-symmetric point, in the presence of a six-spin ring exchange perturbation. At low temperatures, the model features collinear single-$q$ zigzag and noncollinear triple-$q$ ground states, depending on the sign of the ring exchange coupling. We show that in the vicinity of the hidden-SU(2)-symmetric point, the magnetic long-range orders melt in two stages. The corresponding finite-temperature transitions are continuous and fall into two-dimensional (2D) Ising and 2D Potts universality classes, respectively. The two fluctuation-induced phases at intermediate temperatures spontaneously break spin rotational and lattice translational symmetries, respectively, but both leave time-reversal symmetry intact. They are characterized by finite expectation values of a real, symmetric, traceless, second-rank tensor and are naturally understood as vestigial orders of the underlying magnetic states. We identify these vestigial orders as $Z_3$ spin nematic and $Z_4$ spin current density wave phases, respectively. For increasing ring exchange perturbations, the width of the vestigial phases decreases, eventually giving rise to a direct first-order transition from the magnetically ordered phase to the disordered paramagnet. We propose the $Z_4$ spin current density wave phase, which is the vestigial phase of the primary triple-$q$ magnetic order, as a natural candidate for the paramagnetic 2D long-range-ordered state observed in $Na_2Co_2TeO_6$ in a small window above the antiferromagnetic ordering temperature.

@article{PhysRevB.109.075104, abstract = {The honeycomb magnet ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ has recently been argued to realize an approximate hidden SU(2) symmetry that can be understood by means of a duality transformation. Using large-scale classical Monte Carlo simulations, we study the finite-temperature phase diagram of the pertinent Heisenberg-Kitaev-$\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ model near the hidden-SU(2)-symmetric point, in the presence of a six-spin ring exchange perturbation. At low temperatures, the model features collinear single-$\mathbf{q}$ zigzag and noncollinear triple-$\mathbf{q}$ ground states, depending on the sign of the ring exchange coupling. We show that in the vicinity of the hidden-SU(2)-symmetric point, the magnetic long-range orders melt in two stages. The corresponding finite-temperature transitions are continuous and fall into two-dimensional (2D) Ising and 2D Potts universality classes, respectively. The two fluctuation-induced phases at intermediate temperatures spontaneously break spin rotational and lattice translational symmetries, respectively, but both leave time-reversal symmetry intact. They are characterized by finite expectation values of a real, symmetric, traceless, second-rank tensor and are naturally understood as vestigial orders of the underlying magnetic states. We identify these vestigial orders as ${\mathbb{Z}}_{3}$ spin nematic and ${\mathbb{Z}}_{4}$ spin current density wave phases, respectively. For increasing ring exchange perturbations, the width of the vestigial phases decreases, eventually giving rise to a direct first-order transition from the magnetically ordered phase to the disordered paramagnet. We propose the ${\mathbb{Z}}_{4}$ spin current density wave phase, which is the vestigial phase of the primary triple-$\mathbf{q}$ magnetic order, as a natural candidate for the paramagnetic 2D long-range-ordered state observed in ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$ in a small window above the antiferromagnetic ordering temperature.}, added-at = {2024-02-06T14:36:42.000+0100}, author = {Francini, Niccoló and Janssen, Lukas}, biburl = {https://www.bibsonomy.org/bibtex/2366a697b204ab32e37132c3f0c40067d/ctqmat}, day = 05, description = {Phys. Rev. B 109, 075104 (2024) - Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to ${\mathrm{Na}}_{2}{\mathrm{Co}}_{2}{\mathrm{TeO}}_{6}$}, doi = {10.1103/PhysRevB.109.075104}, interhash = {ad8ced133236057420e6860fde10f9b7}, intrahash = {366a697b204ab32e37132c3f0c40067d}, journal = {Phys. Rev. B}, keywords = {b}, month = {02}, number = 7, numpages = {17}, pages = 075104, publisher = {American Physical Society}, timestamp = {2024-02-23T10:18:21.000+0100}, title = {Spin vestigial orders in extended Heisenberg-Kitaev models near hidden SU(2) points: Application to Na$_{\mathbf{2}}$Co$_{\mathbf{2}}$TeO$_{\mathbf{6}}$}, url = {https://link.aps.org/doi/10.1103/PhysRevB.109.075104}, volume = 109, year = 2024 }