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Register a new userNoncollinear Antiferromagnetic Order and Effect of Spin-Orbit Coupling in Spin-1 Honeycomb Lattice
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Motivated by the recently synthesized insulating nickelate Ni$_2$Mo$_3$O$_8$, which has been reported to have an unusual non-collinear magnetic order of Ni$^{2+}$ $S=1$ moments with a nontrivial angle between adjacent spins, we construct an effective spin-1 model on the honeycomb lattice, with the exchange parameters determined with the help of first principles electronic structure calculations. The resulting bilinear-biquadratic model, supplemented with the realistic crystal-field induced anisotropy, favors the collinear Neel state. We find that the crucial key to explaining the observed noncollinear spin structure is the inclusion of the Dzyaloshinskii--Moriya (DM) interaction between the neighboring spins. By performing the variational mean-field and linear spin-wave theory (LSWT) calculations, we determine that a realistic value of the DM interaction $Dapprox 2.78$ meV is sufficient to quantitatively explain the observed angle between the neighboring spins. We furthermore compute the spectrum of magnetic excitations within the LSWT and random-phase approximation (RPA) which should be compared to future inelastic neutron measurements.
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Single crystal neutron diffraction, inelastic neutron scattering, bulk magnetization measurements, and first-principles calculations are used to investigate the magnetic properties of the honeycomb lattice $rm Tb_2Ir_3Ga_9$. While the $Rln2$ magnetic contribution to the low-temperature entropy indicates a $rm J_{eff}=1/2$ moment for the lowest-energy crystal-field doublet, the Tb$^{3+}$ ions form a canted antiferromagnetic structure below 12.5 K. Due to the Dzyalloshinskii-Moriya interactions, the Tb moments in the $ab$ plane are slightly canted towards $b$ by $6^circ$ with a canted moment of 1.22 $mu_{rm B} $ per formula unit. A minimal $xxz$ spin Hamiltonian is used to simultaneously fit the spin-wave frequencies along the high symmetry directions and the field dependence of the magnetization along the three crystallographic axes. Long-range magnetic interactions for both in-plane and out-of-plane couplings up to the second nearest neighbors are needed to account for the observed static and dynamic properties. The $z$ component of the exchange interactions between Tb moments are larger than the $x$ and $y$ components. This compound also exhibits bond-dependent exchange with negligible nearest exchange coupling between moments parallel and perpendicular to the 4$f$ orbitals. Despite the $J_{{rm eff}}=1/2$ moments, the spin Hamiltonian is denominated by a large in-plane anisotropy $K_z sim -1$ meV. DFT calculations confirm the antiferromagnetic ground state and the substantial inter-plane coupling at larger Tb-Tb distances.
We used single-crystal x-ray and neutron diffraction to investigate the crystal and magnetic structures of trigonal lattice iridate Ca2Sr2IrO6. The crystal structure is determined to be $Rbar3$ with two distinct Ir sites. The system exhibits long-range antiferromagnetic order below $T_N = 13.1$ K. The magnetic wave vector is identified as $(0,0.5,1)$ with ferromagnetic coupling along the $a$ axis and antiferromagnetic correlation along the $b$ axis. Spins align dominantly within the basal plane along the [1,2,0] direction and tilt 34$^circ$ towards the $c$ axis. The ordered moment is 0.66(3) $mu_B$/Ir, larger than other iridates where iridium ions form corner- or edge-sharing $rm IrO_6$ octahedral networks. The tilting angle is reduced to $approx19^circ$ when a magnetic field of 4.9 Tesla is applied along the $c$ axis. Density functional theory calculations confirm that the experimentally determined magnetic configuration is the most probable ground state with an insulating gap $sim0.5$~eV.
Co4Ta2O9 exhibits a three-dimensional magnetic lattice based on the buckled honeycomb motif. It shows unusual magnetoelectric effects, including the sign change and non-linearity. These effects cannot be understood without the detailed knowledge of the magnetic structure. Herein, we report neutron diffraction and direction-dependent magnetic susceptibility measurements on Co4Ta2O9 single crystals. Below 20.3 K, we find a long-range antiferromagnetic order in the alternating buckled and flat honeycomb layers of Co2+ ions stacked along the c axis. Within experimental accuracy, the magnetic moments lie in the ab plane. They form a canted antiferromagnetic structure with a tilt angle of ~ 14 degrees at 15 K in the buckled layers, while the magnetic moments in each flat layer are collinear. This is directly evidenced by a finite (0, 0, 3) magnetic Bragg peak intensity, which would be absent in the collinear magnetic order. The magnetic space group is C2/c. It is different from the previously reported C2/c group, also found in the isostructural Co4Nb2O9. The revised magnetic structure successfully explains the major features of the magnetoelectric tensor of Co4Ta2O9 within the framework of the spin-flop model.
Most of the searches for Kitaev materials deal with $4d/5d$ magnets with spin-orbit-coupled ${J=1/2}$ local moments such as iridates and $alpha$-RuCl$_3$. Here we propose the monoclinic YbCl$_3$ with a Yb$^{3+}$ honeycomb lattice for the exploration of Kiteav physics. We perform thermodynamic, $ac$ susceptibility, angle-dependent magnetic torque and neutron diffraction measurements on YbCl$_3$ single crystal. We find that the Yb$^{3+}$ ion exhibits a Kramers doublet ground state that gives rise to an effective spin ${J_{text{eff}}=1/2}$ local moment. The compound exhibits short-range magnetic order below 1.20 K, followed by a long-range Neel-type antiferromagnetic order at 0.60 K, below which the ordered Yb$^{3+}$ spins lie in the $ac$ plane with an angle of 16(11)$^{circ}$ away from the $a$ axis. These orders can be suppressed by in-plane and out-of-plane magnetic fields at around 6 and 10 T, respectively. Moreover, the Neel temperature varies non-monotonically under the out-of-plane magnetic fields. The in-plane magnetic anisotropy and the reduced order moment 0.8(1) $mu_B$ at 0.25 K indicate that YbCl$_3$ could be a two-dimensional spin system to proximate the Kitaev physics.
Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Neel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1 approx 0.23$. Close to the transition point, the Gutzwiller-projected uniform resonating valence bond state gives an excellent approximation to the exact ground-state energy. For $0.23 lesssim J_2/J_1 lesssim 0.4$, a gapless $Z_2$ spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the Neel order melts, this ordered state becomes clearly favored only for $J_2/J_1 gtrsim 0.3$. Finally, for $0.36 lesssim J_2/J_1 le 0.5$, a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the Neel antiferromagnet from the plaquette valence-bond solid.
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