Triple-meron crystal in high-spin Kitaev magnets

Abstract

Skyrmions hold great promise in future spintronics applications since they are robust against local deformations. The meron, due to its topological equivalence to a half skyrmion, has been widely found to appear in pairs. Motivated by recent progresses in high-spin Kitaev magnets, here we investigate numerically a classical Kitaev-$\Gamma$ model with a single-ion anisotropy. An exotic spin texture consisting of three merons is discovered. Such a state features a peculiar property with an odd number of merons in one magnetic unit cell. Therefore, these merons cannot be dissociated from skyrmions as reported in the literature and their origin is briefly discussed. Moreover, we find that these three merons contribute a finite topological number and thus it can induce the topological Hall effect. Experimentally this spin texture can be observed by the Lorentz transmission electron microscopy and the topological Hall effect can be used to identify the finite topological number. Our work demonstrates that high-spin Kitaev magnets can host robust unconventional spin textures and thus they offer a versatile platform for exploring exotic spin textures as well as their applications in spintronics.

Beyond Kitaev physics in strong spin-orbit coupled magnets

“…While such orders with large (or infinite) unit cells are challenging to detect in finite-size simulations, the associated multi-peaked spin structure factors [219] offer distinctive fingerprints for their experimental detection by, e.g., neutron diffraction, nuclear magnetic resonance, or µSR. (iv) One of the proposed intermediate phases is the so-called 'K-state' of figures 5(b) and (c), discussed in [208,[216][217][218][219], which is analogous to the K-state proposed in [46] for β-Li 2 IrO 3 (see section 6). This state has a six-site magnetic unit cell and shows a characteristic 'period-3 chain' structure with counter-rotating spin sublattices, that has the following form:…”

“…This leads to two, qualitatively different regions in parameter space, the ones where K and Γ have the same sign, and the ones where they have opposite signs. The ground states of the former regions are known exactly, whereas the ones of the latter are not fully understood [16,183,208,[216][217][218][219].…”

“…While a slight variation of this recipe can still be applied on individual chains (see section 7.1), the bonds connecting the chains remain frustrated, which gives rise to a rich interplay of various complex phases. Figures 5(a)-(c) show the classical phase diagrams for positive Γ and negative K, as proposed from various classical energy minimization approaches, including machine learning [183] (figure 5(a)), Monte Carlo simulations [216,218] (figure 5(b)), hybrid Monte Carlo and iterative variational minimizations [219] (figure 5(c)). Let us summarize the main features:…”

“…threefold-symmetric order with 18 spin sublattices, whose stability region is varied across the different studies, see figures 5(a)-(c). This state is dubbed 18C 3 order in [216,219], modulated S 3 ×Z 3 phase in [183], and triplemeron crystal in [218]. Applying the symmetries R x,y,z of equation (32) to the 18C 3 state delivers other ground states with 54 sublattices.…”

“…(iii) The number and exact nature of the phases that appear in between the 18C 3 and the zigzag regions are debated. Nevertheless, it seems that this intermediate region is occupied by phases with large magnetic unit cells or longwavelength, IC modulations thereof [183,208,211,[216][217][218][219]. While such orders with large (or infinite) unit cells are challenging to detect in finite-size simulations, the associated multi-peaked spin structure factors [219] offer distinctive fingerprints for their experimental detection by, e.g., neutron diffraction, nuclear magnetic resonance, or µSR.…”