We present a thorough theoretical assessment of the stability of non-collinear spin arrangements in small palladium clusters. We generally find that ferromagnetic order is always preferred, but that antiferromagnetic and non-collinear configurations of different sorts exist and compete for the first excited isomers. We also show that the relative stability of all these states is rather insensitive to the choice of atomic configuration for the pseudopotential used and to the approximation taken for the exchange and correlation potential. This result stands in stark contrast with the situation found for the bulk phases of palladium.
The modification of the magnetization dissipation or Gilbert damping caused by an inhomogeneous magnetic structure and expressed in terms of a wave vector dependent tensor $underline{alpha}(vec{q})$ is investigated by means of linear response theory. A corresponding expression for $underline{alpha}(vec{q})$ in terms of the electronic Green function has been developed giving in particular the leading contributions to the Gilbert damping linear and quadratic in $q$. Numerical results for realistic systems are presented that have been obtained by implementing the scheme within the framework of the fully relativistic KKR (Korringa-Kohn-Rostoker) band structure method. Using the multilayered system (Cu/Fe$_{1-x}$Co$_x$/Pt)$_n$ as an example for systems without inversion symmetry we demonstrate the occurrence of non-vanishing linear contributions. For the alloy system bcc Fe$_{1-x}$Co$_x$ having inversion symmetry, on the other hand, only the quadratic contribution is non-zero. As it is shown, this quadratic contribution does not vanish even if the spin-orbit coupling is suppressed, i.e. it is a direct consequence of the non-collinear spin configuration.
We propose that non-collinear magnetic order in quantum magnets can harbor a novel higher-order topological magnon phase with non-Hermitian topology and hinge magnon modes. We consider a three-dimensional system of interacting local moments on stacked-layers of honeycomb lattice. It initially favors a collinear magnetic order along an in-plane direction, which turns into a non-collinear order upon applying an external magnetic field perpendicular to the easy axis. We exploit the non-Hermitian nature of the magnon Hamiltonian to show that this field-induced transition corresponds to the transformation from a topological magnon insulator to a higher-order topological magnon state with a one-dimensional hinge mode. As a concrete example, we discuss the recently-discovered monoclinic phase of the thin chromium trihalides, which we propose as the first promising material candidate of the higher-order topological magnon phase.
The orthoperovskites TbCoO$_3$ and DyCoO$_3$ with Co$^{3+}$ in a non-magnetic low-spin state have been investigated by neutron diffraction down to 0.25 K. Magnetic ordering is evidenced below $T_N=3.3$ K and 3.6 K, respectively, and the ordered arrangements are of canted type, A$_x$G$_y$ for TbCoO$_3$ and G$_x$A$_y$ for DyCoO$_3$ in Bertauts notation. The experiments are confronted with the first-principle calculations of the crystal field and magnetism of Tb$^{3+}$ and Dy$^{3+}$ ions, located in the $Pbnm$ structure on sites of $C_s$ point symmetry. Both these ions exhibit an Ising behavior, which originates in the lowest energy levels, in particular in accidental doublet of non-Kramers Tb$^{3+}$ ($4f^8$ configuration) and in ground Kramers doublet of Dy$^{3+}$ ($4f^9$) and it is the actual reason for the non-collinear AFM structures. Very good agreement between the experiment and theory is found. For comparison, calculations of the crystal field and magnetism for other systems with Kramers ions, NdCoO$_3$ and SmCoO$_3$, are also included.
The influence of the spin-orbit coupling on the magnetic structure of deposited transition metal nanostructure systems has been studied by fully relativistic electronic structure calculations. The interplay of exchange coupling and magnetic anisotropy was monitored by studying the corresponding magnetic torque calculated within ab-initio and model approaches. It is found that a spin-orbit induced Dzyaloshinski-Moriya interaction can stabilise a non-collinear spin structure even if there is a pronounced isotropic ferromagnetic exchange interaction between the magnetic atoms.
By the first-principles electronic structure calculations, we find that the ground state of PbO-type tetragonal $alpha$-FeTe is in a bi-collinear antiferromagnetic state, in which the Fe local moments ($sim2.5mu_B$) are ordered ferromagnetically along a diagonal direction and antiferromagnetically along the other diagonal direction on the Fe square lattice. This bi-collinear order results from the interplay among the nearest, next nearest, and next next nearest neighbor superexchange interactions $J_1$, $J_2$, and $J_3$, mediated by Te $5p$-band. In contrast, the ground state of $alpha$-FeSe is in the collinear antiferromagnetic order, similar as in LaFeAsO and BaFe$_2$As$_2$.