In spinels ACr 2 O 4 (A=Mg, Zn) realisation of the classical pyrochlore Heisenberg antiferromagnet model is complicated by a strong spin-lattice coupling: the extensive degeneracy of the ground state is lifted by a magneto-structural transition at T N =12.5 K. We study the resulting low-temperature low-symmetry crystal structure by synchrotron x-ray diffraction. The consistent features of x-ray low-temperature patterns are explained by the tetragonal model of Ehrenberg et. al [Pow. Diff. 17, 230( 2002)], while other features depend on sample or cooling protocol. Complex partially ordered magnetic state is studied by neutron diffraction and spherical neutron polarimetry. Multiple magnetic domains of configuration arms of the propagation vectors k 1 =( 1 2 1 2 0), k 2 =(1 0 1 2 ) appear. The ordered moment reaches 1.94(3) µ B /Cr 3+ for k 1 and 2.08(3)µ B /Cr 3+ for k 2 , if equal amount of the k 1 and k 2 phases is assumed. The magnetic arrangements have the dominant components along the [110] and [1-10] diagonals and a smaller c-component. By inelastic neutron scattering we investigate the spin excitations, which comprise a mixture of dispersive spin waves propagating from the magnetic Bragg peaks and resonance modes centered at equal energy steps of 4.5 meV. We interpret these as acoustic and optical spin wave branches, but show that the neutron scattering cross sections of transitions within a unit of two corner-sharing tetrahedra match the observed intensity distribution of the resonances. The distinctive fingerprint of cluster-like excitations in the optical spin wave branches suggests that propagating excitations are localized by the complex crystal structure and magnetic orders.3

Magnetoelectric phenomena are intimately linked to relativistic effects and also require the material to break spatial inversion symmetry and time-reversal invariance. Magnetoelectric coupling can substantially affect light–matter interaction and lead to non-reciprocal light propagation. Here, we confirm on a fully experimental basis, without invoking either symmetry-based or material-specific assumptions, that the optical magnetoelectric effect in materials with non-parallel magnetization (M) and electric polarization (P) generates a trilinear term in the refractive index, δn ∝ k ⋅ (P × M), where k is the propagation vector of light. Its sharp magnetoelectric resonances in the terahertz regime, which are simultaneously electric and magnetic dipole active excitations, make Co2Mo3O8 an ideal compound to demonstrate this fundamental relation via independent variation of M, P, and k. Remarkably, the material shows almost perfect one-way transparency in moderate magnetic fields for one of these magnetoelectric resonances.

We study magnetic behaviour of the Yb 3+ ions on a frustrated pyrochlore lattice in the spinel CdYb 2 Se 4 . The crystal-electric field parameters deduced from high-energy inelastic neutron scattering reveal well-isolated ytterbium ground state doublet with a weakly Ising character. Magnetic order studied by powder neutron diffraction evolves from the XY -type antiferromagnetic Γ 5 state to a splayed ice-like ferromagnet (both with k=0) in applied magnetic field with B c =3 T. Lowenergy inelastic neutron scattering identifies weakly dispersive magnetic bands around 0.72 meV starting at | Q | = 1.1Å −1 at zero field, which diminish with field and vanish above 3 T. We explain the observed magnetic behaviour in framework of the nearest-neighbour anisotropic exchange model for effective S = 1/2 Kramers doublets on the pyrochlore lattice. The estimated exchanges position the CdYb 2 Se 4 spinel close to the phase boundary between the Γ 5 and splayed ferromagnet states, similar to the Yb-pyrochlores suggesting an important role of the competition between these phases.

We theoretically and experimentally study the stability of the unconventional fractional antiferromagnetic skyrmion lattice (AF-SkL) in MnSc 2 S 4 spinel under magnetic fields applied along the [1-10] crystal direction. By performing numerical Monte Carlo simulations for the minimal effective spin model that we proposed in S. Gao et al., Nature 586, 37 (2020), we show that the lattice is aligned within the equivalent and symmetric [1][2][3][4][5][6][7][8][9][10][11] or [1-1-1] planes, which are equally inclined to the applied magnetic-field H . We attribute this behavior to the magnetic anisotropy of the host material. Neutron single-crystal diffraction presents a very good agreement with the predictions of the effective model. It reveals that the topological spin texture gets destabilized at low temperatures and moderate magnetic fields and is replaced by a conical phase for H // [1-10]. The present study elucidates the central role of the magnetic anisotropy in the stabilization of AF-Sk states.