Linear spin wave theory provides the leading term in the calculation of the excitation spectra of long-range ordered magnetic systems as a function of 1/ √ S. This term is acquired using the Holstein-Primakoff approximation of the spin operator and valid for small δS fluctuations of the ordered moment. We propose an algorithm that allows magnetic ground states with general moment directions and single-Q incommensurate ordering wave vector using a local coordinate transformation for every spin and a rotating coordinate transformation for the incommensurability. Finally we show, how our model can determine the spin wave spectrum of the magnetic C-site langasites with incommensurate order.

α-CaCr2O4 is a distorted triangular antiferromagnet. The magnetic Cr 3+ ions which have spin-3/2 and interact with their nearest neighbors via Heisenberg direct exchange interactions, develop long-range magnetic order below TN = 42.6 K. Powder and single-crystal neutron diffraction reveal a helical magnetic structure with ordering wavevector k = (0, ∼ 1/3, 0) and angles close to 120• between neighboring spins. Spherical neutron polarimetry unambiguously proves that the spins lie in the ac plane perpendicular to k. The magnetic structure is therefore that expected for an ideal triangular antiferromagnet where all nearest neighbor interactions are equal, in spite of the fact that α-CaCr2O4 is distorted with two inequivalent Cr 3+ ions and four different nearest neighbor interactions. By simulating the magnetic order as a function of these four interactions it is found that the special pattern of interactions in α-CaCr2O4 stabilizes 120• helical order for a large range of exchange interactions.

The magnetic insulator yttrium iron garnet can be grown with exceptional quality, has a ferrimagnetic transition temperature of nearly 600 K, and is used in microwave and spintronic devices that can operate at room temperature. The most accurate prior measurements of the magnon spectrum date back nearly 40 years, but cover only 3 of the lowest energy modes out of 20 distinct magnon branches. Here we have used time-of-flight inelastic neutron scattering to measure the full magnon spectrum throughout the Brillouin zone. We find that the existing models of the excitation spectrum fail to describe the optical magnon modes. Using a very general spin Hamiltonian, we show that the magnetic interactions are both longer-ranged and more complex than was previously understood. The results provide the basis for accurate microscopic models of the finite temperature magnetic properties of yttrium iron garnet, necessary for next-generation electronic devices.

In this Letter, we explore the phase diagram and excitations of a distorted triangular lattice antiferromagnet. The unique two-dimensional distortion considered here is very different from the "isosceles"-type distortion that has been extensively investigated. We show that it is able to stabilize a 120° spin structure for a large range of exchange interaction values, while new structures are found for extreme distortions. A physical realization of this model is α-CaCr(2)O(4), which has a 120° structure but lies very close to the phase boundary. This is verified by inelastic neutron scattering which reveals unusual rotonlike minima at reciprocal space points different from those corresponding to the magnetic order.