Small-angle neutron scattering experiments were performed on a bulk single crystal of chiral-lattice multiferroic insulator Cu 2 OSeO 3 . In the absence of an external magnetic field, helical spin order with magnetic modulation vector q 001 was identified. When a magnetic field is applied, a triple-q magnetic structure emerges normal to the field in the A phase just below the magnetic ordering temperature T c , which suggests the formation of a triangular lattice of skyrmions. Notably, the favorable q direction in the A phase changes from q 110 to q 001 upon approaching T c . Near the phase boundary between these two states, the external magnetic field induces a 30 • rotation of the skyrmion lattice. This suggests a delicate balance between the magnetic anisotropy and the spin texture near T c , such that even a small perturbation significantly affects the ordering pattern of the skyrmions.
Using single crystal inelastic neutron scattering with and without the application of an external magnetic field and powder neutron diffraction, we have characterized magnetic interactions in Ba3Cr2O8. Even without a field, we found that there exist three singlet-to-triplet excitation modes in the (h, h, l) scattering plane. Our complete analysis shows that the three modes are due to spatially anisotropic interdimer interactions that are induced by lattice distortions of the tetrahedron of oxygens surrounding the Jahn-Teller active Cr5+(3d1). The strong intradimer coupling of J0=2.38(2) meV and weak interdimer interactions (|Jinter|< or =0.52(2) meV) makes Ba3Cr2O8 a good model system for weakly coupled s=1/2 quantum spin dimers.
In this paper, we calculated the linear spin wave energies using incorrectly normalized exchange constants such thatJ ij = S i S j J ij andD i = S 2 i D i . In this Erratum we provide the results of our revised analysis, but also argue that the main conclusion of the original paper is still intact. First, the correct way for normalization should have beenJ ij = S i S j J ij andD i = S i D, respectively, since the spin wave frequency is proportional to S. The best-fit values of the exchange constants given in Table I of the original paper thus correspond toJ ij = S i S j J ij orD i = S i D, respectively.The above treatment in fact still ignores the cross terms that occur between different spin moments. To clarify this issue, we performed new calculations without using normalization. The spin moments were explicitly fixed to be S A = 5 2 and S B = 2 (for Mn 3 O 4 ) or 1 (for MnV 2 O 4 ). The new parameters are summarized in Table I, which replaces Table I of the original paper. The dispersions and intensities calculated using the new parameters for MnV 2 O 4 are summarized in the revised Fig. 3, which replaces Fig. 3 of the original paper. The new results for Mn 3 O 4 are essentially identical to what was shown in Fig. 2 of the original paper. We note that the new parameters provided in this Erratum are comparable to those shown in the original paper when converted by the corrected normalization. Most importantly, the ratio indicating the spatial anisotropy of the B-B exchange, J BB /J BB = 0.3 ± 0.1, is equal to the value reported in the original paper. It is thus confirmed that the conclusions of the original paper still stand without any reservations.TABLE I. The best-fit parameters used to calculate spin wave energies and intensities of Mn 3 O 4 and MnV 2 O 4 (J and D are in meV).
Using neutron scattering techniques, we have investigated spin wave excitations in noncollinear ferrimagnetic spinels MnB 2 O 4 ͑B =Mn,V͒ with e g and t 2g orbital degeneracies, respectively, that lead to tetragonal distortions along opposite directions. Linear spin wave analysis of the excitations yields spatially inhomogeneous nearest neighbor interactions in both tetragonal spinels. We find the ratio J c / J ab Ϸ −0.06͑4͒ for Mn 3 O 4 ͑c Ͼ a = b͒ and Ϸ0.3͑1͒ for MnV 2 O 4 ͑c Ͻ a = b͒. Resulting exchange couplings of Mn 3 O 4 can be qualitatively explained in terms of possible overlaps of t 2g and e g electrons of Mn 2+ and Mn 3+ ions. On the other hand, those of MnV 2 O 4 , in particular, the strong J c , seem to contradict with the antiferro-orbital state of V 3+ ͑t 2g 2 ͒ ions that was proposed by a recent synchrotron x-ray study ͓T. Suzuki et al., Phys. Rev. Lett. 98, 127203 ͑2007͔͒. Theoretical implications to the orbital physics are also discussed. DOI: 10.1103/PhysRevB.77.054412 PACS number͑s͒: 75.30.Et, 75.30.Ds, 75.50.Gg TABLE I. The optimal parameters used to calculate spin wave dispersions of Mn 3 O 4 ͓Fig. 2͑b͔͒ and MnV 3 O 4 ͑Fig. 3͒ ͑J and D are in meV͒.
Magnetic multiferroic materials become simultaneously ferroelectric and magnetic at low temperatures and are thus attractive for use in technological devices that can exploit both sets of properties [1][2][3][4][5] Various theories have been proposed to explain the magneto-electric coupling in magnetic multiferroics [6][7][8][9][10][11][12] : the symmetry-based phenomenological Ginzburg-Landau theory 8 , spin-current mechanism 6,7,9 , magneto-striction mechanism 11 , and delocalized spin density wave model 12 .In the spin-current model, the spontaneous electric polarization, P, occurs when the magnetic ground state has a non-collinear transverse (cycloidal) spiral structure and yields a non-zero spin current e ij ! (S i ! S j ) where 3 e ij = r i ! r j r i ! r j is the unit vector connecting the two magnetic ions: P = !e ij " (S i " S j ) .This model explains the magneto-electric phenomena found in many different materials such as TbMnO 3 1,13,14 and CoCr 2 O 4 15 . On the other hand, in the magneto-striction model P ! S i " S j can occur for a collinear spin structure that has !!"" configuration.Previous powder neutron diffraction studies on AMn 2 O 5 (A = Y and Tb) 16,17 have reported nearly collinear spin structures for their ferroelectric phases and thus presented these systems as where the magneto-striction mechanism not the spin-current model is at work. In the previous study, the decrease in P at the transition from the ITC-FE to the LTI-FE phase was attributed to a magnetic transition from a structure with magnetic moments of similar amplitudes to an amplitude-modulated sinusoidal spin structure.The same result was also referred as experimental evidence for a recent theory based on delocalized spin density waves. and polarized neutron diffraction (PND) measurements. In the FCD measurements relative spin directions and magnitudes in a magnetic system give arise to relative intensities of magnetic Bragg reflections, while in the PND measurements they give rise to different intensities in the non-spin-flip and the spin-flip channels at each reflection.Thus, in the FCD technique, enough information for the structure determination can only be obtained by measuring a large number of reflections. As the complexity of the structure increases, the required number of reflections grows. In the PND technique, on the other hand, information about particular spin directions and magnitudes can be achieved at each reflection. Thus, the two techniques can be complimentary and powerful, when combined, in determining a complex spin structure. Our FCD measurements were performed at the Paul Scherrer Institute to collect about 300 magnetic reflections in each FE phase. Our PND measurements were done at two neutron facilities using two different experimental configurations: at the National Institute of Standards and Technology, the conventional PND measurements with two sets of transmission neutron polarizers and spin flippers before and after the sample, and a vertical guide field along the beam path to maintain the select...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.