Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the E 8 Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material CoNb 2 O 6. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six E 8 particles, m 1 to m 6 , and the two-particle (m 1 + m 2) continuum in an applied transverse magnetic field of B 1D c = 4.75 T, before the three-dimensional magnetic order is suppressed above B 3D c ≈ 5.3 T. The observation of the higher-energy particles (m 3 to m 6) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.
Spin excitations of magnetoelectric LiNiPO4 are studied by infrared absorption spectroscopy in the THz spectral range as a function of magnetic field through various commensurate and incommensurate magnetically ordered phases up to 33 T. Six spin resonances and a strong two-magnon continuum are observed in zero magnetic field. Our systematic polarization study reveals that some of the excitations are usual magnetic-dipole active magnon modes, while others are either electromagnons, electric-dipole active, or magnetoelectric, both electric-and magnetic-dipole active spin excitations. Field-induced shifts of the modes for all three orientations of the field along the orthorhombic axes allow us to refine the values of the relevant exchange couplings, single-ion anisotropies, and the Dzyaloshinskii-Moriya interaction on the level of a four-sublattice mean-field spin model. This model also reproduces the spectral shape of the two-magnon absorption continuum, found to be electric-dipole active in the experiment. a b c J xy J xz J y J yz
Competing exchange interactions can produce complex magnetic states together with spin-induced electric polarizations. With competing interactions on alternating triangular and kagome layers, the swedenborgite CaBaCo4O7 may have one of the largest measured spin-induced polarizations of ∼ 1700 nC/cm 2 below its ferrimagnetic transition temperature at 70 K. Upon rotating our sample about c = [0, 0, 1] while the magnetic field is fixed along [1, 0, 0], the three-fold splitting of the spinwave frequencies indicates that our sample is hexagonally twinned. Magnetization measurements then indicate that roughly 20% of the sample is in a domain with the a axis along [1, 0, 0] and that 80% of the sample is in one of two other domains with the a axis along either [−1/2, √ 3/2, 0] or [−1/2, − √ 3/2, 0]. Powder neutron-diffraction data, magnetization measurements, and THz absorption spectroscopy reveal that the complex spin order in each domain can be described as a triangular array of bitetrahedral c-axis chains ferrimagnetically coupled to each other in the ab plane. The electric-field dependence of bonds coupling those chains produces the large spin-induced polarization of CaBaCo4O7.
We have studied spin excitations in a single-domain crystal of antiferromagnetic LiCoPO4 by THz absorption spectroscopy. By analysing the selection rules and comparing the strengths of the absorption peaks in the different antiferromagnetic domains, we found electromagnons and magnetoelectric (ME) spin resonances besides conventional magnetic-dipole active spin-wave excitations. Using the sum rule for the ME susceptibility we determined the contribution of the spin excitations to all the different off-diagonal elements of the static ME susceptibility tensor in zero as well as in finite magnetic fields. We conclude that the ME spin resonances are responsible for the static ME response of the bulk, when the magnetic field is along the x axis, and the symmetric part of the ME tensor with zero diagonal elements dominates over the antisymmetric components.
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