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It is known that the longitudinal and transverse excitation modes can exist in the vicinity of a quantum critical point in the ordered phase of quantum magnetic systems. The total moment sum rule for such systems is derived on the basis of the extended spin-wave theory, where both longitudinal and transverse magnetic excitations are taken into account. The sum rule is resolved into elastic, one-magnon, and two-magnon components. The formulation is applicable to spin systems with the longitudinal mode, such as S = 1 systems with single-ion anisotropy of easy-plane type and spin dimer systems. The result helps us analyze and understand measured data of inelastic neutron scattering. [ABSTRACT FROM AUTHOR]

Magnetoelectric effects in honeycomb antiferromagnet Co4Nb2O9 are investigated on the basis of symmetry analyses of Co2+ ions in trigonal P3¯c1 space group. For each Co2+ ion, the possible spin dependence is classified by C3 point-group symmetry. This accounts for the observed main effect that an electric polarization rotates in the opposite direction at the twice speed relative to the rotation of the external magnetic field applied in the ab-plane. Inversion centers and twofold axes in the unit cell restrict the active spin-dependence of the electric polarization, which well explains the observed experimental results. Expected optical properties of quadrupolar excitation and various types of dichroism are also discussed. [ABSTRACT FROM AUTHOR]

Crystal field triplet ground states in f² configurations such as Pr ions have quadrupolar coupling as well as magnetic coupling to conduction electrons, leading to a nontrivial non-Fermi liquid Kondo physics associated with quadrupole degrees of freedom. In particular, a magnetic-field-induced quadrupole moment exhibits the same power-law temperature dependence as a magnetic moment, which is demonstrated by a numerical renormalization group analysis. Both thermodynamic quantities are also scaled by a single energy parameter as well as a quadrupole susceptibility, indicating that magnetic dipoles and electric quadrupoles are closely correlated. The field-induced quadrupoles may be relevant for confirmation of the Kondo effect of triplet origin, which could cause unusual heavy fermion properties of Prbased metallic compounds. [ABSTRACT FROM AUTHOR]

We study the local antisymmetric spin-orbit (ASO) coupling effect on spin, orbital, and charge degrees of freedom for the Kondo effect in a triangular triple quantum dot (TTQD). Here, one of the three QDs is coupled to a metallic lead through electron tunneling, and a local electric polarization is induced by the Kondo effect. The ASO interaction is introduced in the other two coupled QDs on the opposite side of the lead. Generally, the ASO coupling effect is very weak and not easily detectable, but it essentially causes spin and charge reconfigurations in the TTQD through the Kondo effect. Using an extended Anderson model for the TTQD Kondo system, we elucidate that the ASO coupling gives rise to a considerable reduction of the emergent electric polarization, as a consequence of the parity mixing of molecular orbitals in the triangular loop as well as the spin-up and spin-down coupling of local electrons. The latter leads to a local diamagnetic susceptibility owing to the ASO coupled spins. We also show that the Kondo-induced electric polarization can be controlled by the ASO coupling as well as by the magnetic flux penetrating through the TTQD. [ABSTRACT FROM AUTHOR]

Spin-dependent electric dipole operators are investigated group-theoretically for the emergence of an electric dipole induced by a single spin or by two spins, where the spin dependences are completely classified up to the quadratic order. For a single spin, a product of spin operators behaves as an even-parity electric quadrupole operator, which differs from an odd-parity electric dipole. The lack of the inversion symmetry allows the even- and odd-parity mixing, which leads to the electric dipole described by the electric quadruple operators. Point-group tables are given for classification of the possible spin-dependent electric dipoles and for the qualitative analysis of multiferroic properties, such as an emergent electric dipole moment coexisting with a magnetic moment, electromagnon excitation, and directional dichroism. The results can be applied to a magnetic ion in crystals or embedded in molecules at a site without the inversion symmetry. In the presence of an inversion symmetry, the electric dipole does not appear for a single spin. This is not the case for the electric dipole induced by two spins with antisymmetric spin dependence, which is known as vector spin chirality, in the presence of the inversion center between the two spins. In the absence of the inversion center, symmetric spin-dependent electric dipoles are also relevant. The detailed analysis of various symmetries of two-spin states is applied to spin dimer systems and the related multiferroic properties. [ABSTRACT FROM AUTHOR]

Magnetic excitation in the interacting spin dimer system NH4CuCl3 is investigated on the basis of an extended spinwave theory, assuming a doubled unit cell with four dimer sublattices of inequivalent intradimer interactions as suggested by neutron scattering measurements. In the magnetically ordered phase, there are both transverse (Nambu-Goldstone) and longitudinal (Higgs) excitation modes as in the pressure-induced ordered phase of the isostructural spin dimer compounds TlCuCl3 and KCuCl3. The inequivalent dimer model is consistent with the magnon dispersion relation at zero magnetic field and with the field dependence of the excitation energies obtained by neutron scattering and ESR measurements. This supports the existence of four dimer sublattices with inequivalent dimers in NH4CuCl3. [ABSTRACT FROM AUTHOR]

A magnetic flux effect is studied theoretically on an electric polarization induced by the Kondo effect in a triangular triple-quantum-dot system, where one of the three dots is connected to a metallic lead. This electric polarization exhibits an Aharonov-Bohm oscillation as a function of the magnetic flux penetrating through the triangular loop. The numerical renormalization group analysis reveals how the oscillation pattern depends on the Kondo coupling of a local spin with lead electrons, which is sensitive to the point contact with the lead. It provides an experimental implication that the Kondo effect is the origin of the emergent electric polarization. [ABSTRACT FROM AUTHOR]

Electromagnon excitation is investigated on the basis of the symmetric spin-dependent electric polarization in both collinear and noncollinear magnetically ordered states. We focus on quantum spin systems with a large easy-plane single-ion anisotropy, where both massive longitudinal (Higgs) and massless transverse (Nambu-Goldstone) modes exist in the magnetic excitations. In the one-magnon excitation, it is found that the symmetric spin-dependent electric polarization is connected with the longitudinal fluctuation of the ordered moment and that the Higgs mode appears as the electromagnon excitation in collinear states. In noncollinear states, both the Higgs and Nambu-Goldstone modes are observable as the electromagnon excitation. [ABSTRACT FROM AUTHOR]

We present a microwave electron spin resonance study of the quantum spin dimer system TlCuCl3, which shows the magnetic-field-induced ordering with both antiferromagnetic spin order and ferroelectricity by the Bose-Einstein condensation (BEC) of triplon quasiparticles. Our main achievement is an electrical switching of the nonreciprocal directional microwave response in the triplon BEC phase. High-speed directional control of microwave absorption by applying an electric field has been accomplished in this Letter. The strength of the observed nonreciprocal microwave response well agrees with the calculation based on Kubo theory with the parameters, evaluated from the static electric polarization in this material. [ABSTRACT FROM AUTHOR]

We measured the temperature dependence of the magnetic susceptibility and specific heat and the magnetic-field dependence of the magnetization of CuInVO5. An antiferromagnetically ordered state appears below TN = 2.7 K. We observed a 1/2 quantum magnetization plateau above 30 T at 1.3 K. We consider that the probable spin model for CuInVO5 is an interacting spin-1/2 tetramer model. We evaluated values of the intratetramer interactions as J1 = 240±20 K (antiferromagnetic) and J2 = -142±10 K (ferromagnetic). The ground state of the isolated spin tetramer with the J1 and J2 values is spin singlet. The shrinkage of ordered magnetic moments by quantum fluctuation can be expected. Detectable low-energy longitudinal-mode magnetic excitations may exist in CuInVO5. [ABSTRACT FROM AUTHOR]

Quantum phase transitions in quantum matter occur at zero temperature between distinct ground states by tuning a nonthermal control parameter. Often, they can be accurately described within the Landau theory of phase transitions, similarly to conventional thermal phase transitions. However, this picture can break down under certain circumstances. Here, we present a comprehensive study of the effect of hydrostatic pressure on the magnetic structure and spin dynamics of the spin-1/2 ladder compound C9H18N2CuBr4. Single-crystal heat capacity and neutron diffraction measurements reveal that the Néel-ordered phase breaks down beyond a critical pressure of Pc ∼ 1.0 GPa through a continuous quantum phase transition. Estimates of the critical exponents suggest that this transition may fall outside the traditional Landau paradigm. The inelastic neutron scattering spectra at 1.3 GPa are characterized by two well-separated gapped modes, including one continuum-like and another resolution-limited excitation in distinct scattering channels, which further indicates an exotic quantum-disordered phase above Pc. There is a class of quantum phase transitions that do not fit into the traditional Landau paradigm, but are described in terms of fractionalized degrees of freedom and emergent gauge fields. Hong et al. find evidence of such a transition in a molecular spin-1/2 antiferromagnetic ladder compound under hydrostatic pressure. [ABSTRACT FROM AUTHOR]

KCuCl 3 is known to show a quantum phase transition from the disordered to antiferromagnetically ordered phases by applying pressure. There is a longitudinal excitation mode (Higgs amplitude mode) in the vicinity of the quantum critical point in the ordered phase. To detect the Higgs amplitude mode, high-pressure ESR measurements are performed in KCuCl 3 . The experimental data are analyzed by the extended spin-wave theory on the basis of the vector spin chirality. We report the first ESR detection of the Higgs amplitude mode and the important role of the electric dipole described by the vector spin chirality. [ABSTRACT FROM AUTHOR]

We review electric dipole active magnetic resonance and nonreciprocal directional dichroism in magnetoelectric multiferroic materials in terahertz and millimeter wave regions. Owing to dynamical magnetoelectric coupling generated by the spin-dependent electric polarization, magnetic resonance, which usually occurs owing to magnetic dipole transition, can be induced by the oscillating electric fields of electromagnetic wave. This electric dipole active magnetic resonance can be useful for microscopic investigations of magnetic excitation in unconventional spin systems. The magnetoelectric coupling also induces the nonreciprocal directional dichroism, which provides a novel functionality to materials as an optical diode, in teraheltz and microwave absorption by magnetic resonance. As examples, we describe the results of the high field ESR measurements of the triangular lattice antiferromagnet CuFeO 2 and the interacting quantum spin dimer systems TlCuCl 3 and KCuCl 3 . [ABSTRACT FROM AUTHOR]

We performed inelastic neutron scattering experiments on Cu2114Cd11B2O6 powder. The magnetic excitations at low temperatures are similar to those of the interacting spin-1/2 tetramers in the ordered state. The weak excitations existing above 3 meV suggest that the Higgs mode appears in Cu2CdB2O6 at ambient pressure and zero magnetic field. We evaluated J1=27.3±1.0 and J2=-14.0±1.4 meV for the intratetramer interactions and J3=-0.4±0.2 and J4=1.4±0.2meV for the intertetramer interactions. The spin gap in the isolated spin tetramer was calculated to be 1.6 meV, which is less than the effective intertetramer interaction value (3.6±0.8 meV). Therefore, antiferromagnetic long-range order is possible, although the ground state of the isolated spin tetramer is the spin-singlet state. We discuss the temperature dependence of the magnetic excitations. [ABSTRACT FROM AUTHOR]

We measured the temperature dependence of the magnetic susceptibility χ(T) and the specific heat C(T) and the magnetic-field dependence of the magnetization M(H) of A2Ni2Mo3O12(A = Rb or K) powder. We consider that the probable spin model is an interacting spin-1 antiferromagnetic tetramer model. We evaluated values of the intratetramer interactions as J1=9 K and J2=18 K, and the effective intertetramer interaction as Jeff=4 K for Rb2Ni2Mo3O12. The susceptibility and magnetization at 1.3 K of K2Ni2Mo3O12 are very close to those of Rb2Ni2Mo3O12. We observed a phase transition to a magnetically ordered state in C(T)/T in magnetic fields above 3 T. The transition temperature increases with magnetic field. Probably, the ordered state appears around 1.8 K even in 0 T. The ordered state in 0 T, however, is not stable enough like an order in the vicinity of a quantum critical point. Longitudinal-mode magnetic excitations may be observable in single crystalline A2Ni2Mo3O12(A = Rb or K). [ABSTRACT FROM AUTHOR]

We measured magnetization, specific heat, electron spin resonance, neutron diffraction, and inelastic neutron scattering of CrVMoO7 powder. An antiferromagnetically ordered state appears below TN=26.5±0.8 K. We consider that the probable spin model for CrVMoO7 is an interacting antiferromagnetic spin-3/2 dimer model. We evaluated the intradimer interaction J to be 25±1 K and the effective interdimer interaction Jeff to be 8.8±1 K. CrVMoO7 is a rare spin dimer compound that shows an antiferromagnetically ordered state at atmospheric pressure and zero magnetic field. The magnitude of ordered moments is 0.73(2)μB. It is much smaller than a classical value ~3μB. Longitudinal-mode magnetic excitations may be observable in single crystalline CrVMoO7. [ABSTRACT FROM AUTHOR]