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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 $$\hbox {CuFeO}_{\mathrm{2}}$$ and the interacting quantum spin dimer systems $$\hbox {TlCuCl}_{\mathrm{3}}$$ and $$\hbox {KCuCl}_{\mathrm{3}}$$ .

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., 24 pages, 12 figures

The status of a project to measure spin-isospin responses of neutron drip-line nuclei using a new low-energy neutron detector, PANDORA (Particle Analyzer Neutron Detector Of Real-time Acquisition), is reported. The performance of PANDORA was characterized by the 6He(p,n)6Li reaction in inverse kinematics at the HIMAC facility in Chiba. Observation of the strong transition to the ground state in 6Li is discussed. Preliminary results of 11Li(p,n)11Be and 14Be(p,n)14B experiments in inverse kinematics at RI Beam Factory (RIBF) of RIKEN Nishina Center are also presented including the exotic decay channel of 11Be→9Li + d. Details of the experimental setup based on PANDORA and the SAMURAI large-acceptance magnetic spectrometer, as well as the combined data-acquisition system are described. The neutron-gamma discrimination capability of PANDORA was evaluated, Figure-of-Merit (FoM) values higher than those found in the literature for similar materials were derived from experimental data.

A theory of magnetoacoustic resonance is proposed to measure quadrupole-strain couplings in a spin-triplet state with the $C_{3v}$ point group symmetry, considering the spin-strain interaction in a diamond nitrogen-vacancy (NV) center. Based on the Floquet theory, we demonstrate how the single- and two-phonon transition probabilities depend on the change in the longitudinal and transverse quadrupole couplings, which can be controlled by rotating an applied magnetic field, around the threefold axis. The obtained quadrupole dynamics results are useful for realizing mechanical or ac strain-control of the NV spin as an alternative to the conventional magnetic control by spin resonance., 13 pages, 5 figures

In this study, dielectric constant and pyroelectric current measurements under high pressure up to 16.7 kbar have been performed for the interacting spin dimer system ${\mathrm{TlCuCl}}_{3}$, which exhibits spin-driven ferroelectricity in the magnon Bose-Einstein condensation (BEC) phase with strong quantum spin fluctuation. When pressure is applied, the magnon BEC phase becomes significantly stabilized, whereas the value of the electric polarization decreases in high-pressure regions. It is also observed that electric polarization becomes harder under pressure. Analyses based on both a Landau theory and a microscopic spin Hamiltonian demonstrate that the suppression of quantum fluctuation on the application of pressure caused the observed pressure effects. Consequently, it is revealed that the ferroelectricity in ${\mathrm{TlCuCl}}_{3}$ is highly governed by the quantum spin fluctuation.

We present a microwave electron spin resonance study of the quantum spin dimer system TlCuCl_{3}, 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.

We study a local antisymmetric spin-orbit (ASO) coupling effect on a triangular-triple-quantum-dot (TTQD) system as a theoretical proposal for a new application of the Kondo physics to nanoscale devices. The electric polarization induced by the Kondo effect is strongly correlated with the spin configurations and molecular orbital degrees of freedom in the TTQD. In particular, an abrupt sign reversal of the emergent electric polarization is associated with a quantum critical point in a magnetic field, which can also be controlled by the ASO coupling that changes the mixing weight of different orbital components in the TTQD ground state.

The presence of a Higgs amplitude mode is revealed in a two-dimensional spin-half quantum antiferromagnet, C9H18N2CuBr4 by means of neutron scattering. Spontaneous symmetry-breaking quantum phase transitions play an essential role in condensed-matter physics1,2,3. The collective excitations in the broken-symmetry phase near the quantum critical point can be characterized by fluctuations of phase and amplitude of the order parameter. The phase oscillations correspond to the massless Nambu–Goldstone modes whereas the massive amplitude mode, analogous to the Higgs boson in particle physics4,5, is prone to decay into a pair of low-energy Nambu–Goldstone modes in low dimensions2,6,7. Especially, observation of a Higgs amplitude mode in two dimensions is an outstanding experimental challenge. Here, using inelastic neutron scattering and applying the bond-operator theory, we directly and unambiguously identify the Higgs amplitude mode in a two-dimensional S = 1/2 quantum antiferromagnet C9H18N2CuBr4 near a quantum critical point in two dimensions. Owing to an anisotropic energy gap, it kinematically prevents such decay and the Higgs amplitude mode acquires an infinite lifetime.

Magnetoelectric effects in honeycomb antiferromagnet Co4Nb2O9 are investigated on the basis of symmetry analyses of Co ions in trigonal P-3c1 space group. For each Co 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., Comment: 15 pages, 12 figures

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., Comment: 16 pages, 10 figures

The spin-isospin responses of the 11Li drip-line nucleus has been measured. Preliminary results of the 11Li(p, n)11Be experiment in inverse kinematics at RI Beam Factory (RIBF) of RIKEN Nishina Center are presented including the observation of 1n, 2n, t, d, 2α and 6He+α decay channels of 11Be reaction product. Details of the experimental setup based on PANDORA (Particle Analyzer Neutron Detector Of Real-time Acquisition) low-energy neutron detector and the SAMURAI large-acceptance magnetic spectrometer are described.

Motivated by the recent progress of high-frequency ultrasonic measurements, we propose a theory of magnetoacoustic resonance as a microscopic probe for quadrupole degrees of freedom hidden in magnetic materials. A local strain driven by an acoustic wave couples to electronic states of a magnetic ion through various quadrupole-strain couplings, and this provides a periodically time-dependent oscillating field. As a typical two-level system with the quadrupole, we consider a non-Kramers doublet and investigate single- and multiphonon-mediated transition processes on the basis of the Floquet theory. An analytic form of the transition probability is derived within the weak coupling theory, which helps us analyze the magnetoacoustic quadrupole resonance. We apply the theory to realistic non-Kramers doublet systems for the f2 configuration in Oh and D4h symmetries, and discuss how to identify the relevant quadrupole by controlling the quadrupole-strain coupling with an applied magnetic field in ultrasonic measurements., 13 pages, 5 figures

Magnetic field-induced nonreciprocal magnon in noncollinear magnet is investigated in detail from symmetry viewpoint. To understand the nonreciprocal dispersion relation, we discuss similarity to t...

Motivated by the recent progress of phonon-mediated control in quantum spin devices, we propose a possibility of hybrid measurement using electron paramagnetic resonance (EPR) and a surface acoustic wave (SAW). Considering quadrupole-strain (QS) couplings suggested for silicon vacancies, we present a minimum model of the two-level system to investigate a magnetoacoustic resonance (MAR) coupled to various strain modes driven by the SAW. The longitudinal and transverse QS couplings can be changed by rotating a magnetic field, which depends on a combination of the strain modes. Using the Floquet theory, we elucidate each coupling effect on the time-averaged transition probability, especially focus on a single-phonon transition process. The important result is that the longitudinal QS coupling brings about a sharp photon-assisted resonance and leads to an abrupt change in the field-angle dependent transition probability. Since this phonon transition process is always accompanied by the photon transition, the field angle for the sharp resonance peak can be detected by the EPR measurement. The hybrid EPR-MAR measurement is useful to confirm the existence of quadrupole degrees of freedom strongly coupled to elastic strains, and thus it is expected to be a complementary probe for the precise evaluation of quadrupole properties., Comment: 10 pages, 12 figures

Magnetic excitations in the multiferroic ${\mathrm{Ba}}_{2}{\mathrm{CoGe}}_{2}{\mathrm{O}}_{7}$ are measured by combination of unpolarized and polarized neutron-scattering techniques. The unpolarized neutron spectrum reveals an anisotropic $\mathbf{Q}$ dependence of the intensity of the electromagnon mode at 4 meV. The analysis of the polarized neutron spectra identifies the directions of the magnetic fluctuations of the observed modes. The determined modes are consistent with the calculation by the extended spin-wave theory. A couple of transverse modes and a single longitudinal mode are involved in the magnetic excitation of ${\mathrm{Ba}}_{2}{\mathrm{CoGe}}_{2}{\mathrm{O}}_{7}$. The longitudinal fluctuation takes on a main role in the electromagnon mode.

In this Rapid Communication, we propose a mechanism for electric dipole active spin resonance caused by spin-dependent electric polarization in a quantum spin gapped system. This proposal was successfully confirmed by high-frequency electron spin resonance (ESR) measurements of the quantum spin dimer system ${\mathrm{KCuCl}}_{3}$. ESR measurements by an illuminating linearly polarized electromagnetic wave reveal that the optical transition between the singlet and triplet states in ${\mathrm{KCuCl}}_{3}$ is driven by an ac electric field. The selection rule of the observed transition agrees with the calculation by taking into account spin-dependent electric polarization. We suggest that spin-dependent electric polarization is effective in achieving fast control of quantum spins by an ac electric field.

We measured the temperature dependence of the magnetic susceptibility $\ensuremath{\chi}(T)$ and the specific heat $C(T)$ and the magnetic-field dependence of the magnetization $M(H)$ of ${A}_{2}{\mathrm{Ni}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}\phantom{\rule{4pt}{0ex}}(A$ = 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 ${J}_{1}=9$ K and ${J}_{2}=18$ K, and the effective intertetramer interaction as ${J}_{\mathrm{eff}}=4$ K for ${\mathrm{Rb}}_{2}{\mathrm{Ni}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}$. The susceptibility and magnetization at 1.3 K of ${\mathrm{K}}_{2}{\mathrm{Ni}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}$ are very close to those of ${\mathrm{Rb}}_{2}{\mathrm{Ni}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}$. 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 ${A}_{2}{\mathrm{Ni}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{12}\phantom{\rule{4pt}{0ex}}(A$ = Rb or K).

The notion of a quasiparticle, such as a phonon, a roton, or a magnon, is used in modern condensed matter physics to describe an elementary collective excitation. The intrinsic zero-temperature magnon damping in quantum spin systems can be driven by the interaction of the one-magnon states and multi-magnon continuum. However, detailed experimental studies on this quantum many-body effect induced by an applied magnetic field are rare. Here we present a high-resolution neutron scattering study in high fields on an S=1/2 antiferromagnet C9H18N2CuBr4. Compared with the non-interacting linear spin-wave theory, our results demonstrate a variety of phenomena including field-induced renormalization of one-magnon dispersion, spontaneous magnon decay observed via intrinsic linewidth broadening, unusual non-Lorentzian two-peak structure in the excitation spectra, and a dramatic shift of spectral weight from one-magnon state to the two-magnon continuum., 8 pages, 6 figures, some typos were corrected in the revised version

Quantum magnets, which involve strong quantum fluctuation stemming from noncommutative properties of spin operators, have attracted much attention because of those fascinating properties. In this paper, we report detailed behaviors of the ferroelectricity, driven by the field-induced Bose-Einstein condensation of magnon quasiparticles in the quantum spin gap system ${\mathrm{TlCuCl}}_{3}$. Superposition of the wave functions inherent in a quantum magnet in its ground state plays a key role in the appearance of this ferroelectricity. The field dependence of the spontaneous electric polarization clearly demonstrates that the ferroelectricity is caused by the emergence of the vector spin chirality in the magnon Bose-Einstein condensate. The ferroelectricity is suggested to be significantly enhanced by quantum entanglement in the spin dimer. Furthermore, reflecting the isotropic nature of ${\mathrm{TlCuCl}}_{3}$, the ferroelectricity is very soft with a low electric coercive field ${E}_{\mathrm{r}}\ensuremath{\simeq}0.03$ MV/m. Our analysis indicates that vector components of the electric polarization, which are not caused by the spin current mechanism, appear in ${\mathrm{TlCuCl}}_{3}$.

We measured magnetization, specific heat, electron spin resonance, neutron diffraction, and inelastic neutron scattering of ${\mathrm{CrVMoO}}_{7}$ powder. An antiferromagnetically ordered state appears below ${T}_{\mathrm{N}}=26.5\ifmmode\pm\else\textpm\fi{}0.8$ K. We consider that the probable spin model for ${\mathrm{CrVMoO}}_{7}$ is an interacting antiferromagnetic spin-$\frac{3}{2}$ dimer model. We evaluated the intradimer interaction $J$ to be $25\ifmmode\pm\else\textpm\fi{}1$ K and the effective interdimer interaction ${J}_{\mathrm{eff}}$ to be $8.8\ifmmode\pm\else\textpm\fi{}1$ K. ${\mathrm{CrVMoO}}_{7}$ 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 $0.73(2){\ensuremath{\mu}}_{\mathrm{B}}$. It is much smaller than a classical value $\ensuremath{\sim}3{\ensuremath{\mu}}_{\mathrm{B}}$. Longitudinal-mode magnetic excitations may be observable in single crystalline ${\mathrm{CrVMoO}}_{7}$.

We measured the temperature dependence of the magnetic susceptibility and specific heat and the magnetic-field dependence of the magnetization of CuInVO$_5$. An antiferromagnetically ordered state appears below $T_{\rm N} = 2.7$ K. We observed a $\frac{1}{2}$ quantum magnetization plateau above 30 T at 1.3 K. We show that the spin system consists of antiferromagnetic spin-$\frac{1}{2}$ tetramers with $J_1 = 240 \pm 20$ and $J_2 = -142 \pm 10$ K for the intratetramer interactions.

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 Kon...

The Bose–Einstein condensation is a fascinating phenomenon, which results from quantum statistics for identical particles with an integer spin. Surprising properties, such as superfluidity, vortex quantization or Josephson effect, appear owing to the macroscopic quantum coherence, which spontaneously develops in Bose–Einstein condensates. Realization of Bose–Einstein condensation is not restricted in fluids like liquid helium, a superconducting phase of paired electrons in a metal and laser-cooled dilute alkali atoms. Bosonic quasi-particles like exciton-polariton and magnon in solids-state systems can also undergo Bose–Einstein condensation in certain conditions. Here, we report that the quantum coherence in Bose–Einstein condensate of the magnon quasi particles yields spontaneous electric polarization in the quantum magnet TlCuCl3, leading to remarkable magnetoelectric effect. Very soft ferroelectricity is realized as a consequence of the O(2) symmetry breaking by magnon Bose–Einstein condensation. The finding of this ferroelectricity will open a new window to explore multi-functionality of quantum magnets., Magnons, quantized spin excitations in magnetic materials, may undergo Bose-Einstein condensation into a macroscopic correlated quantum state at low temperature. Here, the authors demonstrate how magnon condensation in quantum magnet TlCuCl3 generates an electrical polarization.

${\mathrm{Ba}}_{2}{\mathrm{CoGe}}_{2}{\mathrm{O}}_{7}$ exhibits a collinear-antiferromagnetic structure with the easy axis along $\ensuremath{\langle}100\ensuremath{\rangle}$ directions and an antiferroelectric order with the polarization axis along the [001] direction. By applying the electric field the magnetic moment rotates from $\ensuremath{\langle}100\ensuremath{\rangle}$ to [110] directions and, simultaneously, the antiferroelectric state changes to the ferroelectric state gradually. This magnetoelectric effect, i.e., continuous control of the local magnetic moment by the electric field, is quantitatively explained by the Hamiltonian including the dielectric energy.

A triangular triple quantum dot gives various Kondo effects, such as the emergence of an electric polarization accompanied by a complete compensation of spin degrees of freedom. The interplay of spin and charge of electrons in quantum dots is investigated using an Anderson model with an equilateral triangular spin cluster, in which a single electron state at one site is hybridized with a conduction band in a lead. The numerical renormalization group analysis shows how a nonzero electric polarization develops with local electrons traveling in the loop and how it depends on the hybridization strength as an experimentally controllable parameter in the Kondo effect., Comment: 5 pages, 5 figures

We performed inelastic neutron scattering experiments on ${\mathrm{Cu}}_{2}^{114}\mathrm{Cd}{}^{11}{\text{B}}_{2}{\mathrm{O}}_{6}$ powder. The magnetic excitations at low temperatures are similar to those of the interacting spin-$\frac{1}{2}$ tetramers in the ordered state. The weak excitations existing above 3 meV suggest that the Higgs mode appears in ${\mathrm{Cu}}_{2}{\mathrm{CdB}}_{2}{\mathrm{O}}_{6}$ at ambient pressure and zero magnetic field. We evaluated ${J}_{1}=27.3\ifmmode\pm\else\textpm\fi{}1.0$ and ${J}_{2}=\ensuremath{-}14.0\ifmmode\pm\else\textpm\fi{}1.4$ meV for the intratetramer interactions and ${J}_{3}=\ensuremath{-}0.4\ifmmode\pm\else\textpm\fi{}0.2$ and ${J}_{4}=1.4\ifmmode\pm\else\textpm\fi{}0.2$ meV 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 $(3.6\ifmmode\pm\else\textpm\fi{}0.8$ 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.

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 T N = 2.7 K. We observed a quantum magnetization plateau above 30 T at 1.3 K. The probable spin model for CuInVO5 is an interacting spin- tetramer model. We evaluated the values of the intratetramer interactions as J 1 = 240 ± 20 K (antiferromagnetic) and J 2 = −142 ± 10 K (ferromagnetic) and the value of the effective intertetramer interaction as J eff = 30 ± 4 K. The ground state of the isolated spin tetramer with the J 1 and J 2 values is spin singlet. The shrinkage of ordered magnetic moments by quantum fluctuation can be expected. Longitudinal-mode magnetic excitations may be observable in CuInVO5.

We performed inelastic neutron scattering experiments on Cu$_2$$^{114}$Cd$^{11}$B$_2$O$_6$ 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 Cu$_2$CdB$_2$O$_6$ at ambient pressure and zero magnetic field. We evaluated $J_1 = 27.3 \pm 1.0$ and $J_2 = -14.0 \pm 1.4$ meV for the intra-tetramer interactions and $J_3 = -0.4 \pm 0.2$ and $J_4 = 1.4 \pm 0.2$ meV for the inter-tetramer interactions. The spin gap in the isolated spin tetramer was calculated to be 1.6 meV, which is less than the effective inter-tetramer interaction value ($3.6 \pm 0.8$ 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., Comment: 9 pages, 7 figures, 1 table

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., 11 pages, 5 figures

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., Comment: 28 pages, 9 figures

Magnetic excitation in a spin dimer system on a bilayer honeycomb lattice is investigated in the presence of a zigzag edge, where disordered and ordered phases can be controlled by a quantum phase transition. In analogy with the case of graphene with a zigzag edge, a flat edge magnon mode appears in the disordered phase. In an ordered phase, a finite magnetic moment generates a mean-field potential to the magnon. Since the potential is nonuniform on the edge and bulk sites, it affects the excitation, and the dispersion of the edge mode deviates from the flat shape. We investigate how the edge magnon mode evolves when the phase changes through the quantum phase transition and discuss the similarities to ordered spin systems on a monolayer honeycomb lattice., Comment: 17 pages, 13 figures

We study an orbitally degenerate Kondo effect in a triangular triple quantum dot (TTQD), where the three dots are connected vertically with a single metallic lead through electron tunneling. Both spin and orbital degrees of freedom play an important role in the SU(4) Kondo effect. This is demonstrated by an equilateral TTQD Kondo system at half-filling, by Wilson's numerical renormalization group method. We show how an emergent electric polarization of the TTQD is associated with a crossover from SU(4) to SU(2) symmetry in the low-temperature state. A marked sign reversal of the electric polarization is generated by the fine-tuning of Kondo coupling with degenerate orbitals, which can be utilized to reveal orbital dynamics in the SU(4) Kondo effect., 5 pages, 5 figures

Since a symmetric spin-dependent electric polarization makes quantum spin systems couple to an electric field, it is one of a possible origin of electromagnon excitations in noncollinear (spiral) magnetically ordered states. In collinear ordered states, however, it is believed that the electromagnon excitation is difficult to realize. In the present study, we focus on the symmetric spin-dependent electric polarization and study the electromagnon excitation in both collinear and noncollinear states. In one-magnon excitation process, it is found that the symmetric spin-dependent polarization couples to a longitudinal fluctuation of the ordered moment and that the electromagnon measurements probe the longitudinal (Higgs) mode selectively. In noncollinear states, we report that both Higgs and Nambu-Goldstone (transverse) modes are observable.

The Kondo effect plays an important role in emergence of electric polarization in a triangular triple-quantum-dot system, where one of the three dots is point-contacted with a single lead, and a magnetic flux penetrates through the triangular loop. The Kondo-induced electric polarization exhibits an Aharonov-Bohm type oscillation as a function of the magnetic flux. Our theoretical study shows various oscillation patterns associated with the field-dependent mixing of twofold orbitally degenerate ground states and their sensitivity to the point contact.

Magnetic excitation in the interacting spin dimer system NH4CuCl3 is investigated on the basis of an extended spin-wave 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.