We report a comprehensive neutron scattering study of low energy magnetic excitations in the breathing pyrochlore helimagnetic $\text{Cu}_2\text{OSeO}_3$. Fully documenting the four lowest energy magnetic modes that leave the ferrimagnetic configuration of the "strong tetrahedra" intact ($|\hbarω|<13$ meV), we find gapless quadratic dispersion at the $Γ$ point for energies above 0.2 meV, two doublets separated by 1.6(2) meV at the $R$ point, and a bounded continuum at the $X$ point. Our constrained rigid spin cluster model relates these features to Dzyaloshinskii-Moriya (DM) interactions and the incommensurate helical ground state. Combining conventional spin wave theory with a spin cluster form-factor accurately reproduces the measured equal time structure factor through multiple Brillouin zones. An effective spin Hamiltonian describing the complex anisotropic inter-cluster interactions is obtained.
We report on the observation of magnon thermal conductivity $κ_m\sim$ 70 W/mK near 5 K in the helimagnetic insulator Cu$_2$OSeO$_3$, exceeding that measured in any other ferromagnet by almost two orders of magnitude. Ballistic, boundary-limited transport for both magnons and phonons is established below 1 K, and Poiseuille flow of magnons is proposed to explain a magnon mean-free path substantially exceeding the specimen width for the least defective specimens in the range 2 K $<T<$ 10 K. These observations establish Cu$_2$OSeO$_3$ as a model system for studying long-wavelength magnon dynamics…
We report studies of thermal conductivity as functions of magnetic field and temperature in the helimagnetic insulator Cu$_2$OSeO$_3$ that reveal novel features of the spin-phase transitions as probed by magnon heat conduction. The tilted conical spiral and low-temperature skyrmion phases, recently identified in small-angle neutron scattering studies, are clearly identified by sharp signatures in the magnon thermal conductivity. Magnon scattering associated with the presence of domain boundaries in the tilted conical phase and regions of skyrmion and conical-phase coexistence are identified.
Linear dichroism -- the polarization dependent absorption of electromagnetic waves -- is routinely exploited in applications as diverse as structure determination of DNA or polarization filters in optical technologies. Here filamentary absorbers with a large length-to-width ratio are a prerequisite. For magnetization dynamics in the few GHz frequency regime strictly linear dichroism was not observed for more than eight decades. Here, we show that the bulk chiral magnet Cu$_{2}$OSeO$_{3}$ exhibits linearly polarized magnetization dynamics at an unexpectedly small frequency of about 2 GHz. Unlik…
We present a thorough $^{77}$Se NMR study of a single crystal of the magnetoelectric compound Cu$_2$OSeO$_3$. The temperature dependence of the local electronic moments extracted from the NMR data is fully consistent with a magnetic phase transition from the high-T paramagnetic phase to a low-T ferrimagnetic state with 3/4 of the Cu$^{2+}$ ions aligned parallel and 1/4 aligned antiparallel to the applied field of 14.09 T. The transition to this 3up-1down magnetic state is not accompanied by any splitting of the NMR lines or any abrupt modification in their broadening, hence there is no observa…
Chiral magnets with topologically nontrivial spin order such as Skyrmions have generated enormous interest in both fundamental and applied sciences. We report broadband microwave spectroscopy performed on the insulating chiral ferrimagnet Cu$_{2}$OSeO$_{3}$. For the damping of magnetization dynamics we find a remarkably small Gilbert damping parameter of about $1\times10^{-4}$ at 5 K. This value is only a factor of 4 larger than the one reported for the best insulating ferrimagnet yttrium iron garnet. We detect a series of sharp resonances and attribute them to confined spin waves in the mm-si…
In this work, we present a comprehensive study of the low energy optical magnetic response of the skyrmionic Mott insulator Cu$_2$OSeO$_3$ via high resolution time-domain THz spectroscopy. In zero field, a new magnetic excitation not predicted by spin-wave theory with frequency $f$ = 2.03 THz is observed and shown, with accompanying time-of-flight neutron scattering experiments, to be a zone folded magnon from the $\mathrm{R}$ to $\mathrmΓ$ points of the Brillouin zone. Highly sensitive polarimetry experiments performed in weak magnetic fields, $μ_0$H $<$ 200 mT, observe Faraday and Kerr rotat…
We theoretically study the intrinsic thermal Hall and spin Nernst effect in collinear ferrimagnets on a honeycomb lattice with broken inversion symmetry. The broken inversion symmetry allows in-plane Dzyaloshinskii-Moriya interaction between the nearest neighbors, which does not affect the magnon spectrum in the linear spin wave theory. However, the Dzyaloshinskii-Moriya interaction can induce large Berry curvature in the magnetoelastic excitation spectrum through the magnon-phonon interaction to produce thermal Hall current. Furthermore, we find that the magnetoelastic excitations transport s…
Within the Dyson-Maleev boson formalism, we study the zero-temperature magnon dispersions in a family of one-dimensional quantum Heisenberg ferrimagnets composed of two different spins $(S_1,S_2)$ in the elementary cell. It is shown that the spin-wave theory can produce precise quantitative results for the low-energy excitations. The spin-stiffness constant $ρ_s$ and the optical magnon gap $Δ$ of different $(S_1,S_2)$ ferrimagnetic systems are calculated, respectively, to second and third order in the quasiparticle interaction. The spin-wave results are compared with available numerical estima…
We present a theory of magnetoelectric magnon-photon coupling in cavities hosting noncentrosymmetric magnets. Analogously to nonreciprocal phenomena in multiferroics, the magnetoelectric coupling is time-reversal and inversion asymmetric. This asymmetry establishes a means for exceptional tunability of magnon-photon coupling, which can be switched on and off by reversing the magnetization direction. Taking the multiferroic skyrmion-host Cu$_2$OSeO$_3$ with ultralow magnetic damping as an example, we reveal the electrical activity of skyrmion eigenmodes and propose it for magnon-photon splittin…
We compare the ground-state features of alternating ferrimagnetic chains $(1/2, S)$ with $S=1,3/2,2,5/2$ in a magnetic field and the corresponding Holstein-Primakoff bosonic models up to order $\sqrt{s/S}$, with $s=1/2$, considering the fully polarized magnetization as the boson vacuum. {The single-particle Hamiltonian is a Rice-Mele model with uniform hopping and modified boundaries, while the interactions have a correlated (density-dependent) hopping term and magnon-magnon repulsion.} The magnon-magnon repulsion increases the many-magnon energy and the density-dependent hopping decreases the…
The strongly correlated cuprate Cu$_2$OSeO$_3$ has recently been identified as the first insulating system exhibiting a skyrmion lattice phase. Using a microscopic multi-boson theory for its magnetic ground state and excitations, we establish the presence of two distinct types of modes: a low energy manifold that includes a gapless Goldstone mode and a set of weakly dispersive high-energy magnons. These spectral features are the most direct signatures of the fact that the essential magnetic building blocks of Cu$_2$OSeO$_3$ are not individual Cu spins, but rather weakly-coupled Cu$_4$ tetrahed…
We present long-wavelength neutron diffraction data measured on both single crystal and polycrystalline samples of the skyrmion host material Cu$_{2}$OSeO$_{3}$. We observe magnetic satellites around the $(0\bar{1}1)$ diffraction peak not accessible to other techniques, and distinguish helical from conical spin textures in reciprocal space. We confirm successive transitions from helical to conical to field polarised ordered spin textures as the external magnetic field is increased. The formation of a skyrmion lattice with propagation vectors perpendicular to the field direction is observed in …
Chiral Magnon Mixing by Symmetry-Breaking in Collinear Ferrimagnets
Ames National Laboratory（艾姆斯国家实验室）；Department of Physics and Astronomy, Iowa State University（爱荷华州立大学物理与天文系）；Neutron Scattering Division, Oak Ridge National Laboratory（橡树岭国家实验室中子散射部）
Nuclear spin-lattice relaxation in one-dimensional Heisenberg ferrimagnets is studied by means of a modified spin-wave theory. We consider the second-order process, where a nuclear spin flip induces virtual spin waves which are then scattered thermally via the four-magnon exchange interaction, as well as the first-order process, where a nuclear spin directly interacts with spin waves via the hyperfine interaction. We point out a possibility of the three-magnon relaxation process predominating over the Raman one and suggest model experiments.
Recent proton spin-lattice relaxation-time (T_1_) measurements on the ferrimagnetic chain compound NiCu(C_7_H_6_N_2_O_6_)(H_2_O)_3_2H_2_O are explained by an elaborately modified spin-wave theory. We give a strong evidence of the major contribution to 1/T_1_ being made by the three-magnon scattering rather than the Raman one.
Nuclear spin-lattice relaxation in one-dimensional Heisenberg ferrimagnets is studied by means of a modified spin-wave theory. Calculating beyond the first-order mechanism, where a nuclear spin directly interacts with spin waves through the hyperfine coupling, we demonstrate that the exchange-scattering-enhanced three-magnon nuclear relaxation may generally predominate over the Raman one with increasing temperature and decreasing field. Recent proton spin-lattice relaxation-time (T_1_) measurements on the ferrimagnetic chain compound NiCu(C_7_H_6_N_2_O_6_)(H_2_O)_3_2H_2_O suggest that the majo…
Clusters of single spins form the relevant spin entities in the formation of long-range magnetic order in spin cluster Mott insulators. Such type of spin order bears resemblance to molecular crystals, and we therefore may expect a prototypical spin wave spectrum which can be divided into low-energy external and high-energy internal cluster spin wave modes. Here, we study high-energy spin cluster excitations in the spin cluster Mott insulator Cu$_{2}$OSeO$_{3}$ by means of spontaneous Raman scattering. Multiple high-energy optical magnon modes are observed, of which the Raman-activity is shown …
Magnetic field effects on spin-split band and magnon transport in altermagnets and emergent compensated ferrimagnets
Graduate School of Advanced Science and Engineering, Hiroshima University（广岛大学先进理工学研究科）；Center for Life Photonic Innovation, Kobe University（神户大学生命光子创新中心）
Spin excitations were studied by absorption spectroscopy in CaBaCo4O7 which is a type-I multiferroic compound with the largest magnetic-order induced ferroelectric polarization (ΔP=17mC/m2) reported, so far. We observed two optical magnon branches: a solely electric dipole allowed one and a mixed magnetoelectric resonance. The entangled magnetization and polarization dynamics of the magnetoelectric resonance gives rise to unidirectional light absorption, i.e. that magnon mode absorbs the electromagnetic radiation for one propagation direction but not for the opposite direction. Our systematic …
The spinel MnV_2O_4 is a two-sublattice ferrimagnet, with site A occupied by the Mn^{2+} ion and site B by the V^{3+} ion. The magnon of the system, the transversal fluctuation of the total magnetization, is a complicated mixture of the sublattice A and B transversal magnetic fluctuations. As a result, the magnons' fluctuations suppress in a different way the manganese and vanadium magnetic orders and one obtains two phases. At low temperature (0,T^*) the magnetic orders of the Mn and V ions contribute to the magnetization of the system, while at the high temperature (T^*,T_N), the vanadium ma…
We theoretically study the optical generation of dc spin current (i.e., a spin-current solar cell) in ordered antiferromagnetic and ferrimagnetic insulators, motivated by a recent study on the laser-driven spinon spin current in noncentrosymmetric quantum spin chains [H. Ishizuka and M. Sato, Phys. Rev. Lett. 122, 197702 (2019)]. Using a non-linear response theory for magnons, we analyze the dc spin current generated by a linearly-polarized electromagnetic wave (typically, terahertz or gigahertz waves). Considering noncentrosymmetric two-sublattice magnets as an example, we find a finite dc sp…
In response to recent nuclear-magnetic-resonance measurements on a ferrimagnetic chain compound NiCu(C_7H_6N_2O_6)(H_2O)_3 2H_2O [Solid State Commun. {\bf 113} (2000) 433], we calculate the nuclear spin-lattice relaxation rate 1/T_1 in terms of a modified spin-wave theory. Emphasizing that the dominant relaxation mechanism arises from the direct (single-magnon) process rather than the Raman (two-magnon) one, we explain the observed temperature and applied-field dependences of 1/T_1. Ferrimagnetic relaxation phenomena are generally discussed and novel ferrimagnets with extremely slow dynamics a…
We experimentally study magnetic resonances in the helical and conical magnetic phases of the chiral magnetic insulator Cu$_2$OSeO$_3$ at the temperature $T$=5 K. Using a broadband microwave spectroscopy technique based on vector network analysis, we identify three distinct sets of helimagnon resonances in the frequency range 2 GHz $\leq f \leq$ 20 GHz. The extracted resonance frequencies are in accordance with calculations of the helimagnon bandstructure found in an intrinsic chiral magnonic crystal. The periodic modulation of the equilibrium spin direction that leads to the formation of the …
We provide evidence of a superfluid-insulator transition (SIT) of magnons in a quasi-one-dimensional quantum ferrimagnet with {\it isotropic} competing antiferromagnetic spin interactions. This SIT occurs between two distinct ferrimagnetic phases due to the frustration-induced closing of the gap to a magnon excitation. It thus causes a coherent superposition of singlet and triplet states at lattice unit cells and a power-law decay on the staggered spin correlation function along the transverse direction to the spontaneous magnetization. A hard-core boson map suggests that asymptotically close …
Two-sublattice ferrimagnet, with spin-$s_1$ operators $\bf{S_{1i}}$ at the sublattice $A$ site and spin-$s_2$ operators $\bf{S_{2i}}$ at the sublattice $B$ site, is considered. The magnon of the system, the transversal fluctuation of the total magnetization, is a complicate mixture of the transversal fluctuations of the sublattice $A$ and $B$ spins. As a result, the magnons' fluctuations suppress in a different way the magnetic orders of the $A$ and $B$ sublattices and one obtains two phases. At low temperature $(0,T^*)$ the magnetic orders of the $A$ and $B$ spins contribute to the magnetizat…
We discuss that a low-energy effective Lagrangian relying on SO(3) $\rightarrow$ SO(2) is applicable for a ferrimagnet as well as a ferromagnet and an antiferromagnet. The analysis of the particle states shows that there exist not only massless modes with the dispersion relations $ω\propto |\bm{k}|,\, |\bm{k}|^2$, i.e., the so-called type-I and type-II Nambu-Goldstone modes, respectively, but also gapped modes with $ω\propto m^2+|\bm{k}|^2$. We clarify how the coefficients of the terms with one time derivative and those with two time derivatives in the effective Lagrangian determine the order …
The present paper is a sequel to the paper by Karchev (2008 J.Phys.:Condens.Matter {\bf 20} 325219). A two-sublattice ferrimagnet, with spin-$s_1$ operators $\bf{S_{1i}}$ at the sublattice $A$ site and spin-$s_2$ operators $\bf{S_{2i}}$ at the sublattice $B$ site, is considered. Renormalized spin-wave theory, which accounts for the magnon-magnon interaction, and its extension are developed to describe the two ferrimagnetic phases $(0,T^*)$ and $(T^*,T_N)$ in the system, and to calculate the magnetization as a function of temperature. The influence of the parameters in the theory on the charact…
The nuclear spin-lattice relaxation time $T_1$ of $^{31}P$ nuclei in the title compound is measured for the first time and interpreted in terms of a modified spin-wave theory. We establish a novel scenario for one-dimensional ferrimagnetic spin dynamics -- it is three-magnon processes enhanced by exchange scattering, rather than Raman processes, that make the major contribution to $1/T_1$.
Spin-1/2 Heisenberg diamond-like decorated honeycomb lattice in a magnetic field from the perspective of localized magnons and exact diagonalization
Faculty of Science, P. J. Šafárik University（帕·约·沙法里克大学理学院）；Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université（CY塞尔吉巴黎大学，CNRS UMR 8089理论物理与建模实验室）
A two-sublattice spin-fermion model of ferrimagnetic spinel, with spin-$1/2$ itinerant electrons at the sublattice $A$ site and spin-$s$ localized electrons at the sublattice $B$ site is considered. The exchange between itinerant and localized electrons is antiferromanetic. As a result the external magnetic field, applied along the magnetization of the localized electrons, compensates the Zeeman splitting due to the spin-fermion exchange and magnon-fermion interaction induces spin anti-parallel p-wave superconductivity which coexists with magnetism. We have obtained five characteristic values …
We use a semiclassical large-$S$ expansion to study a plateau at $1/3$ saturation in the magnetization curve of a frustrated ferrimagnet on a spatially anisotropic kagomé lattice. The spins have both ferromagnetic and antiferromagnetic nearest-neighbor Heisenberg couplings, and a frustrating next-nearest-neighbor coupling in one lattice direction. The magnetization plateau appears at the classical level for a certain range of couplings, and quantum fluctuations significantly broaden it at both ends. Near the region of the phase diagram where the classical plateau destabilizes, we find an exoti…
The magnetic insulator yttrium iron garnet (YIG) with a ferrimagnetic transition temperature of $\sim$560 K has been widely used in microwave and spintronic devices. Anomalous features in the spin Seeback effect (SSE) voltages have been observed in Pt/YIG and attributed to the magnon-phonon coupling. Here we use inelastic neutron scattering to map out low-energy spin waves and acoustic phonons of YIG at 100 K as a function of increasing magnetic field. By comparing the zero and 9.1 T data, we find that instead of splitting and opening up gaps at the spin wave and acoustic phonon dispersion int…
We propose an effective theory for the critical phase of a quantum ferrimagnetic chain with alternating spins 1 and 1/2 in an external magnetic field. With the help of the matrix product variational approach, the system is mapped to a spin-1/2 XXZ chain in an (effective) magnetic field; as a byproduct, we obtain an excellent description of the optical magnon branch in the gapped phase. Recent finite-temperature DMRG results for the low-temperature part of the specific heat are well described by the present approach, and the ``pop-up'' peaks, developing near the critical field values and in the…
TbMn6Sn6 is a metallic ferrimagnet displaying signatures of both topological electrons and topological magnons arising from ferromagnetism and spin-orbit coupling within its Mn kagome layers. Inelastic neutron scattering measurements find strong ferromagnetic (FM) interactions within the Mn kagome layer and reveal a magnetic bandwidth of ~230 meV. The low-energy magnetic excitations are characterized by strong FM Mn-Mn and antiferromagnetic (AFM) Mn-Tb interlayer magnetic couplings. We observe weaker, competing long-range FM and AFM Mn-Mn interlayer interactions similar to those driving helica…
The ferrimagnetic spinels MnB2O4 (B = Mn,V) exhibit a similar series of closely spaced magnetic and structural phase transitions at low temperatures, reflecting both magnetic frustration and a strong coupling between the spin and lattice degrees of freedom. Careful studies of excitations in MnB2O4 (B = Mn,V), and the evolution of these excitations with temperature, are important for obtaining a microscopic description of the role that magnetic excitations and spin-lattice coupling play in the low temperature phase transitions of these materials. We report an inelastic light (Raman) scattering …
We report on an investigation of optical properties of multiferroic CoCr$_{2}$O$_{4}$ at terahertz frequencies in magnetic fields up to 30 T. Below the ferrimagnetic transition (94 K), the terahertz response of CoCr$_{2}$O$_{4}$ is dominated by a magnon mode, which shows a steep magnetic-field dependence. We ascribe this mode to an exchange resonance between two magnetic sublattices with different $g$-factors. In the framework of a simple two-sublattice model (the sublattices are formed by Co$^{2+}$ and Cr$^{3+}$ ions), we find the inter-sublattice coupling constant, $λ= - (18 \pm 1)$ K, and t…
