Magnon Pairs Research Articles

Electron spin resonance for the detection of long-range spin nematic order

In this paper we propose that electron spin resonance (ESR) measurements enable us to detect the long-range spin nematic order. We show that the frequency of the paramagnetic resonance peak in the ESR spectrum is shifted by the ferroquadrupolar order parameter together with other quantities. The ferroquadrupolar order parameter is extractable from the angular dependence of the frequency shift. In contrast, the antiferroquadrupolar order parameter is usually invisible in the frequency shift. Instead, the long-range antiferroquadrupolar order yields a characteristic resonance peak in the ESR spectrum, which we call a magnon-pair resonance peak. This resonance corresponds to the excitation of the bound magnon pair at the wave vector $\bm k={\bm 0}$. Reflecting the condensation of bound magnon pairs, the field dependence of the magnon-pair resonance frequency shows a singular upturn at the saturation field. Moreover, the intensity of the magnon-pair resonance peak shows a characteristic angular dependence and it vanishes when the magnetic field is parallel to one of the axes that diagonalize the weak anisotropic interactions. We confirm these general properties of the magnon-pair resonance peak in the spin nematic phase by studying an $S=1$ bilinear-biquadratic model on the square lattice in the linear flavor-wave approximation. In addition, we argue applications to the $S=1/2$ frustrated ferromagnets and also the $S=1/2$ orthogonal dimer spin system SrCu$_2$(BO$_3$)$_2$, both of which are candidate materials of spin nematics. Our theory for the antiferroquadrupolar ordered phase is consistent with many features of the magnon-pair resonance peak experimentally observed in the low-magnetization regime of SrCu$_2$(BO$_3$)$_2$.

Dynamics of bound magnon pairs in the quasi-one-dimensional frustrated magnet LiCuVO4

We report on the dynamics of the spin-1/2 quasi-one-dimensional frustrated magnet LiCuVO$\mathrm{_4}$ measured by nuclear spin relaxation in high magnetic fields 10--34 T, in which the ground state has spin-density-wave order. The spin fluctuations in the paramagnetic phase exhibit striking anisotropy with respect to the magnetic field. The transverse excitation spectrum probed by $^{51}$V nuclei has an excitation gap, which increases with field. On the other hand, the gapless longitudinal fluctuations sensed by $^7$Li nuclei grow with lowering temperature, but tend to be suppressed with increasing field. Such anisotropic spin dynamics and its field dependence agree with the theoretical predictions and are ascribed to the formation of bound magnon pairs, a remarkable consequence of the frustration between ferromagnetic nearest neighbor and antiferromagnetic next-nearest-neighbor interactions.

Tunneling between chiral magnets: Spin current generation without external fields

Magnons can generate a spin current, and the standard generating mechanism requires at least one external field. Since this mechanism is often applied to a multilayer system including a magnet and a paramagnetic metal, the system can possess not only the charge current induced by the spin current but also the charge current induced by the external field. The latter is an unnecessary accompaniment. Here we show that the tunneling of a magnon pair between chiral magnets can generate a spin current even without external fields. This phenomenon originates from a phase difference between magnon pairs of separate, weakly coupled chiral magnets, and is essentially different from the mechanism using the angle degree of freedom of the magnon Bose-Einstein condensates. The pair's tunneling is possible in chiral magnets due to lack of the Goldstone-type gapless excitations. This phenomenon opens the door to spintronics not requiring any external field and using the magnon pair tunneling.

Semiclassical analysis of a magnetization plateau in a two-dimensional frustrated ferrimagnet

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 kagom\'{e} 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 exotic "chiral liquid" phase that preserves translational and $U(1)$ spin symmetry, in which bound pairs of magnons with opposite spins are condensed. We show how this state is obtained naturally from a relativistic field theory formulation. We comment on the relevance of the model to the material $\text{Cu}_3\text{V}_2\text{O}_7\text{(OH)}_2 \cdot 2\text{H}_2\text{O}$ (volborthite).

Anisotropic Spin Fluctuations in the Quasi One-Dimensional Frustrated Magnet LiCuVO4

We report results of NMR experiments on a single crystal of the quasi one-dimensional frustrated magnet LiCuVO_4. The NMR spectra of ^7Li and ^{51}V nuclei indicate a helical spin order in a magnetic field of 4 T with the helical spin plane perpendicular to the field and a spin-density-wave (SDW) order at 10 T with modulation in the magnitude of the moments aligned along the field, in agreement with earlier reports. The nuclear spin-lattice relaxation rate 1/T_1 at ^{51}V nuclei, which is selectively coupled to the transverse spin fluctuations perpendicular to the field, shows a pronounced peak near the helical ordering temperature in the field of 4 T applied along the a-axis. In the field of 10 T, however, such a peak is absent. Instead 1/T_1 at ^7Li nuclei probing longitudinal spin fluctuations shows divergent behavior towards the SDW ordering temperature. These results are qualitatively consistent with the theoretical description that the SDW correlation is due to bound magnon pairs, which produce an energy gap in the transverse spin excitation spectrum.

Microscopic origin of magnetic linear dichroism in the antiferromagnetic insulator MnF2

Magnetically ordered crystals often show unique magneto-optical phenomena that are not found without magnetic order. For example, MnF${}_{2}$, a two-sublattice antiferromagnet with different sublattice symmetries shows magnetic linear dichroism (MLD), which is odd with respect to the external magnetic field in the Faraday geometry. In particular, the magnon sideband of an exciton with a particular orbital function exhibits MLD, and the commonly found magnetic circular dichroism (MCD) is almost absent. In this study, we clarify the microscopic origin of this characteristic feature. We found that the symmetry of the exciton orbital determines the polarization eigenstate of the light to create the exciton magnon pair. These eigenstates can even be two cross-linear polarizations, depending in which sublattice the exciton is created. In this case, only MLD is allowed and MCD is forbidden.

Magnetooptic coupling coefficients for one- and two-magnon Raman scattering in rutile-structure antiferromagnets FeF2, MnF2, CoF2, and NiF2

Inelastic light scattering intensities in response to magnetic excitations are governed by magnetooptic coupling coefficients, which have been previously evaluated, for instance, for the ferrimagnetic Y3Fe5O12 (YIG) and the metamagnetic FeCl2 and FeBr2. However, by far the most detailed studies to date were performed on the classic rutile-structure antiferromagnets, and here we summarize the results obtained from the many experimental and theoretical investigations of these compounds for both one-magnon and two-magnon excitations. A comparison of the magnitudes of the various coupling coefficients for MnF2, FeF2, CoF2, and NiF2 reveals a surprising similarity in many coefficients. In one-magnon Raman scattering the in-phase linear magnetooptic coefficient dominates, and the main differences between MnF2, FeF2, and NiF2 lie in the relative significance of the in-phase quadratic magnetooptic coefficient. Thus, the quadratic coefficients now appear to be of particular importance in determining the strength of one-magnon scattering in a variety of magnetic insulators. In two-magnon Raman scattering one magnetooptic coefficient is dominant for all of these antiferromagnets. However, the other six coefficients are in general remarkably similar in magnitude and not negligible in most cases, indicating some similarity in the way light interacts with the pairs of magnons of opposite and equal wave vectors in rutile structure antiferromagnets.

Phase diagram and continuous pair-unbinding transition of the bilinear-biquadraticS=1Heisenberg chain in a magnetic field

We investigate the properties of the Heisenberg $S=1$ chain with bilinear and biquadratic interactions in a magnetic field using the density- matrix renormalization-group, Bethe ansatz, and field-theoretical considerations. In a large region of the parameter space, we identify a magnetized ferroquadrupolar Luttinger liquid consisting of a quasicondensate of bound magnon pairs. This liquid undergoes a continuous pair-unbinding transition to a more conventional Luttinger liquid region obtained by polarizing the system above the Haldane gap region. This pair-unbinding transition is shown to be in the Ising universality class on top of a Luttinger liquid, leading to an effective central charge 3/2. We also revisit the nature of the partially polarized Luttinger liquid around and above the Uimin-Lai-Sutherland point. Our results confirm that this is a two-component liquid and rule out the formation of a single-component vector-chiral phase.

Theory of coherence in Bose-Einstein condensation phenomena in a microwave-driven interacting magnon gas

Strong experimental evidences of the formation of quasi-equilibrium Bose-Einstein condensation (BEC) of magnons at room temperature in a film of yttrium iron garnet (YIG) excited by microwave radiation have been recently reported. Here we present a theory for the magnon gas driven by a microwave field far out of equilibrium showing that the nonlinear magnetic interactions create cooperative mechanisms for the onset of a phase transition leading to the spontaneous generation of quantum coherence and magnetic dynamic order in a macroscopic scale. The theory provides rigorous support for the formation of a BEC of magnons in a YIG film magnetized in the plane. We show that the system develops coherence only when the microwave driving power exceeds a threshold value and that the theoretical result for the intensity of the Brillouin light scattering from the BEC as a function of power agrees with the experimental data. The theory also explains quantitatively experimental measurements of microwave emission from the uniform mode generated by the confluence of BEC magnon pairs in a YIG film when the driving power exceeds a critical value.

Theory of microwave superradiance from a Bose-Einstein condensate of magnons

We show that the nearly uniform mode generated by the confluence of Bose-Einstein condensate (BEC) magnon pairs produced by microwave radiation in a film of yttrium iron garnet (YIG) is a coherent magnon state. This state corresponds to a macroscopic precessing magnetization which emits a superradiant microwave signal as a result of the cooperative action of the spins. The theory explains quantitatively recent experimental observations of microwave emission from a BEC of magnons in a YIG film when the driving power exceeds a critical value.

Frustrated ferromagnetic spin-12chain in a magnetic field: The phase diagram and thermodynamic properties

The frustrated ferromagnetic spin-1/2 Heisenberg chain is studied by means of a low-energy field theory as well as the density-matrix renormalization group and exact diagonalization methods. Firstly, we study the ground-state phase diagram in a magnetic field and find an `even-odd' (EO) phase characterized by bound pairs of magnons in the region of two weakly coupled antiferromagnetic chains. A jump in the magnetization curves signals a first-order transition at the boundary of the EO phase, but otherwise the curves are smooth. Secondly, we discuss thermodynamic properties at zero field, where we confirm a double-peak structure in the specific heat for moderate frustrating next-nearest neighbor interactions.

Failure of geometric frustration to preserve a quasi-two-dimensional spin fluid

Using spin-wave theory, we show that geometric frustration fails to preserve a two-dimensional spin fluid. Even though frustration can remove the interlayer coupling in the ground-state of a classical anti-ferromagnet, spin layers innevitably develop a quantum-mechanical coupling via the mechanism of ``order from disorder''. We show how the order from disorder coupling mechanism can be viewed as a result of magnon pair tunneling, a process closely analogous to pair tunneling in the Josephson effect. In the spin system, the Josephson coupling manifests itself as a a biquadratic spin coupling between layers, and for quantum spins, these coupling terms are as large as the inplane coupling. An alternative mechanism for decoupling spin layers occurs in classical XY models in which decoupled "sliding phases" of spin fluid can form in certain finely tuned conditions. Unfortunately, these finely tuned situations appear equally susceptible to the strong-coupling effects of quantum tunneling, forcing us to conclude that in general, geometric frustration cannot preserve a two-dimensional spin fluid.

Two-magnon excitations observed by neutron scattering in the two-dimensional spin-52Heisenberg antiferromagnetRb2MnF4

The low-temperature magnetic excitations of the two-dimensional spin-5/2 square-lattice Heisenberg antiferromagnet Rb2MnF4 have been probed using pulsed inelastic neutron scattering. In addition to dominant sharp peaks identified with one-magnon excitations, a relatively weak continuum scattering is also observed at higher energies. This is attributed to neutron scattering by pairs of magnons and the observed intensities are consistent with predictions of spin wave theory.

Noise pumping of nuclear spin waves in an antiferromagnet

Parametric excitation and the above-threshold behavior of a nonequilibrium system of nuclear magnons are investigated both under microwave noise pumping and under monochromatic pumping with noise modulation of the magnon spectrum. It is established that there exist two critical pumping amplitudes: the first corresponds to the onset of nonlinear absorption of the microwave field, and the second corresponds to the development of strong phase correlations—a nonequilibrium Bose condensate (NBC)—in a system of excited magnon pairs. The formation of the NBC was recorded by two methods: by intense electromagnetic radiation from a sample and by a coherent response of parametric magnons to a harmonic modulation of their spectrum (by a modulation response). The existing theories provide a satisfactory description for the functional dependence of pumping thresholds on the parameters of experiment, except for the region of minimal temperatures. The observed discrepancy between theoretical and experimental results can be explained under the assumption that quasi-elastic two-magnon relaxation processes make a nonadditive contribution to the threshold amplitudes of noise pumping.

Nonlinear interaction of resonator photons with parametric magnon pairs

We consider the process of parametric resonance of magnons in magneto-ordered crystals in a microwave resonator. The nonlinear interaction of the resonator photons with the parametric magnon pairs is analysed theoretically and the result expressed by the deviation frequencies relative to the pump frequency further demonstrates that the dynamics of resonator modes plays an important role once the pump power exceeds the threshold of parallel pumping.

Characterization of the nonlinearly excited magnon pair

The Hamilton's equations of motion were derived by analyzing the process of excitation for magnon pair in magneto-ordered medium placed in a microwave oscillator. The result showed that the magnon pair couples with the microwave resonator with nonlinearly oscillatory characterization.

Observation of the coherent state in a system of nuclear spin-wave pairs excited by microwave noise pumping

The parametric excitation of nuclear magnons by a microwave noise field was observed in an antiferromagnet. Two critical pumping amplitudes were found to exist. The first one corresponds to the onset of nonlinear microwave absorption. Above the second amplitude, strong phase correlations appear in a system of excited magnon pairs to form a nonequilibrium Bose condensate, which produces intense coherent electromagnetic radiation from the sample and gives rise to the coherent response of parametric magnons to the modulation of their spectrum (modulation response). It was found that, for the noise pumping, the contribution from the processes of elastic magnon relaxation to the threshold pumping amplitudes becomes nonadditive.

Nonlinear radiation damping of parametrically excited spin waves

We consider the process of microwave parametric excitation of spin waves in a resonator. The interaction of the resonator cavity photon with the parametric magnon pair is expected to cause additional nonlinearity: nonlinear radiation damping which is proportional to the quality factor Q of the resonator. Estimations of this positive nonlinear magnon relaxation in ferromagnets and antiferromagnets (for electronic and nuclear spin waves, magnetoelastic waves) show that it can play an important role in forming the stationary state. The threshold of the autooscillations of microwave absorption in a ferromagnet is found to increase with increasing Q.

Theory of phonon-assisted multimagnon optical absorption and bimagnon states in quantum antiferromagnets.

We calculate the effective charge for multimagnon infrared absorption assisted by phonons in a perovskitelike antiferromagnet and we compute the spectra for two-magnon absorption using interacting spin-wave theory. The full set of equations for the interacting two-magnon problem is presented in the random-phase approximation for arbitrary total momentum of the magnon pair. The spin-wave theory results fit very well the primary peak of recent measured bands in the parent insulating compounds of cuprate superconductors. The line shape is explained as being due to the absorption of one phonon plus a new quasiparticle excitation of the Heisenberg Hamiltonian that consists of a long-lived virtual bound state of two magnons (bimagnon). The bimagnon states have well-defined energy and momentum in a substantial portion of the Brillouin zone. The higher-energy bands are explained as one phonon plus higher multimagnon absorption processes. Other possible experiments for observing bimagnons are proposed. In addition we predict the line shape for the spin-1 system ${\mathrm{La}}_{2}$${\mathrm{NiO}}_{4}$.

Phonon assisted multimagnon optical absorption and long lived two-magnon states in undoped lamellar copper oxides.

We calculate the effective charge for multimagnon infrared (IR) absorption assisted by phonons in the parent insulating compounds of cuprate superconductors and the spectra for two-magnon absorption using interacting spin-wave theory. Recent measured bands in the mid-IR [Perkins et al., Phys. Rev. Lett. 71, 1621 (1993)] are interpreted as involving one phonon plus a two-magnon virtual bound state, and one phonon plus higher multimagnon absorption processes. The virtual bound state consists of a narrow resonance occurring when the magnon pair has total momentum close to $(\ensuremath{\pi},0)$.