Phonon Avalanche Research Articles

Nonlinear regimes of coherent optical phonon generation in quantum wells under electric current pumping

We present an analysis of nonlinear regimes of the coherent optical phonon generation under the electron drift in quantum wells. The phonon and electron subsystems are treated self-consistently. This allows us to find thesteady-state generation regimes with macroscopic populations of optical phonon modes and the electron transport controlled in part by the generated phonons. The generation regimes demonstrate a pronounced threshold character. At high electric fields above the threshold, practically single-mode generation occurs and the current-voltage characteristic is considerably changed. We demonstrate high efficiency generation of the coherent optical phonons by the electric current. The coherent macroscopic optical displacements and the amplitudes of oscillating electrostatic fields are evaluated. The proposed model based on the electron nonlinearities predicts a range of the pumping electric fields under which the steady state phonon generation is realized. Our results suggest that the phonon avalanche occurs beyond this field range.

The evolution of longitudinal and transverse acoustic waves in a medium with paramagnetic impurities

We study the bipartial interaction of longitudinal and transverse acoustic pulses with a system of paramagnetic impurities with an effective spin S=1/2 in a crystalline layer or on a surface in the presence of an arbitrarily directed external constant magnetic field. We derive a new system of evolution equations that describes this interaction and show that, in the absence of losses, for equal phase velocities of these acoustic components, and under the condition of their unidirectional propagation, the original system reduces to a new integrable system of equations. The derived integrable system describes the pulse dynamics outside the scope of the slow-envelope approximation. For one of the reductions of the general model that corresponds to the new integrable model, we give the corresponding equations of the inverse scattering transform method and find soliton solutions. We investigate the dynamics and formation conditions of the phonon avalanche that arises when the initial completely or incompletely inverted state of the spin system decays. We discuss the application of our results to describing the interaction dynamics of spins and acoustic pulses in various systems with an external magnetic field.

Butterfly hysteresis and slow relaxation of the magnetization in (Et 4N) 3Fe 2F 9: manifestations of a single-molecule magnet

(Et 4N) 3Fe 2F 9 exhibits a butterfly-shaped hysteresis below 5 K when the magnetic field is parallel to the threefold axis, in accordance with a very slow magnetization relaxation in the timescale of minutes. This is attributed to an energy barrier Δ=2.40 K resulting from the S=5 dimer ground state of [Fe 2F 9] 3− and a negative axial anisotropy. The relaxation partly occurs via thermally assisted quantum tunneling. These features of a single-molecule magnet are observable at temperatures comparable to the barrier height, due to an extremely inefficient energy exchange between the spin system and the phonons. The butterfly shape of the hysteresis arises from a phonon avalanche effect.

Laser-induced explosive desorption

A theory of the explosive desorption, observed by Chuang and Domen [Phys. Rev. Lett. 59, 1484 (1987); J. Vac. Sci. Technol. A 5, 473 (1987); J. Chem. Phys. (90, 3318 1989; Chem. Phys. Lett. (with A. Mödl). (154, 187 (1989)] is developed. When adsorbates are subjected to UV laser action, an explosive, molecular nonselective desorption takes place. This phenomenon is explained as follows: adsorbate molecules are excited by an UV laser to the higher electronic states. The electronic energy is delivered to the low energy vibronic states. The energy differences of these states are resonant to the corresponding phonon modes. This leads to the excitation of these phonons. When the energy input to the phonon modes exceeds their decay, phonon numbers start to increase exponentially. The phonon avalanche takes place. This in turn causes molecular nonselective desorption. The main result of the theory is the finding of the fluence and coverage dependent threshold conditions.

Acoustic superradiance, phonon avalanche, and propagation effects

New quantum equations for superradiance in extended systems are presented, and some preliminary considerations concerning the possibility for acoustic superradiance to prevail over incoherent phonon avalanche are developed.

Theory of ESR dipolar splitting of a spin pair in the presence of avalanche phonons

The ESR spectrum of a pair of paramagnetic spins $S=\frac{1}{2}$, interacting via dipolar magnetic forces, is calculated in the presence of an incoherent phonon avalanche, which is coupled to the spin pair by linear spin-phonon interaction. The problem is approximately solved by a Green's-function approach. Two cases are discussed, the first for an infinitely narrow phonon spectrum, and the second for finite bandwidth of the avalanche phonons. When the ESR frequency falls out of the avalanche band, the spectrum of the pair is shown to consist of two lines shifted from the no-avalanche resonant field and more closely spaced than in the no-avalanche situation. When the ESR frequency is within the avalanche band, a sharp decrease of the ESR intensity is expected. These results are interpreted in terms of ac Stark shift and of screening of dipolar interaction by the avalanche phonons. Their relationships to electromagnetic power narrowing of ESR lines and to the "magic angle" effect in NMR are discussed. Finally the theoretical results are examined in connection with phonon-avalanche experiments on ${\mathrm{Ce}}^{3+}$-doped lanthanum magnesium nitrate.

Kinetics of Dilute Solid Paramagnets under “Bottleneck” Conditions

AbstractKinetic equations, describing a dilute paramagnet in “bottleneck” (BN) conditions, are obtained in the case of spin‐lattice mechanism of longitudinal and transverse relaxation of electron spins (direct processes). The spectral distribution function of phonons, obtained in stationary conditions, is compared with the corresponding function for a concentrated paramagnet. The influence of the resonance phonons on the spin‐system is considered. The possibility of studying the phonon avalanche in dilute paramagnets by pulse techniques is mentioned.

Reduction of dipolar interaction by off-resonance phonon avalanche

An off-resonance phonon avalanche is shown to reduce effectively the magnetic dipolar interaction between paramagnetic spins 1 2 in a crystal and to change the Larmor frequency of the spins. Both effects are obtained by a unitary transformation which eliminates approximately the phonon field from the Hamiltonian of the system.

Nonlinear paramagnetic relaxation: II. The properties of kinetic equations solutions for two-level systems

For pt.I see ibid., vol.9, p.511 (1976). The detailed mathematical discussion of the properties of solutions of the set of equations describing the nonlinear paramagnetic relaxation is given. The authors show exactly that the equations admit the existence of a phenomenon usually called the phonon avalanche. The Provotorov-like equation has such properties that the stationary generation of the high-frequency phonons is not excluded. The considered equations can be applied to the whole class of two-level interacting systems.

Effect of Exchange Interactions on a Phonon Bottleneck Effect and on a Phonon Avalanche Formation

Effect of Exchange Interactions on a Phonon Bottleneck Effect and on a Phonon Avalanche Formation

Theory of the spin-phonon avalanche in paramagnetic crystals: I. Spatial phonon transport

A system of nonlinear integro-differential equations was constructed to describe the phenomenon of the phonon avalanche as a function of space and time in a paramagnetic crystal. The spatial effects were taken into account by a transport probability kernel which is similar to the Holstein-Biberman model of photon imprisonment in gases. The equations were then applied to the simplified one dimensional case simulating the geometry of an infinite slab. Calculations were made for dilute Ce2Mg3(NO3)12.24H2O. Semiquantitative agreement between theory and earlier experimental data was obtained. The remaining discrepancies are thought to be due to the neglect of consideration of spectral spin diffusion in the present model.

Theory of the spin-phonon avalanche in paramagnetic crystals: II. Spectral diffusion of magnetic energy

For Pt. I see ibid., vol.5, 828 (1972). The theory of the phonon avalanche in paramagnetic crystals is generalized to include diffusion of the magnetic excitation in addition to the spatial transport of acoustical excitation treated in Pt.I. Quantitative agreement between theory and earlier experimental data is found to be further improved.

Brillouin scattering from a phonon avalanche

Microwave acoustic phonons generated during a phonon avalanche in a paramagnetic crystal have been detected by means of the optical technique of Brillouin scattering. The avalanche was generated in Ni-doped MgO during the direct paramagnetic relaxation of the ΔM = 1 transitions of Ni 2+. An expression for the minimum detectable avalanche phonon excitation was derived and compared with the observed values for the transverse acoustical modes. The measurements showed a peak avalanche phonon temperature of 10 3 to 10 4 °K.

On the Phonon Avalanche Generated by Spin‐Lattice Relaxation in a Bottlenecked Crystal

AbstractThe phonon avalanche phenomenon is investigated using Zubarev's density‐matrix formalism. A system of differential equations is derived which determines the time dependence of the spin and phonon temperatures. This system essentially differs from that gained from simple rate equations. The relevance of the phase‐memory time T2 for the decay of the inverted spin system is revealed.

Phonon Avalanche in Ce-Doped Lanthanum Magnesium Double Nitrate. Measurement of the Phonon Lifetime and of the Acoustic Spectrum

We have investigated the phonon avalanche in Ce-doped lanthanum magnesium double nitrate using pulsed microwave and pulsed magnetic-field techniques. In these experiments we have been able to determine the lifetime of the avalanche phonons and to obtain some evidence for coherence in the spin-phonon interaction.

Spatial Effects in the Theory of the Phonon Avalanche

A set of coupled, nonlinear integro-differential equations is proposed to describe the space-time variation of the spin and phonon excitations in a paramagnetic crystal under conditions appropriate to a phonon avalanche. An effective phonon lifetime is derived and found to exceed the simple time-of-flight lifetime by orders of magnitude. For the case of an infinite slab, the theory is shown to be capable of remedying the inability of earlier models to describe the time evolution of the average magnetization.

Suppressed and Accelerated Spin-Lattice Relaxation

The transient magnetic behavior of a paramagnetic substance, after an initial disturbance, is considered theoretically for a variety of situations in which the lattice temperature rises as a result of energy flow from the magnetic (electron spin) system. The direct and ${T}^{9}$ Raman spin-phonon processes are considered. Coupling between phonon modes, and leakage of energy into a bath are taken into account. Graphs of the resultant behavior are presented. Effects such as suppressed and accelerated spin relaxation, and rapid decay (phonon avalanche) after spin inversion, are discussed. It is pointed out that experiments performed without the usual helium bath may provide reliable measurements of inelastic phonon-boundary scattering.

Paramagnetic Relaxation to a Bottlenecked Lattice: Development of the Phonon Avalanche

Paramagnetic Relaxation to a Bottlenecked Lattice: Development of the Phonon Avalanche