Two-phonon Processes Research Articles

Nuclear spin relaxation of methane in solid xenon

Nuclear spin relaxation of methane in solid xenon has been studied by infrared spectroscopy. From the analysis of the temporal changes of the rovibrational peaks, the rates of the nuclear spin relaxation of I = 2 ← 1 correlated to the rotational relaxation of J = 0 ← 1 were obtained at temperatures of 5.1–11.5 K. On the basis of the temperature dependence of the relaxation rate, the activation energy of the indirect two-phonon process was determined to be 50 ± 6 K, which is in good agreement with the rotational transition energies of J = 2 ← 1 and J = 3 ← 1. Taking into account this result and the spin degeneracy, we argue that the lowest J = 3 level in which the I = 1 and I = 2 states are degenerate acts as the intermediate point of the indirect process.

Two-phonon Absorption Spectra in the Layered Honeycomb Compound α-RuCl3

We performed infrared absorption spectroscopy for α-RuCl3 with a two-dimensional honeycomb lattice of Ru3+ ions. In the mid-infrared range, we observed three absorption peaks corresponding to intra-atomic d–d transitions among Ru3+ ions in accordance with a previous report. In the far-infrared range, we observed conspicuous broad absorption structures near 600 cm−1 in addition to several sharp single phonon peaks. Our first-principles calculations for the isolate sandwich model together with the factor group analysis revealed that the peak structures near 600 cm−1 are absorptions related to a two-phonon process. Our results stimulate further study on the spin–lattice coupling in α-RuCl3 as well as the optical detection of Majorana excitations in Kitaev spin liquids.

Giant acoustic atom: A single quantum system with a deterministic time delay

We investigate the quantum dynamics of a single transmon qubit coupled to surface acoustic waves (SAWs) via two distant connection points. Since the acoustic speed is five orders of magnitude slower than the speed of light, the travelling time between the two connection points needs to be taken into account. Therefore, we treat the transmon qubit as a giant atom with a deterministic time delay. We find that the spontaneous emission of the system, formed by the giant atom and the SAWs between its connection points, initially decays polynomially in the form of pulses instead of a continuous exponential decay behaviour, as would be the case for a small atom. We obtain exact analytical results for the scattering properties of the giant atom up to two-phonon processes by using a diagrammatic approach. We find that two peaks appear in the inelastic (incoherent) power spectrum of the giant atom, a phenomenon which does not exist for a small atom. The time delay also gives rise to novel features in the reflectance, transmittance, and second-order correlation functions of the system. Furthermore, we find the short-time dynamics of the giant atom for arbitrary drive strength by a numerically exact method for open quantum systems with a finite-time-delay feedback loop.

Probing microstructures of molybdenum disulfide quantum dots by resonant Raman scattering

Research on the photoluminescence (PL) mechanism of MoS2 quantum dots (MQDs) has entered into a new age that involves analyzing the complicated microstructures of MQDs that are presumably significant for PL emission. However, microstructures of MQDs have not been clearly observed and thoroughly identified by conventional detection techniques. In this work, pure MQDs were fabricated by pulsed laser ablation along the direction parallel to basal planes of the MoS2 crystal in deionized water to enable resonant Raman measurements. Resonant Raman scattering (RRS) that corresponds to microstructures of MQDs, especially defects and disorders at the edges and surfaces of MQDs, is obtained, which is distinctly different from that of bulk and monolayer MoS2 and has not been characterized in such a direct method by RRS spectroscopy. The highest intensity of the defect-induced LA(M) peak at approximately 217 cm−1, which is similar to the D band of graphene, indicates the existence of enormous defects and disorders. Furthermore, the LA(M) peak is split into a shoulder at 212 cm−1 and a peak at 217 cm−1 which are due to double resonance processes derived from defects on the edges and disorders in the planes, respectively. More resonant two-phonon Raman processes appear because of the strong electron-phonon coupling at resonance. In addition, the typical phonon modes of MoS2 and Raman-silent phonon modes are analyzed and identified. This work indicates that the features of microstructures of MQDs can be convincingly and experimentally characterized by RRS spectroscopy.

Effect of flexural phonons on the hole states in single-layer black phosphorus

Flexural thermal fluctuations in crystalline membranes affect the band structure of the carriers, which leads to an exponential density-of-states (DOS) tail beyond the unperturbed band edge. We present a theoretical description of this tail for a particular case of holes in single-layer black phosphorus, a material which exhibits an extremely anisotropic quasi-one-dimensional dispersion ($m_y/m_x\gg1$) and, as a result, an enhanced Van Hove singularity at the valence band top. The material parameters are determined by {\it ab initio} calculations and then are used for quantitative estimation of the effect of two-phonon (flexural) processes have on the charge carrier DOS. It is shown that unlike the isotropic case, the physics is determined by the phonons with wavevectors of the order of $q^*$, where $q^*$ determines the crossover between harmonic and anharmonic behavior of the flexural phonons. The spectral density of the holes in single-layer black phosphorus at finite temperatures is calculated.

Molecular and electronic structure of terminal and alkali metal-capped uranium(V) nitride complexes.

Determining the electronic structure of actinide complexes is intrinsically challenging because inter-electronic repulsion, crystal field, and spin–orbit coupling effects can be of similar magnitude. Moreover, such efforts have been hampered by the lack of structurally analogous families of complexes to study. Here we report an improved method to U≡N triple bonds, and assemble a family of uranium(V) nitrides. Along with an isoelectronic oxo, we quantify the electronic structure of this 5f1 family by magnetometry, optical and electron paramagnetic resonance (EPR) spectroscopies and modelling. Thus, we define the relative importance of the spin–orbit and crystal field interactions, and explain the experimentally observed different ground states. We find optical absorption linewidths give a potential tool to identify spin–orbit coupled states, and show measurement of UV···UV super-exchange coupling in dimers by EPR. We show that observed slow magnetic relaxation occurs via two-phonon processes, with no obvious correlation to the crystal field.

Quadratic Zeeman effect and spin-lattice relaxation of Tm3+ :YAG at high magnetic fields

Anisotropy of the quadratic Zeeman effect for the $^3{\rm H}_6 \rightarrow \, ^3{\rm H}_4$ transition at 793 nm wavelength in $^{169}$Tm$^{3+}$-doped Y$_3$Al$_5$O$_{12}$ is studied, revealing shifts ranging from near zero up to + 4.69 GHz/T$^2$ for ions in magnetically inequivalent sites. This large range of shifts is used to spectrally resolve different subsets of ions and study nuclear spin relaxation as a function of temperature, magnetic field strength, and orientation in a site-selective manner. A rapid decrease in spin lifetime is found at large magnetic fields, revealing the weak contribution of direct-phonon absorption and emission to the nuclear spin-lattice relaxation rate. We furthermore confirm theoretical predictions for the phonon coupling strength, finding much smaller values than those estimated in the limited number of past studies of thulium in similar crystals. Finally, we observe a significant -- and unexpected -- magnetic field dependence of the two-phonon Orbach spin relaxation process at higher field strengths, which we explain through changes in the electronic energy-level splitting arising from the quadratic Zeeman effect.

Two Polymorphic Forms of a Six-Coordinate Mononuclear Cobalt(II) Complex with Easy-Plane Anisotropy: Structural Features, Theoretical Calculations, and Field-Induced Slow Relaxation of the Magnetization

A mononuclear cobalt(II) complex [Co(3,5-dnb)2(py)2(H2O)2] {3,5-Hdnb = 3,5-dinitrobenzoic acid; py = pyridine} was isolated in two polymorphs, in space groups C2/c (1) and P21/c (2). Single-crystal X-ray diffraction analyses reveal that 1 and 2 are not isostructural in spite of having equal formulas and ligand connectivity. In both structures, the Co(II) centers adopt octahedral {CoN2O4} geometries filled by pairs of mutually trans terminal 3,5-dnb, py, and water ligands. However, the structures of 1 and 2 disclose distinct packing patterns driven by strong intermolecular O-H···O hydrogen bonds, leading to their 0D→2D (1) or 0D→1D (2) extension. The resulting two-dimensional layers and one-dimensional chains were topologically classified as the sql and 2C1 underlying nets, respectively. By means of DFT theoretical calculations, the energy variations between the polymorphs were estimated, and the binding energies associated with the noncovalent interactions observed in the crystal structures were also evaluated. The study of the direct-current magnetic properties, as well as ab initio calculations, reveal that both 1 and 2 present a strong easy-plane magnetic anisotropy (D > 0), which is larger for the latter polymorph (D is found to exhibit values between +58 and 117 cm(-1) depending on the method). Alternating current dynamic susceptibility measurements show that these polymorphs exhibit field-induced slow relaxation of the magnetization with Ueff values of 19.5 and 21.1 cm(-1) for 1 and 2, respectively. The analysis of the whole magnetic data allows the conclusion that the magnetization relaxation in these polymorphs mainly takes place through a virtual excited state (Raman process). It is worth noting that despite the notable difference between the supramolecular networks of 1 and 2, they exhibit almost identical magnetization dynamics. This fact suggests that the relaxation process is intramolecular in nature and that the virtual state involved in the two-phonon Raman process lies at a similar energy in polymorphs 1 and 2 (∼20 cm(-1)). Interestingly, this value is recurrent in Co(II) single-ion magnets, even for those displaying different coordination number and geometry.

Surface Temperature Dependence of Hydrogen Ortho-Para Conversion on Amorphous Solid Water.

The surface temperature dependence of the ortho-to-para conversion of H_{2} on amorphous solid water is first reported. A combination of photostimulated desorption and resonance-enhanced multiphoton ionization techniques allowed us to sensitively probe the conversion on the surface of amorphous solid water at temperatures of 9.2-16K. Within a narrow temperature window of 8K, the conversion time steeply varied from ∼4.1×10^{3} to ∼6.4×10^{2} s. The observed temperature dependence is discussed in the context of previously suggested models and the energy dissipation process. The two-phonon process most likely dominates the conversion rate at low temperatures.

Intrinsic Charge Carrier Mobility in Single-Layer Black Phosphorus.

We present a theory for single- and two-phonon charge carrier scattering in anisotropic two-dimensional semiconductors applied to single-layer black phosphorus (BP). We show that in contrast to graphene, where two-phonon processes due to the scattering by flexural phonons dominate at any practically relevant temperatures and are independent of the carrier concentration n, two-phonon scattering in BP is less important and can be considered negligible at n≳10^{13} cm^{-2}. At smaller n, however, phonons enter in the essentially anharmonic regime. Compared to the hole mobility, which does not exhibit strong anisotropy between the principal directions of BP (μ_{xx}/μ_{yy}∼1.4 at n=10^{13} cm^{-2} and T=300 K), the electron mobility is found to be significantly more anisotropic (μ_{xx}/μ_{yy}∼6.2). Absolute values of μ_{xx} do not exceed 250 (700) cm^{2} V^{-1} s^{-1} for holes (electrons), which can be considered as an upper limit for the mobility in BP at room temperature.

Evidence of Slow Magnetic Relaxation in Co(AcO)2(py)2(H2O)2

The monometallic pseudo-octahedral complex, [Co(H2O)2(CH3COO)2(C5H5N)2], is shown to exhibit slow magnetic relaxation under an applied field of 1500 Oe. The compound is examined by a combination of experimental and computational techniques in order to elucidate the nature of its electronic structure and slow magnetic relaxation. We demonstrate that any sensible model of the electronic structure must include a proper treatment of the first-order orbital angular momentum, and we find that the slow magnetic relaxation can be well described by a two-phonon Raman process dominating at high temperature, with a temperature independent quantum tunnelling pathway being most efficient at low temperature.

The spin relaxation of nitrogen donors in 6H SiC crystals as studied by the electron spin echo method

We present the detailed study of the spin kinetics of the nitrogen (N) donor electrons in 6H SiC wafers grown by the Lely method and by the sublimation “sandwich method” (SSM) with a donor concentration of about 1017 cm−3 at T = 10–40 K. The donor electrons of the N donors substituting quasi-cubic “k1” and “k2” sites (Nk1,k2) in both types of the samples revealed the similar temperature dependence of the spin-lattice relaxation rate (T1−1), which was described by the direct one-phonon and two-phonon processes induced by the acoustic phonons proportional to T and to T9, respectively. The character of the temperature dependence of the T1−1 for the donor electrons of N substituting hexagonal (“h”) site (Nh) in both types of 6H SiC samples indicates that the donor electrons relax through the fast-relaxing centers by means of the cross-relaxation process. The observed enhancement of the phase memory relaxation rate (Tm−1) with the temperature increase for the Nh donors in both types of the samples, as well as for the Nk1,k2 donors in Lely grown 6H SiC, was explained by the growth of the free electron concentration with the temperature increase and their exchange scattering at the N donor centers. The observed significant shortening of the phase memory relaxation time Tm for the Nk1,k2 donors in the SSM grown sample with the temperature lowering is caused by hopping motion of the electrons between the occupied and unoccupied states of the N donors at Nh and Nk1,k2 sites. The impact of the N donor pairs, triads, distant donor pairs formed in n-type 6H SiC wafers on the spin relaxation times was discussed.

Calomel-made crystalline acousto-optical cell designed for an advanced regime of noncollinear two-phonon light scattering

We study the potentials of a wide-aperture crystalline calomel-made acousto-optical cell. Characterizing this cell is nontrivial due to the chosen regime based on an advanced noncollinear two-phonon light scattering. Recently revealed important features of this phenomenon are essentially exploited in the cell and are investigated in more detail. These features can be observed more easily and simply in tetragonal crystals, e.g., calomel, exhibiting specific acousto-optical nonlinearity caused by the acoustic waves of finite amplitude. This parametric nonlinearity manifests itself at low acoustic powers in calomel possessing linear acoustic attenuation. The formerly identified additional degree of freedom, unique to this regime, is exploited for designing the cell with an eye to doubling the resolution due to two-phonon processes. We clarify the role of varying the central acoustic frequency and acoustic attenuation using that degree of freedom. Then the efficiency of calomel is exploited to expand the cell’s bandwidth with a cost of its efficiency. Proof-of-principle experiments confirm the developed approaches and illustrate their applicability to innovative techniques of optical spectrum analysis with the improved resolution. The achieved spectral resolution of 0.205 A at 405 nm and the resolving power 19,800 are the best for acousto-optical spectrometers dedicated to space or airborne operations to date as far as we know.

Electrodynamic characteristics of berillium oxide in the submillimeter-infrared band

Single-crystal beryllium oxide has been studied by submillimeter-infrared spectroscopy and nonlinear optics methods in the wavenumber range of 2–5000 cm–1 in the temperature interval of 80–300 K. With the aid of computation models, the dispersion parameters of phonons and nonresonance absorption bands have been determined. The mechanisms responsible for dielectric loss in the terahertz band have been revealed. It has been shown that the decisive contribution is made by low-frequency dipole excitations, including two-phonon difference processes, and this contribution exceeds the phonon contribution by two orders of magnitude. Coherent anti-Stokes Raman scattering has been used to determine the coefficients of absorption by polaritons of the low-frequency dispersion branch.

Lattice sites, charge states and spin–lattice relaxation of Fe ions in 57Mn+ implanted GaN and AlN

The lattice sites, valence states, resulting magnetic behaviour and spin–lattice relaxation of Fe ions in GaN and AlN were investigated by emission Mössbauer spectroscopy following the implantation of radioactive 57Mn+ ions at ISOLDE/CERN. Angle dependent measurements performed at room temperature on the 14.4keV γ-rays from the 57Fe Mössbauer state (populated from the 57Mn β− decay) reveal that the majority of the Fe ions are in the 2+ valence state nearly substituting the Ga and Al cations, and/or associated with vacancy type defects. Emission Mössbauer spectroscopy experiments conducted over a temperature range of 100–800K show the presence of magnetically split sextets in the “wings” of the spectra for both materials. The temperature dependence of the sextets relates these spectral features to paramagnetic Fe3+ with rather slow spin–lattice relaxation rates which follow a T2 temperature dependence characteristic of a two-phonon Raman process.

Spectral collapse via two-phonon interactions in trapped ions

Two-photon processes have so far been considered only as resulting from frequency-matched second-order expansions of light-matter interaction, with consequently small coupling strengths. However, a variety of novel physical phenomena arises when such coupling values become comparable with the system characteristic frequencies. Here, we propose a realistic implementation of two-photon quantum Rabi and Dicke models in trapped-ion technologies. In this case, effective two-phonon processes can be explored in all relevant parameter regimes. In particular, we show that an ion chain under bichromatic laser drivings exhibits a rich dynamics and highly counterintuitive spectral features, such as interaction-induced spectral collapse.

Microscopic models for charge-noise-induced dephasing of solid-state qubits

Several experiments have shown qubit coherence decay of the form $exp[\ensuremath{-}{(t/{T}_{2})}^{\ensuremath{\alpha}}]$ due to environmental charge-noise fluctuations. We present a microscopic description for temperature dependencies of the parameters ${T}_{2}$ and $\ensuremath{\alpha}$. Our description is appropriate to qubits in semiconductors interacting with spurious two-level charge fluctuators coupled to a thermal bath. We find distinct power-law dependencies of ${T}_{2}$ and $\ensuremath{\alpha}$ on temperature depending on the nature of the interaction of the fluctuators with the associated bath. We consider fluctuator dynamics induced by first- and second-order tunneling with a continuum of delocalized electron states. We also study one- and two-phonon processes for fluctuators in either GaAs or Si. These results can be used to identify dominant charge-dephasing mechanisms and suppress them.

Thermal conductance of metal-diamond interfaces at high pressure.

The thermal conductance of interfaces between metals and diamond, which has a comparatively high Debye temperature, is often greater than can be accounted for by two-phonon processes. The high pressures achievable in a diamond anvil cell (DAC) can significantly extend the metal phonon density of states to higher frequencies, and can also suppress extrinsic effects by greatly stiffening interface bonding. Here we report time-domain thermoreflectance measurements of metal-diamond interface thermal conductance up to 50 GPa in the DAC for Pb, Au0.95Pd0.05, Pt and Al films deposited on type 1A natural [100] and type 2A synthetic [110] diamond anvils. In all cases, the thermal conductances increase weakly or saturate to similar values at high pressure. Our results suggest that anharmonic conductance at metal-diamond interfaces is controlled by partial transmission processes, where a diamond phonon that inelastically scatters at the interface absorbs or emits a metal phonon.

Rigorous theory of the radiative and gain characteristics of silicon and germanium lasing media

A generalized numerical model for the phonon-assisted optical interband transition based on the Green's function formalism was developed and implemented to investigate optical processes in germanium and silicon media intended for on-chip light emitter and laser applications. High-fidelity full band structures obtained from the empirical pseudopotential method, self-energies, and the corresponding spectral density functions for the phonon-perturbed electron and holes have been computed numerically as a function of strain, temperature, and doping level. Validation has been carried out by showing the model's ability to accurately reproduce the measured temperature dependent absorption coefficient data for both germanium and silicon. Absorption coefficients, radiative recombination rates of germanium and silicon active media were investigated with different biaxial tensile strain, doping concentrations and injection conditions. Furthermore, when the model is employed to compute the optical gain in strained germanium, we find that the use of tensile strain and high injection are the preferable approaches to obtain population inversion. At the same time, strong absorption from the spin-orbit to the heavy-hole band limits the maximum injection density that can be applied. Finally, when applied to study silicon, the proposed model also successfully reproduces the experimentally observed radiative recombination peak due to the two-phonon process.

Crystal field simulation and NMR study of19F in a EuF3Van Vleck paramagnet

The temperature dependence of the nuclear spin-lattice relaxation rate of 19F nuclei is measured for a powder sample of a EuF3 Van Vleck paramagnet, in a broad temperature range (55–300 K). The increase in the nuclear relaxation rate observed at T > 100 K is caused by fluctuations in the magnetic fields, induced at the fluorine nuclei by the magnetic moments of the europium ions, the lifetime of which is determined by a two-phonon relaxation process with input from the first excited state of the electron shell of Eu3+ ions (Δ1 = 370 K). The set of crystal field parameters allowing for a satisfactory description of the electron energy spectrum of the Eu3+ ions in the EuF3 crystal, is calculated within the framework of the semi-phenomenological exchange charge model.