S. Cojocaru - Academia.edu (original) (raw)

Papers by S. Cojocaru

Research paper thumbnail of Effetti DI Correlazione a Bassa Dimensionalita

IV o Congresso del Dipartimento

Research paper thumbnail of Quantum Spin Excitations on 1 D and 2 D Continua

Symmetry and Structural Properties of Condensed Matter, 2001

ABSTRACT

Research paper thumbnail of Magnon excitations in a mesoscopic Heisenberg ferromagnet

Research paper thumbnail of Magnon gas and deviation from the Bloch law in a nanoscale Heisenberg ferromagnet

Philosophical Magazine, 2011

ABSTRACT It is known that saturation magnetization of ferromagnetic nanoparticles and nanocluster... more ABSTRACT It is known that saturation magnetization of ferromagnetic nanoparticles and nanoclusters deviates strongly from the Bloch T 3/2 law. To describe the deviation one usually uses a modified power law T α with a size dependent exponent α, which is motivated simply by its flexibility in fitting the observed behavior. By considering the Heisenberg spin model we derive an explicit expression in terms of a magnon gas which generalizes the Bloch formula to a finite size system. Comparison to the experimental data shows good agreement with the observed behavior and gives a better understanding of its physics.

Research paper thumbnail of Electron–phonon heat exchange in layered nano-systems

We analyze the heat power P from electrons to phonons in thin metallic films deposited on free-st... more We analyze the heat power P from electrons to phonons in thin metallic films deposited on free-standing dielectric membranes in a temperature range in which the phonon gas has a quasi two-dimensional distribution. The quantization of the electrons wavenumbers in the direction perpendicular to the film surfaces lead to the formation of quasi two-dimensional electronic sub-bands. The electron–phonon coupling is treated in the deformation potential model. If we denote by T e the electrons temperature and by T ph the phonons temperature, we find that P P ð0Þ ðT e ÞÀP ð1Þ ðT e ; T ph Þ. Due to the quantization of the electronic states, both P ð0Þ and P ð1Þ , plotted vs ðT e ; dÞ show very strong oscillations with d, forming sharp crests almost parallel to T e. From valley to crest, both P ð0Þ and P ð1Þ increase by more than one order of magnitude. In the valleys between the crests, P p T 3:5 e À T 3:5 ph in the low temperature limit, whereas on the crests P does not have a simple power law dependence on temperature. The strong modulation of P with the thickness of the film may provide a way to control the electron-phonon heat power and the power dissipation in thin metallic films. On the other hand, the surface imperfections of the metallic films can smoothen these modulations.

Research paper thumbnail of Electronic structure of A4C60: Joint effect of electron correlation and vibronic interactions

Physical Review B, 1999

Effects of electron correlation, intrasite vibronic interaction, and merohedral disorder on the e... more Effects of electron correlation, intrasite vibronic interaction, and merohedral disorder on the electronic structure of K 4 C 60 are investigated with a model approach taking into account all essential interactions in the lowest unoccupied molecular orbital ͑LUMO͒ band. The self-energy was calculated within the GW approximation with self-consistency after the quasiparticle Green function starting from Hartree-Fock band structure. The insulating state arises due to interorbital charge disproportionation within the LUMO band while the band gap is strongly reduced by effects of long-range electron correlation. The results of the calculations are in reasonable agreement with experiment, providing evidence for a Jahn-Teller induced transition from a Mott-Hubbard to a band insulator state. ͓S0163-1829͑99͒51020-5͔

Research paper thumbnail of Effect of electron–phonon interaction on the single-particle spectral properties of the Hubbard model

The effect of electron-phonon interaction on quasiparticle dispersion and spectral density is con... more The effect of electron-phonon interaction on quasiparticle dispersion and spectral density is considered within second order adiabatic approximation of the two-dimensional Holstein-Hubbard model. The electron-phonon interaction gives rise to a kink in the dispersion along the nodal direction of the Brillouin zone whose dependence on isotope substitution and doping is discussed in relation to recent photoemission experiments on the nodal quasiparticles in high-temperature superconductors. It is shown that various experimental features can be qualitatively explained in a framework that considers both strong correlations effect and the usual electron-phonon interaction. r

Research paper thumbnail of Role of electron-phonon interaction on quasiparticle dispersion in the strongly correlated cuprate superconductors

Physical Review B, 2006

The role of the electron-phonon ͑el-ph͒ interaction in high-T c cuprates is investigated theoreti... more The role of the electron-phonon ͑el-ph͒ interaction in high-T c cuprates is investigated theoretically by considering correlated electrons interacting with Holstein phonons within the two-dimensional single-band Hubbard model in the limit of large Coulomb interaction. It is shown that the electron-phonon interaction gives rise to a kink in the dispersion along the nodal direction and to a peak/dip/hump structure in the one-electron spectral weight whose dependence on temperature, isotope substitution, and doping is discussed in relation to recent photoemission experiments on the nodal quasiparticles in Bi2201 and LSCO. A comparison with these experiments shows that electron correlations play a crucial role in the determination of the kink position, size, and doping dependence. We also show that the "unusual" oxygen isotope shift in the real part of the selfenergy, experimentally observed in the optimally doped Bi2212 samples, can be qualitatively explained within the framework that incorporates both strong electron correlations and the adiabatic electron-phonon interaction.

Research paper thumbnail of Effective electron–phonon coupling in the Hubbard–Holstein model in presence of strong correlations and density fluctuations

Physica C: Superconductivity, 2007

We study the Hubbard-Holstein model in the strong coupling regime and discuss the role of electro... more We study the Hubbard-Holstein model in the strong coupling regime and discuss the role of electron-electron correlations, doping and phonon frequency (isotope substitution) on the effective electron-phonon coupling. A comparison with recent dynamical mean field (DMF) studies and connection with recent experimental findings in cuprate superconductors is also discussed.

Research paper thumbnail of High-energy kink in the single-particle spectra of cuprates

Physica B: Condensed Matter, 2008

Within a phenomenological model where electrons are coupled to a bosonic mode in a generic form o... more Within a phenomenological model where electrons are coupled to a bosonic mode in a generic form of damped oscillator, we analyze the high-energy kink recently observed in ARPES experiments on cuprates. It is shown that the model allows to describe the main anomalous features found in experiments, such as the broad incoherent spectral weight, the ''waterfall dispersion'', its doping and temperature dependence. In contrast to the low-energy kink, presence of significant damping is required to account for the anomalies. The ''bosonic mode'' is related to the incoherent excitation peak observed in optical conductivity spectra of cuprates. r

Research paper thumbnail of Renormalization of the electron–phonon interaction in the Hubbard model

Physica B: Condensed Matter, 2005

We calculate the electron-phonon vertex in the two-dimensional Hubbard model by a strong coupling... more We calculate the electron-phonon vertex in the two-dimensional Hubbard model by a strong coupling approach based on cumulant expansion. The role of the on-site Coulomb interaction on the coupling of the electrons to the Holstein phonons is investigated in different regions of the Brillouin zone. The results reveal the presence of a strong forward scattering and an effective increase of the vertex function at low temperatures above a certain critical U. Comparison with other approaches is also discussed. r

Research paper thumbnail of Bond stretching phonon softening and isotope effect in a phenomenological model for cuprate superconductors

Journal of Physics: Conference Series, 2010

Lattice and charge degrees of freedom of cuprate superconductors remain an intensively debated to... more Lattice and charge degrees of freedom of cuprate superconductors remain an intensively debated topic, both experimentally and theoretically, because of the strong anomalies observed in some of the phonon branches. In particular, the bond-stretching phonon modes show a knee like softening and a large damping for momenta around 0.25−0.3 r.l.u. along, e.g., (1, 0, 0) direction of the Brillouin zone. We discuss a phenomenological model where these anomalies are caused by coupling to electron charge fluctuations and explore a possibility to extract the spectrum of the latter from the phonon data. In particular, we predict a significant deviation from the standard value of the oxygen isotope substitution effect on the phonon spectrum itself. The phonon dispersion and linewidth are shown to contain complementary information related to the isotope effect which could allow a detailed description of the electronic spectrum.

Research paper thumbnail of Modification of the Bloch law in ferromagnetic nanostructures

EPL (Europhysics Letters), 2014

Research paper thumbnail of Bond stretching phonon anomalies due to incommensurate charge density wave instabilities in high-Tc cuprates

The European Physical Journal B, 2008

Phonon anomalies observed in various high Tc cuprates are analyzed theoretically within the Hubba... more Phonon anomalies observed in various high Tc cuprates are analyzed theoretically within the Hubbard-Holstein model in the limit of strong local electron correlations and in presence of long-range Coulomb interaction. The phonon self-energy is evaluated by taking into account the charge collective modes that become critical upon doping approaching an instability towards an incommensurate charge density wave (ICDW) driven by electron correlations. The doping dependence of phonon softening features and the highly distinctive phonon self-energy dependence on the wave vector agree with experiments. We discuss relevance of dynamical corrections to the density correlation function to achieve a sizeable bond-stretching phonon softening with a kink-like profile away from the zone boundary. PACS. 71.10.Fd Lattice fermion models -74.72.-h Cuprate superconductors -71.38.-k Polarons and electron-phonon interactions -71.27.+a Strongly correlated electron systems; heavy fermions 180 The European Physical Journal B

Research paper thumbnail of Isotope effect and bond-stretching phonon anomaly in high-Tc cuprates

The European Physical Journal B, 2010

We analyse a model where the anomalies of the bond-stretching LO phonon mode are caused by the co... more We analyse a model where the anomalies of the bond-stretching LO phonon mode are caused by the coupling to electron dynamic response in the form of a damped oscillator and explore the possibility to reconstruct the spectrum of the latter from the phonon measurements. Preliminary estimates point to its location in the mid infrared region and we show how the required additional information can be extracted from the oxygen isotope effect on the phonon spectrum. The model predicts a significant measurable deviation from the "standard value" of the isotope effect even if the phonon frequency is far below the electron excitation spectrum, provided the latter is strongly incoherent. In this regime, which corresponds to the "mid infrared scenario", the phonon linewidth becomes a sensitive and informative probe of the isotope effect.

Research paper thumbnail of Bessel functions of integer order in terms of hyperbolic functions

Using Jacobi's identity we derive a simple expression for the Bessel functions of integer or... more Using Jacobi's identity we derive a simple expression for the Bessel functions of integer order in terms of combinations of powers and hyperbolic functions of the same argument.

Research paper thumbnail of Green's function and excitation spectrum of finite lattices

physica status solidi (b), 2006

PACS 71.15.Mb, 75.10.Jm New analytical results are obtained for the Green's function of a finite ... more PACS 71.15.Mb, 75.10.Jm New analytical results are obtained for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction using discrete Fourier transform. The method offers an alternative to the Bethe Ansatz, but does not require any a priori assumption on the form of the wavefunction. This makes it suitable for extensions to nano-ferromagnets of higher dimensions. Solutions of the Heisenberg spin chain with periodic and open boundary conditions are considered as examples.

Research paper thumbnail of Spin excitations on finite lattices and the discrete Fourier transform

Journal of Magnetism and Magnetic Materials, 2006

The method of discrete Fourier transform (DFT) is applied to obtain the exact one-or bi-magnonic ... more The method of discrete Fourier transform (DFT) is applied to obtain the exact one-or bi-magnonic states in several finite onedimensional spin systems. The advantage of DFT method, compared to Bethe ansatz, is that no assumption is made on the form of the wave function and that its limit of infinite system reduces to the standard approach to excitation spectra in condensed matter. So the method has, in principle, no limitation on lattice dimensionality and its physical interpretation is relatively transparent. It is demonstrated that the two approaches (DFT and BA) give identical results for the solution of the Schrodinger equation on the 1D lattice, although the structure of the methods is rather different. The excitation spectrum of the XXZ chain with arbitrary end fields is analyzed in detail and an analogy with atomic wires is briefly discussed. r

Research paper thumbnail of Low-temperature electron-phonon heat transfer in metal films

We consider the deformation potential mechanism of the electron-phonon coupling in metal films an... more We consider the deformation potential mechanism of the electron-phonon coupling in metal films and investigate the intensity of the associated heat transfer between the electron and phonon subsystems. The focus is on the temperature region below dimensional crossover T < T * where the thermally relevant vibrations are described in terms of a quasi-two-dimensional elastic medium, while electron excitations behave as a three-dimensional Fermi gas. We derive an explicit expression for the power P (T) of the electron-phonon heat transfer which explains the behavior observed in some experiments including the case of metallic film supported by an insulating membrane with different acoustic properties. It is shown that at low temperatures the main contribution is due to the coupling with Lamb's dilatational and flexural acoustic modes.

Research paper thumbnail of Effetti DI Correlazione a Bassa Dimensionalita

IV o Congresso del Dipartimento

Research paper thumbnail of Quantum Spin Excitations on 1 D and 2 D Continua

Symmetry and Structural Properties of Condensed Matter, 2001

ABSTRACT

Research paper thumbnail of Magnon excitations in a mesoscopic Heisenberg ferromagnet

Research paper thumbnail of Magnon gas and deviation from the Bloch law in a nanoscale Heisenberg ferromagnet

Philosophical Magazine, 2011

ABSTRACT It is known that saturation magnetization of ferromagnetic nanoparticles and nanocluster... more ABSTRACT It is known that saturation magnetization of ferromagnetic nanoparticles and nanoclusters deviates strongly from the Bloch T 3/2 law. To describe the deviation one usually uses a modified power law T α with a size dependent exponent α, which is motivated simply by its flexibility in fitting the observed behavior. By considering the Heisenberg spin model we derive an explicit expression in terms of a magnon gas which generalizes the Bloch formula to a finite size system. Comparison to the experimental data shows good agreement with the observed behavior and gives a better understanding of its physics.

Research paper thumbnail of Electron–phonon heat exchange in layered nano-systems

We analyze the heat power P from electrons to phonons in thin metallic films deposited on free-st... more We analyze the heat power P from electrons to phonons in thin metallic films deposited on free-standing dielectric membranes in a temperature range in which the phonon gas has a quasi two-dimensional distribution. The quantization of the electrons wavenumbers in the direction perpendicular to the film surfaces lead to the formation of quasi two-dimensional electronic sub-bands. The electron–phonon coupling is treated in the deformation potential model. If we denote by T e the electrons temperature and by T ph the phonons temperature, we find that P P ð0Þ ðT e ÞÀP ð1Þ ðT e ; T ph Þ. Due to the quantization of the electronic states, both P ð0Þ and P ð1Þ , plotted vs ðT e ; dÞ show very strong oscillations with d, forming sharp crests almost parallel to T e. From valley to crest, both P ð0Þ and P ð1Þ increase by more than one order of magnitude. In the valleys between the crests, P p T 3:5 e À T 3:5 ph in the low temperature limit, whereas on the crests P does not have a simple power law dependence on temperature. The strong modulation of P with the thickness of the film may provide a way to control the electron-phonon heat power and the power dissipation in thin metallic films. On the other hand, the surface imperfections of the metallic films can smoothen these modulations.

Research paper thumbnail of Electronic structure of A4C60: Joint effect of electron correlation and vibronic interactions

Physical Review B, 1999

Effects of electron correlation, intrasite vibronic interaction, and merohedral disorder on the e... more Effects of electron correlation, intrasite vibronic interaction, and merohedral disorder on the electronic structure of K 4 C 60 are investigated with a model approach taking into account all essential interactions in the lowest unoccupied molecular orbital ͑LUMO͒ band. The self-energy was calculated within the GW approximation with self-consistency after the quasiparticle Green function starting from Hartree-Fock band structure. The insulating state arises due to interorbital charge disproportionation within the LUMO band while the band gap is strongly reduced by effects of long-range electron correlation. The results of the calculations are in reasonable agreement with experiment, providing evidence for a Jahn-Teller induced transition from a Mott-Hubbard to a band insulator state. ͓S0163-1829͑99͒51020-5͔

Research paper thumbnail of Effect of electron–phonon interaction on the single-particle spectral properties of the Hubbard model

The effect of electron-phonon interaction on quasiparticle dispersion and spectral density is con... more The effect of electron-phonon interaction on quasiparticle dispersion and spectral density is considered within second order adiabatic approximation of the two-dimensional Holstein-Hubbard model. The electron-phonon interaction gives rise to a kink in the dispersion along the nodal direction of the Brillouin zone whose dependence on isotope substitution and doping is discussed in relation to recent photoemission experiments on the nodal quasiparticles in high-temperature superconductors. It is shown that various experimental features can be qualitatively explained in a framework that considers both strong correlations effect and the usual electron-phonon interaction. r

Research paper thumbnail of Role of electron-phonon interaction on quasiparticle dispersion in the strongly correlated cuprate superconductors

Physical Review B, 2006

The role of the electron-phonon ͑el-ph͒ interaction in high-T c cuprates is investigated theoreti... more The role of the electron-phonon ͑el-ph͒ interaction in high-T c cuprates is investigated theoretically by considering correlated electrons interacting with Holstein phonons within the two-dimensional single-band Hubbard model in the limit of large Coulomb interaction. It is shown that the electron-phonon interaction gives rise to a kink in the dispersion along the nodal direction and to a peak/dip/hump structure in the one-electron spectral weight whose dependence on temperature, isotope substitution, and doping is discussed in relation to recent photoemission experiments on the nodal quasiparticles in Bi2201 and LSCO. A comparison with these experiments shows that electron correlations play a crucial role in the determination of the kink position, size, and doping dependence. We also show that the "unusual" oxygen isotope shift in the real part of the selfenergy, experimentally observed in the optimally doped Bi2212 samples, can be qualitatively explained within the framework that incorporates both strong electron correlations and the adiabatic electron-phonon interaction.

Research paper thumbnail of Effective electron–phonon coupling in the Hubbard–Holstein model in presence of strong correlations and density fluctuations

Physica C: Superconductivity, 2007

We study the Hubbard-Holstein model in the strong coupling regime and discuss the role of electro... more We study the Hubbard-Holstein model in the strong coupling regime and discuss the role of electron-electron correlations, doping and phonon frequency (isotope substitution) on the effective electron-phonon coupling. A comparison with recent dynamical mean field (DMF) studies and connection with recent experimental findings in cuprate superconductors is also discussed.

Research paper thumbnail of High-energy kink in the single-particle spectra of cuprates

Physica B: Condensed Matter, 2008

Within a phenomenological model where electrons are coupled to a bosonic mode in a generic form o... more Within a phenomenological model where electrons are coupled to a bosonic mode in a generic form of damped oscillator, we analyze the high-energy kink recently observed in ARPES experiments on cuprates. It is shown that the model allows to describe the main anomalous features found in experiments, such as the broad incoherent spectral weight, the ''waterfall dispersion'', its doping and temperature dependence. In contrast to the low-energy kink, presence of significant damping is required to account for the anomalies. The ''bosonic mode'' is related to the incoherent excitation peak observed in optical conductivity spectra of cuprates. r

Research paper thumbnail of Renormalization of the electron–phonon interaction in the Hubbard model

Physica B: Condensed Matter, 2005

We calculate the electron-phonon vertex in the two-dimensional Hubbard model by a strong coupling... more We calculate the electron-phonon vertex in the two-dimensional Hubbard model by a strong coupling approach based on cumulant expansion. The role of the on-site Coulomb interaction on the coupling of the electrons to the Holstein phonons is investigated in different regions of the Brillouin zone. The results reveal the presence of a strong forward scattering and an effective increase of the vertex function at low temperatures above a certain critical U. Comparison with other approaches is also discussed. r

Research paper thumbnail of Bond stretching phonon softening and isotope effect in a phenomenological model for cuprate superconductors

Journal of Physics: Conference Series, 2010

Lattice and charge degrees of freedom of cuprate superconductors remain an intensively debated to... more Lattice and charge degrees of freedom of cuprate superconductors remain an intensively debated topic, both experimentally and theoretically, because of the strong anomalies observed in some of the phonon branches. In particular, the bond-stretching phonon modes show a knee like softening and a large damping for momenta around 0.25−0.3 r.l.u. along, e.g., (1, 0, 0) direction of the Brillouin zone. We discuss a phenomenological model where these anomalies are caused by coupling to electron charge fluctuations and explore a possibility to extract the spectrum of the latter from the phonon data. In particular, we predict a significant deviation from the standard value of the oxygen isotope substitution effect on the phonon spectrum itself. The phonon dispersion and linewidth are shown to contain complementary information related to the isotope effect which could allow a detailed description of the electronic spectrum.

Research paper thumbnail of Modification of the Bloch law in ferromagnetic nanostructures

EPL (Europhysics Letters), 2014

Research paper thumbnail of Bond stretching phonon anomalies due to incommensurate charge density wave instabilities in high-Tc cuprates

The European Physical Journal B, 2008

Phonon anomalies observed in various high Tc cuprates are analyzed theoretically within the Hubba... more Phonon anomalies observed in various high Tc cuprates are analyzed theoretically within the Hubbard-Holstein model in the limit of strong local electron correlations and in presence of long-range Coulomb interaction. The phonon self-energy is evaluated by taking into account the charge collective modes that become critical upon doping approaching an instability towards an incommensurate charge density wave (ICDW) driven by electron correlations. The doping dependence of phonon softening features and the highly distinctive phonon self-energy dependence on the wave vector agree with experiments. We discuss relevance of dynamical corrections to the density correlation function to achieve a sizeable bond-stretching phonon softening with a kink-like profile away from the zone boundary. PACS. 71.10.Fd Lattice fermion models -74.72.-h Cuprate superconductors -71.38.-k Polarons and electron-phonon interactions -71.27.+a Strongly correlated electron systems; heavy fermions 180 The European Physical Journal B

Research paper thumbnail of Isotope effect and bond-stretching phonon anomaly in high-Tc cuprates

The European Physical Journal B, 2010

We analyse a model where the anomalies of the bond-stretching LO phonon mode are caused by the co... more We analyse a model where the anomalies of the bond-stretching LO phonon mode are caused by the coupling to electron dynamic response in the form of a damped oscillator and explore the possibility to reconstruct the spectrum of the latter from the phonon measurements. Preliminary estimates point to its location in the mid infrared region and we show how the required additional information can be extracted from the oxygen isotope effect on the phonon spectrum. The model predicts a significant measurable deviation from the "standard value" of the isotope effect even if the phonon frequency is far below the electron excitation spectrum, provided the latter is strongly incoherent. In this regime, which corresponds to the "mid infrared scenario", the phonon linewidth becomes a sensitive and informative probe of the isotope effect.

Research paper thumbnail of Bessel functions of integer order in terms of hyperbolic functions

Using Jacobi's identity we derive a simple expression for the Bessel functions of integer or... more Using Jacobi's identity we derive a simple expression for the Bessel functions of integer order in terms of combinations of powers and hyperbolic functions of the same argument.

Research paper thumbnail of Green's function and excitation spectrum of finite lattices

physica status solidi (b), 2006

PACS 71.15.Mb, 75.10.Jm New analytical results are obtained for the Green's function of a finite ... more PACS 71.15.Mb, 75.10.Jm New analytical results are obtained for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction using discrete Fourier transform. The method offers an alternative to the Bethe Ansatz, but does not require any a priori assumption on the form of the wavefunction. This makes it suitable for extensions to nano-ferromagnets of higher dimensions. Solutions of the Heisenberg spin chain with periodic and open boundary conditions are considered as examples.

Research paper thumbnail of Spin excitations on finite lattices and the discrete Fourier transform

Journal of Magnetism and Magnetic Materials, 2006

The method of discrete Fourier transform (DFT) is applied to obtain the exact one-or bi-magnonic ... more The method of discrete Fourier transform (DFT) is applied to obtain the exact one-or bi-magnonic states in several finite onedimensional spin systems. The advantage of DFT method, compared to Bethe ansatz, is that no assumption is made on the form of the wave function and that its limit of infinite system reduces to the standard approach to excitation spectra in condensed matter. So the method has, in principle, no limitation on lattice dimensionality and its physical interpretation is relatively transparent. It is demonstrated that the two approaches (DFT and BA) give identical results for the solution of the Schrodinger equation on the 1D lattice, although the structure of the methods is rather different. The excitation spectrum of the XXZ chain with arbitrary end fields is analyzed in detail and an analogy with atomic wires is briefly discussed. r

Research paper thumbnail of Low-temperature electron-phonon heat transfer in metal films

We consider the deformation potential mechanism of the electron-phonon coupling in metal films an... more We consider the deformation potential mechanism of the electron-phonon coupling in metal films and investigate the intensity of the associated heat transfer between the electron and phonon subsystems. The focus is on the temperature region below dimensional crossover T < T * where the thermally relevant vibrations are described in terms of a quasi-two-dimensional elastic medium, while electron excitations behave as a three-dimensional Fermi gas. We derive an explicit expression for the power P (T) of the electron-phonon heat transfer which explains the behavior observed in some experiments including the case of metallic film supported by an insulating membrane with different acoustic properties. It is shown that at low temperatures the main contribution is due to the coupling with Lamb's dilatational and flexural acoustic modes.