High-energy phonon confinement in nanoscale metallic multilayers

Cuenya, Beatriz Roldán; Keune, W.; Peters, Robert; Schuster, E.; Sahoo, Balaram; Hörsten, U. von; Sturhahn, W.; Zhao, Jiyong; Toellner, T. S.; E., E.; Bader, S. D.

doi:10.1103/physrevb.77.165410

Cited by 28 publications

(25 citation statements)

References 36 publications

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“…3(a)]. The typical features in the VDOS of Fe/Ag and Fe/Cr center and interface Fe layers, respectively, are summarized in Table I. A qualitatively similar reduction of the LA-phonon peak height at ∼35 meV combined with an enhancement of the low-energy part of the VDOS below ∼18 meV, as in the present Fe/Ag samples, was previously observed in nanoscale polycrystalline [ 57 Fe/Ag(40Å)] 15 multilayers containing homogeneous 57 Fe layers 1.5 to 4 nm in thickness when the 57 Fe layer thickness decreases down to 1.5 nm [21]. This effect was attributed to Fe phonon confinement and interface localization due to the VDOS energy mismatch between of Fe and Ag.…”

Section: Resultssupporting

confidence: 88%

“…The data marked with * correspond to polycrystalline references samples discussed in Ref. [21]. Fe/Cr multilayer, where no significant change in these quantities between the interface and the center layer is observed.…”

Section: Resultsmentioning

confidence: 96%

“…Reddy et al [20] pointed out the limitations of the Debye approximation in DMM calculations, and Dechaumphai et al emphasized the use of DMM-calculated bulk (three-dimensional) full phonon dispersion relations in order to correctly describe the ITR in Au/Si multilayers [18]. However, the use of the bulk phonon dispersion for the interface in A/B multilayers is very problematic, as the phonon DOS in metallic multilayers is known from experiment [21] to depend on the individual nanoscale film thickness as well as on the ratio of the upper phonon cut-off frequencies (i.e., on the phonon contrast) of the two multilayer materials A and B. Therefore knowledge of the phonon DOS at interfaces becomes of paramount interest for the basic understanding and engineering of low-dimensional devices.…”

Section: Introductionmentioning

confidence: 99%

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Influence of interfaces on the phonon density of states of nanoscale metallic multilayers: Phonon confinement and localization

Keune

Hong

et al. 2018

Phys. Rev. B

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Isotope-selective 57 Fe nuclear resonant inelastic x-ray scattering (NRIXS) measurements and atomic-layer resolved density functional theory (DFT) calculations were used to investigate the effect of interfaces on the vibrational (phonon) density of states (VDOS) of (001)-oriented nanoscale Fe/Ag and Fe/Cr multilayers. The multilayers in the experiment contained isotopically enriched 57 Fe monolayers as probe layers located either at the Fe/Ag or Fe/Cr interfaces or in the center of the Fe films. This allows probing of the vibrational dynamics of Fe sites either at the buried interfaces or in the center of the Fe films. For Fe/Ag multilayers, distinct differences were observed experimentally between the Fe-partial VDOS at the interface and in the center. At the Fe/Ag interface, the high-energy longitudinal-acoustic (LA) phonon peak of Fe near ∼35 meV is suppressed and slightly shifted to lower energy, and the low-energy part of the VDOS below ∼20 meV is drastically enhanced, as compared to the Fe-specific VDOS in the center Fe layers or in bulk Fe. Similar phenomena are found to a less degree in the Fe/Cr multilayers. The measured Fe-partial VDOS was used to determine the Fe site-selective vibrational thermodynamic properties of the multilayers. Our theoretical findings for the layer-dependent VDOS of the multilayers are in qualitative agreement with the experimental results obtained by NRIXS. For Fe/Ag multilayers, which are characterized by a large atomic mass ratio, the experimental and theoretical results demonstrate phonon confinement in the Fe layers and phonon localization at the Fe/Ag interfaces due to the energy mismatch between Ag and Fe LA phonons. These phenomena are reduced or suppressed in the Fe/Cr multilayers with their about equal atomic masses. Moreover, direction-projected Fe VDOS along the (nearly in-plane) incident x-ray beam was computed in order to address the intrinsic vibrational anisotropy of the Fe/Ag multilayer. We have also performed spin-resolved electronic band structure (DFT) calculations, predicting an enhanced magnetic moment (μ Fe = 2.8 μ B ) of the interfacial Fe atoms and a high electron spin polarization (79%) at the Fermi energy for the Fe/Ag interface, as compared to the case of Fe center layers. This is a result of charge transfer from Fe to Ag at the interface. On the contrary, Cr tends to donate electrons to Fe, thus reducing the interfacial Fe moment (μ Fe = 1.9 μ B ). This implies strong chemical bonding at the Fe/Ag and Fe/Cr interfaces, affecting the interfacial VDOS.

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Section: Resultssupporting

confidence: 88%

Section: Resultsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

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Influence of interfaces on the phonon density of states of nanoscale metallic multilayers: Phonon confinement and localization

Keune

Hong

et al. 2018

Phys. Rev. B

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“…Clear differences between g(E) of the NP samples and bulk bcc Fe are observed. First, a strong suppression of the longitudinal acoustic (LA) phonon peak at ~35 meV is detected for the NPs, an effect that may be attributed to phonon damping due to confinement 9,44,51,67 . In addition, a shift of the LA peak to lower energies (up to 1.3 meV shift for S5) is found.…”

Section: -66mentioning

confidence: 99%

Size-dependent evolution of the atomic vibrational density of states and thermodynamic properties of isolated Fe nanoparticles

et al. 2012

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We have gained insight into the internal degree of atomic disorder in isolated sizeselected Fe nanoparticles (NPs) (~2 -6 nm in size) supported on SiO 2 /Si(111) and Al 2 O 3 (0001) from precise measurements of the low-energy (low-E) part of the phonon density of states [PDOS, g(E)] via 57 Fe nuclear resonant inelastic X-ray scattering (NRIXS), combined with transmission electron microscopy (TEM) measurements. An intriguing size-dependent trend was observed, namely, an increase of the low-E excess density of phonon states (as compared to the PDOS of bulk bcc Fe) with increasing NP size. This is unexpected, since usually the enhancement of the density of low-E phonon modes is attributed to low-coordinated atoms at the NP surface, whose relative content increases with decreasing NP size due to the increase in the surface-to-volume ratio. OurNPs are covered by a Ti coating layer, which essentially restores the local neighbourhood of surface Fe surface atoms towards bulk-like coordination, reducing the surface effect.Our data can be qualitatively explained by the existence of low-coordinated Fe atoms 2 located at grain boundaries or other defects with structural disorder in the interior of the large NPs (~3 -6 nm), while our small NPs (~2 nm) are single-grain and, therefore, characterized by a higher degree of structural order. This conclusion is corroborated by the observation of Debye behaviour at low energy [g(E) ~ E n with n ~ 2] for the small NPs, but non-Debye behaviour (with n ~ 1.4) for the large NPs. The PDOS was used to determine thermodynamic properties of the Fe NPs. Finally, our results demonstrate that, in combination with TEM, NRIXS is a suitable technique to investigate atomic disorder/defects in NPs. We anticipate that our findings are universal for similar NPs with bcc structure.Keywords: Fe, nanoparticle, nuclear resonant inelastic x-ray scattering, atomic force microscopy, transmission electron microscopy, x-ray photoelectron spectroscopy, phonon density of states.

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“…In a separate NRIXS study, Roldan Cuenya, et al studied phonons in thin, 8 nm layers of 57 Fe confined between layers of Cr, Co, Cu, Pd, Au, or Ag [284]. There was a clear suppression of high-frequency longitudinal modes of bcc Fe when it was confined between metals having a lower cutoff of their phonon DOS.…”

Section: Low-energy Vibrations Of Nanostructuresmentioning

confidence: 99%

Vibrational thermodynamics of materials

Fultz¹

2010

Progress in Materials Science

558

428

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Abstract. The literature on vibrational thermodynamics of materials is reviewed. The emphasis is on metals and alloys, especially on the progress over the last decade in understanding differences in the vibrational entropy of different alloy phases and phase transformations. Some results on carbides, nitrides, oxides, hydrides and lithium-storage materials are also covered.Principles of harmonic phonons in alloys are organized into thermodynamic models for unmixing and ordering transformations on an Ising lattice, and extended for non-harmonic potentials. Owing to the high accuracy required for the phonon frequencies, quantitative predictions of vibrational entropy with analytical models prove elusive. Accurate tools for such calculations or measurements were challenging for many years, but are more accessible today. Ab-initio methods for calculating phonons in solids are summarized. The experimental techniques of calorimetry, inelastic neutron scattering, and inelastic x-ray scattering are explained with enough detail to show the issues of using these methods for investigations of vibrational thermodynamics. The explanations extend to methods of data analysis that affect the accuracy of thermodynamic information.It is sometimes possible to identify the structural and chemical origins of the differences in vibrational entropy of materials, and the number of these assessments is growing. There has been considerable progress in our understanding of the vibrational entropy of mixing in solid solutions, compound formation from pure elements, chemical unmixing of alloys, order-disorder transformations, and martensitic transformations. Systematic trends are available for some of these phase transformations, although more examples are needed, and many results are less reliable at high temperatures. Nanostructures in materials can alter sufficiently the vibrational dynamics to affect thermodynamic stability. Internal stresses in polycrystals of anisotropic materials also contribute to the heat capacity. Lanthanides and actinides show a complex interplay of vibrational, electronic, and magnetic entropy, even at low temperatures.A "quasiharmonic model" is often used to extend the systematics of harmonic phonons to high temperatures by accounting for the effects of thermal expansion against a bulk modulus. Non-harmonic effects beyond the quasiharmonic approximation originate from the interactions of thermally-excited phonons with other phonons, or with the interactions of phonons with electronic excitations. In the classical high temperature limit, the adiabatic electron-phonon coupling can have a surprisingly large effect in metals when temperature causes significant changes in the electron density near the Fermi level. There are useful similarities in how temperature, pressure, and composition alter the conduction electron screening and the interatomic force constants. Phononphonon "anharmonic" interactions arise from those non-harmonic parts of the interatomic potential that cannot be accounted for by the quasiharmonic ...

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High-energy phonon confinement in nanoscale metallic multilayers

Cited by 28 publications

References 36 publications

Influence of interfaces on the phonon density of states of nanoscale metallic multilayers: Phonon confinement and localization

Influence of interfaces on the phonon density of states of nanoscale metallic multilayers: Phonon confinement and localization

Size-dependent evolution of the atomic vibrational density of states and thermodynamic properties of isolated Fe nanoparticles

Vibrational thermodynamics of materials

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