Site-Specific Phonon Density of States Measuredusing Nuclear Resonant Scattering

Fig. 1. Energy spectrum of nuclear resonantscattering of all 57Fe atoms in Fe3O4.

It is well known that all atoms oscillate in a solidmaterial even at low temperature, and their quantizedvibrations are known as phonons. Except for simplematerials, different kinds of atoms are usually containedin a material, and the properties of their oscillationsare generally not the same. The atomic motion of acertain atom sometimes plays an important role in thecharacteristics of the material such as the vibration ofthe impurity or doped atoms in metals or semiconductors,the carrier ionʼs motions in ionic conductors, and theoscillations of rare-earth atoms in filled skutteruditeantimonides. Therefore, each atomic motion providesimportant information. The nuclear resonant inelasticscattering of synchrotron radiation offers element-(isotope)-specific phonon energy spectra [1]. In thismethod, the nuclear resonant excitation is attainedwith synchrotron radiation, the bandwidth of which isreduced to the order of meV, and the energy dependenceof the delayed emission from the relatively long-livedexcited state yieds the inelastic excitation spectrum,i.e., the phonon energy spectrum. Usually, the excitationenergy level is inherent to each nucleus and simultaneousexcitation of more than two nuclei can be ignored.Therefore, if we tune the incident photon energyaround the excitation energy of a certain nuclide, we

individual site through hyperfine interactions isobtained from the incoherent inelastic scattering, wecan identify each phonon component of every site bymeasuring the hyperfine interactions. The effect ofhyperfine interactions can be observed in the timeevolution of the delayed scattering. Therefore, themeasurements of time evolution of the incoherentinelastic scattering at different phonon energies permitus to observe the site-specific phonon energy spectra.

We have performed the measurement of site-specific phonons in magnetite (Fe3O4). In magnetite,the iron atoms are located in two nonequivalentpositions in the unit cell at room temperature; one-third of the Fe ions (Fe3+) occupy the A sitestetrahedrally coordinated by four oxygen ions and two-thirds of the Fe ions (Fe2.5+) occupy the B sitesoctahedrally surrounded by six oxygen ions. Apolycrystalline sample pressed into the pellet formwas used. The measurements were performed at thenuclear resonant scattering beamline BL09XU andthe JAERI beamline BL11XU. The incident radiationwas monochromatized to the bandwidth of 3.2 meV(FWHM), and the energy of the radiation was variedaround the first nuclear resonant excitation energy of57Fe (14.413 keV). The scattered 14.413 keV γ rays

can obtain the element-specific phonon energysp ec t r um . Howeve r , i n t h e cas e o fcompounds with two or more different states ofa toms o f t h e same e l emen t , suc h asmagnet i te , which is a mixed valent Fecompound [2], the observed phonon energyspectrum is the superposition of the partialp hono n spec t r a o f i nd i v i dua l a tom s .Therefore, even this method seems unable todistinguish the “site-specific” phonon energyspectrum. Although the phonon is one of themost fundamental concepts in solids, it wasimpossible to discern the site-specific atomicmotions by previous methods. However, wecou ld use a new method , wh ich is anextension of the nuclear resonant scatteringmethod, and it led to the observation of thesite-specific phonons [3]. In general, nuclearenergy levels are split and/or shifted owing tothe surrounding electronic states; theseinteractions are small compared to the nuclearexcitation energy and known as hyperfineinteractions. Because the information of the

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Makoto Seto

Research Reactor Institute, Kyoto University

E-mail: seto@rri.kyoto-u.ac.jp

Fig. 2. Time spectra measured at different incidentphoton energies (deviations from nuclear resonantenergy; diamonds: 16 meV, circles: 22 meV,triangles: 35 meV). Lines are least-square fittedspectra with two exponential functions accompaniedby sinusoidal quantum beats.

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at the deexcitation from a resonantly excited nucleuswere measured using a multielement Si-avalanchephotodiode (APD) detector Nuclear resonant inelastic scattering spectrum of57Fe in Fe3O4 is shown in Fig. 1, which is thesuperposition of the inelastic scattering from both Aand B sites.

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Typical time spectra measured atdifferent incident photon energies are shown in Fig. 2,and the component ratios of A site to B site wereobtained at each phonon energy. From a measurednuclear resonant inelastic scattering spectrum (Fig. 1),phonon density of states (PDOS) of all Fe atoms inFe3O4 was reduced and is shown in Fig. 3 as closedcircles. Site-specific partial PDOS of A and B sitesobtained using the total Fe PDOS and the componentratios in time spectra are shown in Fig. 3 as downwardand upward triangles, respectively, and the differencesare clearly seen. Around the first peak of 17 meV, theintensity of the B site is larger than that of the A sitewhile their intensities are almost the same at around35 meV. The observed characteristics indicate theircouplings to surrounding atoms, and the phonons ataround 17 meV and at around 35 meV are consideredto be mainly due to the iron atom’s motions and thecoupled motions of iron and oxygen atoms, respectively. We could observe for the first time the partialPDOS identified using the electronic states. Thismethod is applicable not only to solids but also to softmaterials and liquids if only their electronic states canbe identified in the time spectra. The method allowsus to study site-specific phonons in various systems,which we could not access, and will enable theextensive study of the relationships of the electronicstates to the local phonon states.

Fig. 3. Phonon densities of states of 57Fe in the Fe3O4 sample. The phonondensity of states of all Fe is shown in solid circles. The partial phonondensities of states of the A and B sites obtained experimentally are shown asdownward and upward triangles, respectively. Lines are guides for the eye.

References[1] M. Seto et al.: Phys. Rev. Lett. 74(1995) 3828.[2] For a review, see N. Tsuda et al. :Electronic Conduction in Oxides, 2nded. (Springer-Verlag, Berlin, 2000).[3] M. Seto, S. Kitao, Y. Kobayashi, R.Haruki , Y. Yoda, T. Mitsui and T.Ishikawa: Phys. Rev. Lett. 91 (2003)185505; P. Schewe et al.: PhysicsNews Update 661 (2003), (http://www.a i p . o r g /e n e w s / p h y s n e w s / 2 0 0 3 /661.html)

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