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the role of phonons in the mechanism of high - temperature superconductivity in ferropnictides remains poorly understood . while density function theory ( dft ) calculations indicate that conventional electron - phonon coupling is not responsible for superconductivity @xcite , there is nevertheless a strong relationship between the lattice and electronic properties , including both magnetism and superconductivity . for example , there is an isotope effect due to fe @xcite , and the superconducting temperature strongly depends upon the fe - as - fe bond angle @xcite ( or alternatively the height of the pnictogen atom above the plane of the transition metal@xcite ) . in addition , the lattice and magnetism are strongly coupled , which manifests in several ways . first , in order to correctly refine the internal parameters of the structure , dft calculations must be performed with spin - polarization @xcite . second , cafe@xmath1as@xmath1  enters a `` collapsed '' tetragonal state at mild isotropic pressures @xcite , in which the c - axis contracts by @xmath010% and the magnetism becomes quenched @xcite ; this is the result of strong coupling between the fe moment and interplanar as - as bonding @xcite . third , the increase of the static moment with as - fe separation can be described by a landau / stoner theory @xcite , in which a larger volume around each fe atom allows a larger magnetic moment . this dependence of the moment on as position has been confirmed experimentally @xcite for the static moment in the cefeas@xmath2p@xmath3o series . this strong magnetostructural coupling can in turn influence the phonon spectrum . for instance , the frequency of the raman - active mode corresponding to vibration of the as atoms is not predicted correctly unless the fe moment is taken into account @xcite . in addition , the phonon density of states in lafeaso is appreciably softer than predicted by nonmagnetic dft @xcite , especially for the higher - energy modes corresponding to in - plane motion of the fe and as atoms . while the dispersion of the c - axis modes has been studied elsewhere @xcite ) , we are not aware of any reports regarding the in - plane fe and as phonons .    here we present measurements of the phonon dispersion in srfe@xmath1as@xmath1  obtained through time - of - flight ( tof ) inelastic neutron scattering , focusing on the closely - spaced higher - energy modes which are sensitive to fe - as coupling and compare these results to the dft calculations . in order to isolate the dispersions of different phonons from nearby branches , we developed a novel approach that utilizes the entire tof spectrum across many brillouin zones ( bz ) , which we call multizone phonon refinement ( mpr ) . we show that the experimental phonon dispersions agree well with dft calculations performed with the structure constrained to the measured structure . we also found that there is no significant temperature dependence across the magnetic ordering transition of any of the phonons for which it was measured . phonon dispersion along ( 2,k,0 ) . this is the inelastic scattering for the regions shown as red boxes in panels @xmath4 and @xmath5 . near ( 2,0,0 ) the phonons are strictly transverse , but near ( 2,6,0 ) the longitudinal phonons are also evident . @xmath6 map of elastic scattering in the ( 2,k , l ) plane , showing many bragg peaks . @xmath7 map of elastic scattering in the ( h , k,0 ) plane , showing 8 bragg peaks . ] the experiment was performed using the arcs time - of - flight spectrometer at the spallation neutron source , located at the oak ridge national laboratory @xcite . data were collected using the recently - developed rotating sample technique @xcite , which allows us to collect a 4-dimensional dataset ( h , k , l , energy ) . the sample was a single crystal of srfe@xmath1as@xmath1 , grown from self - flux in glassy carbon crucibles @xcite , using extra - low cooling rates of @xmath8 - @xmath9 c / h . the sample mass was @xmath0  1.5  g , and the mosaic was @xmath0  @xmath10 . at room temperature the material is tetragonal ( space group 139 , _ i4/mmm _ ) , and at @xmath0  210  k undergoes an afm / orthorhombic transition @xcite ( space group 69 , _ fmmm _ ) . because the orthorhombic distortion is quite small ( @xmath11  @xmath0  1% ) , we use tetragonal notation throughout this paper . the sample was mounted using twisted aluminum foil , and placed in a closed - cycle refrigerator . no exchange gas was used , so the temperatures are accurate to within 10  k.    data were collected over a period of 6 days ; approximately 3 days over an angular range of @xmath12 at t  = 10  k , and approximately 1.5 days over a range of @xmath13 at both t  = 220  k and t  = 320  k. this corresponds to roughly 45 bz in the energy range of interest for 10  k and 20 bz for 220  k ( just slighly above the magnetic ordering temperature ) , and 320  k. the sample was mounted in the hk0 plane , but the out - of - plane detector coverage allows access up to l @xmath0  @xmath14  4 . the incident energy was 70  mev , with a fwhm of @xmath0  3  mev at the elastic line , and @xmath0  1.5  mev in the range of interest . the details of the dft calculations have been described previously @xcite . we used the non - magnetic tetragonal unit cell , with the experimental lattice parameters and atomic positions taken from previously - published work @xcite . the eigenvectors are closely related to the atomic displacements , which in turn determine the intensities of the phonon peaks in various bz . these eigenvectors can be calculated quite well at the high - symmetry points , and the calculation allows for the phonon intensity at other points to be calculated using a perturbative method . these energies and intensities are then used as a starting point for the refinement , as described below . $ ] ( gamma point ) . the background ( solid red line ) can be subtracted from the raw data ( red diamonds ) to produce a remarkably clean spectrum ( blue circles ) . dashed lines show the refined values of the peak centers . the intensities shown are predicted from dft , which provides reasonable initial conditions for least - squares fitting . ]    = [ 0.7 , 0 , 0 ] from selected brillouin zones . the left panel displays the data ( points with error bars ) together with phonon energies and intensities as predicted by dft ; the right panel displays the same data , along with the energies and intensities after multizone phonon refinement . although data from only 5 symmetry points are shown here , a total of 154 symmetry points were used for the fitting . data from different @xmath15 are vertically offset for clarity . the model consists of 6 phonons each constrained to have the same energy and lineshape in all bz . the individual phonons broadened by experimental resolution are shown with thin lines , and the summation with solid lines . the dashed vertical lines mark the phonon energies , and facilitate comparison between the different @xmath15 . ] optical phonons in many compounds with a large unit cell form dense `` spaghetti '' of branches in large parts of reciprocal space . in such a case energies of different phonons at the reduced wavevector are separated by much less than the energy - resolution of the spectrometer . quite often it is easy to mistake two nearby peaks for a single broad peak . here we outline a novel technique , multizone phonon refinement ( mpr ) that allows accurate determination of phonon dispersions in such cases . we use this technique to resolve a group of branches between 24 and 36 mev in srfe@xmath1as@xmath1 ,  measured as described in the previous section .      in neutron - scattering experiments the inelastic background arises from a combination of factors , primarily incoherent phonon scattering by the sample , powder - averaged phonon scattering from the mount ( in this case aluminum foil ) , secondary scattering ( a bragg peak and a phonon ) , and multiphonon scattering ( strongest at high temperature ) . the first factor necessarily produces isotropic scattering with a @xmath16 dependence characteristic of phonons . for this work all contributions to the inelastic background are assumed to follow this form .    in order to determine the background , we divided measured reciprocal space into equally - sized volume elements ( known as `` voxels '' ) , normalizing by @xmath16 . each voxel corresponds to an energy scan at a fixed @xmath15 . for a given energy , the mean of the lowest - intensity voxels was taken to be the background ( see fig . [ fig : bg_subt ] ) . in other words , for each energy we found the lowest intensities over the entire measured dataset ( after dividing by @xmath16 ) and took that to be the background . figure [ fig : bg_subt ] shows such energy spectra plotted together in thin lines . the thick solid line corresponding to the average intensity of the lowest 1% of the @xmath15-voxels . we experimented with using the lowest 1% to the lowest 5% of the @xmath15-voxels at each energy , and found only minor changes to the resulting background function . since our primary interest here was the higher - energy phonons , we made no attempt to subtract the elastic line . in future experiments we can subtract the elastic line separately from each voxel of @xmath15 , and then subtract the background . an additional linear term was included in the fitting to account for any residual intensity , but was generally insignificant . at lower @xmath15 there is some additional background , but these data have little effect on the overall fit . as can be seen in fig . [ fig : bg_subt ] , the subtraction works quite well in the sense that it results in spectra that consist of phonon peaks on top of a very small linear background .    note that because this method measures the background empirically , the source of the background ( sample , aluminum , multiphonon , elastic line , etc . ) is irrelevant ; the only stipulation is that the angular range of data collection be large enough so that at some point of the measured range of s@xmath17 , the phonon structure factor goes to zero . the precise range of @xmath15 required to meet that condition varies depending on symmetry of the sample and the energy range of interest . in the worst - case scenario ( collecting over the entire energy range ) , the _ i4/mmm _ symmetry of this sample would require a rotation of @xmath18 , plus an additional range of @xmath0  @xmath13 to account for the different region of reciprocal space which is measured at different energy transfers . in practice the actual range covered may be substantially less ; we found no appreciable difference whether gathering the background from a @xmath12 or @xmath13 range . one potential limit of the background subtraction procedure is in the case of a non - dispersive mode . if a mode maintained both a constant energy and a nonzero structure factor , then some of its intensity might be incorrectly assigned to the background . however , this situation can only occur for an isolated atom in an isotropic environment ( a rattling mode inside of a rigid cage might approximate this condition ) . other than this special case , the intensity of a well - behaved mode must vary with @xmath15 , due to either the phase factor , or to the projection of the eigenvector onto @xmath15 . traditionally , phonon measurements have been made at specific wavevectors in one or two bz . this works when phonons are well - separated in energy , but in cases of multiple overlapping peaks it is often impossible to distinguish a single broad peak from two or more narrow peaks . tof inelastic neutron scattering instruments capture data over many bz . thus phonon peaks belonging to a multiplet of overlapping peaks at a specific reduced wavevector will have different intensities in different bz , but they will have the same energies and intrinsic linewidths . to perform the fitting , we first start with predictions of dft calculations , which give approximate phonon frequencies and structure factors . some of these are very accurate and agree with the data without any fitting , whereas others are significantly off . ( see left panel in fig . [ fig : multizone ] ) by simultaneously fitting the experimental phonon spectrum at the same reduced wavevector in multiple bz , we can identify experimental positions of individual phonons them quite well if we constrain their widths and energies to be bz - independent while letting their intensities vary from zone to zone ( see right panel in fig . [ fig : multizone ] ) . the energy resolution of arcs is nearly independent of @xmath15 over the entire instrument , so values for resolution widths were calculated as a function of energy , as described elsewhere @xcite . because arcs has an asymetric resolution function , the peaks were modeled as split gaussians , with the lower ( higher ) side of the peak having 60% ( 40% ) of the fwhm . the peak width and asymmetry were checked at several @xmath15 for which dft predicted only a single phonon was allowed in the 32 - 35 mev range , and this modeling of the energy resolution was found to be satisfactory .    while on a triple - axis instrument the momentum and energy resolutions are strongly coupled , for arcs they are largely independent . the @xmath15-resolution at higher momentum transfer ( where phonons are strongest ) is determined primarily by the sample mosaic . our sample mosaic of @xmath10 sets @xmath19/@xmath15 @xmath03% , on the same order as the @xmath15-resolution set by size of the detector pixels ( @xmath01% ) . the in - plane voxel size ( q - binning ) was either @xmath14 .025 r.l.u . , or @xmath14 0.05 r.l.u . , which makes @xmath19/@xmath15 between 1 - 2% or 2 - 4% , respectively . the out - of - plane voxel size was @xmath14 0.5 r.l.u . in all cases ; this puts @xmath19/@xmath15 @xmath06% , but the dft calculation indicates that the energy should vary by less than 1% over this range ( c - axis modes are generally fairly non - dispersive in layered systems such as this one ) , reducing the effect of @xmath15-resolution on determination of the phonon energies .    in order to simulate the combined effect of dispersion and finite bin size on the energy resolution , we increased the calculated energy fwhm by 10% . for weakly ( strongly ) dispersive branches , this will cause the refined separation between overlapping modes to be smaller ( larger ) than the true separation . a more detailed analysis could modify the energy broadening based upon bin size and local dispersion as calculated from dft . other than this broadening , no attempt was made to account for the effect of @xmath15-resolution on the energy linewidth . the fitting program was written in matlab , using a standard least - squares algorithm . each reduced-@xmath20 symmetry point was fit separately . the heights of the peaks were constrained to be positive , but could vary between bz . peak centers were constrained to be identical in various bz . resolution widths were fixed as described above . for each voxel , the empirical background was subtracted , and an additional linear term was included in the fitting to account for any residual background ( but was generally small ) . the energy linewidth was fixed to be resolution - limited , but can be made a fitted parameter in the future . solid lines are from t  = 10  k , dashed lines from t  = 220  k , and dotted lines from t  = 320  k. the data from t  = 220  k and 320  k were taken over a shorter time and smaller angular region and are correspondingly noisier . the endpoints are labelled with the same numbers used in fig . [ fig : disp ] . ]        figure [ fig : disp ] shows extracted dispersions and branch assignments for narrowly - spaced phonon branches in srfe@xmath1as@xmath1 . note that their separation in energy was often much smaller than the experimental resolution . our method of determining the phonon peak positions automatically provides bz - dependence of peak intensities for each reduced @xmath20 , which is determined by the phonon eigenvectors . thus we assign phonon peaks to the same branch if their eigenvectors vary smoothly throughout the zone ( a similar method has been previously used to assign eigenvectors using triple - axis ins @xcite ) . symmetry constraints and comparison of experimental results with the dft calculations of peak positions and eigenvectors served as additional guides in peak assignments . because the detector banks extend out - of - plane , we were able to determine the c - axis modes as well ( albeit with less precision ) . figure [ fig : disp ] shows that dft calculations reproduce the phonon dispersions and intensities quite well . although some small deviations from the calculated dispersions have been observed , they are on the order of 5% , which is typical for the agreement between experiment and dft calculations in general . this good agreement has been achieved despite the fact that the calculations were carried out without inclusion of magnetism , although the structure was constrained to the experimental structure . our results for the raman - active modes at the @xmath21-point are in good agreement with previous raman studies @xcite . we have not been able to establish the extent to which different branches mix with each other when they cross . such mixing should occur , but the resulting anti - crossing gaps were too small to be observed in our experiment . the gaps could likely be determined by using a sample which is larger ( for better statistics ) and has a smaller mosaic ( for better resolution ) . successful mapping of phonon dispersions allowed us to investigate temperature dependence of these phonon branches in order to look for phonon anomalies associated with magnetic ordering . [ fig : temp ] shows that temperature - dependence of these phonons is weak and is consistent with small changes in lattice constants due to thermal expansion , i.e. these phonons are not particularly sensitive to the magnetic ordering transition . we note some temperature variation does appear near points 4 and 8 . however , the polarization in those regions is primarily along the c - axis , and the weak intensity produces larger errors . along with the narrower range of data aquisition for t  = 220  k and 320  k , the uncertainty at these points are large enough to account for the variation seen here . there is no measurable effect of the onset of long range magnetic order on any phonon branch measured so far as a part of this study ( fig . [ fig : temp ] ) or in previous studies , with the exception of transverse acoustic phonons whose eigenvectors correspond directly to the associated structural deformation @xcite . it is also possible that phonons couple to the nematic fluctuations found at higher energies @xcite and do not feel the effects of the phase transition . these fluctuations may vary as a function of doping @xcite , and may in turn influence the phonon spectrum . the effect of doping on these high - energy phonons can now be investigated using the multizone approach . one advantage of mpr can be the identification of enhanced electron - phonon coupling at wavevectors away from high symmetry directions that previously would have remained unobserved . for example , such anomalies have been found in cr @xcite . we examined temperature - dependence of phonons away from high - symmetry directions in srfe@xmath1as@xmath1  and found that there are no anomalies there either . we developed a multizone phonon refinement ( mpr ) technique for using time - of - flight neutron chopper spectrometers to extract phonon dispersions even when the phonon frequencies are spaced much more closely than the experimental resolution . it is based on fitting scattering intensities in multiple bz . we used this technique to reliably measure closely - spaced phonons above 23  mev in ferropnictide superconductors . we assigned eigenvectors to these phonons and showed that they do not exhibit any unconventional temperature - dependence related to the magnetic ordering transition . our results pave the way for future detailed comparison of experimental and calculated phonon frequencies in iron - based superconductors and for future studies of materials with large unit cells where closely spaced phonon branches are expected , such as thermoelectrics and complex oxides . d.p and d.r . were supported by the doe , office of basic energy sciences , office of science , under contract no . de - sc0006939 . the research at ornl s spallation neutron source was sponsored by the scientific user facilities division , office of basic energy sciences , u.s . department of energy . 26ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12  & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1103/physrevlett.101.026403 [ * * ,   ( ) ] link:\doibase 10.1038/nature07981 [ * * , ( ) ] link:\doibase    10.1143/jpsj.77.083704 [ * * , ( ) ] link:\doibase 10.1088/0953 - 2048/23/5/054013 [ * * ,   ( ) ] ,   link:\doibase 10.1038/nphys1160 [ * * , ( ) ] link:\doibase    10.1103/physrevb.78.184517 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.79.024513 [ * * ,   ( ) ] link:\doibase 10.1103/physrevlett.102.037003 [ * * ,   ( ) ] link:\doibase    10.1155/2010/164916 [ * * ,   ( ) ] link:\doibase    10.1016/j.physc.2009.11.167 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.80.214534 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.79.220511 [ * * ,   ( ) ] link:\doibase    10.1143/jpsj.77.103715 [ * * , ( ) ] link:\doibase 10.1063/1.3680104 [ * * ,   ( ) ] link:\doibase 10.1103/physrevlett.109.057001 [ * * ,   ( ) ] @noop `` , ''   link:\doibase    10.1103/physrevb.81.060501 [ * * ,   ( ) ] link:\doibase    10.1103/physrevb.78.212502 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.60.r3709 [ * * , ( ) ] link:\doibase    10.1088/0953 - 8984/20/45/452201 [ * * , ( ) ] ,   link:\doibase 10.1103/physrevb.71.092301 [ * * ,   ( ) ] link:\doibase    10.1103/physrevb.78.060503 [ * * ,   ( ) ] link:\doibase 10.1107/s0108768112008294 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.84.054544 [ * * ,   ( ) ] link:\doibase 10.1038/nphys1512 [ * * ,   ( ) ] link:\doibase    10.1103/physrevb.82.195121 [ * * ,   ( ) ]
the ferropnictide superconductors exhibit a sensitive interplay between the lattice and magnetic degrees of freedom , including a number of phonon modes that are much softer than predicted by nonmagnetic calculations using density functional theory ( dft ) . 
 however , it is not known what effect , if any , the long - range magnetic order has on phonon frequencies above 23  mev , where several phonon branches are very closely spaced in energy and it is challenging to isolate them from each other . 
 we measured these phonons using inelastic time - of - flight neutron scattering in @xmath0 40  brillouin zones , and developed a technique to determine their frequencies . 
 we find this method capable of determining phonon energies to @xmath0  0.1  mev accuracy , and that the dft calculations using the experimental structure yield qualitatively correct energies and eigenvectors . 
 we do not find any effect of the magnetic transition on these phonons .