Temperature dependence of the paramagnetic spin excitations in BaFe{}_{2}As{}_{2}

Temperature dependence of the paramagnetic spin excitations in BaFeAs

Leland W. Harriger Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA    Mengshu Liu Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA    Huiqian Luo Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China    R. A. Ewings ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK    C. D. Frost ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK    T. G. Perring ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK    Pengcheng Dai pdai@utk.edu Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
Abstract

We use inelastic neutron scattering to study temperature dependence of the paramagnetic spin excitations in iron pnictide BaFeAs throughout the Brillouin zone. In contrast to a conventional local moment Heisenberg system, where paramagnetic spin excitations are expected to have a Lorentzian function centered at zero energy transfer, the high-energy ( meV) paramagnetic spin excitations in BaFeAs exhibit spin-wave-like features up to at least 290 K (). Furthermore, we find that the sizes of the fluctuating magnetic moments per Fe are essentially temperature independent from the AF ordered state at to , which differs considerably from the temperature dependent fluctuating moment observed in the iron chalcogenide FeTe [I. A. Zaliznyak et al., Phys. Rev. Lett. 107, 216403 (2011).]. These results suggest unconventional magnetism and strong electron correlation effects in BaFeAs.

pacs:
75.30.Ds, 25.40.Fq, 75.50.Ee

The elementary magnetic excitations (spin waves and paramagnetic spin excitations) in a ferromagnet or an antiferromagnet can provide direct information about the itinerancy of the unpaired electrons contributing to the ordered moment. In a local moment system, spin waves are usually well-defined throughout the Brillouin zone and can be accurately described by a Heisenberg Hamiltonian in the magnetically ordered state. The total moment sum rule requires that the dynamical structure factor , when integrated over all wave vectors () and energies (), is a temperature independent constant and equals to , where is the Land factor () and is the spin of the system lorenzana . Upon increasing temperature to the paramagnetic state, spin excitations in the low- limit can be described by a simple Lorentzian scattering function , where is the temperature dependent inverse spin-spin correlation length and is the wave vector dependent characteristic energy scale tucciarone ; wicksted ; jwlynn . At sufficiently high temperatures above the magnetic order, spin excitations should be purely paramagnetic with no spin-wave-like correlations. Therefore, a careful investigation of the wave vector and energy dependence of spin excitations across the magnetic ordering temperature can provide important information concerning the nature of the magnetic order and spin-spin correlations. For example, a recent inelastic neutron scattering study of spin excitations in one of the parent compounds of iron-based superconductors, the iron chalcogenide FeTe which has a bicollinear antiferromagnetic (AF) structure and Nel temperature of K Hsu ; Fang ; Bao ; Li ; lipscombe ; Johnston ; dai , reveals that the effective spin per Fe changes from in the AF state to in the paramagnetic state, thus providing evidence that FeTe is not a conventional Heisenberg antiferromagnet but a nontrivial local moment system coupled with itinerant electrons igor .

Since antiferromagnetism may be responsible for electron pairing and superconductivity in iron-based superconductors scalapino ; Hirschfeld , it is important to determine if the observed anomalous spin excitation behavior in iron telluride FeTe is a general phenomenon in the parent compounds of iron-based superconductors. For this purpose, we study the spin excitations of another parent compound of iron-based superconductors, the iron pnictide BaFeAs which has a collinear AF structure with K Kamihara ; cruz ; rotter ; qhuang , over a wide temperature range (). In the low-temperature orthorhombic phase ( K), previous inelastic neutron scattering experiments found that a Heisenberg Hamiltonian with highly anisotropic effective magnetic exchange couplings and damping along the orthorhombic and axes directions can describe the observed spin-wave spectra lharriger , similar to the spin waves in the collinear AF ordered CaFeAs jzhao . However, similar measurements on iron pnictide SrFeAs suggest that spin waves can be better described by calculations from a five-band itinerant mean-field model ewings ; kaneshita . Therefore, it is unclear whether a localized Heisenberg Hamiltonian lharriger ; jzhao or itinerant magnetism ewings ; kaneshita ; diallo09 is a more appropriate description for spin waves in pnictides. In the high-temperature tetragonal phase, the spin-wave anisotropy of BaFeAs appears to persist at 150 K () suggesting the presence of an electronic nematic phase lharriger ; fradkin ; tmchuang ; jhchu ; myi ; kasahara ; ruff . However, these paramagnetic spin excitations can also be understood by considering both the localized and itinerant electrons using dynamic mean field theory hpark or a biquadratic spin-spin interactions within a Heisenberg Hamiltonian without the need for electronic nematicity wysocki ; ryu .

By studying spin excitations in BaFeAs over a wide temperature range throughout the Brillouin zone in absolute units, we can determine the temperature dependence of the paramagnetic scattering and its spectral weight. This will reveal if itinerant electrons in BaFeAs are coupled with local moments on warming across similar to that of the iron telluride FeTe igor . Surprisingly, we find that the total fluctuating magnetic moments per Fe in BaFeAs, corresponding to an effective spin per Fe msliu , are essentially unchanged on warming from 7 K at to room temperature at , much different from that of FeTe igor . In addition, while paramagnetic spin excitations at small wave vectors near the AF zone center follow a simple Lorentzian scattering function as expected tucciarone , they change only slightly from the low-temperature spin waves for wave vectors near the zone boundary up to room temperature. This is different from the expectation of a local moment Heisenberg system, and indicate a strong electron correlation effect in BaFeAs.

Figure 1: (Color online) Panels a)-c) compare the meV magnetic scattering deep inside the ordered state (7 K) to scattering in the paramagnetic phase for temperatures (225 K and 290 K) well away from the K phase transition. Panels d)-f) and g)-i) are a similar comparison for energy transfers of 100 meV and 150 meV, respectively. The dotted ellipses and boxes are guides to the eye to more easily facilitate comparison. Data in panels a)-f) and g)-i) were collected using meV and 450 meV respectively. All data was background subtracted using the average intensity from the region , r.l.u. as the background point. Data in the region was folded into the equivalent positions in order to improve statistics.

We have used the MAPS time-of-flight inelastic neutron spectrometer at ISIS, Rutherford-Appleton Laboratory, UK, to determine the paramagnetic excitations of BaFeAs. For the experiment, we have used the same sample and experimental set-up as described previously lharriger . Below , BaFeAs has an orthorhombic structure with and Å and forms a collinear AF order at the ordering wave vector qhuang . In the paramagnetic state, BaFeAs changes to tetragonal structure. Figure 1 presents an overview of the temperature evolution of the spin excitations at different energies. The data has been normalized to a vanadium standard and plotted in absolute units of mbarn sr meV f.u., without correction for the magnetic form factor, leading to a decrease in magnetic scattering with increased . At meV, spin waves form ellipses along the transverse direction centered at and , where and , at 7 K (Fig. 1a) lharriger . Upon warming to the paramagnetic state at 225 K (, Fig. 1b) and 290 K (, Fig. 1c), the signal becomes weaker, and the ellipses broader, compared to the spin wave peak seen at 7 K, similar to the low-energy paramagnetic spin excitations seen in CaFeAs diallo . However, the spin waves at (Figs. 1d-1f) and meV (Figs. 1g-1i) only decrease slightly in intensity on warming, and become more diffusive at 290 K.

Figure 2: (Color online) Panels a)-d) compare the Energy versus intensity slices for 7 K, 125 K, 225 K, and 290 K. All data is background subtracted and folded in an identical manner as described in the caption of Fig. 1. The solid line is the Heisenberg dispersion obtained using anisotropic exchange couplings , , , meV determined by fitting the full cross section to the 7 K data lharriger .

Figures 2a-2d show the background subtracted scattering for the meV data projected in the wave vector () and energy space at , 125, 225, and 290 K, respectively. The solid lines represent the expected dispersion from the anisotropic Heisenberg Hamiltonian lharriger . At 7 K, three plumes of spin waves stem from where , and reach to the zone boundary at 200 meV (Fig. 2a). On warming to 125 (Fig. 2b), 225 (Fig. 2c), and 290 K (Fig. 2d), spin excitations become broader in momentum space but their zone boundary energies appear to be unchanged. For the classical insulating Heisenberg ferromagnet or antiferromagnet, spin excitations in the paramagnetic state should be uncorrelated and display Lorentzian-like peaks centered at meV at sufficiently high temperatures tucciarone ; wicksted . If electron correlations are important, spin excitations in the paramagnetic state should exhibit spin-wave like peaks in energy for wave vectors near the zone boundary jwlynn . While previous work found that spin excitations near the zone boundary for energies above meV are indeed similar between 7 K and 150 K lharriger , it is unclear what happens to zone boundary spin excitations at higher temperatures.

Figure 3: (Color online) a-f) Temperature overplot of the evolution of the spin excitations as a function of increasing energy. The green diamonds, yellow squares, red circles, cyan upward facing triangles, and blue downward facing triangles are for the 7 K, 125 K, 150 K, 225 K, and 290 K data respectively. The data has been artificially offset for clarity and empirically fit using Gaussian functions. The insets are the fits without offset.

Figure 3 summarizes the wave vector and temperature dependence of the spin excitations from 7 K to 290 K along the direction. For each of the wave vector cuts along the -direction, the -direction integration range is slightly different. At meV, the spin wave intensity increases on warming from 7 K to 125 K. Upon further warming to above , the spin excitation peak centered at becomes weaker and broader with increasing temperature, and is very broad at 290 K. For spin wave energies meV (Fig. 3b), meV (Fig. 3c), and meV (Fig. 3d), the situation is similar although spin excitations have less temperature dependence with increasing energy. Finally, spin excitations only change marginally from 9 K to 290 K for meV (Fig. 3e) and meV (Fig. 3f).

Figure 4: (Color online) a) Dispersion along the direction as determined by energy and cuts of the raw data. The solid line is the anisotropic Heisenberg dispersion lharriger . b) Dispersion along the direction built using the same method. The light blue upward facing triangular points in c)-f) are constant- cuts at , (1, 0.2), (1, 0.35), and (1, 0.5), respectively, at 225 K. The dark blue downward facing triangular points in c)-f) are identical constant- cuts at 290 K. The solid green and red lines are guides to the eye describing the observed 7 K and 150 K scattering, respectively. These constant- cuts correspond to cuts across the dispersion as depicted in the inset of panel c). The horizontal bars in d) and f) are instrumental energy resolution.

Based on the data in Figures 2 and 3, we construct in Fig. 4a spin excitation dispersions along the and directions at 225 K (the upper triangles) and 290 K (the lower triangles). Comparing the outcome with the spin waves at 7 K (the solid lines) reveals essentially the same dispersion for spin excitations in the paramagnetic state for temperatures up to (Figs. 4a and 4b). Figures 4c-4f show constant- cuts of the spin excitations along the direction throughout the Brillouin zone (see inset in Fig. 4c). Previous measurements at 7 K and 150 K are plotted as green and red solid lines, respectively. For wave vector near the zone center at and , we see that the well-defined spin wave peaks in the AF phase become Lorentzian like in the paramagnetic state at 150 K (Fig. 4c and 4d). On further warming to 225 and 290 K, quasielastic intensity near meV becomes weaker, consistent with the expectations for paramagnetic scattering tucciarone ; wicksted ; jwlynn . However, the low-temperature spin wave peaks at the wave vectors and near the zone boundary are still clearly present up to 290 K, and only become slightly broader and weaker (Figs. 4e and 4f), thus suggesting a strong electron correlation effect in BaFeAs.

Figure 5: (Color online) The local susceptibility plots in panels a)-e) represent the total -integrated intensity across the magnetic zone of size , r.l.u. In practice, it is not possible to use the actual full zone size in and because of gaps in the detector array and consequent limited accessibility of certain reciprocal space regions. Thus, for each a smaller region that either contains all of the scattering and/or has the requisite symmetry is chosen instead. These regions are then all normalized to the entire zone area as required by . The solid black lines in panels a)-e) are empirical fits of the local susceptibility. f) An overplot of these fits to aid in a cross-comparison of the temperature dependence. g) The dynamic moment as determined by integrating the fits from the previous panels. The static moment is reproduced from qhuang .

Finally, we show in Figure 5 the temperature dependence of the local dynamic susceptibility for BaFeAs msliu ; clester . In the AF ordered state at 7 K, there is a spin anisotropy gap below 10 meV matan and the local susceptibility peaks at 180 meV (Fig. 5a). On warming to 125 K just below , the spin anisotropy gap disappears while at higher energies the local susceptibility remains essentially unchanged (Fig. 5c). Upon further warming to the paramagnetic state at 150 K (Fig. 5e), 225 K (Fig. 5b), and 290 K (Fig. 5d), we see that the local dynamic susceptibility becomes slightly weaker and broader with increasing temperature (Fig. 5f). Figure 5g shows the temperature dependence of the ordered moment (solid line) qhuang and integrated local susceptibility, which is dominated by spectral weight from spin excitations above 100 meV. For comparison, we note that the integrated magnetic spectral weight of FeTe were reported to concentrate almost entirely within 30 meV igor .

In earlier triple-axis spectrometry studies of paramagnetic spin excitations of metallic ferromagnets such as iron and nickel, there was considerable controversy concerning whether persistent spin wave like excitations can exist in the paramagnetic state above wicksted ; mook ; lynn75 ; steinsvoll ; endoh . For BaFeAa, we see spin-wave-like excitations above 100 meV at temperatures up to . This is different from the usual paramagnetic scattering in a Heisenberg antiferromagnet. The lack of temperature dependence of the integrated local moment, per Fe, suggests that the effective spin of iron in BaFeAs () is unchanged from the AF orthorhombic phase to the paramagnetic tetragonal phase up to room temperature. Therefore, there is no exotic entanglement of itinerant electrons with localized magnetic moments, much different from that of the FeTe igor . We also note that the size of the dynamic moment per Fe in BaFeAs is larger than the local moment of per Fe determined from x-ray emission spectroscopy gretarsson , but similar to the local moment of per Fe in SrFeAs obtained from the Fe core level photoemission spectra measurements vilmercati .

In summary, we have studied the temperature dependent paramagnetic spin excitations in iron pnictide BaFeAs, one of the parent compounds of iron-based superconductors. In contrast to a conventional Heisenberg system, we find spin-wave-like paramagnetic excitations near the zone boundary for temperatures up to with no evidence for the expected zone boundary magnon softening. In addition, the integrated local magnetic moment is remarkably temperature independent from the AF ordered orthorhombic phase to the paramagnetic tetragonal phase, and corresponds to an effective iron spin of . This is different from the temperature dependent spin excitations in the iron chalcogenide FeTe. Our results indicate a strong electron correlation effect and suggest that the entanglement of itinerant electrons with localized magnetic moments in FeTe igor is not fundamental to the magnetism in the parent compounds of iron-based superconductors. Furthermore, correctly modeling the pnictides requires taking into account a mixed state where correlations are important. Indeed, both dynamic mean field theory hpark and biquadratic exchange wysocki ; ryu are approaches that pick up electron correlations and appear to provide necessary features for describing the physics of these systems.

We are grateful to Jeffrey Lynn for helpful discussions. The work at UTK is supported by the US NSF DMR-1063866. Work at the IOP,CAS is supported by the MOST of China 973 programs (2012CB821400, 2011CBA00110) and NSFC-11004233.

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