Anisotropic inplane spin correlation in the parent and Co-doped BaFe2As2: a neutron scattering study
aa r X i v : . [ c ond - m a t . s up r- c on ] O c t Anisotropic inplane spin correlation in the parent and Co-doped BaFe As : aneutron scattering study S. Ibuka a,b,1, ∗ , Y. Nambu a,b,2 , T. Yamazaki a,b,3 , M. D. Lumsden c , T. J. Sato a,b,2 a Neutron Science Laboratory, Institute of Solid State Physics, University of Tokyo, Tokai, Ibaraki 319-1106, Japan b TRIP, JST, Chiyoda, Tokyo 102-0075, Japan c Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
Abstract
Antiferromagnetic spin fluctuations were investigated in the normal states of the parent ( x = x = .
04) and optimally-doped ( x = .
06) Ba(Fe − x Co x ) As single crystals using inelastic neutron scattering tech-nique. For all the doping levels, quasi-two-dimensional antiferromagnetic fluctuations were observed as a broad peaklocalized at Q = (1 / , / , l ). At lower energies, the peak shows an apparent anisotropy in the hk x = As . Keywords:
Iron superconductor, Magnetic excitation, Inelastic neutron scattering
1. Introduction
For iron-based superconductors [1], the conventionaltheory of phonon-mediated superconductivity has di ffi -culty in explaining the high superconducting transitiontemperatures [2–4]. Accordingly, various other candi-dates for the superconducting pairing mechanism havebeen proposed to date, such as spin-fluctuation medi-ated s + − model [3, 5–7], as well as orbital-fluctuationmediated s ++ model [8–11]. To determine which pair-ing mechanism is indeed appropriate, it is crucial toknow the details of the spin and orbital fluctuations inthe normal paramagnetic state. Since direct observa-tion of the orbital fluctuations is di ffi cult, experimen-tal e ff orts have been focused on observation of the spin ∗ Corresponding author
Email address: [email protected] (S. Ibuka) Present address: High Energy Accelerator Research Organiza-tion, Tokai, Ibaraki 319-1106, Japan. Present address: Institute of Multidisciplinary Research for Ad-vanced Materials, Tohoku University, Katahira, Sendai 980-8577,Japan. Present address: Faculty of Science and Technology, Tokyo Uni-versity of Science, Noda, Chiba 278-8510, Japan. fluctuations using neutron inelastic scattering technique.Among a number of Fe-based superconductor com-pounds, A Fe As ( A = Ca, Sr, Ba and K) 122-type com-pounds have been most intensively studied due to theavailability of large single crystals with various dopinglevels. Both in the parent and doped compounds, rod-like low energy spin excitation with weak spin corre-lation along l was observed around the zone boundary Q = (1 / , / , l ) in the tetragonal paramagnetic state,for example, in Ba(Fe − x Co x ) As (0 ≤ x ≤ .
08) [12–18]. The Q vector connects hole Fermi surface sheetsat the antiferromagnetic zone centre to electron sheetsat the zone corner, and satisfies the nesting condition.Moreover, in the heavily-overdoped Ba(Fe − x Co x ) As ( x = . < x < Preprint submitted to Physica C September 8, 2018 ion in the two-dimensional hk ~ ω >
80 meV), the el-liptical peak enlarges and splits, with no clear changeon entering in the orthorhombic phase. As Park et al explained [24], the anisotropy preserves C symmetrywith the symmetry axis (0, 0, l ), and is di ff erent fromrotational symmetry breaking. They suggest [24, 35]that such inplane anisotropy, at least in the low-energyrange, can be consistently reproduced by a simple ran-dom phase approximation (RPA) calculation taking ac-count of orbital characters. It has been an issue ifsuch a anisotropic spin correlations may be naturallyattributed to the multiband nature of the Ba-122 com-pounds, or much intriguing idea has to be introduced,such as the frustrated J − J model [21, 23], quasipropagating mode with di ff erent velocity [23], and in-terplay between anisotropies of the correlation lengthand of Landau damping [30, 36]. Above controversymay be due to the lack of consistent dataset in one com-pound family; Park et al [24] compared the low energyanisotropy in Ba(Fe − x Co x ) As ( x = . As [21], whereas another comparison was madewith the hole doped KFe As [25]. Hence, it is ob-vious that direct comparison between the parent com-pound and electron doped compound, such as BaFe As and Ba(Fe,Co) As , under the same condition is es-sential. Luo et al elaborately studied the anisotropyboth in the antiferromagnetic and paramagnetic phasein Ba(Fe − x Ni x ) As crystals (0 . ≤ x ≤ .
09) [29],however it is hard to see the doping dependence ofthe anisotropy in the paramagnetic phase under thesame energy and temperature. Therefore, in this work,we performed electron-doping dependence study of theinplane anisotropy of low-energy spin fluctuations inBa(Fe − x Co x ) As crystals ( x =
0, 0.04 and 0.06) byinelastic neutron scattering, focusing on the paramag-netic phase. We observed clear anisotropic inplane spincorrelations for all the doping levels. The anisotropyin BaFe As is smaller than the electron doped Ba(Fe,Co) As . This result is consistent with the Fermi sur-face nesting picture and indicates that the anisotropicnature of the spin fluctuations in the low energy regimeare dominated by Fermi surface nesting. Concern-ing the temperature dependence of the peak width, thedoped compounds show consistent behaviour expectedfor nearly antiferromagnetic metals, whereas the peakin the parent compound sharpens much pronouncedly.This suggests that the quasi-two-dimensional spin cor-relations grow much rapidly for decreasing temperature in the x = As .
2. Experimental details
Single crystals of Ba(Fe − x Co x ) As ( x = concentration being about 1 ppm to avoidoxidation. The sealed starting elements were then setin the vertical Bridgman furnace to obtain large singlecrystals; details of the Bridgman technique used in thisstudy are given in [37]. We performed the Bridgmangrowth four times for di ff erent Co compositions, andeach batch obtained was found to contain several smallpieces of single crystals. The mass of the grown piecesof single crystals was between 0.3 and 1.2 grams.Co compositions of the obtained crystals were deter-mined by energy dispersive X-ray analysis using a scan-ning electron microscopy JEOM JSM-5600 and Ox-ford Link ISIS. The resulting sample compositions are x EDX = . x = . c axis. Fig-ure 1 shows the obtained magnetic susceptibility inthe low temperature region. As seen from the sus-ceptibility data, the superconducting transition temper-atures are 13, 16 and 24 K, for the doped three samples x = . T AF ∼ x =
0, 0.04( T c with the help of the previous report [38]are consistent with those determined by energy disper-sive X-ray analysis; x T c ∼ . x = . M agne t i c s u sc ep t i b ili t y χ ( c m / g ) Temperature (K)
FCZFC
Ba(Fe x Co x ) As H a = 10 Oe, H a ⊥ cx = 0.04( x = 0.04( x = 0.06 Figure 1: (Colour online) Temperature dependence of zero-field-cooled (ZFC) and field-cooled (FC) dc magnetic susceptibility ofBa(Fe − x Co x ) As . The (orange) squares stand for x = . study, we regard the two x = .
04 samples ( ff erence in thecompositions for the two samples makes considerablechange in the superconducting transition temperatures,we believe that such slight composition di ff erence doesnot give rise to any significant di ff erence in the inelas-tic response in the paramagnetic phase. This treatmentwill be accepted by the weak dependence of F and Γ parameters on the composition, as we see below.Using the four crystals, we performed inelastic neu-tron scattering experiments. We used two thermal neu-tron triple-axes spectrometers, ISSP-GPTAS installedat JRR-3, Tokai, Japan and HB3 installed at HFIR atOak Ridge National Laboratory, TN, USA. The par-ent compound ( x =
0) and underdoped compound( x = . x = . x = .
06) were measured at HB3. Pyrolytic graphite 002reflections were used both for the monochromator andanalyzer to select an energy of neutrons. Final neutronenergy was set to E f = . ~ ω =
28 meV, where signal becomes weaker,horizontal focusing monochromator with 40’-3 bladesRadial Collimator (3RC)-80’-80’ was employed at GP-TAS. Higher harmonic neutrons were eliminated by us- ing pyrolytic graphite filters.To obtain su ffi cient intensity, two or three pieces ofsingle crystals were co-aligned; the total mass of thesamples was about 1 g for all the doping levels. Mosaicspreads of the co-aligned samples in the scattering planewere within 1.2, 0.5, 0.7 and 0.6 degrees of full widthat half maximum for the samples of x =
0, 0.04( Q direction due to the sam-ple mosaic was negligible compared with that due to theinstrumental resolution. The co-aligned crystals weresealed in aluminum cans and then set in closed cycle He refrigerators.
3. Results ~ ω =
10 meVFirst, doping dependence of anisotropy was investi-gated by measuring the inelastic scattering peak alongthe longitudinal direction ( h , h ,
0) and transverse direc-tion ( h , − h ,
0) around Q = (1 / , / ,
0) at the low en-ergy transfer ~ ω =
10 meV. Figure 2(a) shows direc-tion of the scans in the hk x = T = ab plane are anisotropic at ~ ω =
10 meV.It should be noted that the instrumental resolutions aresu ffi ciently narrow, so that the apparent di ff erence in thepeak widths cannot be due to the resolution e ff ect. (Thispoint will be further confirmed by the resolution convo-luted fitting later.)For the underdoped compounds x = . T =
80 and 180 K are shownin Figs. 2(f) and (g), respectively. By comparing thepeak widths at the same temperature 180 K, we foundthat the longitudinal width in the underdoped compoundis mostly the same as that observed in the parent com-pound, whereas the transverse width becomes signifi-cantly wider. This indicates that the corresponding anti-ferromagnetic correlations become more anisotropic inthe ab plane.3 I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) GPTAS 40’-80’-40’-80’ T = 145 K x = 0 (b) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) GPTAS 40’-80’-40’-80’ T = 145 K x = 0 (b) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) GPTAS 40’-80’-40’-80’ T = 145 K x = 0 (b) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) GPTAS 40’-80’-40’-80’ T = 145 K x = 0 (b) HB3 48’-80’-40’-90’ T = 180 K x = 0 (c) HB3 48’-80’-40’-90’ T = 180 K x = 0 (c) HB3 48’-80’-40’-90’ T = 180 K x = 0 (c) HB3 48’-80’-40’-90’ T = 210 K x = 0 (d) HB3 48’-80’-40’-90’ T = 210 K x = 0 (d) HB3 48’-80’-40’-90’ T = 210 K x = 0 (d) HB3 48’-80’-40’-90’ T = 180 and 210 KBackgrounds (e) HB3 48’-80’-40’-90’ T = 180 and 210 KBackgrounds (e) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) GPTAS 40’-80’-40’-80’ T = 80 K x = 0.04( (f) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) GPTAS 40’-80’-40’-80’ T = 80 K x = 0.04( (f) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) GPTAS 40’-80’-40’-80’ T = 80 K x = 0.04( (f) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) GPTAS 40’-80’-40’-80’ T = 80 K x = 0.04( (f) HB3 48’-80’-40’-90’ T = 180 K x = 0.04( (g) HB3 48’-80’-40’-90’ T = 180 K x = 0.04( (g) HB3 48’-80’-40’-90’ T = 180 K x = 0.04( (g) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) HB3 48’-80’-40’-90’ T = 3 K x = 0.06 (h) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) HB3 48’-80’-40’-90’ T = 3 K x = 0.06 (h) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) HB3 48’-80’-40’-90’ T = 3 K x = 0.06 (h) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,1- h ,0) (r.l.u.) HB3 48’-80’-40’-90’ T = 3 K x = 0.06 (h) HB3 48’-80’-40’-90’ T = 35 K x = 0.06 (i) HB3 48’-80’-40’-90’ T = 35 K x = 0.06 (i) HB3 48’-80’-40’-90’ T = 35 K x = 0.06 (i) HB3 48’-80’-40’-90’ T = 100 K x = 0.06 (j) HB3 48’-80’-40’-90’ T = 100 K x = 0.06 (j) HB3 48’-80’-40’-90’ T = 100 K x = 0.06 (j) HB3 48’-80’-40’-90’ T = 180 K x = 0.06 (k) HB3 48’-80’-40’-90’ T = 180 K x = 0.06 (k) HB3 48’-80’-40’-90’ T = 180 K x = 0.06 (k) k (r . l . u ) h (r.l.u) (a) q tr q lo l = 0 Ba(Fe x Co x ) As , − h ω = 10 meV Figure 2: (Colour online) Longitudinal and transverse scans around Q = (1 / , / ,
0) in the normal paramagnetic state of Ba(Fe − x Co x ) As at ~ ω =
10 meV. (a) Schematic drawing of the directions of the scans. The short thick (blue) arrow indicates the longitudinal direction, and thelong thin (red) arrow the transverse direction. (b)–(d) Scans of x = T = x = x = . T =
80 K. (g) Scans of x = . x = .
06 at T =
3, 35, 100 and180 K. Data (b)–(d), (f)–(g) and (h)–(k) were measured with a counting time of more than 30, 30 and 10 min, respectively, but are normalized. x = . T = T = ab plane for all the dop-ing levels; the widths along the transverse direction areconsiderably wider than those along the longitudinal di-rection. The anisotropy seems to be enhanced for thehigher doping level.To estimate the anisotropy further quantitatively, thedata were fitted to a model scattering function derivedfrom the generalized susceptibility of nearly antiferro-magnetic metals for small q [16, 21, 39]: I ( Q , ω ) ∝ χ ′′ ( q , ω )1 − exp [ − ~ ω/ (k B T)] , (1) χ ′′ ( q , ω ) = χ ( T ) Γ ( T ) ~ ω ( ~ ω ) + Γ ( T ) (cid:16) + F q + F q + D q c (cid:17) , (2)where q = Q − Q AF (3) = h / √ q lo + q tr ) , / √ q lo − q tr ) , q c i . (4) χ ( T ) represents the isothermal susceptibility, Γ ( T ) isthe isotropic damping constant, and q lo , q tr and q c arethe norms of the wave vectors away from an antiferro-magnetic zone centre Q AF along ( h , h , h , − h ,
0) and(0 , , l ), respectively. F lo , F tr and D are the inverse ofthe peak widths along the three directions, correspond-ing to the magnetic correlation lengths.In the fitting procedure, the model scattering func-tion was convoluted by the instrumental resolution func-tion [40], and was used to fit the background-subtracteddata. Temperature dependence of Γ was constrainedto obey the linear form Γ ( T ) = α ( T + Θ ) where α = .
14 meV / K and
Θ =
30 K [16, 18]. D was set to1.3 r.l.u. and was assumed to be temperature indepen-dent [18]. The backgrounds were set to Q and T inde-pendent for x =
0, whereas for x = . F l o and F t r ( Å ) Temperature (K) x = 0 (a) AF PM F lo F tr x = 0.04( (b) AF PM x = 0.04( F lo F tr F lo F tr x = 0.06 (c) Ba(Fe x Co x ) As , − h ω = 10 meV F lo F tr Figure 3: (Colour online) Temperature dependence of F lo and F tr of Q = (1 / , / ,
0) at ~ ω =
10 meV in Ba(Fe − x Co x ) As for (a) x = . T AF =
140 and 70 K, respectively. Thesolid lines show fits with ( T + Θ ) − / . and 0.06, Q independent but slightly T dependent. Thesolid lines in figure 2 indicate fits to (2), and the dashedlines denote fitted backgrounds. All peaks were fittedwell with the above model function.Temperature dependence of obtained optimum pa-rameters F lo and F tr is shown in figure 3(a), (b) and (c)for x =
0, 0.04 and 0.06, respectively. For the super-conducting composition x = . F lo and F tr in the su-perconducting state at T = ff er much fromthose in the normal state at T =
35 K. This agrees withthe earlier reports [16, 24]. For nearly antiferromagneticmetals [39], temperature dependence of F lo and F tr is inproportion to Γ ( T ) − / ∝ ( T + Θ ) − / . The solid linesin figure 3 are the fitting results with ( T + Θ ) − / with Θ =
30 K. The function gives a good fit to F lo and F tr for x = .
04 and 0.06, which is consistent with [16],however, a poor fit for x =
0. Increase of F lo and F tr for x = A n i s o t r op y δ = ( F l o - F t r ) / ( F l o + F t r ) Temperature (K)
Park et al.x = 0.065Luo et al.
Ba(Fe,Ni) As Diallo et al.
CaFe As Ba(Fe x Co x ) As , − h ω = 10 meV x = 0 x = 0.04( x = 0.04( x = 0.06 Figure 4: (Colour online) Temperature dependence of the anisotropyof magnetic correlation δ around Q = (1 / , / ,
0) at ~ ω =
10 meV inBa(Fe − x Co x ) As . The (orange) squares stand for x =
0, (green) cir-cles for 0.04( δ ave for x =
0, 0.04 and 0.06(, respec-tively). The thin dash-dot lines are the anisotropy for x = .
065 [24],and the average anisotropy for Ni-doped BaFe As [29]. The dia-mond shows the anisotropy for CaFe As [21]. those expected for nearly antiferromagnetic metals.Next, we check the relation between F tr and F lo bydefining the anisotropy ratio δ as ( F lo − F tr ) / ( F lo + F tr ).Temperature dependence of δ is shown in figure 4 for x =
0, 0.04 and 0.06, respectively. δ is temperatureindependent in all the composition within the experi-mental uncertainty. The average anisotropy δ ave of eachcompound is 0.15(7), 0.30(13) and 0.33(6) for x = δ ave of x = x = .
04 and 0.06. δ ave of x = ∼ . As at T =
180 K and ~ ω = ± et al [21]. δ ave of x = .
06 is roughly consistent to the anisotropy 0.41(2)of x = .
065 reported by Park et al [24]. A slight in-crease of anisotropy by Ni doping including antiferro-magnetic state is reported by Luo et al [29]. ~ ω =
28 meVAt ~ ω =
28 meV, temperature dependence of theanisotropy was investigated around Q = (3 / , / , x =
0. The results of the constant-energy scans at T = Q dependence exists even at the room tempera-ture T =
300 K ∼ T AF . At all the temperatures, thetransverse scans show larger peak widths compared tothe longitudinal ones, in good agreement with the lowenergy results at ~ ω =
10 meV. These data were fit- I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,3- h ,0) (r.l.u.) GPTAS 40’-RC3-80’-80’ T = 145 K x = 0 (a) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,3- h ,0) (r.l.u.) GPTAS 40’-RC3-80’-80’ T = 145 K x = 0 (a) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,3- h ,0) (r.l.u.) GPTAS 40’-RC3-80’-80’ T = 145 K x = 0 (a) I n t en s i t y ( c oun t s / m i n sc a l ed ) h of ( h , h ,0) or ( h ,3- h ,0) (r.l.u.) GPTAS 40’-RC3-80’-80’ T = 145 K x = 0 (a) GPTAS 40’-RC3-80’-80’ T = 180 K x = 0 (b) GPTAS 40’-RC3-80’-80’ T = 180 K x = 0 (b) GPTAS 40’-RC3-80’-80’ T = 180 K x = 0 (b) GPTAS 40’-RC3-80’-80’ T = 210 K x = 0 (c) GPTAS 40’-RC3-80’-80’ T = 210 K x = 0 (c) GPTAS 40’-RC3-80’-80’ T = 210 K x = 0 (c) GPTAS 40’-RC3-80’-80’ T = 300 K x = 0 (d) Ba(Fe x Co x ) As , − h ω = 28 meV 0 100 200 300 GPTAS 40’-RC3-80’-80’ T = 300 K x = 0 (d) Ba(Fe x Co x ) As , − h ω = 28 meV 0 100 200 300 GPTAS 40’-RC3-80’-80’ T = 300 K x = 0 (d) Ba(Fe x Co x ) As , − h ω = 28 meV Figure 5: (Colour online) (a)–(d) Longitudinal and transverse scansaround (3 / , / ,
0) in the paramagnetic state of BaFe As at ~ ω =
28 meV at T = / F l o and F t r ( Å ) Temperature (K) x = 0 (a) AF PM ( T + Θ ) −1/2 F lo F tr A n i s o t r op y δ x = 0 (b) AF PMBa(Fe x Co x ) As , − h ω = 28 meV Figure 6: (Colour online) (a) Temperature dependence of F lo and F tr of Q = (3 / , / ,
0) at ~ ω =
28 meV in BaFe As . The solidlines indicate fit with ( T + Θ ) − / . (b) Temperature dependence of theanisotropy δ around Q = (3 / , / ,
0) at ~ ω =
28 meV in BaFe As .The dashed line shows the average value of δ for T ≥
210 K. Thevertical (black) dotted lines in (a) and (b) stand for T AF =
140 K. ted to (2) with the fixed D = F lo and F tr isshown in figure 6(a). As inferred from the raw data infigure 5, the obtained optimum parameter F tr is smallerthan the longitudinal F lo . F lo and F tr gradually increaseas the temperature is decreased. F tr shows good fit with( T + Θ ) − / , although F lo shows poor fit as shown bythe solid lines in figure 6(a). The ratio of anisotropy δ is shown in figure 6(b). δ is positive even at T =
300 K ∼ T AF . δ at high temperatures are roughly the same asthose at ~ ω =
10 meV. On the other hand, δ becomeslarge at T =
145 K just above T AF ; this behaviour isdi ff erent from that at ~ ω =
10 meV.
4. Discussion
Three key findings in the present study are summa-rized as follows. First, anisotropy of the inplane spin correlation δ is increased by electron doping from x = x = .
06. Secondly, for x =
0, the inplane anisotropy δ at ~ ω =
28 meV becomes large at T =
145 K, al-though δ above T =
210 K is as small as that at ~ ω =
10 meV. Thirdly, for x = F lo and F tr increase morethan those expected for nearly antiferromagnetic metalsas temperature decreasing, with the inplane anisotropykeeping constant within errors at ~ ω =
10 meV.First and second results are consistent with a simpleRPA calculation taking the multiorbital character of Fe3 d bands into account [24, 35]. The increasing behav-ior of the anisotropy with the electron doping is indeedexpected in the earlier study [24]. The larger inplaneanisotropy at T =
145 K compared to that at 210 K forthe energy ~ ω =
28 meV may be understood as fol-lows: the nesting condition may be more anisotropicat higher energy transfer, as inferred in a high-energystudy by Harriger et al [26]. Such anisotropic nestingmay be clearly seen in the spin excitations at lower tem-perature, however, at high temperatures, thermal fluc-tuations may smear the details of electronic structurearound the Fermi level. This would be the reason whythe observed the pronounced anisotropy at lower tem-peratures, whereas spectra become similar to those at ~ ω =
10 meV. Hence, both the lower- and higher-energyresults indicate that the anisotropic antiferromagneticfluctuations are mostly dominated by the Fermi surfacenesting.In contrast to first and second results, the tempera-ture dependence of the peak width for the parent com-pound is inconsistent with that expected for nearly an-tiferromagnetic metals. A similar discrepancy can befound in another parent compound CaFe As reportedby Diallo et al [21]. It should be noted that the peaksharpening is naturally expected as the temperature be-comes closer to the transition temperature. What is trulyunusual here is that the temperature dependence of thepeak width for x = i.e. , F ∝ Γ − / . The previous neutroninelastic scattering study reported [18] that the criticalslowing down process of the spin fluctuations, Γ ( T ),is interrupted at T AF , implying the first-order magneticphase transition. The interruption is also observed bythe NMR technique through the spin-lattice relaxationrate [41, 42]. For small q and ~ ω region of itinerant an-tiferromagnets [39], the peak width F is connected tothe damping constant Γ ( T ) with Γ ( T ) ∝ F − . There-fore, in the absence of a large critical slowing down,the peak width is expected to show relatively moder-ate temperature dependence even immediately abovethe transition temperature. This disagreement may beanother appearance of the unconventional critical be-7aviour of the first-order magnetic transition in the par-ent compounds. For x ≤ . x ∼ . ff raction measurements showed that the an-tiferromagnetic order parameter exponent β is di ff er-ent between below and above the tricritical point; β is about the two-dimensional Ising value of 0.125 for x = x = .
021 and 0.022 [48], and three-dimensionalIsing value of 0.327 [49] for under-doped compoundsfor 0.039 [48] and x = .
047 [12]. The inconsistencyof the peak width may represent the existence of uncon-ventional spin dynamics even below the tricritical point x ≤ . χ ′′ calculation, on which our above argumentsare based on, may have quantitative shortfalls. Indeed,the inplane peak in the calculated χ ′′ [24, 35] is sig-nificantly broader than the observed one. The orbitaldistribution of the Fe 3 d bands used in the above RPAcalculation is not consistent with the recent ARPES re-sult [50], and hence the quantitative validity of the RPAcalculation may be questioned also from this viewpoint.Nonetheless, the doping dependence of the anisotropyin the nesting picture is caused by the di ff erent sizesof the hole and electron pockets, and hence, smalleranisotropy in the parent compound only requires asmaller di ff erence of the pocket sizes. Therefore, a mi-nor modification of the calculated Fermi surface will nota ff ect the conclusion.
5. Summary
We investigated antiferromagnetic spin fluctuationsin Ba(Fe − x Co x ) As crystals ( x =
0, 0.04 and 0.06)by inelastic neutron scattering technique. The inplaneanisotropy was clearly observed for the low-energy spinfluctuations. The anisotropy is larger in the higherdoping level. The result agrees with the RPA calcu-lations including the orbital character of the electronbands [24, 35]. The large anisotropy observed for ~ ω =
28 meV would also be explained within the Fermisurface nesting picture. We conclude that the inplaneanisotropy of the spin correlations is mostly dominatedby the Fermi surface nesting. Concerning the temper-ature dependence of the peak width, the doped com-pounds show consistent behavior expected for nearly antiferromagnetic metals, whereas the peak in the par-ent compound sharpens much pronouncedly. This sug-gests that the quasi-two-dimensional spin correlationsgrow much rapidly for decreasing temperature in the x = As . For quantitative discussion of theanisotropy, further study of the electronic structure nearthe Fermi level is necessary.
6. Acknowledgments
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