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Localized and itinerant dichotomy of electrons in Ba(Fe,Co)2As2

Variant approaches, either based on the Fermi surface nesting or started from the proximity to a Mott-insulator, were proposed to elucidate the physics in iron pnictides, but no consensus has been reached. A fundamental problem concerns the nature of their 3d electrons. Here we report the magnetoresistivity (\rho_xx) and the Hall resistivity (\rho_xy) of Ba(Fe1-xCox)2As2 (x=0 and 0.05) in a magnetic field of up to 55T. The magnetic transition is extremely robust against magnetic field, giving strong evidence that the magnetic ordering is formed by local moments. The magnetic state is featured with a huge magnetoresistance and a distinguished Hall resistivity, \rho_xy(H), which shows a pronounced parabolic field dependence, while the paramagnetic state shows little magnetoresistance and follows a simple linear magnetic field dependence on the Hall resistivity. Analyses of our data, based on a two-carrier model, demonstrate that the electron carriers in the magnetic state rapidly increase upon applying a magnetic field, partially compensating the loss of electron carriers at T_M. We argue that the 3d-electrons in Ba(Fe1-xCox)2As2 are divided into those who are close to forming localized moments controlling the magnetic transition and the others giving rise to complex transport properties through their interaction with the former.

Ba(Fe 1-x Co x ) 2 As 2 are divided into those who are close to forming localized moments controlling the magnetic transition and the others giving rise to complex transport properties through their interaction with the former.

Introduction
Dichotomy of localized/itinerant characters of electrons has been demonstrated in some correlated electron systems. For example, in the heavy fermion compounds CeRhIn 5 and UPd 2 Al 3 1,2 , it was shown that the magnetic order originates from the localized 4f-electrons but superconductivity develops from the attractions of "heavy" itinerant electrons. Reminiscent of the heavy fermion compounds 3 and the high T c cuprates 4 , superconductivity recently discovered in the iron pnictides seems to be tied up with magnetism as well [5][6][7][8][9][10][11][12][13] . Intensive efforts have been devoted to the study of magnetism and superconductivity in these compounds, but their origins remain a puzzle.
It was initially proposed that the magnetic order in iron pnictides is of spin-densitywave (SDW) type 6,14,15 , driven by Fermi-surface nesting. Such a scenario was supported by some angle-resolved photoemission spectroscopy (ARPES) 16 and optical measurements 6 , in which an energy gap was observed below T M . In contrast, a strongcoupling approach was also suggested to describe the physics of iron pnictides [17][18][19][20][21][22] , in which the magnetic ordering stems from the superexchange interactions of nearly localized 3d-electrons. Early measurements of quantum oscillations 23 , Hall resistivity 11,24 and ARPES 25 in the 122-type compounds have shown a rather low charge carrier density in the magnetic state, with a possible Fermi surface reconstruction at the magnetic/structural transition temperature (T M ). The strong Fermi surface reconstruction, together with the reduction of charge carriers at T M , could be attributed to electronic localization as well as a gap opening induced by magnetic ordering.
In an itinerant electron system with a spin density wave transition, a strong external magnetic field may significantly affect the SDW transition. The robustness of a magnetic transition to external magnetic field can be used to check the degree of electronic itinerancy. Thus, strong pulsed magnetic fields, reaching an energy scale similar to the magnetic transition temperature T M , may provide evidence to the nature of the 3d electrons and, therefore, probe the mechanism of magnetism and superconductivity in iron pnictides. Figure 1 shows the magnetoresistivity,  xx ( 0 H)/ 0 , of BaFe 2 As 2 at various temperatures. We find that the magnetoresistivity is nearly zero at temperatures above T M (T M 142K, see below). In contrast, a huge magnetoresistivity is observed in the magnetic state, and its value depends on the orientation of the applied magnetic field.

Experimental results
For instance, the magnetoresistivity at 4K reaches 300% and 120% upon applying a field of 50T along the c-axis and the ab-plane, respectively.
To demonstrate the effect of magnetic field on the magnetic transition, the electrical resistivity  xx (T) of both doped and undoped samples is plotted as a function of temperature in Fig.2, from which one can observe the following important points: (i) At zero field, a resistive anomaly is observed at T M 142K and 77K for BaFe 2 As 2 and Ba(Fe 0.95 Co 0.05 ) 2 As 2 respectively, consistent with reports in the literature 10,11 . (ii) The magnetoresistivity  xx (T)/ 0 (see the insets) monotonically decreases with increasing temperature and vanishes at T M . This fact indicates that the resistive anomaly at T M is unlikely driven by the structural distortion, but rather by magnetic interaction, because the former usually causes little magnetoresistance 26  Together with the observation of the insulator-like resistivity in Ba(Fe 0.95 Co 0.05 ) 2 As 2 below T M, it might suggest the importance of electronic localization in BaFe 2 As 2 .
In a conventional SDW state, a sufficiently large magnetic field would suppress the energy gap and, therefore, lead to a decrease of the magnetic transition temperature.
For example, the spin-flip transition (T sf =123K, which is close to T M 142K in BaFe 2 As 2 ) in chromium, an archetypal material for studying the SDW state, is quadratically suppressed by applying a magnetic field 27 . In contrast, the magnetic transition is extremely robust against the magnetic field of over 55T in Ba(Fe 1-x Co x ) 2 As 2 .
It is noted that the energy scale of magnetic excitations at a field of 55T is compatible with that of the thermal excitations at T M (T M 77K for x=0.05) and the spin gap (~10meV for x=0) resolved by neutron scattering 28 . Thus the magnetic transition is expected to be largely suppressed at such a high magnetic field in the conventional SDW scenario. On the other hand, in the strong-coupling local-moment picture the energy scale required to suppress the magnetic transition is of the order of 200meV in terms of the zone-boundary spin-wave energy of CaFe 2 As 2 29 , which is far beyond the magnetic field we applied. Our experimental findings, therefore, provide evidence that the magnetically ordered state in iron pnictides may not be a conventional SDW state, but possibly originates from local moments and is thus rather robust against magnetic field as observed in other strongly correlated materials 30 .
The field induced crossover from metallic to insulator-like behaviour in BaFe 2 As 2 , as demonstrated in the low temperature electrical resistivity  xx (T), indicates that the charge carriers and their mobility might be strongly affected by magnetic field. Such a point is further supported by simultaneous measurements of the Hall resistivity. In Fig.  3 the Hall resistivity,  xy ( 0 H), is plotted as a function of magnetic field for (a) BaFe 2 As 2 and (b) Ba(Fe 0.95 Co 0.05 ) 2 As 2 . One can see that the Hall resistivity has a dramatic change at T M in BaFe 2 As 2 , but it is weakened in the doped case. In the parent compound, the Hall resistivity follows rather linear field dependence at temperatures above T M , but shows a parabolic-like field dependence upon entering the magnetic state might be related to the metal-insulator-like crossover as seen in the resistivity  xx (T).
Indeed, it is difficult to reconcile the striking increase of the Hall coefficient R H s with increasing magnetic field, implying an increase in carrier density, and the small volume of Fermi surface. Similar behaviour is also found in Ba(Fe 0.95 Co 0.05 ) 2 As 2 .

Discussion
It is nonetheless worthwhile to assume the iron pnictides to possess a multi-band electronic structure, consisting of at least two hole pockets and two electron pockets 15 . The

Methods.
The formulas given by Eq.(1) and Eq.(2) are derived by assuming that there are two uncorrelated charge carriers whose densities and mobilities are not affected by applying external magnetic field. For a system in which the physical properties of charge carriers may strongly depend on the external magnetic field, we may still make use of the above formulas to extract the field dependence of the parameters, R e , R h ,  e and  h . In the following, we describe a method of data analysis that naturally extracts these parameters without making any additional assumption.
We notice that the following relation can be derived from Eq.(1) and Eq. (2): Here, R xy (H)= xy (H)/ 0 H. The parameter  can be viewed as the total "mobility" of a two-carrier system and its magnetic field dependence can be directly obtained from the experimental data of  xy (H) and  xx (H) using Eq. (3).
Eq.(1) and Eq.(2) can be rewritten as: where e e h h RR R RR The parameters  xx (0) and R 0 are the electrical resistivity at zero temperature and the Hall coefficient R xy in the limit of H0 respectively, which can be directly obtained from the experimental data. After determining the parameter then one can extract the parameters of R  (H) and   (H) following Eq.(4) and Eq.(5). By substituting the derived parameters R  ,   , R 0 and  xx (0) into Eqs. (6)- (9) and numerically solving the equations, the field dependence of R e , R h ,  e and  h can be uniquely determined, as shown in Fig. 4 for BaFe 2 As 2 .  which an anomaly is observed at T M 142 K and 77K for BaFe 2 As 2 and Ba(Fe 0.95 Co 0.05 ) 2 As 2 , respectively. The insets show the temperature dependence of the magnetoresistivity,  xx / 0 , which vanishes exactly around T M . In both compounds, the transition at T M is nearly independent of the magnetic field up to 55T, suggesting a localized nature of the magnetic order. A metal-insulator-like crossover is observed around 20T in BaFe 2 As 2 . The magetoresistivity is largely reduced in the underdoped compound Ba(Fe 0.95 Co 0.05 ) 2 As 2 , which resistivity increases with decreasing temperature below T M , followed by a superconducting transition at T c 9.5K. Ba(Fe 0.95 Co 0.05 ) 2 As 2 . The Hall resistivity of BaFe 2 As 2 follows linear field dependence above T M , but shows a parabolic-like behaviour in the magnetic state. It is noted that such behaviour is observed in samples coming from different groups and it becomes more pronounced in samples with a higher RRR ratio (ratio of room temperature resistivity to residual resistivity). In the doped compound, the Hall resistivity monotonically decreases with increasing magnetic field, but deviates from the linear field dependence as well. Note that the sharp decrease of  xy ( 0 H) at 1.5K corresponds to the superconducting transition. The inset shows the temperature dependence of the Hall coefficient R H for BaFe 2 As 2 , in which the data marked with empty triangles are from Ref. [24], derived in a dc magnetic field up to 8T.