Upper critical field, Hall effect and magnetoresistance in the iron-based layered superconductor LaFeAsOF
By using a two-step method, we successfully synthesized the iron based new superconductor LaFeAsOF. The resistive transition curves under different magnetic fields were measured, leading to the determination of the upper critical field of this new superconductor. The value of at zero temperature is estimated to be about 50 Tesla roughly. In addition, the Hall effect and magnetoresistance were measured in wide temperature region. A negative Hall coefficient has been found, implying a dominant conduction mainly by electron-like charge carriers in this material. The charge carrier density determined at 100K is about , which is close to the cuprate superconductors. It is further found that the magnetoresistance does not follow Kohler’s law. Meanwhile, the different temperature dependence behaviors of resistivity, Hall coefficient, and magnetoresistance have anomalous properties at about 230K, which may be induced by some exotic scattering mechanism.
pacs:74.70.-b, 74.25.Fy, 73.43.Qt
The recently discovered[1, 2, 3, 4, 5, 6, 7] iron-based superconducting oxides with a transition temperature as high as 55K has attracted much attention. As long as a new superconductor is discovered, the superconducting mechanism is urgent to be understood and the transition temperature is hoped to be enhanced. Thus the fundamental parameters, such as the upper critical field , charge carrier density and its type, the electron scattering mechanism, etc, are very important to identify the superconducting mechanism. It is well perceived that the normal state properties, such as the Hall effect and magnetoresistance, are very important to learn about the electronic scattering feature which is intimately related to the mechanism of a superconductor. For example, the superlinear temperature dependence of the normal state resistivity and the clear temperature dependence of Hall coefficient in wide temperature region in cuprate superconductors have been considered as two important anomalous properties which suggest the unusual scattering process beyond the electron-phonon scattering. In this paper we report the successful fabrication of this material with a two-step method, and the measurements on the resistive transition under different magnetic fields, Hall effect and magnetoresistance. By analyzing the data we obtained fresh information about the upper critical field, the charge carrier density and its type, as well as the scattering times etc.
2 Sample preparation and characterization
The polycrystalline samples were synthesized by using a two-step solid state reaction method. First the starting materials Fe powder (purity 99.95%) and As grains (purity 99.99%) were mixed in 1:1 ratio, ground and pressed into a pellet shape. Then it was sealed in an evacuated quartz tube and followed by heat treating at 700C for 10 hours. The resultant pellet was smashed and ground together with the LaF powder (purity 99.95%), LaO powder (purity 99.9%) and grains of La (purity 99.99%) in stoichiometry as the formula LaFeAsOF. Again it was pressed into a pellet and sealed in an evacuated quartz tube and burned at about 940C for 2 hours, followed by a heat treating at 1150C for 48 hours. Then it was cooled down slowly to room temperature. Since a little amount of F may escape during the second step fabrication, in the formula for our sample, we use as the possible concentration of F. In Figure. 1, we show the X-ray diffraction patterns for the sample LaFeAsOF. Almost all main peaks can be indexed by a tetragonal structure with and . Therefore the dominant component is from LaFeAsOF with only tiny peaks in the same scale as appeared in the data of the original paper. This tiny amount of second phase, perhaps from FeAs, together with the granular behavior of the samples, may give some influence on the zero resistance point, but they should not give any obvious influence on the upper critical field and the normal state properties.
3 Experimental data and discussion
The resistance and Hall effect measurements were done in a physical property measurement system (Quantum Design, PPMS) with magnetic field up to 9T. The six-lead method was used in the measurement on the longitudinal and the transverse resistivity at the same time. The resistance was measured by either sweeping magnetic field at a fixed temperature or sweeping temperature at a fixed field. The temperature stabilization was better than and the resolution of the voltmeter was better than 10nV.
3.1 Resistive transition and upper critical field
In Figure. 2 we present the temperature dependence of resistivity for the LaFeAsOF sample under different magnetic fields. One can see that the onset transition point shifts with the magnetic field weakly, but the zero resistance point shifts more quickly to lower temperatures. This is understandable since the latter is determined by the weak links between the grains as well as the vortex flow behavior, while the former is controlled by the upper critical field of the individual grains. This allows to determine the upper critical field of this material. However, we should mention that the upper critical field determined in this way reflects mainly the situation of -plane since the Cooper pairs within the grains with this configuration will last to the highest field compared to other grains. Taking the onset point of the transition as the upper critical field point means that almost all Cooper pairs are broken at this temperature and magnetic field. By taking a criterion of (referenced by the normal state resistivity marked by the dashed line in Figure. 3) we can determine the upper critical field and shown in Figure. 3. It is seen that the slope of near , i.e., is about T/K. By using the Werthamer-Helfand-Hohenberg (WHH) formula the value of zero temperature upper critical field can be estimated through:
Taking K, we get roughly. We can also determine the by using the formula based on the Ginzburg-Landau (GL) equation. In the GL theory, it is known that and , with the flux quanta, the coherence length, the reduced temperature, thus one has
Although the GL theory is specially applicable near , above equation has been proved to be satisfied in much wider temperature regime. We thus use above equation to fit our data and show them as the solid line in Figure. 3. The zero temperature upper critical fields determined in this way is T. This value is a bit higher than that obtained in using the WHH formula. We note that a recent result reported that the WHH approximation could not be simply applied in this material, and even the is affected by the multiband property. However our result can give a rough magnitude of because of the limit of magnetic field.
In Figure. 4 we show the resistance transition of the sample at zero field in wide temperature region by open circles. From that we can get the zero resistance temperature at about 19K, the onset temperature 28.9K (99% of the normal state resistivity). The resistivity at 30K is 0.133cm, while the residual resistance ratio is about 18.1. This may indicate a good quality of the sample in our experiments. The general shape of the resistivity curve at this doping shows a very good metallic behavior. The inset shown in Figure. 4 gives the zero field cooled and also the field cooled DC magnetization of the sample at 20Oe. The onset critical temperature by magnetic measurement is about 24K (see by an enlarged view), which is corresponding to the middle transition point of resistance.
Magnetoresistance is a very powerful tool to investigate the electronic scattering process and the information about the Fermi surface. For example, in MgB, a large magnetoresistance (MR) was found which is closely related to the multiband property.[12, 13] For this new superconductor, we also measured and found a clear MR. In Figure. 5 (a) we present field dependence of the MR ratio, i.e., , where is the resistivity, is the resistivity at zero field, and . One can see that the MR is about 2.2% at 40K and 9T for this sample. This ratio is one order of magnitude smaller than MgB with the same . However, considering that the sample is a polycrystalline sample, the MR effect may be weakened by mixing the transport components with the magnetic field along different directions of the crystallographic axes. For a single band metal with a symmetric Fermi surface, Kohler’s law is normally obeyed. Kohler’s law shows that the magnetoresistance measured at different temperatures should be scalable with the variable . For MgB, Kohler’slaw is not obeyed because of the multiband property. We also do scaling based on Kohler’slaw for this sample, the result is shown in Figure. 5 (b). Clearly, the data measured at different temperatures do not overlap and Kohler’slaw is violated for this material. This discrepancy may suggest that in this new material there may be multiband effect or other exotic scattering, such as spin scattering which depends on the magnetic field. However, the MR in this sample do show some specialty. For two-band or multiband materials with weak MR, the MR ratios could be well described by the expression in the low field region. This is because the contribution of the higher order even terms of could be omitted at a low field (the odd terms are absent here according to the Boltzmann equation for electronic transport). This effect is also found in NbSe which has a complex Fermi surface structure. It was reported that both LaFeAsO and LaFePO have five orbitals crossing the Fermi level, and Fermi surfaces with both electron and hole type band are present. In this sense, the anomalies mentioned above in the present new superconductor may also be induced by multiband effect together with complex Fermi surfaces. On single crystal samples, when the field is along -axis, a stronger in-plane magnetoresistance is expected.
3.3 Hall effect
For a normal metal with Fermi liquid feature, the Hall coefficient is a constant versus temperature. However, this situation is changed for a multiband material or a sample with non-Fermi liquid behavior, such as the cuprate superconductors. We also do the Hall effect measurement for this sample. As shown in Figure. 6, the transverse resistivity remains negative at all temperatures above the critical temperature, indicating that the electric transport is dominated by electron-like charge carriers, not hole-like ones. For a clean sample, the nonlinear Hall effect is also a sign of multiband, and the effect is weaker in dirtier samples.  In our measurements, all curves shown in Figure. 6 have good linearity versus the magnetic field which may be caused by the disorders within the sample. From this set of data, the Hall coefficient is determined and shown in Figure. 7 (a). It is clear that is almost a constant below about 250K, and there is a kink at about 150K considering the small error showing in the figure. The charge carrier density calculated by is about which is very close to the cuprate superconductors. This may imply that the superfluid density in this superconductor is also very diluted, as suggested by a recent theoretical proposal. However, it should be noted that the Hall coefficient could not be simply expressed as for a multiband material,  so it needs further consideration if multiband property dominates the electric transport. From Figure. 6, the transverse resistivity curves almost overlap at K. However at the temperature above 250K, the absolute value of the slope, i.e., the Hall coefficient decreases quickly. As shown in Figure. 7(a), behaves a little different from another recent work on La(OF)FeAs. In our sample, shows a weak dependence at the temperature below 225K; while at K, the absolute value of has a rapid decrease. This is similar to the situation of MgCNi, which may be caused by the exotic scattering when a ferromagnetic fluctuation is present. The temperature dependent Hall coefficient also tells us that either the multiband effect or some unusual scattering process may be involved in the electron conduction in the material.
In order to reveal an anomalous behavior at about 230K, here we make a further discussion. The differential of the curve shown in Figure. 4 is given in Figure. 7 (b). It is clear that there is a maximum value at about 240K of the differential slope . This is similar to the situation reported in the underdoped LaOFeAs sample,  where they found a clear kink point of resistivity and marked the temperature point as . In our present sample, this kink is absent, but the resistivity shows a weak downward feature around 240K, as evidenced by a bump on the curve of vs. . Therefore the anomaly at about 240K in our sample may be related to the situation at in the original paper. We also try to fit the normal state curve with the formula . As shown in Figure. 4, the curve below 240K could be well fitted and the fitting results give values of and cm. However, just from this temperature and above, the fitting curve starts deviating from the data. As shown in Figure. 7 (c), there is also a sudden decrease of MR at the temperature of 240K. The origin of this anomaly at about 230K certainly needs further consideration.
So far, a weak magnetic signal has been measured in the sample in the normal state, which is exactly the same as that reported in the original paper by Kamihara et al.. Magnetic measurements show that this magnetic signal even has a small hysteresis in low field region. At this moment, we don’t know whether this magnetic signal is due to an intrinsic feature of the LaFeAsO phase, or is due to the second tiny impure phase. If the former is right, some exotic scattering, like the electron-magnon scattering or magnetic skew scattering would exist. This deserves a further study on improved samples. Our present investigation will thus provide a basic platform for the future studies.
In summary, the temperature dependence of resistivity under different magnetic fields, the magnetoresistance and Hall coefficient have been measured in the newly found layered superconductor LaFeAsOF. The value of at zero temperature is obtained roughly to be about 50 Tesla. The Hall coefficient is negative indicating that the electron-like charge carriers dominate the electrical transport. The charge carrier density at 100K is about manifesting that the superconductor may have a diluted superfluid, as in cuprate superconductors. The Hall coefficient has a weak temperature dependence below 230K, but it rises more rapidly above that temperature. At the similar temperature the magnetoresistance becomes very small, together with a maximum of the differential of the resistivity curve . The curve at low temperature could be fitted by with . Kohler’s law is clearly violated in all temperature region. These observations can be explained by the multi-band effect or some exotic scattering, like the scattering with magnetic moments or in presence of weak magnetic correlation.
This work is supported by the Natural Science Foundation of China, the Ministry of Science and Technology of China (973 project: 2006CB01000, 2006CB921802), the Knowledge Innovation Project of Chinese Academy of Sciences (ITSNEM).
-  Kamihara Y, Watanabe T, Hirano M, and Hosono H, 2008 J. Am. Chem. Soc. 130 3296
-  Wen H H, Mu G, Fang L, Yang H, and Zhu X Y, 2008 Europhys Lett. 82 17009
-  Chen X H, Wu T, Wu G, Liu R H, Chen H, and Fang D F, 2008 Nature. 453 761
-  Chen G F, Li Z, Wu D, Li G, Hu W Z , Dong J, Zheng P, Luo J L, and Wang N L, 2008 Chin. Phys. Lett. 25 2235
-  Ren Z A, Yang J, Lu W, Yi W, Shen X L, Li Z C, Che G C, Dong X L, Sun L L, Zhou F and Zhao Z X, 2008 EuroPhys. Lett. 82 57002
-  Ren Z A, Yang J, Lu W, et al., 2008 Chin. Phys. Lett. 25 2215
-  Chen P, Fang L, Yang H, Zhu X Y, Mu G, Luo H Q, Wang Z S, and Wen H H, 2008 Science. in. China. 51 719
-  Werthamer N R, Helfand E, Hohenberg P C, 1966 Phys. Rev. 147 295
-  Fang L, Wang Y, Zou P Y, Tang L, Xu Z, Chen H, Dong C, Shan L and Wen H H, 2005 Phys. Rev. B. 72 014534
-  Fuchs G, Drechsler S L, Kozlova N, Behr G, Koehler A, Werner J, Nenkov, Hess C, Klingeler R, Hamann-Borrero J E , Kondrat A, Grobosch M, Knupfer M, Freudenberger J, Buechner B, Schultz L, 2008 preprint arXiv:0806.0781.
-  Hunte F, Jaroszynski J, Gurevich A, Larbalestier D C, Jin R, Sefat A.S, McGuire M.A, Sales B.C, Christen D.K, and Mandrus D, 2008 Nature 453, 903.
-  Qi Li, Liu B T, Hu Y F, Chen J, Gao H, Shan L, Wen H H, Pogrebnyakov A V, Redwing J M, and Xi X X, 2006 Phys. Rev. Lett. 96 167003
-  Yang H, Liu Y, Zhuang C G, Shi J R, Yao Y G, Massidda S, Monni M, Jia Y, Xi X X, Li Q, Liu Z K, Feng Q R, 2008 preprint arXiv:0802.3443
-  Zinman J M, 2001 in Electrons and Phonons Classics Series (Oxford University Press., New York,)
-  Corcoran R, Meeson P, Onuki Y, Probst P A, Springford M, Takita K, Harima H, Guo G Y, and Gyorffy B L, 1994 J. Phys.: Condens. Matter 6 4479
-  Singh D J and Du M H, 2008 preprint arXiv:0803.0429
-  Lebgue S, 2007 Phys. Rev. B. 75 035110
-  Chen G F, Li Z, Li G, Zhou J, Wu D, Dong J, Hu W Z, Zheng P, Chen Z J, Luo J L, and Wang N L, 2008 preprint arXiv:0803.0128
-  Li S Y, Fan R, Chen X H, Wang C H, Mo W Q, Ruan K Q, Xiong Y M, Luo X G, Zhang H T, Li L, Sun Z, and Cao L Z, 2001 Phys. Rev. B. 64 132505