content_image/395569.jpg content_image/395564.jpg
T$_{c}$ for different doping levels (x = 0 to 0.1). 

In order to know whether the Zn-impurities are re- ally introduced into the lattice, we have carried out de- tailed analysis on the compositions of the grains in each sample using the EDX analysis. The undoped sample Ba$_{0}$$_{.}$$_{5}$K$_{0}$$_{.}$$_{5}$Fe$_{2}$As$_{2}$ exhibits superconductivity at about T$_{c}$ = 35 K, combining with the lattice constants $^{32}$, we con- clude that our sample is slightly overdoped. The EDX data reveals that the actual doping levels of Mn is very close to the nominal composition up to 8%, while Zn dop- ing has a nonlinear ratio between the really measured composition and the nominal one: 3.1 ± 0.3 % in sam- ple x = 0.04, about 4.5 ± 0.5 % in the one x = 0.10. We randomly selected 10 typical grains and analyzed the compositions on them.Taking the sample with nominal Zn=10% as an example, the SEM image and EDX anal- ysis process were shown in Fig.4 and Table I. This fact indicates that the Zn impurities have been successfully doped into the lattice, although the measured composi- tion is lower than the nominal one. 

Above discussion can be corroborated by the charac- terization of the XRD data. The XRD patterns for all samples were shown in Fig.3(a) and Fig.3(b). For Mn- doped ones, one can see that the phase is rather clean and no impurities could be detected up to x=0.08. The lattice constants of a-axis and the cell volume increase monotonically with doping of Mn (as shown in Fig.3(c)), which indicates that the Mn atoms were successfully in- troduced into the lattice. Assuming that the Mn ionic state is ”+2”, since the ionic radius of Mn 2+ (0.8 ˚ A ) is bigger than that of Fe 2+ (0.74 ˚ A ), it is understandable that the in-plane lattice constant expands and the unit cell volume increases about 1.6%. While for Zn-doped samples, since the ionic radius for Fe 2+ and Zn 2+ are both 0.74 ˚ A , therefore the distortion is much smaller, as evidenced by the slight increase of the unit cell volume (0.34%). In both systems, it is found that the c-axis lat- tice constant does not change obviously compared to the a-axis lattice constant. 

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## B. Structure and composition 

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## C. Hall effect, Magnetoresistance and Magnetizations 

It order to know what has been carried out microscopi- cally through doping Mn and Zn in our samples, we mea- sured the Hall coefficient R$_{H}$ , Magnetoresistance (MR) and DC magnetization. As shown in Fig.5(a), R$_{H}$ is pos- itive in the undoped sample, indicating hole dominant conduction in Ba$_{0}$$_{.}$$_{5}$K$_{0}$$_{.}$$_{5}$Fe$_{2}$As$_{2}$. As we dope Mn into the sample and keep increasing the doped content, the R$_{H}$ reduces systematically. This can be explained by intro- ducing more holes into the system through Mn-doping, though complexity will be brought in understanding the Hall data of the multiband system. 35 Actually doping Mn induces similar effect as doping Cr. 36 The tempera- ture dependence of R$_{H}$ is also shown for the Zn doped sample (x=0.06, 0.08) in Fig. 5(a). One can see that the data of Zn-doped sample overlap roughly with the undoped one in a broad temperature region, indicating that the Zn 2+ is almost identical to Fe 2+ in donating 

