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system Maglab-EXA-12. The resistivity, magnetoresis- tance and Hall effect were measured with a Quantum Design instrument physical property measurement sys- tem (PPMS), and the DC magnetization by a Quantum Design instrument SQUID (MPMS-7). 

## A. Magnetic and resistive transitions 

In Fig.1(a), we show the temperature depen- dence of resistivity of the Mn-doped samples Ba$_{0}$$_{.}$$_{5}$K$_{0}$$_{.}$$_{5}$(Fe$_{1}$ − $_{x}$Mn$_{x}$ )$_{2}$As$_{2}$. One can see that the superconducting transition temperature was suppressed quickly upon the doping of Mn, and the superconduc- tivity vanishes in the sample with x = 0.08. In contrast, 

## III. RESULTS 

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as shown in Fig. 1(b), the Zn-doped sample does not exhibit a clear change of T$_{c}$ with the nominal doping concentration as high as x = 0.10. The Zn-doping effect in the iron pnictide has been under a heavy debate. It was found by Li et al. 33 that the Zn-doping to the Fe sites in LaFeAsO does not change T$_{c}$ clearly. However, also in the Zn-doped but high pressure synthesized LaFeAsO samples, Guo et al. 34 found that the superconductivity can be destroyed completely at a very low doping level of 2%. Actually in our Zn-doped Ba-122 samples, the slight change of T$_{c}$ in the samples with different Zn con- centrations may be attributed to the random scattering of T$_{c}$ values induced in the synthesizing process. The temperature dependence of AC susceptibilities for the Mn-doped and Zn-doped samples are shown in Fig.2(a) and Fig.2(b), respectively. For Mn-doped ones, the suppression of T$_{c}$ is remarkable. The sample with x = 0.08 does not show diamagnetism down to 2 K. This is consistent with the resistivity data. For Zn-doped ones, however, there are not much differences in the values of 

