A neutron scattering study of the under-doped Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$, x=0.09 and 0.17 self-flux grown single crystals and the universality of the tricritical point

We present a combination of elastic neutron scattering measurements in zero and 14.5 T and magnetization measurements in zero and 14 T on under-doped superconducting Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ x=0.17, and the same measurements in zero field ona non-superconducting crystal with x=0.09. The data suggest that the under-doped materials may not be electronic phase separated but rather have slightly inhomogeneous potassium doping. The temperature dependence of the magnetic order parameter (OP) below the transition of the sample with x=0.09 is more gradual than that for the case of the un-doped BaFe$_{2}$As$_{2}$, suggesting that this doping may be in the vicinity of a tricritical point. We advance therefore the hypothesis that the tricritical point is a common feature of all superconducting 122s. For the x=0.17 sample, while T$_{c}$ is suppressed from $approx$17 K to $approx$8 K by a magnetic field of 14 T, the intensity of the magnetic Bragg peaks (1 0 3) at 1.2 K is enhanced by 10$%$ showing competition of superconductivity (SC) and antiferromagnetism (AFM). The intensity of the magnetic Bragg peaks (1 0 3) in the (T$_{c}$, T$_{N}$) temperature interval remain practically unchanged in 14.5 T within a 10$%$ statistical error. The present results are discussed in the context of the existing literature.