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We study an odd-parity magnetic multipole order in Ba$_{1-x}$K$_x$Mn$_2$As$_2$ and related materials. Although BaMn$_2$As$_2$ is a seemingly conventional Mott insulator with G-type antiferromagnetic order, we identify the ground state as a magnetic hexadecapole ordered state accompanied by simultaneous time-reversal and space-inversion symmetry breaking. A symmetry argument and microscopic calculations reveal the ferroic ordering of leading magnetic hexadecapole moment and admixed magnetic quadrupole moment. Furthermore, we clarify electromagnetic responses characterizing the magnetic hexadecapole state of semiconducting BaMn$_2$As$_2$ and doped metallic systems. A magnetoelectric effect and antiferromagnetic Edelstein effect are shown. Interestingly, a counter-intuitive currentinduced nematic order occurs in the metallic state. The electric current along the textit{z}-axis induces the textit{xy}-plane nematicity in sharp contrast to the spontaneous nematic order in superconducting Febased 122-compounds. Thus, the magnetic hexadecapole state of doped BaMn$_2$As$_2$ is regarded as a magnetopiezoelectric metal. The anomalous responses stem from the peculiar symmetry of the parity-violating magnetic order. Other candidate materials for magnetic hexadecapole order are proposed.
Combined neutron and x-ray diffraction experiments demonstrate the formation of a low-temperature minority tetragonal phase in Ba$_{0.76}$K$_{0.24}$Fe$_2$As$_2$ in addition to the majority magnetic, orthorhombic phase. A coincident enhancement in the
We report an angle-resolved photoemission spectroscopy study of the iron-based superconductor family, Ba$_{1-x}$Na$_x$Fe$_2$As$_2$. This system harbors the recently discovered double-Q magnetic order appearing in a reentrant C$_4$ phase deep within t
We report inelastic x-ray scattering measurements of the in-plane polarized transverse acoustic phonon mode propagating along $qparallel$[100] in various hole-doped compounds belonging to the 122 family of iron-based superconductors. The slope of the
The electron band around $M$ point in (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ compound -- completely lifted above the Fermi level for $x > 0.7$ and hence has no Fermi Surface (FS) -- can still form an isotropic s-wave gap ($Delta_e$) and it is the main pairing
Single crystals of Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$, $x<0.37$, have been grown and characterized by structural, magnetic and transport measurements. These measurements show that the structural/magnetic phase transition found in pure BaFe$_2$As$_2$ at 1