We report on the synthesis and magnetic properties of frustrated Na0.22MnO2·0. 39H2O and K0.6MnO2·0.48H2O with the birnessite structure. The structure, static and dynamic magnetic properties of the compounds are investigated in detail. A combination of DC and AC magnetic susceptibility measurements and magnetization decay measurements reveal cluster glass behavior below the freezing temperature of 4 K for Na-birnessite and 6 K for K-birnessite. The frequency dependence of the freezing temperature is analyzed on the basis of dynamic scaling laws including the critical slowing down formula and the Vogel-Fulcher law, which further confirm cluster glass formation in both compounds. I. INTRODUCTIONMagnetically frustrated compounds are promising for the emergence of various exotic magnetic states. For example, they can exhibit spin liquid and spin ice behavior, act as valence-bond solids, or exhibit an array of helical and cycloidal spirals or even a variety of periodic states with non-trivial topologies composed of skyrmions and antiskyrmions. 1,2,3 Magnetic frustration often results from competition between ferromagnetic (FM) and antiferromagnetic (AFM) exchange interactions in crystal lattices based on triangles or tetrahedra that share corners, edges or faces. 4,5 One group of interesting compounds from this point of view is the alkali manganites AxMnO2·yH2O (A = Na, K) with the birnessite structure (hereafter referred to as Na/K-bir). These antiferromagnetic compounds have frustrated 2D triangular planes of magnetic Mn 3+/4+ ions, which form edge-shared MnO6 octahedral structural units. The planes are separated from each other by gaps containing non-magnetic A + cations and H2O molecules. 6 This type of structure, with weakly coupled planes of spins pointing typically in the out-of-plane direction, allows tuning of the interlayer distance, the ratio of Mn 3+ /Mn 4+ and thus the magnetic exchange and anisotropy along the stacking direction.The exact crystal structure of birnessites remains unclear in terms of the placement of the interlayer species and the presence of Mn vacancies. 7,8 Due to high ionic mobility, it is difficult to determine whether the alkali cations and water molecules occupy the same or different positions in the interlayer space. At the same time, this high mobility of the interlayer cations has led to the wide use of birnessite compounds in the field of battery storage as capacitors showing high cycling capability. 9,10,11 Furthermore, birnessite compounds have been demonstrated as molecular sieves for purposes such as water purification. 12 Concerning vacancies in the manganese layers, it has been suggested that their existence probably depends on synthesis conditions. 8 Relatively few studies have been reported on the magnetic properties of birnessite compounds. Birnessite-like MnO2 nanowalls exhibited antiferromagnetic (AFM) behavior with an ordering transition at 9.2 K and a bifurcation of the zero-field-cooled and field-cooled DC susceptibilities. 13 No information is available on K-con...

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The largest single crystals of potassium birnessite thus far reported are grown. The structure is studied at atomic resolution. Mn3+/Mn4+ charge ordering, structural modulation and stacking faults are found.

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