research papers Acta Cryst. (2018). C74, 641–649 https://doi.org/10.1107/S2053229618006034 641 Received 15 March 2018 Accepted 19 April 2018 Edited by T.-B. Lu, Sun Yat-Sen University, People’s Republic of China Keywords: morphotropic series; kagome´ network; frustration; antiferromagnetism; crystal structure; canted antiferromagnet. CCDC reference: 1838351 Supporting information: this article has supporting information at journals.iucr.org/c Canted antiferromagnet superimposed on a buckled kagome´ network in RbMn 4 (PO 4 ) 3 Olga Yakubovich, a * Galina Kiriukhina, a,b Larisa Shvanskaya, a,c Olga Maximova, a,c Anatoliy Volkov, a Olga Dimitrova, a Evgeniy Ovchenkov, a Oleg Yumashev, d Asif Iqbal, e Badiur Rahaman, e Tanusri Saha-Dasgupta f and Alexander Vasiliev a,c,g a M. V. Lomonosov Moscow State University, Leninskye Gory 1, Moscow 119991, Russian Federation, b The Institute of Experimental Mineralogy, RAS, Akademika Osip’yana st 4, Chernogolovka, Moscow Region 142432, Russian Federation, c National University of Science and Technology ‘MISiS’, Leninskiy prospekt 4, Moscow 119049, Russian Federation, d Institute of Applied Mechanics, RAS, Leningradsky prt 7, Moscow 125040, Russian Federation, e Aliah University, IIA/27 Newtown, Kolkata 700 156, India, f S. N. Bose National Centre for Basic Sciences, Salt Lake City, Kolkata 700 098, India, and g National Research South Ural State University, Lenina Avenue 76, Chelyabinsk 454080, Russian Federation. *Correspondence e-mail: yakubol@geol.msu.ru Rubidium tetramanganese tris(phosphate), RbMn 4 (PO 4 ) 3 , has been synthesized as single crystals under hydrothermal conditions. The crystal structure was refined in the space group Pnnm (D 2h 12 ). It is argued that the size factor R M /R A , i.e. the ratio of the A + ionic radius to the M 2+ ionic radius, within the morphotropic series AM 4 (TO 4 ) 3 corresponds to a specific type of crystal structure. At low temperatures, the antiferromagnet superimposed on a buckled kagome´ network in RbMn 4 (PO 4 ) 3 experiences a transition into a long-range ordered state with finite spontaneous magnetization. First principles calculations provide the dominant magnetic exchange interactions both within and between the kagome´ layers. The analysis of these interactions allows us to suggest a model of alternating ferromagnetic and antiferromagnetic arrangements within chains of Mn3 atoms. 1. Introduction Transition and alkaline metal phosphates represent an extensively investigated group of compounds because of their potential applications as superionic, ferroelectric, nonlinear optical, catalytic and ion-exchange materials, to name but a few. Three-dimensional rather dense framework structures built of polyhedra centred by transition-metal cations often show promising magnetic properties. In particular, the mor- photropic series of manganese compounds AMn 4 (TO 4 ) 3 (A = Rb, NH 4 or K; T = P or As) has attracted attention with regard to magneto- and electrochemistry. Antiferromagnetic beha- viour has been observed for KMn 4 (PO 4 ) 3 , RbMn 4 (AsO 4 ) 3 and NH 4 Mn 4 (PO 4 ) 3 (Lo´ pez et al., 2008; MacKay et al., 1996; Neeraj et al., 2002), and encouraging data for ionic conductivity in the KMn 4 (PO 4 ) 3 and NaNi 4 (PO 4 ) 3 phases were obtained (Daidouh, Pico & Veiga, 1999). The sequence of crystal structures of phosphates and arsenates which comprise the morphotropic series under discussion has been described previously (Yakubovich et al., 1986; MacKay et al., 1996; Neeraj et al., 2002) and the crystal structure of RbMn 4 (PO 4 ) 3 was solved on the basis of powder X-ray diffraction using the atomic coordinates of isotypic phases as the starting point (Daidouh, Martinez et al., 1999). As single crystals of RbMn 4 (PO 4 ) 3 were obtained in the course of the synthesis of new manganese phosphates by the hydrothermal method, we found it worthwhile refining the structure anew in order to ISSN 2053-2296 # 2018 International Union of Crystallography