Structure-Property Relationships in α-, β'-, and γ-Modifications of Mn₃(PO₄)₂

The manganese orthophosphate, Mn₃(PO₄)₂, is characterized by the rich variety of polymorphous modifications, α-, β'-, and γ-phases, crystallized in monoclinic P2₁/c (P2₁/n) space group type with unit cell volume ratios of 2:6:1. The crystal structures of these phases are constituted by three-dimensional framework of corner- and edge-sharing [MnO₅] and [MnO₆] polyhedra strengthened by [PO₄] tetrahedra. All compounds experience long-range antiferromagnetic order at Neel temperature T_N = 21.9 K (α-phase), 12.3 K (β'-phase), and 13.3 K (γ-phase). Additionally, second magnetic phase transition takes place at T* = 10.3 K in β'-phase. The magnetization curves of α- and β'-modifications evidence spin-floplike features at B = 1.9 and 3.7 T, while the γ-Mn₃(PO₄)₂ stands out for an extended one-third magnetization plateau stabilized in the range of magnetic field B = 7.5-23.5 T. The first-principles calculations define the main paths of superexchange interaction between Mn spins in these polymorphs. The spin model for α-phase is found to be characterized by collection of uniform and alternating chains, which are coupled in all three directions. The strongest magnetic exchange interaction in γ-phase emphasizes the trimer units, which make chains that are in turn weakly coupled to each other. The spin model of β'-phase turns out to be more complex compared to α- or γ-phase. It shows complex chain structures involving exchange interactions between Mn2 (Mn2', Mn2″) and Mn3 (Mn3', Mn3″). These chains interact through exchanges involving Mn1 (Mn1', Mn1″) spins.