Le Chatelier’s Principle and Field-Induced Change in Magnetic Entropy Leading to Spin–Lattice Partitioning and Magnetization Plateau

For a certain antiferromagnet, the magnetization M(H) does not increase gradually with increasing magnetic field μ0H but exhibits field region(s), where M(H) remains constant typically at an integer fraction of its saturation magnetization Msat. This phenomenon is readily understood by the supposition that, under external magnetic field, such an antiferromagnet undergoes field-induced partitioning of its spin–lattice into ferrimagnetic fragments. We searched for a theoretical basis for this supposition by investigating how external magnetic fields affect the magnetic entropy of such an antiferromagnet, to find that the field region of the magnetization plateau has a single magnetic phase, but a nonzero slope region of the magnetization curve has two magnetic phases of different magnetic entropy. Our analysis predicts that the magnetic entropy of a single-phase region does not depend on magnetic field but that of a two-phase region does, such that the magnetic entropy increases with field if the two phases dynamically shift their spin sites but decreases if their spin sites remain fixed. We tested these predictions by carrying out magnetization and specific heat measurements for γ-Mn3(PO4)2, which exhibits a 1/3-magnetization plateau at 2 K at magnetic fields between ∼6 and ∼23 T and undergoes a long-range antiferromagnetic ordering at TN = 12.9 K. It was found that the magnetic entropy of the two-phase region increases with field, indicating that field-induced breaking of magnetic bonds and hence field-induced partitioning of an antiferromagnetic spin–lattice are time-averaged results of all allowed spin arrangements that occur repeatedly during static magnetization measurements. The temperature-dependent magnetic specific heats Cm(T) of γ-Mn3(PO4)2 between 2 and 6 K shows a larger excitation gap Δ when measured at 9 T than at 0 T (i.e., Δ = 1.4 vs 0.5 K). These energy gaps reflect the two successive local excitations of linear Mn2+–Mn2+–Mn2+ ferrimagnetic trimers embedded in the antiferromagnetic spin–lattice of γ-Mn3(PO4)2 and arise from the Boltzmann factor associated with these excitations. Our work demonstrates that Le Chatelier's principle provides a qualitative basis for understanding a series of events that an external magnetic field can bring about in antiferromagnets exhibiting magnetization plateaus.