Inverse Melting of 3D Antiferromagnetic Order in Multi-sublattice Magnetic Perovskites

In conventional antiferromagnets a long-range ordered 3D ground state transitions to a disordered paramagnetic state on warming, often via lower dimensional spin correlations within the critical regime. Here we demonstrate a striking departure from this paradigm. Through analysis of neutron powder diffraction data, we show that the magnetic ground state of columnar-ordered quadruple perovskites, Na$R$Mn$_2$Ti$_4$O$_{12}$ ($R$ = Dy, Sm), lacks long-range order, hosting only 2D spin correlations. On warming, this disordered state transitions into a 3D long-range ordered antiferromagnetic structure prior to the phase transition to the paramagnetic state. Our results establish an unconventional order-by-heating mechanism in which intrinsic A-site chemical disorder is coupled to competing exchange interactions between the rare earth and Mn sub-lattices, leading to a novel type of magnetic phase transition.