Origins of multi-sublattice magnetism and superexchange interactions in double–double perovskite CaMnCrSbO₆

Abstract

Abstract The multi-sublattice magnetism and electronic structure in double–double perovskite compound CaMnCrSbO 6 is explored using density functional theory. The bulk magnetization and neutron diffraction suggest a ferrimagnetic order ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo>∼</mml:mo> </mml:mrow> </mml:mrow> </mml:math> 49 K) between between Mn 2+ and Cr 3+ spins. Due to the non-equivalent Mn atoms (labelled as Mn(1) and Mn(2) which have tetrahedral and planar oxygen coordinations, respectively) and the Cr atom in the centre of distorted oxygen octahedron in the unit cell, the exchange interactions are more complex than that expected from a two sublattice magnetic system. The separations between the on-site energies of the d -orbitals of Mn(1), Mn(2) and Cr obtained from Wannier function analysis are in agreement with their expected crystal field splitting. While the DOS obtained from non spin-polarized calculations show a metallic character, starting from Hubbard U = 0 eV the spin-polarized electronic structure calculations yield a ferrimagnetic insulating ground state. The band gap increases with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msub> </mml:mrow> </mml:math> ( U − J ), thereby showing a Mott–Hubbard nature of the system. The inclusion of anti-site disorder in the calculations show decrease in band-gap and also reduction in the total magnetic moment. Due to the ∼90 ∘ superexchange, nearest neighbour exchange constants obtained from DFT are an order of magnitude smaller than those reported for various magnetic perovskite and double-perovskite compounds. The Mn(1)–O–Mn(2) (out of plane and in-plane), Mn(1)–O–Cr and Mn(2)–O–Cr superexchange interactions are found to be anti-ferromagnetic, while the Cr–O–O–Cr super-superexchange is found to be ferromagnetic. The Mn(2)–O–Cr superexchange is weaker than the Mn(1)–O–Cr super-exchange, thus effectively resulting in ferrimagnetism. From a simple 3-site Hubbard model, we derived expressions for the antiferromagnetic superexchange strength <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mtext>AFM</mml:mtext> </mml:msub> </mml:mrow> </mml:math> and also for the weaker ferromagnetic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mtext>FM</mml:mtext> </mml:msub> </mml:mrow> </mml:math> . The relative strengths of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>J</mml:mi> <mml:mtext>AFM</mml:mtext> </mml:msub> </mml:mrow> </mml:math> for the various superexchange interactions are in agreement with those obtained from DFT. The expression for Cr–O–O–Cr super-superexchange strength ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mrow> <mml:mover> <mml:mi>J</mml:mi> <mml:mo stretchy="false">~</mml:mo> </mml:mover> </mml:mrow> </mml:mrow> <mml:mtext>SS</mml:mtext> </mml:msub> </mml:mrow> </mml:math> ), which has been derived considering a 4-site Hubbard model, predicts a ferromagnetic exchange in agreement with DFT. Finally, our mean field calculations reveal that assuming a set of four magnetic sub-lattices for Mn 2+ spins and a single magnetic sublattice for Cr 3+ spins yields a much improved T C , while a simple two magnetic sublattice model yields a much higher T C .

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