Abstract:
In this work, we try to understand the inconsistency reported by [Yaresko, Phys. Rev. B. 77, 115106 (2008)] in the theoretically estimated nature and the variation of magnitude of nearest neighbour exchange coupling constant (|J1|) with increasing U in ACr2O4 (A=Zn, Cd, Mg and Hg) compounds by using density functional theory. In unconstrained calculations, the nature and variation of |J1| as a function of U in the present study are not consistent with the experimental data and not according to the relation, J1∝ t 2 U especially for CdCr2O4 and HgCr2O4 for U >3 eV and U=2-6 eV, respectively. Such an inconsistent behavior of |J1| is almost similar to that of Yaresko for these two compounds for U=2-4 eV. For ZnCr2O4 and MgCr2O4, the nature and the variation of |J1| in the present work are in accordance with the experimental data and above mentioned relation for U=2-6 eV and are similar to that of Yaresko for ZnCr2O4 for U=2-4 eV. However, in constrained calculations the nature and variation of |J1c| in the present work are according to experimental data and above above mentioned relation for all four compounds. Hence, the present study shows the importance of constrained calculations in understanding the magnetic behaviour of these spinels. The values of magnitude of Curie-Weiss temperature [|(ΘCW )c|] for ZnCr2O4>MgCr2O4>CdCr2O4>HgCr2O4 for U=2-5 eV, which are according to the order of experimentally observed values for these spinels. The calculated values of (ΘCW )c for ZnCr2O4, MgCr2O4, CdCr2O4 and HgCr2O4 are -982 K, -721 K, -147 K and -122 K, respectively at U=5 eV.
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II. INTRODUCTION
It is well known that the magnetic structure and properties of magnetic materials (eg. Curie-Weiss temperature (ΘCW )) are mainly determined by the magnitude and the sign of the interatomic exchange coupling constants (Jij ) arising among the magnetic ions. Because of the sufficiently high ΘCW (above room temperature), any magnetic material can be used in the new generation electronic devices.1 Hence, the ability of first principles electronic structure calculations to predict the Jij plays an important role for designing of the various materials. Theoretically, the basic mechanisms to predict the Jij are quite well-known.2 However, it is not easy task to predict the sign and magnitude of Jij parameters for real magnetic materials. Liechtenstein et al. proposed a general method to extract the exchange integrals from electronic structure calculations, where the energy of the electronic Hamiltonian is mapped onto a classical Heisenberg model.3 Nowadays, this approach has become a prominent theoretical tool for studying the inter-site magnetic interactions for different materials from ab initio electronic structure calculations.
II. INTRODUCTION
It is well known that the magnetic structure and properties of magnetic materials (eg. Curie-Weiss temperature (ΘCW )) are mainly determined by the magnitude and the sign of the interatomic exchange coupling constants (Jij ) arising among the magnetic ions. Because of the sufficiently high ΘCW (above room temperature), any magnetic material can be used in the new generation electronic devices.1 Hence, the ability of first principles electronic structure calculations to predict the Jij plays an important role for designing of the various materials. Theoretically, the basic mechanisms to predict the Jij are quite well-known.2 However, it is not easy task to predict the sign and magnitude of Jij parameters for real magnetic materials. Liechtenstein et al. proposed a general method to extract the exchange integrals from electronic structure calculations, where the energy of the electronic Hamiltonian is mapped onto a classical Heisenberg model.3 Nowadays, this approach has become a prominent theoretical tool for studying the inter-site magnetic interactions for different materials from ab initio electronic structure calculations.
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