Study On The Impact Mechanism Of Exchange Correlation And Magnetocrystalline Anisotropy In M-Type Strontium Hexaferrites

M-type strontium ferrite is a fantastic choice for motors as its high performance and fairish price.In this article,the exchange correlation and magnetocrystalline anisotropy of SrM hexaferrite and Ca²⁺,La³⁺,Co²⁺substituted hexaferrites were discussed by first principle calculation.Firstly,calculation parameters were discussed in detail.The results indicate that:?1?E_cut=500 eV,K-points=11×11×1 and SIGMA=0.1 eV are reasonable parameters for SrM hexaferrite;?2?The structure optimization gets a reasonable structure for calculation?a=5.86?,c=23.04??.?3?The Gorter magnetic configuration system has the lowest energy,GGA+U_eff(U_eff=6.9eV)obtains a reasonable electronic structure;?4?The calculation with spin-orbit coupling uses GGA+U_eff(U_eff=6.9eV).Secondly,we calculated the exchange correlation of SrM and Ca²⁺,La³⁺and Co²⁺ substituted SrM hexaferrites.The results show that:?1?The experimental curie temperature T_c of the?Ca,Sr?M increases first and then stabilizes as the increase of Ca²⁺substitution.The calculation results show that the shift of 4f₂ site leads the increase of exchange correlation parameter J?2b-4f₂?and the decrease of J_ijj between 2a-4f₁,4f₁-4f₂ and 4f₂-12k.In addition,the change trend of T_c calculation result is consistent with the experimental result;?2?The substitution of La³⁺ions decreases J?2a-4f₁?,J?4f₂-12k?and T_c,increases J?2a-12k?and J?4f₁-12k?;?3?The calculation results show that Co²⁺prefers to occupy 12k site and causes the J_ij between 2a-4f₁,2a-12k,4f₁-12k,2b-4f₂ increase and J_ij between 4f₁-4f₂,2b-12k decrease,curie temperature T_c of the system increases.Finally,we investigated the magnetocrystalline anisotropy of SrM,?Sr,La?M and SrCoM hexaferrite.The results show that:?1?the magnetocrystalline anisotropy MAE of SrM,?Sr,La?M and SrCoM is 0.79 meV,2.83 meV,0.83 meV,respectively.MAE increases with magnetization direction?,2b site has the biggest anisotropy in SrM sites;?2?La³⁺substitution causes partial Fe³⁺change to Fe²⁺in 2a site of SrM hexaferrite,the orbital magnetic moment increases,the substitution of La³⁺leads to the anisotropy of 2a,4f₁ and 4f₂ sites increases,which further increases the anisotropy of the system;?3?Co²⁺substitution slightly increases the magnetocrystalline anisotropy of the system.In the SrCoM system,2b site is still the main contributor to the magnetocrystalline anisotropy of the system.