Correlation induced half-metallicity in a ferromagnetic single-layered compound: Sr$_{2}$CoO$_{4}$ Sudhir K. Pandey ∗ UGC-DAE Consortium for Scientific Research, University Campus, Khandwa Road, Indore - 452001, India (Dated: November 21, 2018) The electronic and magnetic properties of Sr 2 CoO 4 compound have been studied using ab initio electronic structure calculations. As opposed to GGA calculation, which gives ferromagnetic metallic solution, GGA+ U calculations provide two kind of ferromagnetic solutions: (i) half-metallic and (ii) metallic. The half-metallic solution is a ground state of the system and the metallic one is a metastable state. The strong hybridization between Co 3 d and O 2 p orbitals decides the electronic and magnetic properties of the compound. The total magnetic moment per formula unit is found to be ∼ 3 µ B ( S = 3/2). Our calculations give the magnetocrystalline anisotropy energy of ∼ 2.7 meV, which provides a good description of experimentally observed large magnetocrystalline anisotropy. The Heisenberg exchange parameters up to fourth nearest neighbours are also calculated. The mean-field theory gives the T C = 887 K. The possible physical implications of the ferromagnetic half-metallic ground state are also discussed. PACS numbers: 71.27.+a, 71.20.-b, 75.20.Hr arXiv:1001.1405v1 [cond-mat.str-el] 9 Jan 2010 I. INTRODUCTION The single-layered compounds with a general formula of A$_{2}$BO$_{4}$ (A and B stand for rare-earth/alkali metals and transition metals, respectively) have attracted a great deal of attention after the discovery of high temperature superconductor in La$_{2}$$_{−}$$_{x}$Sr$_{x}$CuO$_{4}$. 1 These compounds show many exotic physical phenomena like spin/charge stripes formation in nickelates and manganites $^{1}$; and spin-triplet superconductivity in ruthenates. 2 Among the single-layered compounds recently synthe- sized Sr$_{2}$CoO$_{4}$ has been reported to show ferromagnetic (FM) and metallic behaviours, which have never been found in any other such materials. 3,4 The magnetiza- tion data show T$_{C}$ around 250 K. The large magnetic anisotropy where magnetic easy axis is the c -axis is also observed. Moreover, the resistivity data reveal the quasi- two-dimensional electronic nature for the system. In- terestingly, there are contradicting reports on the mag- netic moments. The Matsuno et al . 3 and Wang et al . 4 have reported the saturation magnetization of about 1.8 and 1.0 µ$_{B}$ /Co, respectively. The effective magnetic mo- ment of 3.72 µ$_{B}$ has also been found by fitting Curie- Wiess behaviour in the paramagnetic phase, which sug- gests the magnetic moment corresponds to S ≈ 3/2 spin configuration. 4 Lee et al . 5 tried to understand the above contradic- tory reports on the saturation magnetization by using LDA+ U calculations. Their studies suggest that such values of magnetization can be intrinsic to the system as they got similar two values for the total magnetic mo- ment for different ranges of U . However, if we read the works of Matsuno et al . and Wang et al . carefully we can easily make out that the different values of satura- tion magnetization they got may not be intrinsic to the system. The M(H) data of both the groups look similar. For example, the values of total magnetization at 5 T found by Wang et al . and Matsuno et al . are about 1.4 Here, we report the detailed electronic and magnetic states of Sr$_{2}$CoO$_{4}$ using ab initio electronic structure cal- culations. The ground state solution is found to be a fer- romagnetic half-metallic state having S = 3/2 spin con- figuration, which is different from that reported by Lee et al . The strong hybridization between Co 3 d and O 2 p orbitals decides the electronic and magnetic properties of the compound. The calculation gives magnetocrystalline anisotropy energy of ∼ 2.7 meV. The nature of mag- netic interactions between the Co atoms is calculated up to fourth nearest neighbours, which shows mixed ferro- magnetic and antiferromagnetic coupling. The estimated ferromagnetic transition temperature within mean-field theory is ∼ 887 K. The partial replacement of Sr by rare-earth elements leads to the formation of interesting magnetic phases keeping the crystal structure intact. 6–8 For example, Sr$_{1}$$_{.}$$_{5}$La$_{0}$$_{.}$$_{5}$CoO$_{4}$ compound retains the FM ground state of Sr$_{2}$CoO$_{4}$, whereas SrLaCoO$_{4}$ manifests spin glass state. 6 Contrary to FM state for Sr$_{1}$$_{.}$$_{5}$La$_{0}$$_{.}$$_{5}$CoO$_{4}$, the ground state of Sr$_{1}$$_{.}$$_{5}$Pr$_{0}$$_{.}$$_{5}$CoO$_{4}$ compound is found to be spin glass. 7 Similarly, the formation of spin glass state is also reported in Sr$_{1}$$_{.}$$_{25}$Nd$_{0}$$_{.}$$_{75}$CoO$_{4}$ compound. 8 The ex- istence of spin glass state in the doped compounds ap- pears to be a generic phenomenon. It is well known that the spin glass state arises due to the presence of com- peting ferromagnetic and antiferromagnetic interactions. Therefore, it would be interesting to calculate the na- ture of magnetic interactions between the neighbouring Co atoms in the Sr$_{2}$CoO$_{4}$ compound. and 1.6 µ$_{B}$ /Co, respectively, which are not very different. The different values of saturation magnetization quoted in the last paragraph appear to arise due to two different approaches the authors used in extracting them.