# 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. 

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 

PACS numbers: 71.27.+a, 71.20.-b, 75.20.Hr 

## I. INTRODUCTION 

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. 

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. 

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. 

