PHYSICAL REVIEW B 105, 214422 (2022) Microscopic origin of room-temperature ferromagnetism in the double perovskite Sr 2 FeReO 6 Shishir K. Pandey, 1, 2, 3 Ashis K. Nandy, 1, 4 Poonam Kumari, 1 and Priya Mahadevan 1 , * 1 Department of Condensed Matter Physics and Material Science, S. N. Bose National Center for Basic Sciences, Kolkata-700106 2 International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China 3 Artificial Intelligence for Science Institute, Beijing, China 4 School of Physical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Jatni-752050, India (Received 2 February 2022; accepted 27 May 2022; published 21 June 2022) The puzzling observation of room temperature ferromagnetism in double perovskites (A 2 BB  O 6 ), despite having the magnetic lattice of B ions diluted by nonmagnetic B  ions, have been examined for Sr 2 FeReO 6 . Ab initio spin spiral electronic structure calculations along various high symmetry directions in reciprocal space are used to determine the exchange interactions entering an extended Heisenberg model, which is then solved classically using Monte Carlo simulations to determine the ferromagnetic transition temperature T c . We find that one must consider on-site Coulomb interactions at the nonmagnetic Re sites (U ) in order to obtain a T c close to the experimental value. Analysis of the ab initio electronic structure as well as an appropriate model Hamiltonian trace the origin of enhancement in T c with U to the enhanced exchange splitting that is introduced at these sites. This in turn destabilizes the antiferromagnetic exchange channels, thereby enhancing the T c . The role of occupancy at the nonmagnetic sites is examined by contrasting with the case of Sr 2 FeMoO 6 . DOI: 10.1103/PhysRevB.105.214422 I. INTRODUCTION Double perovskite (DP) oxides have the general formula A 2 BB  O 6 with A being the rare earth or alkaline-earth ion, B and B  are the transition metal atoms separated by oxygen atoms in the lattice. In general, a DP oxide consists of two sub- lattices of perovskite ABO 3 and AB  O 3 units in a way that the B and B  sites are arranged alternately in a three- dimensional array. B (B  ) transition metal atoms reside in an octahedra formed by six oxygen atoms. The finding of ferromagnetic behavior in the Re based DP oxides A 2 FeReO 6 (where A = Ba, Sr, Ca) above room temperature (with ferromagnetic transition temperatures 316, 401, and 538 K, respectively) [1] stimulated research in this new ferromagnetic class of DP ox- ides. Another similar example of a high T c ferromagnetic DP oxide is Sr 2 FeMoO 6 (SFMO) with a transition temperature of 410 K [2,3]. In Sr 2 FeReO 6 (SFRO), the separation between the closest magnetic Fe atoms is √ 2 times larger than that found in a Fe-based perovskite oxide. This large separation of Fe atoms arises because of the dilution of the magnetic lattice with nonmagnetic Re atoms. The naive expectation was that it should result in weaker magnetic interactions and hence a lower magnetic ordering temperature. Surprisingly, the Curie temperature for this system is 401 K. In contrast, considering the case of the hole doped manganites [4], where one has smaller separations between the magnetic atoms, one finds a lower magnetic ordering temperature. As the ferromagnetism has been conventionally understood within a double exchange model, the presence of nonmagnetic atoms like Re/Mo present * priya.mahadevan@gmail.com in a double perovskite crystal requires a different mechanism to explain the high ferromagnetic ordering temperature in these compounds. A qualitative model to understand the high magnetic or- dering temperature was proposed by Sarma et al. [5] after analyzing the ab initio electronic structure of SFMO. They concluded that the hopping interactions between first neighbor Fe and Mo atoms in the lattice led to an exchange splitting being induced on the Mo sites which is opposite in direction to that at the Fe site. This led to an antiferromagnetic coupling between the Fe and Mo sites and an effective ferromagnetic coupling between the Fe sites. This results in the high mag- netic ordering temperatures of these materials. Electronic structure calculations reveal that the majority Fe up spin t 2g and e g states are ∼3.75 and 2.25 eV below the Fermi energy, respectively, while the minority spin states have highly hybridized Fe-Re/Mo character. This idea led to the use a Kondo-like model to describe the magnetism in these materials. The majority spin Fe states are approximated by a spin within this model which interacts with the itinerant conduction electrons through an antiferromagnetic coupling. The itinerant conduction electron can delocalize by hopping from the t 2g levels on the nonmagnetic transition metal atom to those on Fe. While this model was able to successfully explain the high magnetic ordering temperature in Sr 2 FeMoO 6 which had just one electron on the nonmagnetic atom, it failed to explain the high magnetic ordering temperature when one had more than one electron on the nonmagnetic atom as in Sr 2 FeReO 6 [6–9]. Brey and coworkers [10] carried out a mean-field study considering a t 2g only model. The suppression of T c was recovered qualitatively by introducing electron-electron 2469-9950/2022/105(21)/214422(9) 214422-1 ©2022 American Physical Society