Article pubs.acs.org/cm
Ca2MnRuO6: Magnetic Order Arising from Chemical Chaos Rohan Mishra,*,† Jennifer R. Soliz,‡ Patrick M. Woodward,‡ and Wolfgang Windl† †
Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus, Ohio 43210, United States ‡ Department of Chemistry, The Ohio State University, 100 West 18th Avenue, Columbus, Ohio 43210, United States S Supporting Information *
ABSTRACT: We predict the existence of half metallicity and thus highly spinpolarized conduction in the completely disordered double-perovskite Ca2MnRuO6, based on first principles calculations. For ordered structures we find the predominantly Ru t2g electrons to be itinerant whereas the Mn eg spins are nearly localized, thus favoring a ferrimagnetic alignment of the Ru and Mn spins. For disordered structures, we find the Mn ions to favor ferromagnetic coupling to other Mn ions in both Mn and Ru sublattices. This explains the overall ferrimagnetic alignment of Mn and Ru ions, irrespective of chemical disorder, that has been found experimentally. The existence of ferrimagnetism and half metallicity in the presence of high levels of chemical disorder is an unexpected combination not seen in other double perovskites. KEYWORDS: spin-polarization, magnetoresistance, perovskite, half-metal, DFT+U
1. INTRODUCTION Although cooperative magnetic ordering is observed in a wide range of perovskites, examples of ferro- or ferrimagnetism are uncommon. Among ternary perovskites the best-known examples are members of the Ln1−xAxMnO3 (Ln = lanthanoid ion, A = alkaline earth ion) family and SrRuO3. In both cases the ferromagnetism is coupled with itinerant carriers that give rise to metallic conductivity. Expanding the compositional complexity to encompass A2B′B″O6 double perovskites provides more freedom to tune the magnetic interactions, as well as the electrical and magnetotransport properties. Using the Goodenough-Kanamori rules,1,2 one can “design” a double-perovskite ferromagnet by combining a transition-metal ion with halffilled eg orbitals (i.e., d5 or d8 ion) with a transition-metal ion whose eg orbitals are empty (i.e., d3 ion). Archetypical examples include La2FeCrO6 and Sr2FeRuO6. Unfortunately, conventional preparation of these materials invariably leads to a product where the transition-metal ions are disordered.3−6 This is problematic because Fe−O−Fe and Cr−O−Cr superexchange interactions are strongly antiferromagnetic, and the resulting chemical disorder leads to frustration and glassy magnetic behavior. Ordered versions of these perovskites can be prepared using layer-by-layer laser molecular beam epitaxy growth, and the resulting films are ferromagnetic,7−9 but growth of such artificial superlattices is both time-consuming and expensive. La2NiMnO6 and La2CoMnO6 are the only other known examples of superexchange mediated ferromagnetism in a double perovskite.10 Both can be made ordered and ferromagnetic in bulk form, but considerable care must be taken to maintain high levels of chemical order. In A2B′B″O6 double perovskites, ferrimagnetic ordering is also possible, where the spins on the B′ ions line up parallel to © 2012 American Chemical Society
each other but antiparallel to the spins on the B″ ion. Ferrimagnetism is particularly attractive when the electrons in one spin channel are itinerant whereas those in the other spin channel are localized, resulting in half-metallic conductivity (i.e., 100% spin-polarized conductivity). Half-metallic ferrimagnetic double perovskites possess tremendous potential for spin-based devices such as in spin-injectors and magnetic tunnel junctions. Since the discovery of room-temperature giant magnetoresistance in Sr2FeMoO6 over a decade ago,11 ferrimagnetic double perovskites have been studied extensively.12 However, successful incorporation of such materials into multilayer thin film devices has been hindered by difficulties in growing highly ordered, stoichiometric films.13 For device applications this complication is a deal breaker because chemical disorder is highly detrimental to the magnetic and magnetotransport properties. For the example of Sr2FeMoO6, even a relatively small amount of chemical disorder significantly reduces its 100% spin-polarization, making it unattractive for device applications.14 Disorder also leads to a linear decrease in the saturation magnetization (Ms) of Sr2FeMoO6 and sufficiently large amounts of disorder lower the Curie temperature (TC).14,15 Given the propensity for chemical disorder in the double-perovskite family, finding a material where magnetic ordering and spin-polarization can be maintained in the presence of high levels of chemical disorder is very attractive. In half-metallic double perovskites the electrons associated with the 3d transition-metal ion are generally localized whereas the electrons nominally belonging to the 4d/5d transitionReceived: March 30, 2012 Revised: June 10, 2012 Published: June 14, 2012 2757
dx.doi.org/10.1021/cm301007m | Chem. Mater. 2012, 24, 2757−2763
Chemistry of Materials
Article
structures are specially designed small unit cell periodic structures that are constructed to reproduce the most important correlation functions of a randomly disordered system. They have been successfully used to simulate random disorder within small periodic supercells convenient for DFT studies.32,34 The most general special quasi-random structure we constructed was an 80 atom supercell which matched the pair correlation function of a randomly disordered system up to the third nearest neighbors in Ca2MnRuO6.35 Strongly correlated transition-metal oxides have localized delectrons which have energies near the Fermi level (EF). Traditional local density approximation (LDA) or GGA within DFT often fail to describe their electronic and magnetic properties correctly. A popular and efficient way to treat the static correlations is the DFT + Hubbard U method, introduced by Anisimov et al.,36 which has allowed study of many transition-metal compounds with significant improvements over LDA and GGA.14,36 To improve the speed of our calculations and thus facilitate the use of large supercells, we used the rotationally invariant Dudarev approach to GGA+U,37 in which only one effective Hubbard parameter Ueff = U − J is used, with U and J being Hubbard repulsion and intra-atomic exchange, respectively, for the electrons in the localized d states. We used the experimental X-ray photoelectron spectra (XPS) of Sr2MnRuO6 to fit the values of Ueff necessary for Mn and Ru.38 Although we were not able to find critical values of Ueff for Mn and Ru that match all features of the experimental valence band spectra perfectly, we do find that Ueff values of 3.1 and 2.1 eV for Mn and Ru, respectively, provide the best match to the overall features of the XPS spectra. However, we note that a small fraction of Mn d-states cut across the Fermi level in the calculated spectra, a feature that is not observed experimentally. As the Sr 4d and Ca 3d states appear far from EF (above ∼5 eV) and do not hybridize with the Mn or Ru states, they are not expected to affect the Coulomb correlation in the d orbitals, which allows use of the same Ueff values for Ca2MnRuO6. With these values for Ueff, we also find good agreement with the experimentally observed valence of Mn and Ru in Ca2MnRuO6 and Sr2MnRuO6.22 Additionally, because of the ambiguity in determining a value of Ueff exactly, we have repeated our calculations with Ueff = (0−6) eV for Mn and (0−4) eV for Ru and find qualitatively similar results for all values.
metal ion are delocalized and responsible for the conductivity. The 3d ion is nearly always either Fe3+, with d5 configuration (e.g., Sr2FeMoO6), or Cr3+, with a d3 configuration (e.g., Sr2CrReO6). In such compounds the presence of chemical disorder leads to antiferromagnetic superexchange interactions between nearest neighbor 3d ions, either Fe−O−Fe or Cr−O− Cr. The presence of both up-spin and down-spin localized electrons opens conductivity pathways for the 4d/5d electrons in both spin channels and degrades the spin-polarization of the conduction electrons. Thus, the magnetic and magnetotransport properties of any double perovskite containing Fe3+ or Cr3+ will always be negatively impacted by chemical disorder. On the other hand, double perovskites containing Mn3+ offer a ray of hope because Mn−O−Mn superexchange interactions can be either ferromagnetic or antiferromagnetic. However, the details of these interactions depend upon the occupation and orientation of the Mn 3d eg orbitals, and as such are very sensitive to a number of factors including the manganese valency and the size of the A-site cation, as illustrated by the complexity of the La1−xCaxMnO3 phase diagram.16 If we look to A2MnB″O6 double perovskites for attractive candidates, several compounds can immediately be ruled out because they contain Mn2+, which has a d5 configuration and therefore behaves like Fe 3+ . Examples include Sr2Mn2+Mo6+O6,17 Sr2Mn2+W6+O6,17 and Sr2Mn2+Re6+O6,18 all of which order antiferromagnetically at low temperatures. Sr2MnRuO6 is more promising because the oxidation state of manganese is intermediate between +3 and +4. This compound magnetically orders in spite of the fact that the Mn and Ru atoms are completely disordered.19−21 Unfortunately, orbital ordering stabilizes a C-type antiferromagnetic structure in Sr2MnRuO6. If however Sr2+ is replaced by the smaller Ca2+, the magnetic ground state becomes ferrimagnetic.22−25 In this paper we use first principles calculations based on density functional theory (DFT) to understand this unexpected behavior. Our results suggest that Ca2MnRuO6 will be a halfmetal, even in the presence of high levels of Mn/Ru disorder.
2. METHODS We used the projector augmented wave (PAW) method26 along with the spin-polarized generalized gradient approximation27 (GGA) to DFT as implemented in the Vienna Ab-initio Simulation Package (VASP).28,29 To ensure convergence, a plane-wave cutoff energy of 525 eV was employed throughout. We used the PAW-GGA pseudopotentials (Sr_sv, Ca_sv, Mn, Ru, and O) from the VASP distribution with valence configurations of 4s24p65s2 for Sr, 3s23p64s2 for Ca, 3d64s1 for Mn, 4d75s1 for Ru, and 2s22p4 for O.26 To sample the Brillouin zone, we used Monkhorst-Pack k-point meshes30 with mesh divisions Ni such that the product of Ni with the corresponding lattice vectors was as close as possible to 35 Å for structural relaxations and 50 Å for final band-structure calculations. Additionally for the latter the tetrahedron method with Blöchl corrections31 was used for the Brillouin zone integration. Relaxations were performed, keeping the low temperature experimental lattice constants fixed and allowing the internal coordinates to change until the forces were
