Spin and orbital ordering in bilayer Sr${}_3$Cr${}_2$O${}_7$

Abstract

Using maximally localized Wannier functions obtained from DFT calculations, we derive an effective Hubbard Hamiltonian for a bilayer of Sr${}_3$Cr${}_2$O${}_7$, the $n=2$ member of the Ruddlesden-Popper Sr${}_{n+1}$Cr${}_n$O${}_{3n+1}$ system. The model consists of effective $t_{2g}$ orbitals of Cr in two square lattices, one above the other. The model is further reduced at low energies and two electrons per site, to an effective Kugel-Khomskii Hamiltonian that describes interacting spins 1 and pseudospins 1/2 at each site describing spin and orbitals degrees of freedom respectively. We solve this Hamiltonian at zero temperature using pseudospin bond operators and spin waves. Our results confirm a previous experimental and theoretical study that proposes spin ordering antiferromagnetic in the planes and ferromagnetic between planes, while pseudospins form vertical singlets, although the interplane separation is larger than the nearest-neighbor distance in the plane. We explain the physics behind this rather unexpected behavior.

arXiv comment9 pages, 5 figures, information on Cr-O covalency added, accepted in Phys. Rev. B

References in corpus (25)

• Maximally-localized Wannier functions for entangled energy bands
• Wien2wannier: From linearized augmented plane waves to maximally localized Wannier functions
• Spin-ladders with spin gaps: A description of a class of cuprates
• Quantum Melting of Magnetic Order due to Orbital Fluctuations
• Field- and pressure-induced magnetic quantum phase transitions in TlCuCl_3
• Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet
• High-precision finite-size scaling analysis of the quantum-critical point of S=1/2 Heisenberg antiferromagnetic bilayers
• Magnetic neutron scattering study of YVO3: Evidence for an orbital Peierls state
• Interplay of spin and orbital ordering in the layered colossal magnetoresistance manganite La2-2xSr1+2xMn2O7 (0.5<=x<=1.0)
• Orbital fluctuations in the different phases of LaVO3 and YVO3
• Dimerization versus Orbital Moment Ordering in the Mott insulator YVO${}_3$
• Quantum Versus Jahn-Teller Orbital Physics in YVO${}_3$ and LaVO${}_3$
• Frustration and entanglement in the $t_{2g}$ spin--orbital model on a triangular lattice: valence--bond and generalized liquid states
• Complete bond-operator theory of the two-chain spin ladder
• Generalized spin-wave theory: application to the bilinear-biquadratic model
• Symmetry-breaking lattice distortion in Sr_3Ru_2O_7
• Multiplicative logarithmic corrections to quantum criticality in three-dimensional dimerized antiferromagnets
• Possible high-$T_c$ superconductivity due to incipient narrow bands originating from hidden ladders in Ruddlesden-Popper compounds
• Spectral evolution of the SU(4) Kondo effect from the single impurity to the two-dimensional lattice
• Effective Hamiltonian for transition-metal compounds. Application to Na_xCoO_2
• Magnetic and orbital ordering of RuO2 planes in RuSr2(Eu,Gd)Cu2O8
• Effect of covalency and interactions on the trigonal splitting in NaxCoO2
• Cooperative effects of Jahn-Teller distortion, magnetism and Hund's coupling in the insulating phase of BaCrO${}_3$
• Spin-Orbital Entanglement Emerging from Frustration in the Kugel-Khomskii Model
• Magnetic and orbital instabilities in a lattice of SU(4) organometallic Kondo complexes

Cited by in corpus (4)

• Origin of the Magnetic and Orbital ordering in $\alpha$-Sr${}_2$CrO${}_4$
• (Anti-)Altermagnetism from Orbital Ordering in the Ruddlesden-Popper Chromates Sr${}_{n+1}$Cr${}_n$O${}_{3n+1}$
• Material-based analysis of spin-orbital Mott insulators
• Effect of spin-orbit coupling on spin and orbital ordering in Sr${}_{n+1}$Cr${}_n$O${}_{3n+1}$, $n=1,2$