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Register a new userN{e}el and stripe ordering from spin-orbital entanglement in $alpha$-Sr$_2$CrO$_4$
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The rich phenomenology engendered by the coupling between the spin and orbital degrees of freedom has become appreciated as a key feature of many strongly-correlated electron systems. The resulting emergent physics is particularly prominent in a number of materials, from Fe-based unconventional superconductors to transition metal oxides, including manganites and vanadates. Here, we investigate the electronic ground states of $alpha$-Sr$_2$CrO$_4$, a compound that is a rare embodiment of the spin-1 Kugel-Khomskii model on the square lattice -- a paradigmatic platform to capture the physics of coupled magnetic and orbital electronic orders. We have used resonant X-ray diffraction at the Cr-$K$ edge to reveal N{e}el magnetic order at the in-plane wavevector $mathbf{Q}_N = (1/2, 1/2)$ below $T_N = 112$ K, as well as an additional electronic order at the stripe wavevector $mathbf{Q}_s = (1/2, 0)$ below T$_s$ $ sim 50$ K. These findings are examined within the framework of the Kugel-Khomskii model by a combination of mean-field and Monte-Carlo approaches, which supports the stability of the spin N{e}el phase with subsequent lower-temperature stripe orbital ordering, revealing a candidate mechanism for the experimentally observed peak at $mathbf{Q}_s$. On the basis of these findings, we propose that $alpha$-Sr$_2$CrO$_4$ serves as a new platform in which to investigate multi-orbital physics and its role in the low-temperature phases of Mott insulators.
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The origin of successive phase transitions observed in the layered perovskite $alpha$-Sr$_2$CrO$_4$ is studied by the density-functional-theory-based electronic structure calculation and mean-field analysis of the proposed low-energy effective model. We find that, despite the fact that the CrO$_6$ octahedron is elongated along the $c$-axis of the crystal structure, the crystal-field level of nondegenerate $3d_{xy}$ orbitals of the Cr ion is lower in energy than that of doubly degenerate $3d_{yz}$ and $3d_{xz}$ orbitals, giving rise to the orbital degrees of freedom in the system with a $3d^2$ electron configuration. We show that the higher (lower) temperature phase transition is caused by the ordering of the orbital (spin) degrees of freedom.
Motivated by recent experimental progress in transition metal oxides with the K$_2$NiF$_4$ structure, we investigate the magnetic and orbital ordering in $alpha$-Sr$_2$CrO$_4$. Using first principles calculations, first we derive a three-orbital Hubbard model, which reproduces the {it ab initio} band structure near the Fermi level. The unique reverse splitting of $t_{2g}$ orbitals in $alpha$-Sr$_2$CrO$_4$, with the $3d^2$ electronic configuration for the Cr$^{4+}$ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multi-orbital systems, we constructed the ground-state phase diagram for the two-dimensional compound $alpha$-Sr$_2$CrO$_4$. We found stable ferromagnetic, antiferromagnetic, antiferro-orbital, and staggered orbital stripe ordering in robust regions of the phase diagram. Furthermore, using the density matrix renormalization group method for two-leg ladders with the realistic hopping parameters of $alpha$-Sr$_2$CrO$_4$, we explore magnetic and orbital ordering for experimentally relevant interaction parameters. Again, we find a clear signature of antiferromagnetic spin ordering along with antiferro-orbital ordering at moderate to large Hubbard interaction strength. We also explore the orbital-resolved density of states with Lanczos, predicting insulating behavior for the compound $alpha$-Sr$_2$CrO$_4$, in agreement with experiments. Finally, an intuitive understanding of the results is provided based on a hierarchy between orbitals, with $d_{xy}$ driving the spin order, while electronic repulsion and the effective one dimensionality of the movement within the $d_{xz}$ and $d_{yz}$ orbitals driving the orbital order.
Motivated by an experimental finding that the successive phase transitions in $alpha$-Sr$_2$CrO$_4$ observed at ambient pressure ceases to exist under high pressures, we carry out the density-functional-theory-based electronic structure calculations and demonstrate that the reversal of the crystal-field splitting reported previously is restored under high pressures, so that the orbital degrees of freedom disappears, resulting in the single phase transition that divides the system into high-temperature Mott insulating and low-temperature antiferromagnetic insulating phases.
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.
We present electronic structure calculations in combination with local and non-local many-body correlation effects for the half-metallic ferromagnet CrO$_2$. Finite-temperature Dynamical Mean Field Theory results show the existence of non-quasiparticle states, which were recently observed as almost currentless minority spin states near the Fermi energy in resonant scattering experients. At zero temperatures, Variational Cluster Approach calculations support the half-metallic nature of CrO$_2$ as seen in superconducting point contact spectroscopy. The combination of these two techniques allowed us to qualitatively describe the spin-polarization in CrO$_2$.
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