Dzyaloshinskii-Moriya interaction and chiral magnetism in3d−5dzigzag chains: Tight-binding model andab initiocalculations

Abstract

We investigate the chiral magnetic order in free-standing planar 3d-5d bi-atomic metallic chains (3d: Fe, Co; 5d: Ir, Pt, Au) using first-principles calculations based on density functional theory. We found that the antisymmetric exchange interaction, commonly known as Dzyaloshinskii-Moriya interaction (DMI), contributes significantly to the energetics of the magnetic structure. For the Fe-Pt and Co-Pt chains, the DMI can compete with the isotropic Heisenberg-type exchange interaction and the magneto-crystalline anisotropy energy (MAE), and for both cases a homogeneous left-rotating cycloidal chiral spin-spiral with a wave length of 51Å and 36Å, respectively, were found. The sign of the DMI, that determines the handedness of the magnetic structure changes in the sequence of the 5d atoms Ir(+), Pt(−), Au(+). We used the full-potential linearized augmented plane wave method and performed self-consistent calculations of homogeneous spin spirals, calculating the DMI by treating the effect of spin-orbit interaction (SOI) in the basis of the spin-spiral states in first-order perturbation theory. To gain insight into the DMI results of our ab initio calculations, we develop a minimal tight-binding model of three atoms and 4 orbitals that contains all essential features: the spin-canting between the magnetic 3d atoms, the spin-orbit interaction at the 5d atoms, and the structure inversion asymmetry facilitated by the triangular geometry. We found that spin-canting can lead to spin-orbit active eigenstates that split in energy due to the spin-orbit interaction at the 5d atom. We show that, the sign and strength of the hybridization, the bonding or antibonding character between d-orbitals of the magnetic and non-magnetic sites, the bandwidth and the energy difference between states occupied and unoccupied states of different spin projection determine the sign and strength of the DMI. The key features observed in the trimer model are also found in the first-principles results.

Domain-wall motion and interfacial Dzyaloshinskii-Moriya interactions inPt/Co/Ir(tIr)/Tamultilayers

“…The experimental data presented here gives a full picture of the DW dynamics and DMI of polycrystalline Pt/Co/Ir(t Ir )/Ta multilayers. The chirality of the DWs proved to be left-handed using asymmetric bubble expansion, which is the usual behaviour reported for DWs in both theoretical 34,35,76 and experimental 7,15,59 studies of Co/Pt interfaces, also for Pt/Co/Ir multilayers 17,30,57 . The experimental v(H InP ) curves for these films that were acquired using asymmetrical bubble expansion ( Fig 5(b-h)) do not have the form expected from the simple creep model 16 that is often used to analyse such data (Fig 5(a)).…”

“…But the Ir/FM case is not as straightforward as Pt/FM interface. Initially, ab initio calculations proposed that Ir introduces the opposite chirality to Pt 34,35,62 , which was supported by various experimental reports of additive effects 17,36,59,63,64 . Later on, the sign of DMI for Ir was debated when several experimental studies observed right-handed chirality in multilayers including Ir/Co 29,38,60 .…”

Ternary superlattice boosting interface-stabilized magnetic chirality

“…[14][15][16] Understanding of the origin of the DMI and tailoring the DMI is desirable for fundamental reasons and for potential spintronics device applications. Kashid et al provided a theoretical picture of the influence of 3d and 5d metals on the DMI, 17 and several experimental efforts are exploring various choices of non-magnetic heavy metal layers. For instance, it has been found that different choices of 5d heavy metal layers can significantly influence the sign and strength of the DMI.…”

“…Moreover, the DMI in trilayers composed of a single layer sandwiched between two elements might also be different than the DMI in a bilayer structure, 28 and the sign of the DMI is very sensitive to the details of hybridization between magnetic layers and heavy metal layers. 17 For these reasons, predicting the chirality that results from inserting 5d spacers in multilayer structures may be complicated by layer thickness dependence of electronic structure and by complicated hybridizations.…”

Dzyaloshinskii-Moriya Interaction and Hall Effects in the Skyrmion Phase ofMn1−xFexGe

“…1). This model is derived in a similar way as our previous model for 3d-5d transition metal chains [28], and it captures the essential physics of the DMI in our Mn 1−x Fe x Ge alloys. Based on the DFT results, in our model we neglect the SOC on the Ge atom, while the effects of non-collinearity and SOC on TMs lead to a finite DMI strength, D = |D|, via contribution to the energy of the type move from above the Fermi energy, become occupied and enter the region of d xy -states of opposite spin with increasing the concentration x − that is responsible for the change of sign and local peak in the DMI strength in the vicinity of x c .…”