Structural distortions and orbital ordering in LaTiO ₃ and YTiO ₃

Abstract

-Electron density of states and band structure of crystalline solids. PACS. 75.25.+z -Spin arrangement in magnetically ordered materials. PACS. 71.27.+a -Strongly correlated electron systems; heavy fermions.Abstract. -Theoretical investigations of the electronic, magnetic and structural properties of LaTiO3 and YTiO3 have been made. In the framework of GGA and GGA+U scheme we analyzed the effect of the local Coulomb interaction (U ) value on the atomic forces acting in the experimental structure. The optimal parameters of the electron-electron on-site interactions as well as the orbital configurations and magnetic properties are determined.Introduction. -Transition-metal perovskite oxides LaTiO 3 and YTiO 3 are classical MottHubbard insulators. In spite of the fact that they are formally isoelectronic with one 3d electron in the t 2g shell LaTiO 3 has a G-type antiferromagnetic (AFM) structure whereas YTiO 3 has a ferromagnetic (FM) one. The most unusual feature of these compounds relates with a nearly isotropic magnon spectrum in both titanates despite of their distorted crystal structures [1,2].There are two theoretical models aimed to explain these effects in LaTiO 3 . One of them originates from the work of Kugel and Khomskii [3] and operates in terms of the lattice distortions and an orbital ordering (OO). Another one is proposed by Khalliulin and Maekawa [4] and describes the above effects by the model of orbital liquid (OL) where the fluctuations of orbital degrees of freedom play an important role. According to [4] the energy of the orbital fluctuations is estimated to be W orb ∼ 160 meV. Thus OL model is applicable only if the splitting of the t 2g orbital in the crystal field ∆ is significantly smaller than W orb . Otherwise the nearly isotropic exchange is likely to be due to an orbital ordering with a peculiar orbital configuration [9].The OL model was supported by neutron experiments of Keimer et al [1] where no OO in LaTiO 3 was found. Fritsch with co-workers [5] made heat capacity and magnetic measurements. Having supposed the nearly cubic structure of LaTiO 3 they concluded that the energy of the spin-orbit coupling for Ti-sites was E SO = 30 meV and the crystal field effect was small. The theoretical estimations made by Solovyev in Ref. [6] in the framework of the local spin density approximation (LSDA) and LSDA+U theory showed that ∆ in LaTiO 3 was as small

Lattice distortion and magnetism of3d−t2gperovskite oxides

“…In this sense, our strategy is completely different from conventional LDA+U calculations, where the on-site Coulomb interaction U is typically treated as an adjustable parameter (e.g., Refs. 27,29,31,32,33). By changing U , one can certainly get a better numerical agreement with some experimental data already at the HF level.…”

“…19,20,21,22,23,24) as well as the first-principles electronic structure calculations (Refs. 25,26,27,28,29,30,31,32,33). The problem is still far from being understood, and remains to be the subject of numerous contradictions and debates.…”

“…Since the magnetic properties of t 2g perovskite oxides are extremely sensitive to all such details, it is not surprising that there is a substantial variation in the results of first-principles calculations, which sometimes yield even qualitatively different conclusions about the CF splitting and the magnetic structure of the distorted t 2g perovskite oxides. 28,31,32,33 These discrepancies put forward a severe demand on the creation of a really parameter-free scheme of electronic structure calculations for the strongly-correlated systems.…”

Role of nonlocal exchange in the electronic structure of correlated oxides

“…Also in ferromagnetic YTiO 3 , in the LDA-HSE06 it increases up to 0.84μ B from 0.7μ B in the LDA, reaching a similar value as in the GGA + U. 73 Also in these compounds, the LDA-HSE06 gives insulating densities of states [see Figs. 7(a) and 8(a) for LaTiO 3 and YTiO 3 , respectively].…”

Instability : the driving force for new physical phenomena

“…We could show that LDA calculations reproduce the well-documented [87] GdFeO 3 -type distortions in this system very well. To study various types of magnetic ordering, we took account of the Coulomb interaction of the partially filled d-shell using a local Coulomb interaction parameter U Ti d [88] which has been shown to describe the ground state of YTiO 3 and LaTiO 3 qualitatively correctly [89]. The LDA+U results are in even closer agreement with experiment as shown in chapter 2.…”