Spin-Orbital Order Modified by Orbital Dilution in Transition-Metal Oxides: From Spin Defects to Frustrated Spins Polarizing Host Orbitals

Abstract

We investigate the changes in spin and orbital patterns induced by magnetic transition metal ions without an orbital degree of freedom doped in a strongly correlated insulator with spin-orbital order. In this context we study the 3d ion substitution in 4d transition metal oxides in the case of 3d 3 doping at either 3d 2 or 4d 4 sites which realizes orbital dilution in a Mott insulator. Although we concentrate on this doping case as it is known experimentally and more challenging than other oxides due to finite spin-orbit coupling, the conclusions are more general. We derive the effective 3d−4d (or 3d − 3d) superexchange in a Mott insulator with different ionic valencies, underlining the emerging structure of the spin-orbital coupling between the impurity and the host sites and demonstrate that it is qualitatively different from that encountered in the host itself. This derivation shows that the interaction between the host and the impurity depends in a crucial way on the type of doubly occupied t2g orbital. One finds that in some cases, due to the quench of the orbital degree of freedom at the 3d impurity, the spin and orbital order within the host is drastically modified by doping. The impurity acts either as a spin defect accompanied by an orbital vacancy in the spinorbital structure when the host-impurity coupling is weak, or it favors doubly occupied active orbitals (orbital polarons) along the 3d−4d bond leading to antiferromagnetic or ferromagnetic spin coupling. This competition between different magnetic couplings leads to quite different ground states. In particular, for the case of a finite and periodic 3d atom substitution, it leads to striped patterns either with alternating ferromagnetic/antiferromagnetic domains or with islands of saturated ferromagnetic order. We find that magnetic frustration and spin degeneracy can be lifted by the quantum orbital flips of the host but they are robust in special regions of the incommensurate phase diagram. Orbital quantum fluctuations modify quantitatively spin-orbital order imposed by superexchange. In contrast, the spin-orbit coupling can lead to anisotropic spin and orbital patterns along the symmetry directions and cause a radical modification of the order imposed by the spin-orbital superexchange. Our findings are expected to be of importance for future theoretical understanding of experimental results for 4d transition metal oxides doped with 3d 3 ions. We suggest how the local or global changes of the spin-orbital order induced by such impurities could be detected experimentally.

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

“…(5.21). Such a collective spin-orbital excitation (bound state) involves spin and orbital flips at many sites and can be written as follows, 22) with the coefficients…”

“…The strong Coulomb interactions and the relativistic spinorbit interaction entangle locally the spin and orbital degrees of freedom [13] which display an amazing variety of fundamentally new and fascinating phenomena, ranging from topologically nontrivial states [14], relativistic Mott-insulating behavior in 5d [15,16] and 4d [17,18] transition-metal oxides and entanglement on superexchange bonds in spin-orbital models [6,19]. Other more recent developments include entangled spin-orbital excitations [20,21], doped spin-orbital systems [22], skyrmion lattices in the chiral metal MnSi [23], multiferroics, spinHall effects [24], Majorana and Weyl fermions [25], topological surface states [26], Kondo systems [27], exotic spin textures in disordered systems, to name just a few.…”

Multibandd−pmodel and self-doping in the electronic structure ofBa2IrO4

“…Recently it has been shown that strong spin-orbit coupling changes radically the electronic states in Mott insulators [16,17]. Within this limit of an insulator, strong spin-orbit interaction accompanied by large crystal-field effects split t 2g orbitals of Ir 4+ ions into fully filled manifold with effective total angular momentum J eff = 3/2 and singly occupied manifold J eff = 1/2 (half-filled ground state) [18,19].…”

Singlet-Triplet Excitations and Long-Range Entanglement in the Spin-Orbital Liquid CandidateFeSc2S4

“…Orbital degrees of freedom can also be disordered by quantum fluctuations [2]. Systems with both spin and orbital fluctuations as well as spin-orbit coupling (SOC) have been proposed to form a "spin-orbital liquid" (SOL) ground state, characterized by entangled spin and orbital degrees of freedom but no long range order [3][4][5][6][7].…”