Strain engineering of magnetic and orbital order in perovskite ${\mathrm{LuMnO}}_3$ epitaxial films

Epitaxial strain has been extensively used to tailor the functionality of perovskite oxides, in which strain control of magnetism is highly desirable, especially for perovskite manganites. Here on the basis of the first-principles calculations we demonstrated the control of magnetic phase and orbital order in ${\mathrm{LuMnO}}_3$ film by epitaxial strain imposed by a square substrate and revealed the surface and interface effects by combining the strain-bulk and heterostructure models. The spiral and $E$ -type multiferroic phases present in perovskite manganites bulks can exist in the tensile strained films, while a ferromagnetic half-metal phase with high Curie temperature and an antiferromagnetic polar-metal phase arise in the range of compressive strain. Increasing compressive strain changes the sign of the $Q_3$ mode of Jahn-Teller distortion, resulting in the transition of the in-plane stagger orbital order to a uniform orbital order. The reconstruction of Jahn-Teller distortion and orbital order occur in the first two layers near the surface. The symmetry breaking of the crystal field at the surface leads to a uniform $d_{3z^2-r^2}$ type orbital order and surface metallization. The electron accumulation at the interface with ${\mathrm{SrTiO}}_3$ substrate has been demonstrated and decreases dramatically with the increase in the number of ${\mathrm{LuMnO}}_3$ layers.

Figure 1

Change of (a) three Mn-O bond length and $c$-axis lattice constant, (b) $Q_2$ and $Q_3$ modes of JT distortion, and (c) the in-plane (${\theta }_{\mathrm{in}}$) and out-of-plane (${\theta }_{\mathrm{out}}$) Mn-O-Mn bond angles with strain. The insets in (a) show the shape of the unoccupied $d$ orbital (i.e., $d$ hole) under large tensile and compressive strain. The insets in (b) show the structural distortion corresponding to the normal $Q_2$ and $Q_3$ modes.

Figure 2

(a) Relative energy (to FM order) of all AFM orders and magnetic transition temperature estimated by MC simulations as a function of strain. The relative energy of spiral and ${\mathrm{spiral}}^{*}$ orders was calculated by the proposed energy minimization method. The relative energy of the higher-energy $C$- and $G$-type orders is not shown for clarity. (b) Magnetic exchange interactions calculated according to the Heisenberg model.

Figure 3

(a) Dependence of energy on the spin direction under zero strain. The angle denotes the degree of spin direction deviating from the $a$ and $c$ axes, respectively. (b) Change of magnetic anisotropy energy with spins oriented along the $a$ and $c$ axes with strain.

Figure 4

Projected band structures of up-spin states on the $3d$ orbitals at (a) tensile strain of $5\%$, (b) 0 strain, and (c) compressive strain of $-5\%$.

Figure 5

Total spin-induced polarization $P_{\mathrm{total}}$, pure electronic polarization $P_{\mathrm{ele}}$, and ion-displacement polarization $P_{\mathrm{ion}}$ in $E$-type phase changed as a function of strain.

Figure 6

Dependence of relative energy of the considered AFM orders in the heterostructures on the number of ${\mathrm{LuMnO}}_3$ layers. The results of strain-bulk method are also shown for comparison.

Figure 7

(a) The layer-resolution projected density of states of $d$ orbitals in the ${\left({\mathrm{LuMnO}}_3\right)}_2/{\left({\mathrm{SrTiO}}_3\right)}_2$ heterostructure and (b) the distribution of $d$ holes of the corresponding transition-metal ions shown by deformation charge density. The arrows represent the directions of the polar axis ($z$ axis) of the local crystal field, and the character l denotes the longest Mn-O bond.

Figure 8

(a) The layer-resolution projected density of states in the ${\left({\mathrm{LuMnO}}_3\right)}_4/{\left({\mathrm{SrTiO}}_3\right)}_2$ heterostructure and (b) the distribution of $d$ holes shown by deformation charge density. The arrows represent the directions of the polar axis ($z$ axis) of the local crystal field. The characters l and s denote the longest and shortest Mn-O bonds, respectively.