Appearance and disappearance of ferromagnetism in ultrathin ${\mathrm{LaMnO}}_3$ on ${\mathrm{SrTiO}}_3$ substrate: A viewpoint from first principles

The intrinsic magnetic state (ferromagnetic or antiferromagnetic) of ultrathin ${\mathrm{LaMnO}}_3$ films on the most commonly used ${\mathrm{SrTiO}}_3$ substrate is a long-existing question under debate. Either strain effect or nonstoichiometry was argued to be responsible for the experimental ferromagnetism. In a recent experiment [X. R. Wang, C. J. Li, W. M. Lü, T. R. Paudel, D. P. Leusink, M. Hoek, N. Poccia, A. Vailionis, T. Venkatesan, J. M. D. Coey, E. Y. Tsymbal, Ariando, and H. Hilgenkamp, Science 349, 716 (2015)], one more mechanism, namely, the self-doping due to polar discontinuity, was argued to be the driving force of ferromagnetism beyond the critical thickness. Here systematic first-principles calculations have been performed to check these mechanisms in ultrathin ${\mathrm{LaMnO}}_3$ films as well as superlattices. Starting from the very precise descriptions of both ${\mathrm{LaMnO}}_3$ and ${\mathrm{SrTiO}}_3$, it is found that the compressive strain is the dominant force for the appearance of ferromagnetism, while the open surface with oxygen vacancies leads to the suppression of ferromagnetism. Within ${\mathrm{LaMnO}}_3$ layers, the charge reconstructions involve many competitive factors and certainly go beyond the intuitive polar catastrophe model established for ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ heterostructures. Our paper not only explains the long-term puzzle regarding the magnetism of ultrathin ${\mathrm{LaMnO}}_3$ films but also sheds light on how to overcome the notorious magnetic dead layer in ultrathin manganites.

Figure 1

Crystalline structures. (a) LMO bulk. (b) (${\mathrm{LMO})}_2$/(${\mathrm{STO})}_2$ superlattice. (c) (${\mathrm{LMO})}_2$/(${\mathrm{STO})}_2$ heterostructure with open surface. Here the ${\mathrm{TiO}}_2$ layer is the interfacial termination and thus ${\mathrm{MnO}}_2$ is the surface termination.

Figure 2

(a) The energy difference between A-AFM and FM states for LMO bulk. Different pseudopotentials and adding-$U$ methods have been compared. L, Liechtenstein's method; D, Dudarev's method. Other magnetic states (e.g., G-type AFM and C-type AFM) are also tested, which are much higher in energy and thus not shown here. The strained LMO case is also shown as the orange dashed curve. (b) The calculated band gap of bulk LMO with respect to different $U_{\mathrm{eff}}$(Mn). For comparison, several experimental values are also presented as dashed lines. (c) The optimized lattice constants of LMO for the A-AFM ground state. The experimental values [18, 68] and previous DFT values [67] are shown for comparison. (d) The optimized lattice constant of cubic STO. Here $\frac{J\left(\mathrm{Mn}\right)}{U\left(\mathrm{Mn}\right)}$ is fixed as 0.286, while $\frac{J\left(\mathrm{Ti}\right)}{U\left(\mathrm{Ti}\right)}$ is fixed as 0.273. More discussions on the choice of $\frac{J}{U}$ can be found in Supplemental Material [59].

Figure 3

Energy differences between two lowest magnetic states: in particular, C-type AFM and FM for $n=1$ and A-AFM and FM for others. Other uniform magnetic orders such as C-type AFM are also calculated, which are much higher in energy. The energy differences between A-AFM and FM in unstrained and strained LMO bulks are also shown as dashed purple and green lines, respectively. Upper inset: the formation energy of one $V_{\mathrm{O}}$ as a function of layer positions in the $n=2$ open surface case. The formation energy of $V_{\mathrm{O}}$ in the outmost layer is taken as the reference. Lower inset: sketch of C-type AFM and A-AFM.

Figure 4

Total DOS (gray shaded area) and pDOS (color lines) of LMO/STO heterostructures. (a–e) (${\mathrm{LMO})}_n$/(${\mathrm{STO})}_2$ heterostructures with open surfaces. (f–h) (${\mathrm{LMO})}_n$/(${\mathrm{STO})}_n$ superlattices. The vertical dashed line denotes the Fermi level. (i) The DOS value (per Mn) at the Fermi level as a function of LMO thickness.

Figure 5

The DOS and pDOS of Mn of nonstoichiometric (a) (${\mathrm{LMO})}_1$/(${\mathrm{STO})}_2$ and (b) (${\mathrm{LMO})}_2$/(${\mathrm{STO})}_2$ heterostructures, within which the surface oxygen is deficient.

Figure 6

Potential and electron density in LMO layers, counted from the surface or ${\mathrm{TiO}}_2$-SrO-${\mathrm{MnO}}_2$ interface. (a, b) Energy profile of O's $1s$ orbital as a function of the ${\mathrm{MnO}}_2$ layer index, which is an indication of on-site potential from electrostatic field over the heterostructures. The O in the interfacial ${\mathrm{MnO}}_2$ layer is taken as the reference. (a) Superlattices. (b) Open surface cases. Insets: The potential difference ($\mathrm{\Delta }E$) between the top and bottom Mn's as a function of thickness. (c, d) Bader charge density of each ${\mathrm{MnO}}_2$ layer. The reference density (value zero) is set as the Bader charge density for the ${\mathrm{MnO}}_2$ layer in LMO bulk. Thus, a positive (negative) value means more electrons (holes) obtained. The oscillation of Bader charge density is very clear, while the unidirectional electron transfer from $p$-type interface (and surface) to $n$-type interface is obscure.

Figure 7

Layer-resolved pDOS of the Mn $3z^2-r^2$ orbital in (a) the top and (b) the bottom ${\mathrm{MnO}}_2$ layer of vacuum/(${\mathrm{LMO})}_2$/(${\mathrm{STO})}_2$. (c) The electron density. The $3z^2-r^2$ character is obvious for the top layer.

Figure 8

Structural modulation in LMO/STO heterostructures. (a, b) Schematic of polar distortions and $M{\mathrm{O}}_6$ octahedra tilting. (c, d) Polar distortions, characterized by the displacements of $M$, as a function of layer index. (e, f) $M$-O-$M^{\prime }$ bond angles along the $c$ axis. All end points in panel (f) are Mn-O-Ti bonds. The case with a $V_{\mathrm{O}}$ is also shown in panel (e) as solid black dots. (g, h) The JT distortions in the LMO portion of vacuum/(${\mathrm{LMO})}_n$/(${\mathrm{STO})}_2$ heterostructures. For comparison, both the experimental and theoretical values for LMO bulks are also presented [18, 69].