Spin-polaron effective magnetic model for ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}\mathrm{Mn}{\mathrm{O}}_3$

The conventional paradigm of charge order for ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x\mathrm{Mn}{\mathrm{O}}_3$ for $x=0.5$ has been challenged recently by a Zener polaron picture emerging from experiments and theoretical calculations. The effective low energy Hamiltonian for the magnetic degrees of freedom has been found to be a cubic Heisenberg model, with ferromagnetic nearest neighbor and frustrating antiferromagnetic next nearest neighbor interactions in the planes, and antiferromagnetic interaction between planes. With linear spin wave theory and diagonalization of small clusters up to 27 sites we find that the behavior of the model interpolates between the A- and CE-type magnetic structures when a frustrating intraplanar interaction is tuned. The values of the interactions calculated by ab initio methods indicate a possible non-bipartite picture of polaron ordering differing from the conventional one.

Figure 1

Schematic illustration of the connectivity of the model: (a) effective exchange interactions between polarons (FM stands for ferromagnetic and AF for antiferromagnetic). (b) Magnetic unit cell. (c) Connectivity of the model in the planes. Interplanar interactions are AF.

Figure 2

Ground state energy and magnetization per site as a function of $J_2∕\mid J_1\mid$ for $J_3∕\mid J_1\mid =0.5$ within linear spin wave theory. Top: solid line: classical energy, dotted line: spin wave energy.

Figure 3

Dispersion relations along different directions in the Brillouin zone for $J_3∕\mid J_1\mid =0.5$ within linear spin wave theory. [(a) Top] $(k,k,\pi )$, [(b) middle] $(k,-k,\pi )$, [(c) bottom] $(0,0,k)$, straight line: $J_2∕\mid J_1\mid =0$ for top and $0⩽J_2∕\mid J_1\mid ⩽0.5$ for middle and bottom, dotted line: $J_2∕\mid J_1\mid =0.5$ for top, dashed line: $J_2∕\mid J_1\mid =1$, long-dashed line: $J_2∕\mid J_1\mid =5$.

Figure 4

Energy and nearest and next nearest neighbor correlation functions of the ground state for $s_i=\frac{7}{2}$ and a $2\times 2\times 2$ cluster as a function of $J_2∕\mid J_1\mid$. [(a) Top] $J_3∕\mid J_1\mid =0.4$ (∘) and $J_3∕\mid J_1\mid =0.5$ (◻). [(b) Bottom] correlation function for bond $J_1$ (∘), for bond $J_2$ (◻), and for bond $J_3$ (◇). The lines are guides for the eye.

Figure 5

Energy and nearest and next nearest neighbor correlation functions of the ground state for $s_i=\frac{1}{2}$ and a $2\times 2\times 2$ cluster as a function of $J_2∕\mid J_1\mid$. [(a) Top] $J_3∕\mid J_1\mid =0.4$ (∘) and $J_3∕\mid J_1\mid =0.5$ (◻). [(b) Bottom] correlation function for bond $J_1$ (∘), for bond $J_2$ (◻), and for bond $J_3$ (◇). The lines are guides for the eye.

Figure 6

Energy and nearest and next nearest neighbor correlation functions of the ground state for $s_i=\frac{1}{2}$ and a $3\times 3\times 3$ cluster as a function of $J_2∕\mid J_1\mid$. [(a) Top] $J_3∕\mid J_1\mid =0.4$ (∘) and $J_3∕\mid J_1\mid =0.5$ (◻). [(b) Bottom] correlation function for bond $J_1$ (∘), for bond $J_2$ (◻), and for bond $J_3$ (◇). The lines are guides for the eye.

Figure 7

Specific heat [(a) top] and susceptibility [(b) bottom] as function of temperature for $J_3∕\mid J_1\mid =0.5$. solid line: $J_2∕\mid J_1\mid =0.4$, dotted line: $J_2∕\mid J_1\mid =0.5$, dashed line: $J_2∕\mid J_1\mid =0.6$, long-dashed line: $J_2∕\mid J_1\mid =0.7$, dot-dashed line: $J_2∕\mid J_1\mid =0.75$, dot-long dashed line: $J_2∕\mid J_1\mid =0.8$.