Magnetism in spin crossover systems: Short-range order and effects beyond the Heisenberg model

To study non-Heisenberg effects in the vicinity of spin crossover in strongly correlated electron systems we derive an effective low-energy Hamiltonian for the two-band Kanamori model. It contains a Heisenberg high-spin term proportional to exchange constant as well as a low-spin term proportional to spin gap parameter ${\varepsilon }_s$. Using cluster mean field theory we obtain several non-Heisenberg effects. Near the critical value of spin gap ${\varepsilon }_s^c$ there is a magnetic phase transition of first order. In the vicinity of ${\varepsilon }_s^c$ in the paramagnetic phase we observe nontrivial behavior of the Curie constant in the paramagnetic susceptibility in the wide range of temperature. Reentrant temperature behavior of nearest-neighbor spin-spin correlations is observed at ${\varepsilon }_s>{\varepsilon }_s^c$. Finally, the pressure-temperature magnetic phase diagram for ferroperriclase is obtained using the effective Hamiltonian.

Figure 1

The crystal field dependence of the two-electron local eigenstates. The red dashed line shows the ground HS term for $\mathrm{\Delta }<{\mathrm{\Delta }}_c$, the green dotted line indicates the ground LS term for $\mathrm{\Delta }>{\mathrm{\Delta }}_c$, black solid lines correspond to the high-energy singlets. Calculation has been carried out for the following parameters: $U=3\text{eV}, V=1\text{eV}, J=0.7\text{eV}$, and $J=0.7\text{eV}$.

Figure 2

The map of the LS occupation number obtained with $2\times 2$ cluster exact diagonalization.

Figure 3

(a) Average staggered magnetization $m$ and (b) LS occupation number obtained with $2\times 2$ CMF. The arrow shows the position of a tricritical point. The dashed line is the $n_{\mathrm{LS}}=0.5$ isoline.

Figure 4

Temperature dependence of the Curie constant defined by Eq. (16) for different values of spin gap (pressure) obtained with $2\times 2$ CMF (a) below, (b) above the critical pressure. The dashed lines indicate the values of the Neel temperature for the data of the same color; ${\mu }^2$ of Eq. (16) is set equal to one.

Figure 5

Bulk site's magnetization calculated in the Heisenberg limit in 2D within MF, CMF with different rectangular clusters, and RPA.

Figure 6

The same as in Fig. 5 in 3D within MF, $2\times 2\times 2$ CMF, and RPA.

Figure 7

Extrapolation to the infinite system limit for the bulk magnetization $m\left(N_c\right)$ and the critical value of the spin gap ${\varepsilon }_s^c\left(N_c\right)$ in the Heisenberg limit.

Figure 8

Bulk site's magnetization obtained within (a) MF, (b) $2\times 2$, (c) $3\times 2$, and (d) $4\times 2$ CMF. The black line shows MF second-order transition line. Arrows show the position of a tricritical point.

Figure 9

(a) Transverse $C_{\perp }$ and (b) longitudinal $C_{\parallel }$ nearest-neighbor spin correlations, obtained within $2\times 2$ CMF.

Figure 10

(a) Average sublattice magnetization $m$ calculated for ferropericlase parameters from Ref. [65] by $2\times 2$ CMF. The black line is the $n_{\mathrm{LS}}=0.5$ isoline. (b) Transverse spin correlations for the same set of parameters.