Conical order, magnetic compensation, and sign reversible exchange bias in spinel structured $A{B}_2{\text{O}}_4$ compounds: A Monte Carlo study

$A{B}_2{\mathrm{O}}_4$ are a special class of spinel structured compounds exhibiting unique multiferroic properties. Recent experimental observation confirms switchable polarization in $A{\text{Cr}}_2{\text{O}}_4$ $(A=\text{Co}, \mathrm{Mn}, \mathrm{Fe})$, arising out of noncollinear magnetic spin order. In this paper we unfold the microscopic origin behind such magnetic spin order, hysteresis, polarization, and the so-called magnetic compensation effect in $A{\text{Cr}}_2{\text{O}}_4$ $(A=\text{Co}, \mathrm{Mn}, \mathrm{Fe}, \mathrm{Ni})$ using Monte Carlo simulation. We have carefully constructed a set of exchange interaction parameters, which help to explain various experimental findings such as magnetization vs temperature $\left(T\right)$, conical stability, magnetic ordering, and polarization in a representative compound ${\text{CoCr}}_2{\text{O}}_4$. When substituted with Fe, ${\text{CoCr}}_2{\text{O}}_4$ shows few exotic phenomena such as sign reversible exchange bias effect and magnetic compensation. ${\text{CoMn}}_2{\text{O}}_4$ and ${\text{CoFe}}_2{\text{O}}_4$ are two other compounds in the spinel family where we found no conical spin order and polarization, and thus facilitate a distinct contrast compared to others.

Figure 1

Temperature dependence of magnetization for six spinel compounds $A{B}_2{\text{O}}_4$. Red line shows the calculated magnetization and plus $(+)$ symbol indicates experimental data [4, 28].

Figure 2

Total and atom projected magnetization ($M$) vs $T$ for $\mathrm{Co}{\mathrm{Mn}}_2{\mathrm{O}}_4$. The transition temperature ($T_c$) is evaluated from the Mn-projected $M$ vs $T$ curve, which is the dominant contributor of magnetism in this system.

Figure 3

The calculated magnetic order for six spinel compounds: (a) ${\text{MnCr}}_2{\text{O}}_4$, (b) ${\text{FeCr}}_2{\text{O}}_4$, (c) ${\text{CoCr}}_2{\text{O}}_4$, (d) ${\text{NiCr}}_2{\text{O}}_4$, (e) ${\text{CoMn}}_2{\text{O}}_4$, and (f) ${\text{CoFe}}_2{\text{O}}_4$.

Figure 4

Sign reversible exchange bias effect (shift of the origin of hysteresis with varying temperature) in ${\text{CoCr}}_2{\text{O}}_4$ with ${\widehat{J}}_{BB}$/${\widehat{J}}_{AB}=1.41$.