Evolution of magnetic and structural transitions and enhancement of magnetocaloric effect in ${\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x{\mathrm{V}}_2{\mathrm{O}}_4$

Magnetic, structural, and magnetocaloric properties have been investigated for a solid-solution system, ${\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x{\mathrm{V}}_2{\mathrm{O}}_4$ ($0.0\le x\le 1.0$) with a spinel structure. As orbital-active ${\mathrm{Fe}}^{2+}$ ions are partially substituted with orbital-inactive ${\mathrm{Mn}}^{2+}$ ions, various interactions, such as the Jahn–Teller interaction, spin-orbit coupling, and the exchange interaction, compete with each other, giving rise to a rich magnetic and structural phase diagram. The magnetocaloric effect exhibits two peaks as a function of temperature for $x\le 0.9$, associated with a higher-temperature ferrimagnetic transition, and with a lower-temperature concomitant spin-canting and orbital-ordering (mostly lattice-structural) transition of the V site. The large magnetocaloric effect as observed in $\mathrm{Mn}{\mathrm{V}}_2{\mathrm{O}}_4$ can thus be attributed to the sum of the entropy changes upon the merged phase transition at $T_{\mathrm{N}1}\sim T_{\mathrm{N}2}$.

Figure 1

(a) Schematic of spinel structure composed of tetrahedral $A$O${}_4$ ($A=\text{Fe}$, Mn) and octahedral VO${}_6$ units. (b) Ground-state (i.e., $T<T_{\mathrm{N}2}$) spin and orbital configuration of Fe${}^{2+}$, Mn${}^{2+}$, and V${}^{3+}$ ions in FeV${}_2$O${}_4$ and MnV${}_2$O${}_4$ as reported in Ref. [11]. Two electrons of V site uniformly occupy $|xy\rangle$ state and $|yz\rangle$ + $i|zx\rangle$ state in the case of FeV${}_2$O${}_4$ while alternately occupying $|xy\rangle$ and $|yz\rangle$ states at V1 site, and $|xy\rangle$ and $|zx\rangle$ states at the V2 site in the case of MnV${}_2$O${}_4$, where V1 and V2 sites are the two sites connected with 4${}_1$ operation in the T3 phase with $I{4}_1/a$ space group. Note that the notation for the crystal axes here is different from that used in Ref. [11], but the same as in Ref. [18].

Figure 2

(a) Magnetic and structural phase diagram of Fe${}_{1-x}$Mn${}_x$V${}_2$O${}_4$. (b) Contour plot of the magnetocaloric effect or isothermal entropy change ($-\Delta S$) of Fe${}_{1-x}$Mn${}_x$V${}_2$O${}_4$ for a field change from 0 to 5 T.

Figure 3

Temperature dependence of (a) magnetization at $H=0.3$ T and (b) magnetocaloric effect ($-\Delta S$) for a field change from 0 to 5 T for selected samples of Fe${}_{1-x}$Mn${}_x$V${}_2$O${}_4$. The blue and purple arrows indicate the ferrimagnetic ($T_{\mathrm{N}1}$) and V spin-canting ($T_{\mathrm{N}2}$) transitions, respectively.

Figure 4

(a) Temperature dependence of the ratio of the $c$-axis and the $a$-axis lattice parameters for several samples. (b) The ratio of V–O bond length along the $c$ axis and within the $ab$ plane ($\equiv Q$) is plotted against temperature for several $x$ members of Fe${}_{1-x}$Mn${}_x$V${}_2$O${}_4$. $\Delta Q$ denotes the difference between the $Q$ values at low temperature and that just above $T_{\mathrm{N}2}$, as indicated by dashed lines. The respective $Q$ values above the ferrimagnetic ($T_{\mathrm{N}1}$) transition (=1) are also indicated by a dashed line as a reference. Both in panels (a) and (b), blue and purple arrows indicate the ferrimagnetic ($T_{\mathrm{N}1}$) and V spin-canting ($T_{\mathrm{N}2}$) transitions, respectively.

Figure 5

(a) Mn concentration ($x$) dependence of the peak value of the magnetocaloric effect associated with the ferrimagnetic ($T_{\mathrm{N}1}$) and V-spin canting ($T_{\mathrm{N}2}$) transitions in Fe${}_{1-x}$Mn${}_x$V${}_2$O${}_4$. The sum of them is also plotted. (b) Magnetocaloric peak values at $T_{\mathrm{N}1}$ are plotted against the square of the magnetization at $T_{\mathrm{N}1}$ and at $H=5$ T. (c) Magnetocaloric peak values at $T_{\mathrm{N}2}$ are plotted against square of magnitude of the distortion ($\Delta Q$) of the VO${}_6$ octahedra across the V-spin-canting transitions. For the definition of $\Delta Q$, see main text. In panels (b) and (c), the ferrimagnetic (light-red dotted lines) and spin-canting-plus-lattice (light-blue solid lines) contributions to $-\Delta S$ of MnV${}_2$O${}_4$ at $T_{\mathrm{N}1}\sim T_{\mathrm{N}2}$ are also indicated.