Magnetism of ${\mathrm{Mg}}_{1-x}{\mathrm{Mn}}_x{\mathrm{O}}_4$ spinels by SQUID magnetometry and muon spin rotation spectroscopy

The magnetic properties of the substituted spinel ${\mathrm{Mg}}_{1-x}{\mathrm{Mn}}_x{\mathrm{Mn}}_2{\mathrm{O}}_4$, with $0⩽x⩽1$, were investigated by means of superconducting quantum interference device (SQUID) magnetometry and $\mu \mathrm{SR}$ spectroscopy. A zero-field muon spin precession is detected in the two end members and the appearance of static internal fields is evidenced in all samples below a weakly $x$-dependent ordering temperature $T_N$, different from that detected by macroscopic magnetization, $T_M$. For $x$ close to 1 a noncollinear spin structure as in ${\mathrm{Mn}}_3{\mathrm{O}}_4$ is compatible with our low temperature results. At the opposite end ($x$ close to zero) SQUID and $\mu \mathrm{SR}$ data suggest an antiferromagnetic arrangement of the Mn ions on the $B$ spinel site. A nontrivial finding is that the uniform $(q=0)$ component of the magnetic moment scales linearly with $x$. This evidence is discussed on the basis of the known magnetic structure of ${\mathrm{Mn}}_3{\mathrm{O}}_4$.

Figure 1

(Color) Sketch of the local structure of the $A$ and $B$ sublattices in the ${\mathrm{Mn}}_3{\mathrm{O}}_4$ spinel structure. In cyan color four superexchange paths are represented.

Figure 2

Molar magnetic susceptibility $\chi$ (open symbols: FC data, full symbols: ZFC data) of: (a) $x=1,0.75,0.5$ samples at $H=10\mathrm{mT}$; (b) $x=0.25,0$ samples at $H=10\mathrm{mT}$; (c) $x=0.5$ sample at three different fields.

Figure 3

Magnetic hysteresis curves at $T=2\mathrm{K}$ for all the samples investigated in this work. Looking at highest field, from top to bottom: ${\mathrm{Mn}}_3{\mathrm{O}}_4$, ${\mathrm{Mg}}_{0.25}{\mathrm{Mn}}_{2.75}{\mathrm{O}}_4$, ${\mathrm{Mg}}_{0.50}{\mathrm{Mn}}_{2.50}{\mathrm{O}}_4$, ${\mathrm{Mg}}_{0.75}{\mathrm{Mn}}_{2.25}{\mathrm{O}}_4$ and $\mathrm{Mg}{\mathrm{Mn}}_2{\mathrm{O}}_4$. Inset: relaxation of the magnetization of $\mathrm{Mg}{\mathrm{Mn}}_2{\mathrm{O}}_4$, performed at $2\mathrm{K}$ in zero field, after a ZFC process and a subsequent application of $H=5\mathrm{T}$ for $5\text{minutes}$.

Figure 4

(Color) ZF-$\mu \mathrm{SR}$ asymmetry vs time for ${\mathrm{Mn}}_3{\mathrm{O}}_4$ (bottom) and $\mathrm{Mg}{\mathrm{Mn}}_2{\mathrm{O}}_4$ (top); the transverse precession at early times is evidenced on the left, whereas the later times, rebinned on the right, show the decay of the longitudinal components; the solid curves are the best fits.

Figure 5

(Color) Temperature dependence of the fit parameters in ${\mathrm{Mn}}_3{\mathrm{O}}_4$: (a) internal fields; (b) total asymmetry, separated, below $T_N$, in total longitudinal component (blue circles) and total longitudinal plus total transverse components (red squares); (c) spin-lattice relaxation rate, with two distinct rates in the range $20–35\mathrm{K}$; (d) spin-spin relaxation rate of the majority component.

Figure 6

(Color) Temperature dependence of the fit parameters, for $\mathrm{Mg}{\mathrm{Mn}}_2{\mathrm{O}}_4$: (a) internal field $B$ (red circles) and its mean square root deviation $\Delta B$ (blue triangles), roughly coinciding above $T=36\mathrm{K}$; (b): asymmetries, total (red triangles), total longitudinal (blue circles) and the two longitudinal components below $T_N$ (left and right pointing triangles), distinguished by their relaxation rates. For ${\mathrm{Mg}}_{0.75}{\mathrm{Mn}}_{2.25}{\mathrm{O}}_4$: internal field (red triangles, left scale) and spin-lattice relaxation rate (circles, right scale); inset: relaxation rate on an expanded scale, including the GPS data below $T=36\mathrm{K}$; (d) asymmetry.

Figure 7

(Color online) Temperature dependence of the fit parameters, for ${\mathrm{Mg}}_{0.5}{\mathrm{Mn}}_{2.5}{\mathrm{O}}_4$: spin-lattice relaxation rate (a) and asymmetry (b); and for ${\mathrm{Mg}}_{0.25}{\mathrm{Mn}}_{2.75}{\mathrm{O}}_4$: spin-lattice relaxation rates (c) (notice the logarithmic scale), with two components below $T_N$, and asymmetry, (d).

Figure 8

(Color online) Evolution of magnetic parameters with composition $x$: (a) phase diagram showing the magnetic order transitions detected by muons $T_N$ (circles), and the SQUID onset temperatures $T_M$ (triangles); (b) macroscopic moment and low temperature spin structures, left, in ${\mathrm{Mn}}_3{\mathrm{O}}_4$, according to Ref. 5, and right, in $\mathrm{Mg}{\mathrm{Mn}}_2{\mathrm{O}}_4$, proposed. $T$ is the spin vector at the $A$ site, $R_{3,4}$ and $S_{5,6}$ are those at the four independent $B$ site sublattices.