Magnetism in antiperovskite (Li$_2$\textit{M})\textit{Ch}O (\textit{M} = Fe, Mn, Co; \textit{Ch} = S, Se) diluted magnets with fixed 1/3 filling: the key role of magnetic anisotropy

Abstract: We report the magnetic properties of a series of lithium-rich antiperovskites (Li$<em>2M$)$Ch$O ($M$ = Fe, Co, Mn and $Ch$ = Se, S) where transition metal and lithium ions are randomly distributed on the X-sites of the X$_3$BA structure, thereby forming a strongly diluted magnetic sublattice. Our study hence enables us to investigate the evolution of magnetic order at fixed 1/3-filling -- which is in the vicinity but slightly above the percolation threshold -- upon variation of the spin size, the magnetic anisotropy, and the orbital configuration. The data imply the absence of a distinct Curie-Weiss behavior up to 350~K but show rather large and weakly temperature-dependent magnetic susceptibility. We observe clear signatures of long-range antiferromagnetic order evolving in the 1/3-filled and strongly diluted magnetic X-site lattice with increasing Néel temperatures from $T</em>{\rm{N}}\simeq 30$~K in (Li$<em>2$Mn)$Ch$O to $\simeq 50$~K in (Li$_2$Fe)$Ch$O and $70-90$~K in (Li$_2$Co)$Ch$O. Except for $M$ = Co, the chalcogenide has no sizable effect on $T</em>{\rm N}$. We conclude significant magnetic coupling and short-range magnetic correlations at well above $T_{\rm N}$ which is in line with the observation of a broad electron spin resonance signal at room temperature. The actual ordering temperatures are strongly diminished by magnetic dilution. While structural parameters such as the tolerance factor and bonding angles do not strongly affect $T_{\rm N}$, a key parameter is the magnetic anisotropy of the transition metals.

• The paper demonstrates long-range antiferromagnetic order in all six 1/3-filled (Li₂M)ChO compounds, with Néel temperatures rising from 28–29 K for Mn to 92 K for Co despite strong dilution near the percolation threshold.
• The study combines SQUID magnetometry, Fisher-specific-heat analysis, high-field magnetization, and ESR to show strong short-range correlations, unusually large weakly temperature-dependent susceptibility, and effective exchange strengths exceeding 100 K.
• The results identify single-ion anisotropy as the main factor controlling ordering trends: nearly isotropic Mn²⁺, intermediate-anisotropy Fe²⁺, and strongly Ising-like Co²⁺ produce progressively higher ordering temperatures, while structural changes do not explain the trend.

Overview and experimental approach

This paper reports a comparative magnetic study of the six lithium-rich antiperovskites (Li$_2M$)$Ch$O with $M$ = Fe, Mn, Co and $Ch$ = S, Se, combining static SQUID magnetometry (FC/ZFC), isothermal high-field magnetization, Fisher's specific heat $\partial(\chi T)/\partial T$, and X-band electron spin resonance (ESR). The materials crystallize in the cubic $Pm\overline{3}m$ antiperovskite X$_3$BA structure, where Li$^+$ and $M^{2+}$ ions statistically share the 3$c$ X-sites, producing a 2/3-diluted magnetic sublattice at fixed filling of exactly 1/3. The Mn- and Co-based compounds were newly synthesized by high-energy ball milling, with stoichiometry confirmed by ICP-OES and pXRD; the metastable nature of this material class inevitably produces tiny ferromagnetic impurity phases, which the authors quantify in an appendix (ranging from nearly vanishing fractions to roughly 5 wt%) and demonstrate—via high-field differential susceptibility—to contribute negligibly ($Ch$0 erg/(G$Ch$1 mol)) to the extracted intrinsic response.

The central experimental design point is that dilution is held fixed while spin size ($Ch$2, 2, 3/2 for high-spin Mn$Ch$3, Fe$Ch$4, Co$Ch$5), orbital configuration, and single-ion anisotropy are systematically varied. This isolates electronic rather than structural parameters as the origin of trends in ordering temperature.

Absence of Curie–Weiss behavior and large Pauli-like susceptibility

Across all six compounds, the intrinsic susceptibility is only weakly temperature dependent up to the measurement limit near 330 K, with no Curie or Curie–Weiss regime observable below 350 K. This is a strong claim against the prevailing model of these materials as wide-gap insulators with fully localized moments: DFT studies predict band gaps $Ch$6 eV and large local moments (e.g., ~4 $Ch$7/Fe for (Li$Ch$8Fe)SO). The measured susceptibilities, $Ch$9 erg/(G$M$0 mol), are one to two orders of magnitude larger than typical uncorrelated-metal Pauli values. Using a literature DOS estimate for (Li$M$1Fe)SO, the discrepancy would require a Stoner factor $M$2, placing the system at the verge of ferromagnetism—which the authors deem implausible.

The authors reconcile the data with localized moments through finite-cluster physics: at 1/3 occupation on the incomplete fcc lattice they calculate cluster probabilities analytically (monomers ≈ 3.9% of $M$3-sites; dimers ≈ 2%; trimers ≈ 1.1%, split into equilateral, L-shaped, linear, and other triangular configurations). A superposition of size-dependent excitation gaps could yield weakly temperature-dependent $M$4, but the small probabilities suppress isolated-cluster signatures, and the absence of any Curie tail implies monomers and odd-numbered ensembles do not behave independently—requiring non-negligible next-nearest-neighbor coupling. The absence of activated behavior also excludes a narrow-gap semiconductor scenario. Itinerant scenarios cannot be entirely ruled out (notably if Li deficiency shifts the Fermi level into the Fe 3$M$5 manifold), but would demand strong correlation effects analogous to enhanced-Pauli systems such as CoS$M$6Se$M$7 or Lu$M$8Ni$M$9B$Ch$0. No Griffiths-type power-law scaling of $Ch$1 is found.

Long-range antiferromagnetic order above percolation

Fisher's specific heat derived from FC susceptibility shows step-like anomalies in all six compounds, which prior NMR and Mössbauer work on (Li$Ch$2Fe)$Ch$3O established as signatures of long-range AFM order. The resulting Néel temperatures increase systematically with transition metal:

Compound	$Ch$4 (K)	$Ch$5 (10$Ch$6 erg/(G$Ch$7 mol))
(Li$Ch$8Mn)SO	28(2)	4.5(1)
(Li$Ch$9Mn)SeO	29(2)	4.7(2)
(Li$\partial(\chi T)/\partial T$0Fe)SO	46(2)	3.6(1)
(Li$\partial(\chi T)/\partial T$1Fe)SeO	50(2)	3.2(1)
(Li$\partial(\chi T)/\partial T$2Co)SO	67(3)	2.37(5)
(Li$\partial(\chi T)/\partial T$3Co)SeO	92(2)	5.2(1)

That long-range order exists at all is itself notable: the estimated site-percolation threshold of the 1/3-filled incomplete fcc lattice is $\partial(\chi T)/\partial T$4 (by analogy with bcc and via the Balankin formula), so the system sits just above threshold. Dilution comparisons (Fe$\partial(\chi T)/\partial T$5Zn$\partial(\chi T)/\partial T$6F$\partial(\chi T)/\partial T$7, Co$\partial(\chi T)/\partial T$8Mg$\partial(\chi T)/\partial T$9O, Fe$Pm\overline{3}m$0Al$Pm\overline{3}m$1) show that near-threshold systems retain only $Pm\overline{3}m$20.1–0.2 of their undiluted $Pm\overline{3}m$3, from which the authors infer hypothetical undiluted $Pm\overline{3}m$4O compounds would order above 300 K—implying effective couplings $Pm\overline{3}m$5 K, consistent with the absence of Curie–Weiss behavior even at room temperature. This is corroborated by cation-deficient $Pm\overline{3}m$6-Fe$Pm\overline{3}m$7SeO (2/3-filled), which orders at 104 K versus 47 K for (Li$Pm\overline{3}m$8Fe)SeO.

Anisotropy, not structure, controls the trend in $Pm\overline{3}m$9

A key negative result is that structural descriptors do not track $_3$0: bond distances, 60°/90° bond angles, and Goldschmidt tolerance factors vary appreciably between sulfides and selenides without corresponding changes in $_3$1 for $_3$2 = Mn and Fe. Instead, the authors identify single-ion magnetic anisotropy as the controlling parameter: Mn$_3$3 (3$_3$4, $_3$5) is nearly isotropic Heisenberg-like; Fe$_3$6 (3$_3$7) has intermediate anisotropy; and Co$_3$8 (3$_3$9) exhibits strong orbital contribution and Ising character. The monotonic rise of $^+$0 along Mn → Fe → Co, and the anomalous enhancement of $^+$1 upon S→Se substitution only for cobalt, are both attributed to how anisotropy modifies correlation-length growth and dilution dependence near the percolation threshold.

The ESR results directly support this assignment. (Li$^+$2Mn)SO shows a Lorentzian line with $^+$3 and linewidth $^+$4 mT at 300 K—the $^+$5 value confirming vanishing orbital momentum, and the linewidth, comparable to other paramagnetic Mn$^+$6 oxides but broadened beyond purely paramagnetic expectation, indicating residual short-range correlations well above $^+$7. The additional Dysonian component is tentatively assigned to ~1% mesoscopic metallic iron inclusions. Crucially, (Li$^+$8Fe)$^+$9O is ESR-silent at X-band, consistent with strong Fe$M^{2+}$0 single-ion anisotropy and rapid spin–lattice relaxation—providing direct spectroscopic evidence for the anisotropy hierarchy underlying the proposed mechanism.

Additional features consistent with near-threshold dilution include ZFC/FC bifurcation extending up to ~100 K (Fe) or room temperature, attributed to uncompensated moments in the short-range-ordered regime, rare-region clusters embedded in a paramagnetic background, and a weak canted moment below $M^{2+}$1 arising from quenched disorder.

Limitations and open questions

Several caveats bear directly on the conclusions. First, measurements were restricted to below ~330 K due to thermal degradation of the metastable compounds, so the claimed absence of Curie–Weiss behavior is bounded by that temperature; the intrinsic high-temperature susceptibility regime remains unexplored. Second, ferromagnetic impurities are unavoidable and only quantified indirectly through saturation magnetization and ICP-OES cross-analysis; while their high-field susceptibility contribution is shown negligible, the impurity assignments (e.g., Fe$M^{2+}$2 vs. nanoscale Fe$M^{2+}$3O$M^{2+}$4 mixtures in the Se-based samples) remain partly inferential. Third, the percolation threshold of the specific incomplete fcc lattice has not been computed exactly—it is approximated via bcc analogy and a semi-empirical formula—and the mean-field estimate $M^{2+}$5 relies on a Heisenberg model whose validity is limited precisely for the anisotropic Fe and Co cases where it matters most. Fourth, the proposed anisotropy mechanism is not yet quantitatively established: the authors note that inelastic neutron scattering, XMCD, magnetostriction combined with numerical work will be needed to disentangle anisotropy from exchange-coupling variations across the series. Finally, whether lithium deficiency induces itinerant behavior cannot be excluded from magnetization alone; temperature-dependent conductivity measurements, not yet reported for these air-sensitive materials, would settle this.

Conclusion

By exploiting the fixed 1/3 filling of the antiperovskite X-sites, this study demonstrates long-range AFM order in strongly diluted magnets sitting just above the percolation threshold, with ordering temperatures increasing from ~30 K (Mn) through ~50 K (Fe) to 70–90 K (Co). The combination of absent Curie–Weiss behavior, large weakly temperature-dependent susceptibility, and room-temperature ESR evidence points to strongly coupled ($M^{2+}$6 K), short-range-correlated localized spins in a fragmented percolating network, rather than itinerant magnetism. Within this series, structural parameters fail to explain the compositional trends, whereas the systematic variation of single-ion anisotropy—from isotropic Mn$M^{2+}$7 to strongly anisotropic Co$M^{2+}$8—emerges as the key parameter governing how dilution suppresses the ordering temperature.