Mean field magnetism and spin frustration in a double perovskite oxide with compositional complexity

Abstract

The rise of high-entropy oxides as a major functional materials design principle in recent years has prompted us to investigate how compositional disorder affects long-range magnetic ordering in double perovskite oxides. Since ferromagnetic insulators are emerging as an important platform for lossless spintronics, we consider the $RE_2$NiMnO$_6$ ($RE$ : rare-earth) family and investigate single-crystalline films of (La$_{0.4}$Nd$_{0.4}$Sm$_{0.4}$Gd$_{0.4}$Y$_{0.4}$)NiMnO$_{6}$ grown on SrTiO$_3$ (001) substrates in this work. Despite configurational disorder and high cationic size variance at the $RE$ site, the material exhibits robust ferromagnetic ordering with a Curie temperature ($T_\mathrm{c}$) of approximately 150 K. This $T_\mathrm{c}$ is consistent with the expectation based on consideration of the average ionic radii of the rare-earth ($RE$) sites in the bulk $RE_2$NiMnO$_6$. Below $T_\mathrm{c}$, Raman spectroscopy measurement finds a deviation from anharmonic behavior, where the phonon renormalization aligns with a mean-field approximation of spin-spin correlation. At lower temperature, magnetic $RE$ ions also contributed to the magnetic behavior and the system displays a reentrant spin-glass-like behavior. This study demonstrates that while a mean-field approach serves as a viable starting point for predicting the long-range transition temperature, microscopic details of the complex magnetic interactions are essential for understanding the low-temperature phase.

Figures (6)

• Figure 1: Film characterization and electronic structure: (a) Schematic depicting the exchange coupling in a square lattice with (a) one kind of atom exhibiting uniform nearest neighbour interactions (b) random distribution of five different kinds of atoms with different nearest neighbour couplings. (c) Crystal structure of an Ni-Mn ordered $RE^5$NMO where the $A$ site is shown for a random distribution of 5 $RE$ cations [Legend for colors representing each $RE$ cation has been shown at the bottom].(d) XRR experimental data and fitting for 6 nm $RE^5$NMO film on STO. (e) The reflectance data were used to derive the Kubelka-Munk function, which is an absorption equivalent commonly used for the diffused reflectance mode given by, $F$($R$) = (1-$R^2$) / 2$R$, where $R$ is the reflectance Lopez:2012p1. The Tauc relation using the reflectance mode is given by $[\left[F(R) \cdot h\nu\right]^n = A(h\nu - E_g)$] where, $F$($R$) is the Kubelka-Munk function described above, $A$ is a characteristic constant independent of the photon energy, $h\nu$ is the photon energy and $E_g$ is the band gap Tauc:1966p627. We use $n$ = 2 here as $RE_2$NiMnO$_6$ exhibit direct optical band gaps Arima:1993p17006Yi:2022p979. The black line is the linear extrapolation for the Tauc plot to find the band gap. (f) XRD for 6 nm (upper panel) and 100 nm (lower panel) $RE^5$NMO film on STO, * denotes the film peak.
• Figure 2: Long range magnetic ordering: XAS spectra for (a) Ni $L_{3,2}$ edge; Inset : zoomed $L_2$ edge highlighting the characteristic Ni$^{2+}$ splitting, and (b) Mn $L_{3,2}$ edge. The reference for Ni$^{2+}$ and Mn$^{4+}$ have been shown for ease of comparison adapted from Ref. Bhattacharya:2025p176201 corresponding to the spectra for a 20 uc Nd$_2$NiMnO$_6$ film on NdGaO$_3$ substrate. $\chi$ vs $T$ for both ZFC and FC conditions recorded in the warming and cooling cycles respectively, under fields of 50 Oe and 1000 Oe applied (c) in-plane to the film ($H \perp c$) (d) out-of-plane to the film ($H$$\parallel$$c$), where $c$ is the out-of-plane crystallographic direction. The schematic of the measurement geometry have been shown in the inset. (e) Temperature derivative of susceptibility, $d\chi/dT$, under 1000 Oe ($H \perp \mathrm{c}$), highlighting the Curie temperature ($T_\mathrm{c}$) and lower temperature anomaly (marked by arrow, $T^*$). (f) $\chi^{-1}$ as a function of temperature for $H \perp c$ under 1000 Oe, fitted with a modified Curie–Weiss formula (black curve).
• Figure 3: Temperature dependence of $A_\mathrm{g}$ raman mode: (a) Temperature-dependent Raman spectra of $RE^5$NMO measured from 4.2 K to 300 K, showing the evolution of the $A_\mathrm{g}$ phonon mode. (b) Temperature dependence of the $A_\mathrm{g}$ mode peak position, fitted using an anharmonic phonon decay model (black curve). FMI and PMI represent ferromagnetic insulating and paramagnetic insulating states respectively. (c) Comparison of phonon frequency shift $\Delta \omega(T)$, obtained by subtracting the peak positions derived from Lorentzian fitting, from the values obtained from anharmonic model, with $M^2(T)/M_{\mathrm{max}}^2$.
• Figure 4: Ferromagnetic hysteresis and Ni/Mn coupling: (a) $M$-$H$ curves at 2 K, 10 K, 50 K, and 100 K for $H \perp c$. Inset: Corresponding zoomed $M$-$H$ curves highlighting the hysteresis. Right and left circularly polarized XAS spectra (denoted by $\mu^+$ and $\mu^-$ respectively) along with their difference XMCD signal at (b) Ni $L_\mathrm{3,2}$ and (c) Mn $L_\mathrm{3,2}$ edge exhibiting ferromagnetic coupling.
• Figure 5: XMCD at $RE$ edges: Right and left circularly polarized XAS spectra measured under 6 Tesla magnetic field for the $RE$ edges, along with their difference XMCD signal at (a) Nd $M_\mathrm{4,5}$, (b) Sm $M_\mathrm{4,5}$, and (c) Gd $M_\mathrm{4,5}$ edges.