Long-range magnetic order with disordered spin orientations in a high-entropy antiferromagnet

Abstract

Disorder in magnetic systems typically suppresses long-range order, promoting short-range states such as spin glasses and magnetic clusters. This is particularly prominent in high-entropy materials, characterized by the random distributions of local magnetic entities and exchange interactions. However, in rare exceptions, long-range magnetic order can persist in high-entropy systems, while the microscopic characters and underlying mechanisms remain elusive, especially the magnetic behaviors of individual elements. Here, combining neutron diffraction and resonant soft x-ray scattering, we have conducted an element-specific investigation into the magnetic order of a high-entropy honeycomb-lattice van der Waals material (Mn1/4Fe1/4Co1/4Ni1/4)PS3. Despite significant atomic disorder, long-range zigzag antiferromagnetic order is observed below 72 K, with all four transition-metal elements participating in a unified phase transition. However, the spin orientations of various elements are distinct, attributed to the competition between single-ion anisotropies and exchange interactions. Our findings showcase a novel form of long-range magnetic order with disordered spin orientations, which is synergically stabilized by distinct magnetic elements in a high entropy magnet, offering a new paradigm for understanding complex magnetic systems.

Figures (4)

• Figure 1: Magnetic properties of TMPX$_3$ and HEPS$_3$.a--d, Schematics of the magnetic structure of MnPS$_3$, FePS$_3$, CoPS$_3$, and NiPS$_3$, respectively. All spin moments lie within the $ac^*$ plane. e, We define $\Theta$ as the angle between the spin moment $\mathbf{M}$ and lattice $\mathbf{a}$ direction. f, Atomic-resolved elemental *STEM mapping of HEPS$_3$, demonstrating the random distributions of various elements. g, Magnetic susceptibility of HEPS$_3$ and other derivatives of TMPX$_3$ measured in the zero-field-cooling (ZFC) and field-cooling (FC) modes, respectively. For each material, the susceptibility exhibits an anomaly at $T_1$, and the ZFC and FC profiles split below $T_2$. h, Schematic of the magnetic structure of HEPS$_3$ determined from neutron diffraction and RSXS measurements. i, Schematic diagram showing the evolution of spin orientations with different exchange interaction ($J$) to single-ion anisotropy ($\Delta$) ratio. When $J$ is negligible, the spin moments tend to preserve their anisotropy as in the non-HE materials, e.g., Mn$^{2+}$/Fe$^{2+}$ and Co$^{2+}$/Ni$^{2+}$ being almost perpendicular and parallel to the $ab$ plane, respectively (left panel). In another aspect, dominant $J$ would enforce a universal parallel alignment (right panel). A compromised case is realized in HEPS$_3$ (middle panel, see also Supplementary Note 6).
• Figure 2: Neutron diffraction measurements on HEPS$_3$ single crystals.a, b, Neutron diffraction patterns in the $HK0$ plane collected at 250 K and 6 K, respectively, with $L$ integrated in the range of [-0.2, 0.2]. c, d, Neutron diffraction patterns in the $0KL$ plane. The black circles highlight the nuclear peaks. e, f, One-dimensional $\mathbf{Q}$ cuts along $H$ and $K$ directions, respectively, across the nuclear [$\mathbf{Q}{}=(0, 2, 0)$] and magnetic reflections [$\mathbf{Q}{}=(0, 1, 0)$] at the indicated temperatures. The solid lines are fits with Gaussian profiles, yielding FWHM (in unit of r.l.u.) of 0.0539(6) (nuclear) and 0.0496(5) (magnetic) along $H$, and 0.070(1) (nuclear) and 0.068(1) (magnetic) along $K$. g,$\mathbf{Q}$ cuts along $L$ direction across the magnetic signals. The shaded area denotes the 3D magnetic signals, which exhibit different peak widths due to different contributions of sample mosaicity. The 250 K data are treated as a background reference. Note that the intensities are presented on a log scale. h, Temperature dependence of the integrated intensities of 3D magnetic signals at $\mathbf{Q}{}=(0, 1, 1)$ and 2D magnetic signals at $\mathbf{Q}{}=(0.5, 0.5, 0)$, which corresponds to $\mathbf{Q}{}=(0, -1, 1/6)$ in another domain Lancon2016Magnetic. The solid line is a fit to $I-\mathrm{BG} \propto (T_{\mathrm{N}}-T)^{2\beta}$ (BG: background), and the dashed line is a guide for the eye. i, Schematic of the spin structure derived from the neutron diffraction refinements with $\Theta=$49$^{\circ}$, which can be regarded as an average result over all the TM elements. All the data were collected at CORELLI, including the temperature dependence. r.l.u., reciprocal lattice units.
• Figure 3: *RSXS measurements on HEPS$_3$.a, Schematic diagram of the RSXS experiment setup. Note that $\theta$ is the sample angle and $\psi$ is the azimuthal angle. Negative $K$ is defined for grazing-incidence conditions. The polarization of the outgoing photons is not distinguished. b--e, Background subtracted RSXS scans across the 2D magnetic signals at the indicated temperatures for each TM element. The solid curves are fits using pseudo-Voigt profiles. f, Temperature dependence of the fitted peak heights of different elements, indicating a unified magnetic transition. The neutron 2D signals are the same as in Fig. \ref{['fig:neutron']}h. All error bars represent 1 standard deviation. g--j, Background subtracted fix-$\mathbf{Q}$ energy dependence of the 2D magnetic signals for each TM element in HEPS$_3$ with different incident photon polarizations. Data presented in b--f were collected at REIXS beamline with $\pi$ polarization, and data in g--j were collected at 13-3 beamline at 12 K with $\psi\approx$ 0$^{\circ}$.
• Figure 4: Azimuthal dependence of the 2D magnetic signals in HEPS$_3$ for each element.$\psi=0$ corresponds to the position with $\mathbf{Q}{}=(0, 1, 0)$ lying in the scattering plane. All the data were collected at 13-3 beamline at 12 K. Note that we use a different data processing protocol here so that the intensities are not directly comparable to Fig. \ref{['fig:RSXS']}g--j (Methods).