Magnetic properties of the CrMnFeCoNi high-entropy alloy

We present experimental data showing that the equiatomic CrMnFeCoNi high-entropy alloy undergoes two magnetic transformations at temperatures below 100 K while maintaining its fcc structure down to 3 K. The first transition, paramagnetic to spin glass, was detected at 93 K and the second transition of the ferromagnetic type occurred at 38 K. Field-assisted cooling below 38 K resulted in a systematic vertical shift of the hysteresis curves. Strength and direction of the associated magnetization bias was proportional to the strength and direction of the cooling field and shows a linear dependence with a slope of $0.006\pm 0.001 \mathrm{emu}\mathrm{T}$. The local magnetic moments of individual atoms in the CrMnFeCoNi quinary fcc random solid solution were investigated by ab initio (electronic density functional theory) calculations. Results of the numerical analysis suggest that, irrespective of the initial configuration of local magnetic moments, the magnetic moments associated with Cr atoms align antiferromagnetically with respect to a cumulative magnetic moment of their first coordination shell. The ab initio calculations further showed that the magnetic moments of Fe and Mn atoms remain strong (between 1.5 and $2{\mu }_{\mathrm{B}}$), while the local moments of Ni atoms effectively vanish. These results indicate that interactions of Mn- and/or Fe-located moments with the surrounding magnetic structure account for the observed macroscopic magnetization bias.

Figure 1

Schematic visualization of the 90-atom computational supercells used for our quantum-mechanical calculations with (a) all local magnetic moments of Cr, Mn, Fe, Co, and Ni atoms initially (before the full relaxation) oriented in a parallel manner in a ferromagnetic state and (b) half of the local magnetic moments within each element's sublattice initially oriented in an antiparallel manner (simulating a paramagnetic state) while the total magnetic moment is zero and is kept zero during the relaxation.

Figure 2

Temperature dependence of the lattice parameter determined by x-ray diffraction. The inset shows the measured x-ray diffraction pattern at 3 and 300 K. Curves in the inset are vertically shifted for clarity.

Figure 3

Temperature dependence of $\left\{111\right\}$ and $\left\{222\right\}$ cell parameters derived from the neutron diffraction data.

Figure 4

Temperature dependence of magnetic moment measured with decreasing temperature in zero field (blue data points), with increasing temperature after zero field cooling in 100 Oe, and with increasing temperature after 5 T (green data points) field cooling in 100 Oe.

Figure 5

Temperature dependencies of magnetic moment measured after zero field cooling with increasing temperature in 50, 100, 200, and 500 Oe magnetic field.

Figure 6

Field dependence of magnetic moment at 120, 180, 210, and 240 K after zero field cooling (a). Field dependence of magnetic moment at 5, 30, and 50 K after zero field cooling (b).

Figure 7

Temperature dependence of dc susceptibility $dMdH$.

Figure 8

Sketch of the relaxation measurement procedure (a). Relaxations of magnetic moment for various waiting times $t_{\mathrm{w}}$ at 70 K (b).

Figure 9

Magnetic moment vs magnetic field measured at 5 K after zero field cooling (ZFC) and field cooling in +5 T and $-5$ T.

Figure 10

Magnetic moment vs magnetic field measured at 70 K after ZFC and field cooling in +5 T and $-5$ T.

Figure 11

Mössbauer spectra taken at 5 K with and without external magnetic field. (a) Measurements were assisted by external magnetic fields 0 and 300 Oe. (b) Measurements were assisted by external magnetic fields 50 kOe. The green data were acquired after ZFC; the orange data correspond to magnetic state established after FC with 50 kOe. The smooth curves were fitted to the individual experimental data sets using the confit program [42].

Figure 12

Temperature dependence of relative electrical resistivity $R\left(T\right)R$(300) without external magnetic field.

Figure 13

Temperature dependence of electrical resistivity in external magnetic field 5 T (red line) and the absolute value of the difference between the measurements in 0 T and 5 T (blue circles).

Figure 14

Magnetoresistance at various temperatures.

Figure 15

Changes of magnetoresistance slope at various temperatures.

Figure 16

Schematic visualization (a) of the quantum-mechanically computed local atomic magnetic moments in the 90-atom computational supercell after a full optimization. The magnitude of the local moments is depicted by the size of the corresponding atomic spheres. Some local magnetic moments reversed their orientation to an antiparallel one (with respect to the initial parallel orientation) and these are shown by brighter colors [compared with those used in Fig. 1]. In particular, Mn atoms with the original orientation are depicted by darker violet color while those with the antiparallel orientation are shown by lighter violet color. Cr atoms with antiparallel orientation of the local magnetic moments are depicted by light blue color (only one Cr atom kept the initial orientation of the local magnetic moment and it is shown by a darker-blue sphere). One Fe atom also reoriented its magnetic moment and it is shown as a small lighter-brown sphere close to the center of the cell. Element-resolved distributions (b) of the values of local magnetic moments in the final quantum-mechanically computed state depicted in part (a) [negative values indicate antiparallel orientation of the final moments with respect to the initial one seen in Fig. 1].

Figure 17

(a) Same as in Fig. 16 but for the initially antiparallel orientation of local magnetic moments [see Fig. 1].

Figure 18

Number of FM and AFM interactions between a central atom and its first coordination shell sorted according to the chemistry of the central atoms and the sign of the central magnetic moment (plus for “up” and minus for “down” orientation). Red and blue columns represent, respectively, the number of ferromagnetic and antiferromagnetic interactions in the initial ferromagnetic arrangement (IFMA) state while light red and light blue columns correspond to similar frequencies in the initial antiferromagnetic arrangement (IAMA) state; see text for details.