Magnetic phase diagram and magnetoresistance of Gd-Tb-Dy-Ho-Lu hexagonal high-entropy alloy

We present a study of the magnetic phase diagram and the magnetoresistance of a Gd-Tb-Dy-Ho-Lu ideal hexagonal high-entropy alloy (HEA), composed of the elements from the heavy half of the rare earth series only. The phase diagram contains an antiferromagnetic (AFM) state, a field-induced ferromagnetic (FM) state above the AFM-to-FM spin-flop transition and a low-temperature spin-glass state. The complex phase diagram is a result of competition between the periodic potential arising from the electronic band structure that favors periodic magnetic ordering, the substitutional-disorder-induced random local potential that favors spin-glass type spin freezing in random directions, the Zeeman interaction with the external magnetic field that favors spin alignment along the field direction and the thermal agitation that opposes any spin ordering. The magnetoresistance reflects complexity of the phase diagram. Its temperature dependence can be explained by a continuous weakening and final disappearance of the periodic potential upon cooling that leads to the destruction of long-range ordered periodic magnetic structures. The magnetoresistance is large only at temperatures, where the AFM and field-induced FM structures are present and exhibits a maximum at the critical field of the AFM-to-FM transition. Within the AFM phase, the magnetoresistance is positive with a quadratic field dependence, whereas it is negative with a logarithmic-like field dependence within the field-induced FM phase. At lower temperatures, the long-range periodic spin order melts and the magnetoresistance diminishes until it totally vanishes within the low-temperature spin glass phase. The magnetoresistance is asymmetric with respect to the field sweep direction, reflecting nonergodicity and frustration of the spin system.