Different universality classes of isostructural $\mathrm{U}\mathit{TX}$ compounds $(T=\mathrm{Rh},\mathrm{Co},{\mathrm{Co}}_{0.98}{\mathrm{Ru}}_{0.02};X=\mathrm{Ga},\mathrm{Al})$

Magnetization isotherms of the $5f$-electron ferromagnets URhGa, UCoGa, and $\mathrm{U}{\mathrm{Co}}_{0.98}{\mathrm{Ru}}_{0.02}\mathrm{Al}$ were measured at temperatures in the vicinity of their Curie temperature to investigate the critical behavior near the ferromagnetic phase transition. These compounds adopt the layered hexagonal ZrNiAl-type structure and exhibit huge uniaxial magnetocrystalline anisotropy. The critical β, γ, and δ exponents were determined by analyzing Arrott-Noakes plots, Kouvel-Fisher plots, critical isotherms, scaling theory, and Widom scaling relations. The values obtained for URhGa and UCoGa can be explained by the results of the renormalization group theory for a two-dimensional (2D) Ising system with long-range interactions similar to URhAl reported by other investigators. On the other hand, the critical exponents determined for $\mathrm{U}{\mathrm{Co}}_{0.98}{\mathrm{Ru}}_{0.02}\mathrm{Al}$ are characteristic of a three-dimensional (3D) Ising ferromagnet with short-range interactions suggested in previous studies also for the itinerant $5f$-electron paramagnet UCoAl situated near a ferromagnetic transition. The change from the 2D to the 3D Ising system is related to the gradual delocalization of $5f$ electrons in the series of the URhGa, URhAl, and UCoGa to $\mathrm{U}{\mathrm{Co}}_{0.98}{\mathrm{Ru}}_{0.02}\mathrm{Al}$ and UCoAl compounds and appears close to the strongly itinerant nonmagnetic limit. This indicates possible new phenomena that may be induced by the change of dimensionality in the vicinity of the quantum critical point.

Figure 1

Modified Arrott plots for URhGa (left) and UCoGa (right). Resulting critical exponents and Curie temperature corresponding to each compound are in the figures. Magnetic curves close to Curie temperature were used for fit of Arrott-Noakes equation.

Figure 2

Logarithmic plot of magnetic isotherms of URhGa (left) and UCoGa (right). Critical isotherms for each compound are highlighted by the dashed line. The critical exponent δ from fit to critical exponent for each compound are part of the figure.

Figure 3

Kouvel-Fisher plot for spontaneous magnetization and susceptibility for URhGa (left) and UCoGa (right). The critical exponents are shown in corresponding figures.

Figure 4

The scaled magnetization plotted against the renormalized magnetic field below and above $T_{\mathrm{C}}$. Results of fit of scaling theory from Eq. (8) for both compounds are shown in figures URhGa (left) and UCoGa (right).

Figure 5

Obtained critical exponents for URhGa and UCoGa in comparison to URhAl [10] and values of three-dimensional (3D) Ising, 3D XY, 3D Heisenberg, two-dimensional Ising, and mean field models.

Figure 6

Arrott-Noakes plots (left) and logarithmic plots (right) of magnetization isotherms for $\mathrm{U}{\mathrm{Co}}_{0.98}{\mathrm{Ru}}_{0.02}\mathrm{Al}$. The results of the fit by Arrott-Noakes equation [Eq. (5)] are displayed in the left figure, while in the right figure, the result of the fit by critical isotherm can be found.

Figure 7

Kouvel-Fisher plot of $\mathrm{U}{\mathrm{Co}}_{0.98}{\mathrm{Ru}}_{0.02}\mathrm{Al}$ with results of fit of Eqs. (6) and (7) (left). Plot of the scaled magnetization vs the rescaled magnetic field for $\mathrm{U}{\mathrm{Co}}_{0.98}{\mathrm{Ru}}_{0.02}\mathrm{Al}$ (right). Results of fit of scaling theory from Eq. (8) are part of the figure.