Kondo-lattice ferromagnets and their peculiar order along the magnetically hard axis determined by the crystalline electric field

We show that Ce- and Yb-based Kondo-lattice ferromagnets order mainly along the magnetically hard direction of the ground-state Kramers doublet determined by crystalline electric field. Here, we argue that this peculiar phenomenon, that was believed to be rare, is instead the standard case. Moreover, it seems to be independent on the Curie temperature $T_C$, crystalline structure, size of the ordered moment, and type of ground-state wave function. On the other hand, all these systems show the Kondo coherence maximum in the temperature dependence of the resistivity just above $T_C$, which indicates a Kondo temperature of a few degrees Kelvin. An important role of fluctuations is indicated by the non-mean-field-like transition in specific heat measurements as well as by the suppression of this effect by a strong Ising-like anisotropy. We discuss possible theoretical scenarios.

Figure 1

Temperature dependence of the magnetic ac susceptibility ${\chi }^{\prime }\left(T\right)$ for ${\mathrm{YbNi}}_4{\mathrm{P}}_2$, $\mathrm{Yb}{\left({\mathrm{Rh}}_{0.73}{\mathrm{Co}}_{0.27}\right)}_2{\mathrm{Si}}_2$, CeRuPO, and ${\mathrm{YbIr}}_3{\mathrm{Ge}}_7$ measured with modulated field along the two principal CEF directions ($H_{ac}\parallel c$ and $H_{ac}\perp c$) of the tetragonal crystalline structure. ${\mathrm{YbNi}}_4{\mathrm{P}}_2$ and $\mathrm{Yb}{\left({\mathrm{Rh}}_{0.73}{\mathrm{Co}}_{0.27}\right)}_2{\mathrm{Si}}_2$ graphs are reproduced from Refs. [13, 17], respectively. Strong noise is seen for CeRuPO due to the very small size of the crystal.

Figure 2

Temperature dependence of the resistivity $\rho$ divided by the room-temperature resistivity ${\rho }_{300K}$ plotted in a logarithmic scale to emphasize the maximum at $T_{\text{K}}^{*}$ in all four materials which is due to the Kondo coherence effect. ${\mathrm{YbNi}}_4{\mathrm{P}}_2$, CeRuPO, $\mathrm{Yb}{\left({\mathrm{Rh}}_{0.73}{\mathrm{Co}}_{0.27}\right)}_2{\mathrm{Si}}_2$, and ${\mathrm{YbIr}}_3{\mathrm{Ge}}_7$ graphs are reproduced from Refs. [32, 21, 33, 22], respectively.

Figure 3

Temperature dependence of the specific heat around the FM phase transition. Transition temperatures are listed in Table 1. To emphasize the presence of critical fluctuations of the ferromagnetic transition, the ${\mathrm{YbNi}}_4{\mathrm{P}}_2$ data are exemplarily plotted in a logarithmic scale and compared to a MFT. ${\mathrm{YbNi}}_4{\mathrm{P}}_2$, CeRuPO, $\mathrm{Yb}{\left({\mathrm{Rh}}_{0.73}{\mathrm{Co}}_{0.27}\right)}_2{\mathrm{Si}}_2$, and ${\mathrm{YbIr}}_3{\mathrm{Ge}}_7$ graphs are reproduced from Refs. [13, 40, 17, 22] respectively.