Doped ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$: Not Only Ferromagnetic Correlations but Ferromagnetic Order

${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ is a prototypical system for studying unconventional antiferromagnetic quantum criticality. However, ferromagnetic correlations are present which can be enhanced via isoelectronic cobalt substitution for rhodium in $\mathrm{Yb}({\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{Si}}_2$. So far, the magnetic order with increasing $x$ was believed to remain antiferromagnetic. Here, we present the discovery of ferromagnetism for $x=0.27$ below $T_C=1.30\mathrm{K}$ in single crystalline samples. Unexpectedly, ordering occurs along the $c$ axis, the hard crystalline electric field direction, where the $g$ factor is an order of magnitude smaller than in the basal plane. Although the spontaneous magnetization is only $0.1{\mu }_B/\mathrm{Yb}$ it corresponds to the full expected saturation moment along $c$ taking into account partial Kondo screening.

Figure 1

(a) Excerpt of the magnetic phase diagram of $\mathrm{Yb}({\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{Si}}_2$ from Ref. 30. The data points correspond to the transition temperatures $T_L$ and $T_N$, respectively. The arrow marks the position of $\mathrm{Yb}({\mathrm{Rh}}_{0.73}{\mathrm{Co}}_{0.27}{)}_2{\mathrm{Si}}_2$. (b) Real part ${\chi }^{\prime }(T)$ of the susceptibility for $x=0.27$ in different magnetic fields with $B\parallel c$. At zero field a sharp peak is observed at $T_C=1.30\mathrm{K}$. With increasing magnetic field the peak decreases rapidly and its position shifts towards higher temperatures. (c) Temperature dependence of the imaginary part ${\chi }^{\prime \prime }(T)$.

Figure 2

(a) Comparison of the susceptibility along (${\chi }^{\prime }\parallel c$) and perpendicular (${\chi }^{\prime }\perp c$) to the $c$ direction in zero external magnetic field. Close to $T_C$, the susceptibility of the CEF hard direction ${\chi }^{\prime }\parallel c$ becomes much larger than ${\chi }^{\prime }\perp c$. (b) Isothermal magnetization curves for different temperatures with $B\parallel c$. The data were measured using different instruments. (c) Isothermal magnetization curves for different temperatures with $B\perp c$.

Figure 3

Specific heat $C/T$ vs $T$ of $\mathrm{Yb}({\mathrm{Rh}}_{0.73}{\mathrm{Co}}_{0.27}{)}_2{\mathrm{Si}}_2$ in different magnetic fields. At $B=0$, $C(T)/T$ features a mean-field-like anomaly at $T_C=1.30\mathrm{K}$. Increasing $B$, the anomaly is shifted towards higher temperatures. Inset: $C(T)/T$ in zero field down to 0.03 K. The solid line is a fit to the magnon contribution and the shaded area depicts a nuclear contribution (see main text).

Figure 4

Magnetization as a function of magnetic field $B\parallel c$ at $T=1.8\mathrm{K}$. The Van Vleck contribution ${\chi }_{\mathrm{VV}}=0.172\times {10}^{-6}{\mathrm{m}}^3/\mathrm{mol}$ was subtracted from the raw data, leaving a saturation magnetization at 7 T of about $0.11{\mu }_B/\mathrm{Yb}$. Inset: data of ${\chi }_{\mathrm{DC}}={\mu }_{0}M/B$ between 2 and 300 K. Below 20 K a Curie-Weiss fit (solid line) was carried out as described in the main text.