Evolution from Ferromagnetism to Antiferromagnetism in $\mathrm{Yb}\mathbf{(}{\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{\mathbf{)}}_2{\mathrm{Si}}_2$

$\mathrm{Yb}({\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{Si}}_2$ is a model system to address two challenging problems in the field of strongly correlated electron systems. The first is the intriguing competition between ferromagnetic (FM) and antiferromagnetic (AFM) order when approaching a magnetic quantum critical point (QCP). The second is the occurrence of magnetic order along a very hard crystalline electric field (CEF) direction, i.e., along the one with the smallest available magnetic moment. Here, we present a detailed study of the evolution of the magnetic order in this system from a FM state with moments along the very hard $c$ direction at $x=0.27$ towards the yet unknown magnetic state at $x=0$. We first observe a transition towards an AFM canted state with decreasing $x$ and then to a pure AFM state. This confirms that the QCP in ${\mathrm{YbRh}}_2{\mathrm{Si}}_2$ is AFM, but the phase diagram is very similar to those observed in some inherently FM systems like ${\mathrm{NbFe}}_2$ and CeRuPO, which suggests that the basic underlying instability might be FM. Despite the huge CEF anisotropy the ordered moment retains a component along the $c$ axis also in the AFM state. The huge CEF anisotropy in $\mathrm{Yb}({\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{Si}}_2$ excludes that this hard-axis ordering originates from a competing exchange anisotropy as often proposed for other heavy-fermion systems. Instead, it points to an order-by-disorder based mechanism.

Figure 1

Phase diagram of $\mathrm{Yb}({\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{Si}}_2$. The ferromagnetic (FM) phase is separated from two antiferromagnetic phases, ${\mathrm{AFM}}_1$ and ${\mathrm{AFM}}_2$, by first order lines. The circles are taken from Refs. [18, 19]. The triangles corresponds to the peaks in ${\chi }^{\prime }(T)$ of this work. The filled point indicates a first order transition. Since we have investigated only samples with $x=0.18$ and 0.21, we do not know the exact location of the line between the FM and the ${\mathrm{AFM}}_2$ phases and we left this area uncolored.

Figure 2

Selection of measurements on $\mathrm{Yb}({\mathrm{Rh}}_{0.79}{\mathrm{Co}}_{0.21}{)}_2{\mathrm{Si}}_2$ with $B\parallel c$ and $B\perp c$. (a) Specific heat $C(T)$, (b) magnetization $M(B)$, (c),(d) ac susceptibility ${\chi }^{\prime }(T)$ and the phase diagrams (e) with $B\parallel c$ and (f) with $B\perp c$.

Figure 3

Selection of measurements on $\mathrm{Yb}({\mathrm{Rh}}_{0.82}{\mathrm{Co}}_{0.18}{)}_2{\mathrm{Si}}_2$ with $B\parallel c$. (a) Specific heat $C(T)$, (b) magnetization $M(B)$, (c),(d) resistivity $\rho (T,B)$, and the phase diagrams (e) with $B\parallel c$ and (f) with $B\perp c$.

Figure 4

Phase diagrams of $\mathrm{Yb}({\mathrm{Rh}}_{0.82}{\mathrm{Co}}_{0.18}{)}_2{\mathrm{Si}}_2$ with (a) $B\parallel c$ and (b) $B\perp c$.