Tuning magnetism by Kondo effect and frustration

Heavy-fermion systems are an ideal playground for studying the quantum phase transition (QPT) between paramagnetic and magnetically ordered ground states arising from the competition between Kondo and RKKY interactions [1]. Two different routes have been identified by various experiments, i. e., the more traditional spin-density-wave (SDW) [2] and the Kondo-breakdown [3] approaches. However, up to now an \textit{a-priori} assignment of a given system to these different routes has not been possible. Yet another route to quantum criticality not included in the above approaches might be geometric frustration of magnetic moments, a route well known for insulating magnets with competing interactions [4]. First experiments on metallic systems have recently been conducted. In the canonical partially frustrated antiferromagnetic system CePd$_{\mathrm{1-x}}$Ni$_{\mathrm{x}}$Al, the N\'{e}el temperature $T_{\mathrm{N}}(x)$ decreases, with $T_{\mathrm{N}}\to $ 0 at the critical concentration $x_{c}\approx $ 0.144. The low-temperature specific heat $C(T)$ evolves toward $C$/$T\alpha $ ln($T_{\mathrm{0}}$/$T)$ for $x\to x_{c}$ [5]. The unusual $T$ dependence of $C$/$T$ is compatible with the Hertz-Millis-Moriya (HMM) scenario of quantum criticality [2] if the quantum-critical fluctuations are two-dimensional in nature. Here two-dimensionality might arise from antiferromagnetic planes that are effectively decoupled by the frustrated Ce atoms in between. An exciting possibility is that the planes of frustrated Ce moments form a two-dimensional spin liquid. In the prototypical heavy-fermion system CeCu$_{\mathrm{6-x}}$Au$_{\mathrm{x}}$ the experiments by Schr\"{o}der et al.[6] provided the initial evidence of local quantum criticality. While concentration and pressure tuning of the quantum phase transition (QPT) are described by this scenario, magnetic-field tuning the QPT is in line with the SDW scenario [7]. Elastic neutron scattering experiments on CeCu$_{\mathrm{5.5}}$Au$_{\mathrm{0.5}}$ under hydrostatic pressure $p$ [8] show that at $p=$ 8 kbar, $T_{\mathrm{N}}$ and the magnetic propagation vector attain almost the values of CeCu$_{\mathrm{5.7}}$Au$_{\mathrm{0.3}}$. This $x-p$ analogy away from the QPT is highly remarkable since the ambient-pressure magnetic structures for $x=$ 0.3 and 0.5 are quite different. These results give clues to a general ($x$,$p$,$B)$ phase diagram at $T=$ 0 and might explain the existence of different universality classes. \\[4pt] [1] H. v. L\"{o}hneysen et al., Rev. Mod. Phys. \textbf{79}, 1015 (2007).\\[0pt] [2] J. A. Hertz, Phys. Rev. B \textbf{14}, 1165 (1976); A. J. Millis, Phys. Rev. B \textbf{48}, 7113 (1993); T. Moriya and T. Takamoto, J. Phys. Soc. Jpn. \textbf{64}, 960 (1995).\\[0pt] [3] Q. Si et al., Nature \textbf{413}, 804 (2001).\\[0pt] [4] B. Keimer and S. Sachdev, Physics Today \textbf{64} (2), 29 (2011).\\[0pt] [5] V. Fritsch et al., arXive 1301.6062, submitted for publication (2013).\\[0pt] [6] A. Schr\"{o}der et al., Nature \textbf{407}, 351-355 (2000).\\[0pt] [7] O. Stockert et al., Phys. Rev. Lett. \textbf{99}, 237203 (2007).\\[0pt] [8] A. Hamann et al., Phys. Rev. Lett. \textbf{110}, 096404 (2013).