A wide range of metals exhibit anomalous electrical and thermodynamic properties when tuned to a quantum critical point (QCP), although the origins of such strange metals have posed a long-standing mystery. The frequent association of strange metals with unconventional superconductivity and antiferromagnetic QCPs1,2,3,4 has led to the belief that they are highly entangled quantum states5. By contrast, ferromagnets are regarded as an unlikely setting for strange metals, because they are weakly entangled and their QCPs are often interrupted by competing phases or first-order phase transitions6,7,8. Here we provide evidence that the pure ferromagnetic Kondo lattice9,10 CeRh6Ge4 becomes a strange metal at a pressure-induced QCP. Measurements of the specific heat and resistivity under pressure demonstrate that the ferromagnetic transition is continuously suppressed to zero temperature, revealing a strange-metal behaviour around the QCP. We argue that strong magnetic anisotropy has a key role in this process, injecting entanglement in the form of triplet resonating valence bonds into the ordered ferromagnet. We show that a singular transformation in the patterns of the entanglement between local moments and conduction electrons, from triplet resonating valence bonds to Kondo-entangled singlet pairs at the QCP, causes a jump in the Fermi surface volume—a key driver of strange-metallic behaviour. Our results open up a direction for research into ferromagnetic quantum criticality and establish an alternative setting for the strange-metal phenomenon. Most importantly, strange-metal behaviour at a ferromagnetic QCP suggests that quantum entanglement—not the destruction of antiferromagnetism—is the common driver of the varied behaviours of strange metals.
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All the data supporting the findings are available from the corresponding authors upon reasonable request.
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We thank C. Krellner and M. Brando for discussions, G. Cao and Z. Wang for assisting with 3He-SQUID measurements and X. Xiao for assistance with single-crystal X-ray diffraction. This work was supported by the National Key R&D Program of China (grants 2017YFA0303100, 2016YFA0300202), the National Natural Science Foundation of China (grants U1632275, 11974306), the Science Challenge Project of China (grant number TZ2016004) and the National Science Foundation of the United States of America, grant number DMR-1830707.
The authors declare no competing interests.
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Extended data figures and tables
a, Temperature dependence of the magnetic susceptibility (χ(T)) of CeRh6Ge4 in a field of 0.1 T applied both along the c axis and in the a–b plane, where both axes are plotted on a logarithmic scale. χ(T) is anisotropic across the whole temperature range; the a–b plane corresponds to the easy direction. b, Magnetization loops measured at 3 K and 0.44 K, above and below TC, respectively. In the FM state, the magnetization increases rapidly at low fields, reaching a value of around 0.28μB per Ce atom, which probably corresponds to the ordered moment, whereas at higher fields the magnetization increases more slowly.
Temperature dependence of the resistivity (ρ(T)) of CeRh6Ge4 and for the non-magnetic analogue LaRh6Ge4, with the current along the c axis. The inset shows the magnetic contribution to the resistivity of CeRh6Ge4 (ρm), obtained from subtracting the data of LaRh6Ge4. This exhibits a broad maximum at around 80 K, probably as a consequence of both the crystalline electric field and Kondo effects.
a, Low-temperature ρ(T) of CeRh6Ge4 versus T2 under pressures up to 0.69 GPa. For clarity, the data at consecutive pressures are offset vertically by 0.2 μΩ cm. The low-temperature data in the magnetic state was fitted with a quadratic temperature dependence, ρ(T) = ρ0 + AT2, as shown by the solid black lines. b, The corresponding derivative dρ(T)/dT, where the position of TC was determined at each pressure from the position of the maximum, as indicated by the vertical arrows. a.u., arbitrary units. c, Low-temperature ρ(T) versus T2 of CeRh6Ge4 at pressures above the QCP; the data at consecutive pressures are offset vertically by 0.02 μΩ cm. The solid lines show the quadratic temperature dependence, indicating the occurrence of Fermi-liquid behaviour at low temperatures. d, Low-temperature enlargement of ρ(T) − ρ0 for two pressures either side of the QCP, where the data at 0.69 GPa are vertically offset by 0.02 μΩ cm. e, Resistivity as a function of temperature plotted as δρ = ρ − ρFL, for various pressures p. ρFL is the Fermi-liquid contribution to the resistivity, obtained from fitting the low-temperature ρ(T) with a quadratic temperature dependence. The deviation of δρ from zero indicates the onset of non-Fermi-liquid behaviour, and hence corresponds to TFL, as marked by the vertical arrows. f, Pressure dependence of the residual resistivity ρ0, obtained from analysing the low-temperature ρ(T) at various pressures, and where the error bars are smaller than the symbol size. This quantity reaches a maximum around the QCP.
a, Temperature dependence of the absolute value of the heat capacity as C/T, at various pressures below pc. For pressures up to 0.72 GPa, TC can be detected, as marked by the vertical arrows. At lower pressures this is determined from the peak positions, whereas close to pc it is determined by the intersection of the solid lines indicated in the figure. b, The data for two pressures near pc, after subtracting the data taken at 0.8 GPa to remove the logarithmic contribution to C/T. In both cases, the peak position of ΔC/T is in good agreement with the value of TC obtained from a. c, Low-temperature C(T)/T for three pressures above the QCP. The strong increase with decreasing temperature corresponds to non-Fermi-liquid behaviour, whereas the flattening of C(T)/T at low temperatures corresponds to the onset of Fermi-liquid behaviour. The position of the temperature below which Fermi-liquid behaviour occurs, TFL, is highlighted by the vertical arrows, and is determined from the deviation from the near-temperature-independent behaviour marked by the dashed lines.
The a.c. heat capacity as C/T at various pressures up to 1.69 GPa. For pressures below 0.83 GPa, the position of TC is marked by the vertical arrows. The dashed lines show the construction used to determine TC near pc. At 0.83 GPa, no transition is detected down to the lowest measured temperature, 0.3 K; instead, C/T continues to increase with decreasing temperature. At 1.69 GPa, well above the QCP, C/T shows little temperature dependence. a.u., arbitrary units.
Supplementary Methods: additional details about the theoretical Kondo lattice model utilized in the main manuscript. It includes four figures showing the results of calculations based on the model.
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Shen, B., Zhang, Y., Komijani, Y. et al. Strange-metal behaviour in a pure ferromagnetic Kondo lattice. Nature 579, 51–55 (2020). https://doi.org/10.1038/s41586-020-2052-z