In contrast to classical phase transitions driven by temperature,a quantum critical point (QCP) defines a transition at zero temperature that is driven by non-thermal parameters1,2,3. In the known quantum critical d-electron systems, tuning the electronic bandwidth by means of changing the applied pressure or unit-cell dimensions, or tuning the d-state population, is used to drive the criticality4,5,6. Here we describe how a novel chemical parameter, the breaking of bonds in Ge–Ge dimers that occurs within the intermetallic framework in SrCo2(Ge1−xPx)2, results in the appearance of a ferromagnetic (FM) QCP. Although both SrCo2P2 and SrCo2Ge2 are paramagnetic, weak itinerant ferromagnetism unexpectedly develops during the course of the dimer breaking, and a QCP is observed at the onset of the FM phase. The use of chemical bond breaking as a tuning parameter to induce QCP opens an avenue for designing and studying novel magnetic materials.
SrCo2(Ge1−xPx)2 belongs to the layered, tetragonal ThCr2Si2 structure type, which has over 600 intermetallic members. This AT2X2 structure is formed by stacking covalently bonded transition metal–metalloid T2X2 layers, made from edge-sharing TX4 tetrahedra, with ionic A atoms (see Fig. 1a inset). These compounds have attracted recent interest owing to the rich physics they exhibit, such as non-Fermi-liquid behaviour in YbRh2Si2 (ref. 7) and unconventional superconductivity in K-doped BaFe2As2 (ref. 8). The existence of a molecule-like X–X dimer that crosses the A atom layer in certain members of this family was noted 20 years ago, providing an explanation for their anomalously low ratio of stacking to in-plane lattice parameters9,10 (c/a). This X–X bonding between neighbouring T2X2 layers pulls the layers closer together and induces a relaxation of the in-plane lattice dimension, leading to what are known as collapsed tetragonal (cT) cells. In contrast, the absence of an X–X dimer results in uncollapsed tetragonal (ucT) cells. The lack of an interlayer X–X bond substantially weakens the electronic interactions between neighbouring T2X2 layers, leading to less three-dimensional (3D)-like electronic structures and Fermi surface topologies for the ucT phases compared with the cT phases11,12,13. Lattice collapse transitions from ucT to cT phases driven by applied pressure or chemical pressure were not shown to have a great impact on the physical properties of the compounds until recently14,15,16,17,18.
SrCo2Ge2 is a typical cT phase, with a c/a ratio of 2.6 due to the presence of a strong interlayer Ge–Ge bond, whereas SrCo2P2, with a c/a ratio of 3.1, is a typical ucT phase. The solid solution of these two compounds should therefore trace the crossover from cT to ucT phases, and, as shown in Fig. 1a, the SrCo2(Ge1−xPx)2 solid solution shows anomalous -shape changes in both a and c as a function of x. Although a and c vary noticeably, the absence of a region of chemical phase separation indicates that the transition from cT to ucT is continuous in nature. Figure 1b, which plots important interatomic distances and bond angles derived from structural refinements, shows that the -shape behaviour of a and c arises from the breaking of the X–X dimer on substitution of P for Ge, which begins at x∼0.4 and is completed by x∼0.8. Therefore, the structural phase diagram consists of a cT phase for x<0.4, a ucT phase for x>0.8 and an intermediate state for 0.4<x<0.8. The X–X bond length within the dimer varies from 2.9 Å for x=0 to 3.4 Å for x=1, crossing from bonded to non-bonded distances9,10. Correspondingly, the Co–Co separation within the T2X2 layers decreases as the layers separate as a result of the dimer breaking, increasing the in-plane Co–Co interactions. The size and shape of the CoX4 tetrahedron (the Co–X distances and Co–X–Co tetrahedral angle in Fig. 1b) also vary considerably in the crossover region, 0.4≤x≤0.8, as the weakening of the X–X bond allows the structure to relax to a state dominated by 2D rather than 3D bonding interactions. The crystal structure characterization therefore implies that although the electronic structures should be quite different for the cT SrCo2Ge2 and ucT SrCo2P2 phases, the properties of the solid solution should vary continuously between the two endmembers.
As shown in Fig. 2, the magnetic properties of SrCo2(Ge1−xPx)2 do not follow the simple trend implied by the structural variation. Both parent compounds, SrCo2Ge2 and SrCo2P2, are Pauli paramagnetic (PM), although the latter compound is Stoner-enhanced. These results are consistent with previous studies15,18,19. A highly unexpected FM state appears, however, for 0.35≤x≤0.7 (Fig. 2a and b). As x increases from 0 towards 1, the series exhibits spontaneous magnetization, which first appears at 2 K with a small saturated moment (μsat=0.02μB/Co) for x=0.35. This μsat increases to a maximum value (0.1μB/Co) at x=0.55 before decreasing again (see Fig. 3). For x>0.8, the FM ground state disappears entirely.
The FM ordering temperature (TC) was determined from the temperature-dependent magnetization and magnetization isotherm (Arrott plot)20 measurements (Fig. 2c). As shown in Fig. 4, TC varies in the same manner as μsat: the highest TC is 35 K for x=0.55. Figure 2d shows that the series exhibits high-temperature Curie–Weiss behaviour for x≥0.35. The effective moment (μeff) increases from 0.64μB/Co for x=0.35 to 1.7μB/Co for x=1. These μeff values are 10–30 times larger than the corresponding μsat values, placing these FM compounds solidly in the weak itinerant FM region of the Rhodes–Wohlfarth plot21.
To understand how the system evolves from Pauli PM to FM, and then back to enhanced PM with increasing x, the samples near the critical region were measured in more detail. Figure 2a,b shows that the FM ground state develops as x increases from 0.3 to 0.4. The Arrott plot measurements show that TC for x=0.35 (Fig. 3a) and 0.4 (data not shown) are 2±0.2 K and 12±1 K respectively. Figure 3b shows the low-temperature magnetic susceptibility (χ) plotted with respect to T−4/3 for x=0.3, 0.325 and 0.35. Although the χ values are highly sensitive to x, the sample with x=0.325 exhibits very close to the power-law behaviour expected near a FM QCP (ref. 1). Figure 3c shows the heat-capacity data as Cp/T versus T on semi-logarithmic axes. Initially, Cp/T is a constant at low temperatures. However, at x=0.325 and 0.35, Cp/T exhibit clear logarithmic behaviour with respect to T, which is characteristic of a system approaching a FM QCP (ref. 22). When x≥0.4, the logarithmic Cp/T behaviour is suppressed and Fermi-liquid behaviour (Cp/T=γ0+β T2) is recovered. There are no signs of spin-glass behaviour23 in any of the magnetization or heat capacity data near x=0.35. All these results demonstrate the presence of a FM QCP driven by x near x=0.325 in SrCo2(Ge1−xPx)2.
In contrast to the QCP near x=0.325, a simple crossover from the FM state to an enhanced PM state appears for x∼0.8. Figure 4b shows that TC maintains a large value (20±2 K) for x=0.7. When x>0.7, the magnetization remains large but the spontaneous magnetization disappears (Fig. 2a,b). Correspondingly, the heat capacity data show Fermi-liquid behaviour with invariant γ0 for 0.5≤x≤1.
As summarized in Fig. 4, the physical properties of SrCo2(Ge1−xPx)2 are strongly correlated with its variation in structure. When x increases, both the zero-temperature susceptibility (χT=0) and γ0 increase, but the QCP occurs exactly when the X–X dimer is beginning to break (Fig. 4b). Furthermore, the FM ground state appears only during the breaking of the dimer. When the dimer is fully broken, the FM state disappears and χT=0 decreases with increasing x, whereas γ0 is invariant. The phase diagram in Fig. 4b clearly demonstrates that the QCP and ferromagnetism are not induced by a simple electron doping effect, but rather by the breaking of the dimer. This result is consistent with continuing studies on CaCo2(Ge1−xPx)2 and BaCo2(Ge1−xPx)2 (refs 24, 25). The X–X dimer is fully intact for the whole CaCo2(Ge1−xPx)2 series, and the magnetic properties vary from non-magnetic to antiferromagnetic with no unexpected FM state in the intermediate composition region. In contrast, the X–X dimer is fully broken throughout the BaCo2(Ge1−xPx)2 series because of the large size of the Ba2+ ions, and only non-magnetic ground states are observed.
As previously reported, chemical pressure drives P–P dimer breaking in Sr1−xCaxCo2P2, which is associated with a transition from a magnetic cT phase (x=1) to a non-magnetic ucT phase (x=0). A simple explanation for the magnetic transition is based on the Zintl concept9,15; for example, the singly bonded P–P dimer in cT phases has the electron formal count (P–P)4−, whereas the non-bonded P in ucT phases has the formal electron count P26−. Charge redistribution therefore occurs in the Co2P2 layers during the lattice collapse transition, and changes in the magnetic ground state may be anticipated. A magnetic to non-magnetic transition is observed in CaFe2As2 when applied pressure induces a lattice collapse17. In contrast, SrCo2(Ge1−xPx)2 shows different behaviour: with both endmembers non-magnetic, a FM ground state arises during the dimer breaking that destabilizes the collapsed phase. Within the Zintl concept, the substitution of P for Ge in this system does not induce a formal electron count change in the d-state because the extra charge contributed by P doping is consumed through the breaking of the dimer. Therefore the unexpected ferromagnetism cannot be understood as simply being a result of a valence change of the Co.
We speculate that a possible explanation may be found by consideration of differences in the band structure between bonded and non-bonded phases26. With the presence of a covalent Ge–Ge interlayer bond, the chemical potential for SrCo2Ge2 must be located between the bonding orbitals (σ) and antibonding orbitals () of the Ge–Ge dimer. In contrast, with the lack of an interlayer P–P bond, both the σ and orbitals are fully occupied in SrCo2P2. The band must therefore straddle the chemical potential during the continuous process of dimer breaking in SrCo2(Ge1−xPx)2. A higher density of states at the Fermi level and strong electron correlations therefore might occur when the orbitals and the Co 3d orbitals, which are possibly hybridized with it, are at the chemical potential at intermediate compositions, surpassing the Stoner criterion and driving the material into a band FM state. Further theoretical treatment is needed to validate this proposed mechanism for the unexpected correlation of dimer breaking and the onset of ferromagnetism at a QCP in this system. Finally, we believe that the presence or absence of X–X bonding in ThCr2Si2-type phases, not generally taken as an influence on structure–property relationships in this large family of compounds, requires more careful consideration.
Polycrystalline samples were prepared from 1.05Sr, 2xCoP and 2−2xCoGe, as described in ref. 18, at 950–1,000 °C for two days. CoP was prepared as in ref. 27 and CoGe was made from arc-melted CoGe1.05. All the samples were characterized by laboratory X-ray powder diffraction with Cu Kα radiation (D8 focus, Bruker). Selected samples with x=0, 0.25, 0.4, 0.5, 0.55, 0.65, 0.8 and 1.0 were measured by synchrotron X-ray powder diffraction at room temperature using beam line 11-BM at Argonne National Laboratory. We analysed the structure using the program GSAS with EXPGUI (refs 28, 29). As the refined x were the same as the nominal x values within ±2% error, the nominal x values were used for all samples. All physical property characterizations were carried out on a Quantum Design Physical Property Measurement System with a 3He option and a Quantum Design Magnetic Property Measurement System.
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The authors thank J. Xiong and D. X. Qu for experimental assistance, as well as N. Ni for helpful discussion. The work at Princeton was supported by the US Department of Energy, Division of Basic Energy Sciences, Grant No. DE-FG02-98ER45706. Use of the Advanced Photon Source at Argonne National Laboratory was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357.
The authors declare no competing financial interests.
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Jia, S., Jiramongkolchai, P., Suchomel, M. et al. Ferromagnetic quantum critical point induced by dimer-breaking in SrCo2(Ge1−xPx)2. Nature Phys 7, 207–210 (2011). https://doi.org/10.1038/nphys1868