The isomorphic collapse of crystalline lattices under pressure is a rare and intriguing phenomenon–the most famous examples being samarium sulphide and cerium metal. Both lattices are cubic under ambient conditions and collapse isomorphically under pressure, remaining cubic with ∼15% volume reduction1,2,3. In SmS the transition results from a change of the 4f chemical valence. The collapse in Ce is connected with the altering contributions of the 4f electrons to the chemical bonding, the details of which are currently much debated4,5. In contrast, YCo5 is a hexagonal metallic compound with a stable valence and no 4f electrons. Here, we present a combination of high-pressure X-ray diffraction measurements and density functional electronic-structure calculations to demonstrate an entirely different type of isomorphic transition under hydrostatic pressure of 19 GPa. Our results suggest that the lattice collapse is driven by magnetic interactions and can be characterized as a first-order Lifshitz transition, where the Fermi surface changes topologically. These studies support the existence of a bistable bonding state due to the magneto-elastic interaction.
For centuries, phase transitions in solids have played a key role in tailoring material properties, for example, in steel technology. More recently, scientists have been intrigued by isomorphic phase transitions under pressure, where a dramatic change of the electronic structure triggers a volume collapse, while the atomic arrangement in the structure is preserved. Such transitions provide a unique opportunity to study the fundamentals of chemical bonding. In general, high pressure is the most appropriate tool to study the effect of modified atomic distances on physical and chemical properties. Alternatively, similar modifications can be achieved by substituting chemically similar elements with different atomic radii. In contrast to the chemical substitution, high pressure has the advantage that the chemical bonding can be modified without changing the composition. Specifically, chemical substitution introduces disorder and local strain in the atomic lattice, whereas external pressure largely preserves the lattice homogeneity. Recent progress in high-pressure technology now makes it possible to study materials under hydrostatic compression, even at low temperatures, up to the megabar region–that is several million times the atmospheric pressure and comparable to pressures in the earth's core. In particular, itinerant magnetism of transition metals is sensitive to pressure. Iron, the prototype ferromagnetic element and main constituent of the earth's core, becomes non-magnetic under a transition pressure of about 65 GPa (0.65 Mbar)6.
Among all known elements and ordered compounds, cobalt metal exhibits the most stable magnetic behaviour, indicated by its magnetic ordering temperature TC of almost 1,400 K, higher than that of any other element or compound. Even under the extreme pressure of 120 GPa the magnetism in Co is only partially suppressed7. If diluted with moderate amounts of non-magnetic metals, Co largely retains its strong magnetic properties. The Co-rich intermetallic compounds Y2Co17 (90% Co,TC≈1,200 K) and YCo5 (83% Co,TC≈1,000 K) are strong ferromagnets with completely filled majority-spin states in the Co-3d band. This means that the Co spin moment almost retains its maximum atomic value, which is only slightly reduced by hybridization. Compounds of such compositions (SmCo5 and Sm2Co17) are frequently used in permanent-magnet applications8. In contrast, YCo2 (67% Co) shows no spontaneous magnetic order, but becomes ferromagnetic when a strong magnetic field of 69 T is applied9.
These facts make YCo5 a most suitable compound for high-pressure studies: it still has a high ordering temperature but is expected to show a much stronger sensitivity to pressure than Co metal. Previous theoretical studies10 suggested the existence of a low-moment phase of YCo5 at a volume close to 90% of that at ambient conditions. This phase has never been observed. On the other hand, the isostructural compound ThCo5 exhibits a metamagnetic transition 11,12 similar to that in YCo2, indicating that YCo5 may also be close to a magnetic instability.
First, we have studied the electronic structure of YCo5 by means of the high-precision full-potential local-orbital (FPLO) computational method (ref. 13 and http://www.fplo.de; see the Methods section) and found the transition pressure within the experimentally available region. Our results predict a collapse of the lattice connected with a reduction of the magnetic moment by one third. Although the transition is isomorphic, that is, it preserves the symmetry of both the lattice and the atomic sites (see Fig. 1), the sudden change of lattice parameters is predicted to be significantly anisotropic. Although the atomic distances in the hexagonal plane are almost unaffected, the interplane spacing shrinks considerably.
High-pressure experiments were carried out (see the Methods section) at the European Synchrotron Radiation Facility, Grenoble, to detect the predicted anomaly. The results (see Fig. 2) show a remarkable agreement between the theoretical and experimental volume dependence of the lattice parameter ratio, c/a.
From the comparison of theoretical and experimental data it is possible to assign the sudden change of c/a at 19 GPa pressure to a magneto-elastic transition. The two segments of the theoretical curve in Fig. 2, where c/a grows with increasing pressure (decreasing volume), belong to the high-moment and low-moment phases, whereas the steep drop at a cell volume of about 74 Å3 belongs to a metastable region. Such a thermodynamically unstable region is characteristic for a first-order phase transition and can be identified by calculating the free enthalpy of the system. Because it is thermodynamically impossible to transfer one phase into the other through a continuous sequence of equilibrium states, the system chooses non-equilibrium paths depending on internal and external parameters, fluctuations and real structure, including the formation of domain patterns. Thus, different paths are taken for increasing and decreasing pressure. This phenomenon, called hysteresis, is a fingerprint of first-order phase transitions. It is clearly observed in the present experiments (see the area between the blue curves in the transition region in Fig. 2).
The calculated volume reduction ΔV/V =1.3% agrees well with the experimental value, ΔV/V 1.6±0.9%, although the observed anomalies are less sharp due to small pressure inhomogeneities.
The measured X-ray diffraction patterns (see Supplementary Information, Fig. S2 and Tables S3–S5) show the predicted anomalies of the lattice parameters but no indication of any other structural or symmetry change. Consequently, the transition that YCo5 undergoes at 19 GPa is an isomorphic first-order phase transition. This is the first observation of a pressure-induced isomorphic volume collapse of an itinerant magnet. A few other systems also exhibit isomorphic transitions under pressure, for example, cerium1,2, samarium sulphide3, barium silicide Ba8Si46 (ref. 14), osmium15 and RFeO3 perovskites16. The physical mechanism of the transition in Ba8Si46 is unknown, and the transition in Os is not of first order. The mentioned perovskites are antiferromagnetic Mott insulators to be distinguished from the other metallic systems. In the first two examples, the number of electrons that contribute to the chemical bonding and the state of the 4f electrons change at the transition, thereby yielding a volume collapse of about 15%. In the present case, a completely different physical mechanism, the magneto-elastic interaction, causes the collapse. The related volume change of about 1.6% is smaller than that in Ce or SmS. This is to be expected because magnetic interactions are weak (TC≈1,000 K≈0.1 eV/kB) in relation to the energy 1 eV characteristic of the chemical bond.
At ambient conditions, YCo5 is a strong ferromagnet like pure cobalt metal, that is, its magnetism is only slightly susceptible to moderate changes of thermodynamic variables. In particular, the magnetic moment is rather stable because the majority-spin Co-3d band is completely filled (Fig. 3, black line). The application of strong pressure reduces the atomic distances and increases the overlap of the valence orbitals. This leads to a broadening of the related bands. As a consequence, the majority Co-3d band edge moves towards the Fermi energy ɛF (Fig. 3, upper panel, blue line). As soon as the sharp peak crosses the Fermi level, the majority density of states (DOS) and the minority DOS have similarly high values, leading to an instability of the thermodynamic state. Quantitatively, this scenario is described by a generalized Stoner criterion17. At the transition pressure the system transforms into a new stable state characterized by a smaller magnetic moment, a smaller volume and a reduced c/a ratio. Microscopically this is achieved by partly depopulating the majority-spin channel. The band-edge peak (Fig. 3, red line) is now situated well above the Fermi level.
The nature of the magneto-elastic coupling, responsible for the transition, can be understood in the framework of the Friedel model18,19. For the non-magnetic 4d transition-metal series (Fig. 4, black curve) the successive filling of the bonding, non-bonding and antibonding states results in a parabolic dependence of the binding energies and therefore the interatomic distances on the number of valence electrons. In the 4d series the magnetic interaction is relatively weak and cannot compete with the elastic energy. In contrast, magnetic order occurs in the second half of the 3d series. Here, the related metals show pronounced deviations from the expected parabolic behaviour (Fig. 4, red curve) towards larger distances and weaker bonds driven by a gain in magnetic energy. The magnetic order shifts the majority states to lower energy and, in the case of Co and also YCo5, increases the occupation of the antibonding majority-spin states resulting in a loss of bonding energy. The corresponding depopulation of the minority spins has less influence because it moves the non-bonding states to the Fermi level (Fig. 4, left inset). In contrast, the application of high pressure to YCo5 favours the elastic part of the energy balance and reduces the magnetic moment. Accordingly the antibonding states are depopulated (Fig. 4, right inset), the system gains additional bonding energy and the volume shrinks suddenly. Although the balance between magnetic and elastic energy is a general feature, a measurable first-order collapse is not expected in all magnetic systems. It is related to the specific electronic structure of YCo5 showing a narrow peak close to the Fermi energy (see Fig. 3). This peak originates solely from the Co-3dx z and 3dy z orbitals (see Fig. 3, inset). Their bonding increases due to the depopulation of the antibonding states leading to the observed anisotropic lattice collapse.
In 1960, Lifshitz had already predicted that elastic anomalies can occur if the topology of the Fermi surface changes under pressure while preserving the number of valence electrons20. Such electronic topological transitions are, in general, not of first order. Only when the related singularity in the DOS is exceptionally strong, does the compressibility become negative and the lattice suddenly collapses. If this transition is isomorphic, it is called a first-order Lifshitz transition20. In the case of YCo5, the topology of the Fermi surface changes (see Supplementary Information, Fig. S1) when the very strong DOS peak gets depopulated (see Fig. 3). This qualifies YCo5 as the first clear example of a first-order Lifshitz transition, related to the existence of a bistable bonding state due to magneto-elastic interaction.
Beyond its fundamental interest21, studies of magneto-elastic properties are of major importance for the development of high-tech materials. Magnetic shape-memory alloys 22,23 exhibit extraordinary magneto-elastic strains and are candidates for actuator or strain-sensor applications. On the other hand, magnetostriction is undesirable in magnetic refrigerants 24 where the aim is to minimize hysteretic losses25.
Mixtures of the elements (stated purity: Y 99.9%, Co 99.95%) in a molar ratio of 1:5 were arc-melted in purified argon atmosphere. The YCo5 button was homogenized by annealing at 1,100 ∘C for 7 days, followed by crushing and milling to a grain size smaller than 20 μm. To reduce residual mechanical stress in the grains, the powder was annealed at 800 ∘C for 30 min in Ar. X-ray diffraction revealed single-phase material. Bulk samples from the same batch were polished and characterized by optical microscopy and wavelength- dispersive electron microprobe.
High pressures were generated using a diamond anvil cell equipped with a samarium-doped strontium borate crystal as a pressure sensor26,27 and helium as a pressure-transmitting medium. Diffraction experiments using synchrotron radiation at ID09 (wavelength 41.753 pm) of the European Synchrotron Radiation Facility were carried out at various pressures (up to 33 GPa) and temperatures (sample 1 measured at T=140 K, sample 2 at T=100 K). Integration of powder rings was realized by means of the computer program Fit2d (see the Supplementary Information)28. For the determination of peak positions, indexing of diagrams, and lattice-parameter refinements, the program package WinCSD 29 was used.
A full-potential non-orthogonal local-orbital (FPLO, release 3.00-5) scheme13 was used to obtain highly accurate total energies. In the scalar-relativistic calculations within the local spin-density approximation we used the exchange and correlation potential of Perdew and Wang30. As the basis set, Co(3s,3p,4s,4p,3d,4d) and Y (4s,4p,4d,5s,5p,5d) states were chosen. The lower-lying states were considered as core states that are treated fully relativistically. A k-mesh of 46,656 (36×36×36) points in the Brillouin zone was used. Convergency with respect to basis set and k-mesh was carefully checked to ensure the required relative accuracy of 10−12 in the total energy. The calculated pressures have been offset-corrected to zero for the experimental unit cell volume.
We thank A. Möbius, H. Eschrig, and Yu. Grin for discussions. The Deutsche Forschungsgemeinschaft (Emmy Noether Programm, SFB 463) and the Alexander von Humboldt Foundation are acknowledged for financial support.
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Sequential Cobalt Magnetization Collapse in ErCo2: Beyond the Limits of Itinerant Electron Metamagnetism
Scientific Reports (2015)