Yejun Feng

Direct measurement of antiferromagnetic domain fluctuations

Measurements of magnetic noise emanating from ferromagnets owing to domain motion were first carried out nearly 100 years ago, and have underpinned much science and technology. Antiferromagnets, which carry no net external magnetic dipole moment, yet have a periodic arrangement of the electron spins extending over macroscopic distances, should also display magnetic noise. However, this must be sampled at spatial wavelengths of the order of several interatomic spacings, rather than the macroscopic scales characteristic of ferromagnets. Here we present a direct measurement of the fluctuations in the nanometre-scale superstructure of spin- and charge-density waves associated with antiferromagnetism in elemental chromium. The technique used is X-ray photon correlation spectroscopy, where coherent X-ray diffraction produces a speckle pattern that serves as a ‘fingerprint’ of a particular magnetic domain configuration. The temporal evolution of the patterns corresponds to domain walls advancing and retreating over micrometre distances. This work demonstrates a useful measurement tool for antiferromagnetic domain wall engineering, but also reveals a fundamental finding about spin dynamics in the simplest antiferromagnet: although the domain wall motion is thermally activated at temperatures above 100 K, it is not so at lower temperatures, and indeed has a rate that saturates at a finite value—consistent with quantum fluctuations—on cooling below 40 K.

Signatures of quantum criticality in pure Cr at high pressure

The elemental antiferromagnet Cr at high pressure presents a new type of naked quantum critical point that is free of disorder and symmetry-breaking fields. Here we measure magnetotransport in fine detail around the critical pressure, Pc ∼ 10 GPa, in a diamond anvil cell and reveal the role of quantum critical fluctuations at the phase transition. As the magnetism disappears and T → 0, the magntotransport scaling converges to a non-mean-field form that illustrates the reconstruction of the magnetic Fermi surface, and is distinct from the critical scaling measured in chemically disordered Cr∶V under pressure. The breakdown of itinerant antiferromagnetism only comes clearly into view in the clean limit, establishing disorder as a relevant variable at a quantum phase transition.

Order parameter fluctuations at a buried quantum critical point

Quantum criticality is a central concept in condensed matter physics, but the direct observation of quantum critical fluctuations has remained elusive. Here we present an X-ray diffraction study of the charge density wave (CDW) in 2H-NbSe2 at high pressure and low temperature, where we observe a broad regime of order parameter fluctuations that are controlled by proximity to a quantum critical point. X-rays can track the CDW despite the fact that the quantum critical regime is shrouded inside a superconducting phase; and in contrast to transport probes, allow direct measurement of the critical fluctuations of the charge order. Concurrent measurements of the crystal lattice point to a critical transition that is continuous in nature. Our results confirm the long-standing expectations of enhanced quantum fluctuations in low-dimensional systems, and may help to constrain theories of the quantum critical Fermi surface.

Invited Article: High-pressure techniques for condensed matter physics at low temperature

Condensed matter experiments at high pressure accentuate the need for accurate pressure scales over a broad range of temperatures, as well as placing a premium on a homogeneous pressure environment. However, challenges remain in diamond anvil cell technology, including both the quality of various pressure transmitting media and the accuracy of secondary pressure scales at low temperature. We directly calibrate the ruby fluorescence R1 line shift with pressure at T=4.5 K using high-resolution x-ray powder diffraction measurements of the silver lattice constant and its known equation of state up to P=16 GPa. Our results reveal a ruby pressure scale at low temperatures that differs by 6% from the best available ruby scale at room T. We also use ruby fluorescence to characterize the pressure inhomogeneity and anisotropy in two representative and commonly used pressure media, helium and methanol:ethanol 4:1, under the same preparation conditions for pressures up to 20 GPa at T=5 K. Contrary to the accepted wisdom, both media show equal levels of pressure inhomogeneity measured over the same area, with a consistent DeltaP/P per unit area of +/-1.8 %/(10(4) microm(2)) from 0 to 20 GPa. The helium medium shows an essentially constant deviatoric stress of 0.021+/-0.011 GPa up to 16 GPa, while the methanol:ethanol mixture shows a similar level of anisotropy up to 10 GPa, above which the anisotropy increases. The quality of both pressure media is further examined under the more stringent requirements of single crystal x-ray diffraction at cryogenic temperature. For such experiments we conclude that the ratio of sample-to-pressure chamber volume is a critical parameter in maintaining sample quality at high pressure, and may affect the choice of pressure medium.

Breakdown of the Bardeen–Cooper–Schrieffer ground state at a quantum phase transition

Advances in solid-state and atomic physics are exposing the hidden relationships between conventional and exotic states of quantum matter. Prominent examples include the discovery of exotic superconductivity proximate to conventional spin and charge order, and the crossover from long-range phase order to preformed pairs achieved in gases of cold fermions and inferred for copper oxide superconductors. The unifying theme is that incompatible ground states can be connected by quantum phase transitions. Quantum fluctuations about the transition are manifestations of the competition between qualitatively distinct organizing principles, such as a long-wavelength density wave and a short-coherence-length condensate. They may even give rise to ‘protected’ phases, like fluctuation-mediated superconductivity that survives only in the vicinity of an antiferromagnetic quantum critical point. However, few model systems that demonstrate continuous quantum phase transitions have been identified, and the complex nature of many systems of interest hinders efforts to more fully understand correlations and fluctuations near a zero-temperature instability. Here we report the suppression of magnetism by hydrostatic pressure in elemental chromium, a simple cubic metal that demonstrates a subtle form of itinerant antiferromagnetism formally equivalent to the Bardeen–Cooper–Schrieffer (BCS) state in conventional superconductors. By directly measuring the associated charge order in a diamond anvil cell at low temperatures, we find a phase transition at pressures of ∼10 GPa driven by fluctuations that destroy the BCS-like state but preserve the strong magnetic interaction between itinerant electrons and holes. Chromium is unique among stoichiometric magnetic metals studied so far in that the quantum phase transition is continuous, allowing experimental access to the quantum singularity and a direct probe of the competition between conventional and exotic order in a theoretically tractable material.

Pressure-tuned spin and charge ordering in an itinerant antiferromagnet.

Elemental chromium orders antiferromagnetically near room temperature, but the ordering temperature can be driven to zero by applying large pressures. We combine diamond anvil cell and synchrotron x-ray diffraction techniques to measure directly the spin and charge order in the pure metal at the approach to its quantum critical point. Both spin and charge order are suppressed exponentially with pressure, well beyond the region where disorder cuts off such a simple evolution, and they maintain a harmonic scaling relationship over decades in scattering intensity. By comparing the development of the order parameter with that of the magnetic wave vector, it is possible to ascribe the destruction of antiferromagnetism to the growth in electron kinetic energy relative to the underlying magnetic exchange interaction.

Chromium at high pressures: Weak coupling and strong fluctuations in an itinerant antiferromagnet

The spin- and charge-density-wave order parameters of the itinerant antiferromagnet chromium are directly measured with nonresonant x-ray diffraction as the system is driven toward its quantum critical point with high pressure using a diamond anvil cell. The exponential decrease of the spin and charge diffraction intensities with pressure confirms the harmonic scaling of spin and charge, while the evolution of the incommensurate ordering vector provides important insight into the difference between pressure and chemical doping as means of driving quantum phase transitions. Measurement of the charge density wave over more than two orders of magnitude of diffraction intensity provides the clearest demonstration to date of a weakly coupled BCS-type ground state. Evidence for the coexistence of this weakly coupled ground state with high-energy excitations and pseudogap formation above the ordering temperature in chromium, the charge-ordered perovskite manganites, and the blue bronzes, among other such systems, raises fundamental questions about the distinctions between weak and strong coupling.

ENERGY DISPERSIVE X-RAY DIFFRACTION OF CHARGE DENSITY WAVES VIA CHEMICAL FILTERING

Pressure tuning of phase transitions is a powerful tool in condensed matter physics, permitting high-resolution studies while preserving fundamental symmetries. At the highest pressures, energy dispersive x-ray diffraction (EDXD) has been a critical method for geometrically confined diamond anvil cell experiments. We develop a chemical filter technique complementary to EDXD that permits the study of satellite peaks as weak as 10^(-4) of the crystal Bragg diffraction. In particular, we map out the temperature dependence of the incommensurate charge density wave diffraction from single-crystal, elemental chromium. This technique provides the potential for future GPa pressure studies of many-body effects in a broad range of solid state systems.

Incommensurate antiferromagnetism in a pure spin system via cooperative organization of local and itinerant moments

Materials with strong correlations are prone to spin and charge instabilities, driven by Coulomb, magnetic, and lattice interactions. In materials that have significant localized and itinerant spins, it is not obvious which will induce order. We combine electrical transport, X-ray magnetic diffraction, and photoemission studies with band structure calculations to characterize successive antiferromagnetic transitions in GdSi. GdSi has both sizable local moments and a partially nested Fermi surface, without confounding contributions from orbital effects. We identify a route to incommensurate order where neither type of moment dominates, but is rooted in cooperative feedback between them. The nested Fermi surface of the itinerant electrons induces strong interactions between local moments at the nesting vector, whereas the ordered local moments in turn provide the necessary coupling for a spin-density wave to form among the itinerant electrons. This mechanism echoes the cooperative interactions between electrons and ions in charge-density–wave materials, and should be germane across a spectrum of transition-metal and rare-earth intermetallic compounds.

Four-probe electrical measurements with a liquid pressure medium in a diamond anvil cell

We describe a technique for making electrical transport measurements in a diamond anvil cell using an alcohol pressure medium, permitting acute sensitivity while preserving sample fidelity. The sample is suspended in the liquid medium by four gold leads that are electrically isolated by a composite gasket made of stainless steel and an alumina-loaded epoxy. We demonstrate the technique with four-probe resistivity measurements of chromium single crystals at temperatures down to 4 K and pressures above 10 GPa. Our assembly is optimized for making high precision measurements of the magnetic phase diagram and quantum critical regime of chromium, which require repeated temperature sweeps and fine pressure steps while maintaining high sample quality. The high sample quality enabled by the quasi-hydrostatic pressure medium is evidenced by the residual resistivity below 0.1 μΩ cm and the relative resistivity ratio ρ(120 K)/ρ(5 K) = 15.9 at 11.4 GPa. By studying the quality of Crs antiferromagnetic transition over a range of pressures, we show that the pressure inhomogeneity experienced by the sample is always below 5%. Finally, we solve for the Debye temperature of Cr up to 11.4 GPa using the Bloch-Gruneisen formula and find it to be independent of pressure.