We report time- and angle-resolved photoemission spectroscopy measurements on the Sb(111) surface. We observe band- and momentum-dependent binding-energy oscillations in the bulk and surface bands driven by $A_{1g}$ and $E_{g}$ coherent phonons. Whil
e the bulk band shows simultaneous $A_{1g}$ and $E_{g}$ oscillations, the surface bands show either $A_{1g}$ or $E_{g}$ oscillations. The observed behavior is reproduced by frozen-phonon calculations based on density-functional theory. This evidences the connection between electron-phonon coupling and coherent binding energy dynamics.
In photoelectron spectroscopy, the measured electron momentum range is intrinsically related to the excitation photon energy. Low photon energies $<10$ eV are commonly encountered in laser-based photoemission and lead to a momentum range that is smal
ler than the Brillouin zones of most materials. This can become a limiting factor when studying condensed matter with laser-based photoemission. An additional restriction is introduced by widely used hemispherical analyzers that record only electrons photoemitted in a solid angle set by the aperture size at the analyzer entrance. Here, we present an upgrade to increase the effective solid angle that is measured with a hemispherical analyzer. We achieve this by accelerating the photoelectrons towards the analyzer with an electric field that is generated by a bias voltage on the sample. Our experimental geometry is comparable to a parallel plate capacitor and, therefore, we approximate the electric field to be uniform along the photoelectron trajectory. With this assumption, we developed an analytic, parameter-free model that relates the measured angles to the electron momenta in the solid and verify its validity by comparing with experimental results on the charge density wave material TbTe$_3$. By providing a larger field of view in momentum space, our approach using a bias potential considerably expands the flexibility of laser-based photoemission setups.
Neutron scattering is a powerful tool to study magnetic structures and dynamics, benefiting from a precisely established theoretical framework. The neutron dipole moment interacts with electrons in materials via their magnetic field, which can have s
pin and orbital origins. Yet in most experimentally studied cases the individual degrees of freedom are well described within the dipole approximation, sometimes accompanied by further terms of a multipolar expansion that usually act as minor corrections to the dipole form factor. Here we report a unique example of neutrons diffracted mainly by magnetic octupoles. This unusual situation arises in a quantum spin ice where the electronic wavefunction becomes essentially octupolar under the effect of correlations. The discovery of such a new type of quantum spin liquid that comes with a specific experimental signature in neutron scattering is remarkable, because these topical states of matter are notoriously difficult to detect.
Quantum well states appear in metallic thin films due to the confinement of the wave function by the film interfaces. Using angle-resolved photoemission spectroscopy, we unexpectedly observe quantum well states in fractured single crystals of CeCoIn$
_5$. We confirm that confinement occurs by showing that these states binding energies are photon-energy independent and are well described with a phase accumulation model, commonly applied to quantum well states in thin films. This indicates that atomically flat thin films can be formed by fracturing hard single crystals. For the two samples studied, our observations are explained by free-standing flakes with thicknesses of 206 and 101 r{A}. We extend our analysis to extract bulk properties of CeCoIn$_5$. Specifically, we obtain the dispersion of a three-dimensional band near the zone center along in-plane and out-of-plane momenta. We establish part of its Fermi surface, which corresponds to a hole pocket centered at $Gamma$. We also reveal a change of its dispersion with temperature, a signature that may be caused by the Kondo hybridization.
Time- and angle-resolved photoemission spectroscopy is a powerful probe of electronic band structures out of equilibrium. Tuning time and energy resolution to suit a particular scientific question has become an increasingly important experimental con
sideration. Many instruments use cascaded frequency doubling in nonlinear crystals to generate the required ultraviolet probe pulses. We demonstrate how calculations clarify the relationship between laser bandwidth and nonlinear crystal thickness contributing to experimental resolutions and place intrinsic limits on the achievable time-bandwidth product. Experimentally, we tune time and energy resolution by varying the thickness of nonlinear $beta$-BaB$_2$O$_4$ crystals for frequency up-conversion, providing for a flexible experiment design. We achieve time resolutions of 58 to 103 fs and corresponding energy resolutions of 55 to 27 meV.
Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles$^1$. Theories typically define such states using gauge fields and deconfined quasiparticle excitations that emerge from a simple rule governing th
e local ground state of a frustrated magnet. For example, the 2-in-2-out ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores - a state described by a lattice gauge theory of quantum electrodynamics$^{2-4}$. However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and hidden orders$^{5-6}$. Here we show that the correlated ground state of a Ce$^{3+}$-based pyrochlore, Ce$_2$Sn$_2$O$_7$, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with the formation of a fluid-like state of matter, but the intensity distribution is weighted to larger scattering vectors, which indicates that the correlated degrees of freedom have a more complex magnetization density than that typical of magnetic dipoles in a spin liquid. The temperature evolution of the bulk properties in the correlated regime below 1 Kelvin is well reproduced using a model of dipole-octupole doublets on a pyrochlore lattice$^{7-8}$. The nature and strength of the octupole-octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a 2-plus-2-minus rule. Our work identifies Ce$_2$Sn$_2$O$_7$ as a unique example of a material where frustrated multipoles form a hidden topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.
Quantum spin ice is an appealing proposal of a quantum spin liquid - systems where the magnetic moments of the constituent electron spins evade classical long-range order to form an exotic state that is quantum entangled and coherent over macroscopic
length scales. Such phases are at the edge of our current knowledge in condensed matter as they go beyond the established paradigm of symmetry-breaking order and associated excitations. Neutron scattering experiments on the pyrochlore material Pr$_2$Hf$_2$O$_7$ reveal signatures of a quantum spin ice state that were predicted by theory.
The compounds BaDy$_2$O$_4$ and BaHo$_2$O$_4$ are part of a family of frustrated systems exhibiting interesting properties, including spin liquid-type ground states, magnetic field-induced phases, and the coexistence of short- and long-range magnetic
orders, with dominant one-dimensional correlations, which can be described as Ising $J_1-J_2$ zigzag chains along the $c$-axis. We have investigated polycrystalline samples of BaDy$_2$O$_4$ and BaHo$_2$O$_4$ with both neutron diffraction and neutron spectroscopy, coupled to detailed crystalline electric field calculations. The latter points to site-dependent anisotropic magnetism in both materials, which is corroborated by the magnetic structures we determined. The two systems show the coexistence of two different long-range orders --- two double Neel $uparrowuparrowdownarrowdownarrow$ orders in the $ab$-plane with propagation vectors $mathbf{k}_1$ = ($frac{1}{2}$,0,$frac{1}{2}$) and $mathbf{k}_2$ = ($frac{1}{2}$,$frac{1}{2}$,$frac{1}{2}$) for BaDy$_2$O$_4$, and two distinct arrangements of simple Neel $uparrowdownarrowuparrowdownarrow$ orders along the $c$-axis, both with the propagation vector $mathbf{k}_0$ = (0,0,0) for BaHo$_2$O$_4$. The order for both wave vectors in BaDy$_2$O$_4$ occurs at $T_mathrm{N}$ = 0.48 K, while in BaHo$_2$O$_4$, the first order sets in at $T_mathrm{N}sim$ 1.3 K and the second one has a lower ordering temperature of 0.84 K. Both compounds show extensive diffuse scattering which we successfully modeled with a one-dimensional axial next-nearest neighbor Ising (ANNNI) model. In both materials, strong diffusive scattering persists to temperatures well below where the magnetic order is fully saturated. The ANNNI model fits indicate the presence of sites which do not order with moments in the $ab$-plane.
We investigated the magnetic structure of the heavy fermion compound CePt$_2$In$_7$ below $T_N~=5.34(2)$ K using magnetic resonant X-ray diffraction at ambient pressure. The magnetic order is characterized by a commensurate propagation vector ${k}_{1
/2}~=~left( frac{1}{2} , frac{1}{2}, frac{1}{2}right)$ with spins lying in the basal plane. Our measurements did not reveal the presence of an incommensurate order propagating along the high symmetry directions in reciprocal space but cannot exclude other incommensurate modulations or weak scattering intensities. The observed commensurate order can be described equivalently by either a single-${k}$ structure or by a multi-${k}$ structure. Furthermore we explain how a commensurate-only ordering may explain the broad distribution of internal fields observed in nuclear quadrupolar resonance experiments (Sakai et al. 2011, Phys. Rev. B 83 140408) that was previously attributed to an incommensurate order. We also report powder X-ray diffraction showing that the crystallographic structure of CePt$_2$In$_7$ changes monotonically with pressure up to $P~=~7.3$ GPa at room temperature. The determined bulk modulus $B_0~=~81.1(3)$ GPa is similar to the ones of the Ce-115 family. Broad diffraction peaks confirm the presence of pronounced strain in polycrystalline samples of CePt$_2$In$_7$. We discuss how strain effects can lead to different electronic and magnetic properties between polycrystalline and single crystal samples.
In a quantum spin liquid, the magnetic moments of the constituent electron spins evade classical long-range order to form an exotic state that is quantum entangled and coherent over macroscopic length scales [1-2]. Such phases offer promising perspec
tives for device applications in quantum information technologies, and their study can reveal fundamentally novel physics in quantum matter. Quantum spin ice is an appealing proposal of one such state, in which the fundamental ground state properties and excitations are described by an emergent U(1) lattice gauge theory [3-7]. This quantum-coherent regime has quasiparticles that are predicted to behave like magnetic and electric monopoles, along with a gauge boson playing the role of an artificial photon. However, this emergent lattice quantum electrodynamics has proved elusive in experiments. Here we report neutron scattering measurements of the rare-earth pyrochlore magnet Pr$_2$Hf$_2$O$_7$ that provide evidence for a quantum spin ice ground state. We find a quasi-elastic structure factor with pinch points - a signature of a classical spin ice - that are partially suppressed, as expected in the quantum-coherent regime of the lattice field theory at finite temperature. Our result allows an estimate for the speed of light associated with magnetic photon excitations. We also reveal a continuum of inelastic spin excitations, which resemble predictions for the fractionalized, topological excitations of a quantum spin ice. Taken together, these two signatures suggest that the low-energy physics of Pr$_2$Hf$_2$O$_7$ can be described by emergent quantum electrodynamics. If confirmed, the observation of a quantum spin ice ground state would constitute a concrete example of a three-dimensional quantum spin liquid - a topical state of matter which has so far mostly been explored in lower dimensionalities.
