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Stock, C.

Publications and source records attributed to Stock, C..

Spin-orbital correlations from complex orbital order in MgV 2⁢ O 4

MgV 2 ⁢O 4 is a spinel based on magnetic V 3+ ions, which host both spin (𝑆 = 1) and orbital (𝑙 eff = 1) moments. Owing to the underlying pyrochlore coordination of the magnetic sites, the spins in MgV 2 ⁢O 4 only antiferromagnetically order once the frustrating interactions imposed by the 𝐹⁡𝑑⁢$\overline{3}$⁢𝑚 lattice are broken through an orbitally-driven structural distortion at T 𝑆 ≃ ⁢60 K. Consequently, a Néel transition occurs at T 𝑁 ≃ ⁢40 K. Low-temperature spatial ordering of the electronic orbitals is fundamental to both the structural and magnetic properties; however, considerable discussion on whether it can be described by complex or real orbital ordering is ambiguous. We apply neutron spectroscopy to resolve the nature of the orbital ground state and characterize hysteretic spin-orbital correlations using x-ray and neutron diffraction. Neutron spectroscopy finds multiple excitation bands and we parametrize these in terms of a multilevel (or excitonic) theory based on the orbitally degenerate ground state. Meaningful for the orbital ground state, we report an “optical-like” mode at high energies that we attribute to a crystal-field-like excitation from the spin-orbital 𝑗 eff = 2 ground-state manifold to an excited 𝑗 eff =1 energy level. We parametrize the magnetic excitations in terms of a Hamiltonian with spin-orbit coupling and local crystalline electric field distortions resulting from deviations from perfect octahedra surrounding the V 3+ ions. We suggest that this provides compelling evidence for complex orbital order in MgV 2⁢ O 4 . We then apply the consequences of this model to understand hysteretic effects in the magnetic diffuse scattering where we propose that MgV 2⁢ O 4 displays a high-temperature orbital memory of the low-temperature spin order.

Frustrated magnetism↗

Orbital character of the spin-reorientation transition in TbMn 6 Sn 6

Ferromagnetic (FM) order in a two-dimensional kagome layer is predicted to generate a topological Chern insulator without an applied magnetic field. The Chern gap is largest when spin moments point perpendicular to the kagome layer, enabling the capability to switch topological transport properties, such as the quantum anomalous Hall effect, by controlling the spin orientation. In TbMn 6 Sn 6 , the uniaxial magnetic anisotropy of the Tb 3+ ion is effective at generating the Chern state within the FM Mn kagome layers while a spin-reorientation (SR) transition to easy-plane order above T SR = 310 K provides a mechanism for switching. Here, we use inelastic neutron scattering to provide key insights into the fundamental nature of the SR transition. The observation of two Tb excitations, which are split by the magnetic anisotropy energy, indicates an effective two-state orbital character for the Tb ion, with a uniaxial ground state and an isotropic excited state. The simultaneous observation of both modes below T SR confirms that orbital fluctuations are slow on magnetic and electronic time scales < ps and act as a spatially-random orbital alloy. A thermally-driven critical concentration of isotropic Tb ions triggers the SR transition.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Metastable antiphase boundary ordering in CaFe 2 O 4

CaFe 2 O 4 is an $\textit{S}$ = 5/2 antiferromagnet exhibiting two magnetic orders that shows regions of coexistence at some temperatures. Using a Green’s function formalism, we model neutron scattering data of the spin wave excitations in this material, elucidating the microscopic spin Hamiltonian. In doing so, we suggest that the low-temperature A phase order (↑↑↓↓) finds its origins in the freezing of antiphase boundaries created by thermal fluctuations in a parent B phase order (↑↓↑↓). In this work, the low-temperature magnetic order observed in CaFe 2 O 4 is thus the result of a competition between the exchange coupling along $\textit{c}$, which favors the B phase, and the single-ion anisotropy, which stabilizes thermally generated antiphase boundaries, leading to static metastable A phase order at low temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Absence of moment fragmentation in the mixed B -site pyrochlore Nd 2 GaSbO 7

Nd-based pyrochlore oxides of the form Nd 2 GaSbO 7 have garnered a significant amount of interest owing to the moment fragmentation physics observed in Nd 2 GaSbO 7 and speculated in Nd 2 GaSbO 7 . Notably this phenomenon is not ubiquitous in this family, as it is absent in Nd 2 GaSbO 7 , which features a smaller ionic radius on the B site. Here, we explore the necessary conditions for moment fragmentation in the Nd pyrochlore family through a detailed study of the mixed B-site pyrochlore Nd 2 GaSbO 7 . Furthermore, the B site of this system is characterized by significant disorder and an extremely small average ionic radius. Similarly to Nd 2 GaSbO 7 , we find no evidence for moment fragmentation through our bulk characterization and neutron scattering experiments, indicating that chemical pressure (and not necessarily the B-site disorder) plays a key role in the presence or absence of this phenomenon in this material family. Surprisingly, the presence of significant B-site disorder in Nd 2 GaSbO 7 does not generate a spin-glass ground state and instead the same all-in-all-out magnetic order identified in other Nd pyrochlores is found here.

36 MATERIALS SCIENCE↗

Dynamical ground state in the XY pyrochlore Yb2GaSbO7

Abstract The magnetic ground state of the pyrochlore Yb 2 GaSbO 7 has not been established. The persistent spin fluctuations observed by muon spin-relaxation measurements at low temperatures have not been adequately explained for this material using existing theories for quantum magnetism. Here we report on the synthesis and characterisation of Yb 2 GaSbO 7 to revisit the nature of the magnetic ground state. Through DC and AC magnetic susceptibility, heat capacity, and neutron scattering experiments, we observe evidence for a dynamical ground state that makes Yb 2 GaSbO 7 a promising candidate for disorder-induced spin-liquid or spin-singlet behaviour. This state is quite fragile, being tuned to a splayed ferromagnet in a modest magnetic field μ 0 H c ~ 1.5 T.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

From One- to Two-Magnon Excitations in the S = 3 / 2 Magnet β - CaCr 2 O 4

Here, we apply neutron spectroscopy to measure the magnetic dynamics in the S = 3 / 2 magnet β-CaCr 2 O 4 ( T N = 21 K ). The low-energy fluctuations, in the ordered state, resemble large- S linear spin waves from the incommensurate ground state. However, at higher energy transfers, these semiclassical and harmonic dynamics are replaced by an energy and momentum broadened continuum of excitations. Applying kinematic constraints required for energy and momentum conservation, sum rules of neutron scattering, and comparison against exact diagonalization calculations, we show that the dynamics at high-energy transfers resemble low- S one-dimensional quantum fluctuations. β-CaCr 2 O 4 represents an example of a magnet at the border between classical Néel and quantum phases, displaying dual characteristics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Absolute crystal and magnetic chiralities in the langasite compound Ba 3 NbFe 3 Si 2 O 14 determined by polarized neutron and x-ray scattering

Here, we present a combined polarized neutron and x-ray scattering study on two enantiopure langasite single crystals aimed at the determination of their absolute structural and magnetic chiralities and the coupling between them. Our respective data sets unambiguously reveal two samples of opposite structural chirality, where the magnetic handedness is pinned by the structural one. Simple energy considerations of the magnetic exchange and single-ion anisotropy parameters reveal that it is not the Dzyaloshinskii-Moriya interaction but the local single-ion anisotropy on a triangular plaquette which plays a key role in stabilizing one of the two magnetic helices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nonlinear soliton confinement in weakly coupled antiferromagnetic spin chains

In this work, we analyze the low-energy dynamics of quasi-one-dimensional, large-$\textit{S}$ quantum antiferromagnets with easy-axis anisotropy, using a semiclassical nonlinear sigma model. The saddle point approximation leads to a sine-Gordon equation which supports soliton solutions. These correspond to the movement of spatially extended domain walls. Long-range magnetic order is a consequence of a weak interchain coupling. Below the ordering temperature, the coupling to nearby chains leads to an energy cost associated with the separation of two domain walls. From the kink-antikink two-soliton solution, we compute the effective confinement potential. At distances large compared to the size of the solitons the potential is linear, as expected for pointlike domain walls. At small distances the gradual annihilation of the solitons weakens the effective attraction and renders the potential quadratic. From numerically solving the effective one-dimensional Schrödinger equation with this nonlinear confinement potential we compute the soliton bound state spectrum. We apply the theory to CaFe 2 O 4 , an anisotropic $\textit{S}$ = 5/2 magnet based upon antiferromagnetic zigzag chains. Using inelastic neutron scattering, we are able to resolve seven discrete energy levels for spectra recorded slightly below the Néel temperature $T_N$ ≈ 200 K. These modes are well described by our nonlinear confinement model in the regime of large spatially extended solitons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Imitation of spin density wave order in Cu 3 Nb 2 O 8

Spin density waves, based on modulated local moments, are usually associated with metallic materials, but have recently been reported in insulators which display coupled magnetic and structural order parameters. Here, we discuss one such example, the multiferroic Cu 3 Nb 2 O 8 , which is reported to undergo two magnetic phase transitions, first to an unknown antiferromagnetic phase at $T_N$ ≈ 26.5 K , and then to a helicoidal structure coupled to an electric polarization below $T_2$ ≈ 24 K which breaks the crystallographic inversion symmetry. By analogy with other complex oxides, one might naturally expect this intermediate phase to be a spin density wave phase. We apply spherical polarimetry to confirm the low-temperature magnetic structure, yet only observe a single magnetic phase transition to helicoidal order. We argue that the reported unknown phase actually supports an imitation spin density wave which originates from a decoupling of the components of the magnetic order parameter, as allowed by symmetry and driven by thermal fluctuations. This provides a mechanism for the magnetic, but not nuclear, structure to break inversion symmetry thereby creating an intermediate phase in the proximity of $T_N$ which imitates a spin density wave. As the temperature is reduced, this intermediate structure destabilizes the crystal such that a structural chirality is induced, as reflected by the emergence of the electric polarization, and the imitation spin density wave relaxes into a generic helicoid. This scenario in which critical fluctuations allow the magnetic structure to break inversion symmetry while the crystal structure remains centrosymmetric might be relevant to other complex multiferroics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Magnetic fluctuations and the spin–orbit interaction in Mott insulating CoO

Motivated by the presence of an unquenched orbital angular momentum in CoO, a team at Chalk River, including a recently hired research officer Roger Cowley, performed the first inelastic neutron scattering experiments on the classic Mott insulator. Despite identifying two magnon modes at the zone boundary, the team was unable to parameterise the low energy magnetic excitation spectrum below TN using conventional pseudo-bosonic approaches, instead achieving only qualitative agreement. It would not be for another 40 years that Roger, now at Oxford and motivated by the discovery of the high-Tc cuprate superconductors, would make another attempt at the parameterisation of the magnetic excitation spectrum that had previously alluded him at the start of his career. Upon his return to CoO, Roger found a system embroiled in controversy, with some of its most fundamental parameters still remaining undetermined. Faced with such a formidable task, Roger performed a series of inelastic neutron scattering experiments in the early 2010s on both CoO and a magnetically dilute structural analogue Mg 0.97 Co 0.03 O. These experiments would prove instrumental in the determination of both single-ion and cooperative magnetic parameters for CoO. Both these sets of parameters would eventually be used in a spin–orbit exciton model, developed by his longtime friend and collaborator Bill Buyers, to successfully parameterise the complex spectrum that both measured at Chalk River almost 50 years prior. The story of CoO is of one that has come full circle, one filled with both spectacular failures and intermittent, yet profound, little victories.

36 MATERIALS SCIENCE↗