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E. Blackburn

Publications and source records attributed to E. Blackburn.

At least 19 recordsLinked to original sources
arXiv2024

Two characteristic contributions to the superconducting state of 2$H$-NbSe$_2$

Multiband superconductivity arises when multiple electronic bands contribute to the formation of the superconducting state, allowing distinct pairing interactions and gap structures. Here, we present field- and temperature-dependent data on the vortex lattice structure in 2$H$-NbSe$_2$ as a contribution to the ongoing debate on the nature of the superconductivity in this material. The field-dependent data clearly show that there are two distinct superconducting bands, and the contribution of one of them to the vortex lattice signal is completely suppressed for magnetic fields above $\sim$ 0.8 T, well below $B\mathrm{_{c2}}$. By combining the temperature and field scans, we can deduce that there is a moderate degree of interband coupling. From the observed temperature dependences, we find that at low field and zero temperature, the two gaps in temperature units are 13.1 $\pm$ 0.2 and 6.5 $\pm$ 0.3 K ($\Delta_{0}$ = 1.88 and 0.94 $k\mathrm{_{B}} T\mathrm{_{c}} $); the band with the larger gap gives just under two-thirds of the superfluid density. The penetration depth extrapolated to zero field and zero temperature is 160 $\pm$ 2 nm.

cond-mat.supr-con↗
arXiv2024

Investigating the superconducting state of 2$H$-NbS$_2$ as seen by the vortex lattice

2$H$-NbS$_2$ is a classic example of an anisotropic multi-band superconductor, with significant recent work focussing on the interesting responses seen when high magnetic fields are applied precisely parallel to the hexagonal niobium planes. It is often contrasted with its sister compound 2$H$-NbSe$_2$ because they have similar onset temperatures for superconductivity, but 2$H$-NbS$_2$ has no charge density wave whereas in 2$H$-NbSe$_2$ the charge density wave order couples strongly to the superconductivity. Using small-angle neutron scattering, a bulk-sensitive probe, we have studied the vortex lattice and how it responds to the underlying superconducting anisotropy. This is done by controlling the orientation of the field with respect to the Nb planes. The superconducting anisotropy, $Γ_{ac} = 7.07 \pm 0.2$, is found to be field independent over the range measured (0.15 to 1.25 T), and the magnetic field distribution as a function of the applied magnetic field is found to be in excellent quantitative agreement with anisotropic London theory modified with a core-size cut-off correction, providing the first complete validation of this model. We find values of $λ_{ab} = 141.9 \pm 1.5 $ nm for the in-plane London penetration depth, and $λ_{c} \sim$ 1 \textmu m for the out-of-plane response. The field-independence indicates that we are primarily sampling the larger of the two gaps generating the superconductivity in this material.

cond-mat.supr-con↗
arXiv2023

Unconventional gap structures and the intermediate mixed state: a vortex lattice study of the noncentrosymmetric superconductor BiPd

We report on neutron scattering measurements on the vortex lattice of the noncentrosymmetric superconductor BiPd. We observe the existence of the intermediate mixed state, a region where Meissner and vortex lattice phases coexist, which is a feature of low $κ$ Type-II superconductors. Following this, we obtain an estimate of the value of $κ$ using the extended London model, which confirms the expectation that $κ$ should be small. Finally, we find that the temperature dependence of the vortex lattice form factor fits well to a model designed to describe singlet-triplet mixing in non-centrosymmetric superconductors, which may shed light on the question of the gap structure in BiPd.

cond-mat.supr-con↗
arXiv2023

Interplay between atomic fluctuations and charge density waves in La$_{2-x}$Sr$_{x}$CuO$_{4}$

In the cuprate superconductors, the spatial coherence of the charge density wave (CDW) state grows rapidly below a characteristic temperature $T_\mathrm{CDW}$, the nature of which is debated. We have combined a set of x-ray scattering techniques to study La$_{1.88}$Sr$_{0.12}$CuO$_{4}$ ($T_\mathrm{CDW}$~$\approx$~80\,K) to shed light on this discussion. We observe the emergence of a crystal structure, which is consistent with the CDW modulation in symmetry, well above $T_\mathrm{CDW}$. This global structural change also induces strong fluctuations of local atomic disorder in the intermediate temperature region. At $T_\mathrm{CDW}$, the temperature dependence of this structure develops a kink, while the atomic disorder is minimized. We find that the atomic relaxation dynamics cross over from a cooperative to an incoherent response at $T_\mathrm{CDW}$. These results reveal a rich interplay between the CDWs and atomic fluctuations of distinct spatio-temporal scales. For example, the CDW coherence is enhanced on quasi-elastic timescales by incoherent atomic relaxation.

cond-mat.supr-con↗
arXiv2023

Orthogonal magnetic structures of Fe4O5:representation analysis and DFT calculations

The magnetic and electronic structures of Fe4O5 have been investigated at ambient and high pressures via a combination of representation analysis, density functional theory (DFT+U) calculations, and Mössbauer spectroscopy. A few spin configurations corresponding to the different irreducible representations have been considered. The total-energy calculations reveal that the magnetic ground state of Fe4O5 corresponds to an orthogonal spin order. Depending on the magnetic propagation vector k two spin ordered phases with minimal energy differences are realized. The lowest energy magnetic phase is related to k = (0, 0, 0) and is characterized by the ferromagnetic ordering of the iron magnetic moments at prismatic sites along the b axis and antiferromagnetic ordering of iron moments at octahedral sites along the c axis. For the k = (1/2, 0, 0) phase, the moments in the prisms are antiferromagnetically ordered along the b axis and the moments in the octahedra are still antiferromagnetically ordered along the c axis. Under high pressure, the Fe4O5 exhibits magnetic transitions with corresponding electronic transitions of the metal-insulator type. At a critical pressure PC ~ 60 GPa the Fe ions at the octahedral sites undergo a high-spin to low-spin state crossover with a decrease in the unit-cell volume of ~ 4%, while the Fe ions at the prismatic sites remain in the high-spin state up to 130 GPa. This site-dependent magnetic collapse is experimentally observed in the transformation of Mössbauer spectra measured at room temperature and high pressures.

cond-mat.mtrl-sci↗
arXiv2022

Probing superconducting order in overdoped Ca$_{x}$Y$_{1-x}$Ba$_{2}$Cu$_{3}$O$_{7}$ by neutron diffraction measurements of the vortex lattice

We present small angle neutron scattering studies of the magnetic vortex lattice (VL) in Ca$_{0.04}$Y$_{0.96}$Ba$_{2}$Cu$_{3}$O$_{7}$ up to a field of 16.7 T, and Ca$_{0.15}$Y$_{0.85}$Ba$_{2}$Cu$_{3}$O$_{7}$ up to 25 T. We find that the series of vortex lattice structure transitions have shifted down in field relative to those reported for the undoped compound. We attribute this mainly to the weakening of the 1-D superconductivity in the Cu-O chains by the disorder introduced by doping. The hole doping by calcium is also expected to alter the Fermi velocity and it reduces the upper critical field of the system. The high-field structure of the vortex lattice is similar to recent measurements on the parent compound in fields of 25~T, which indicates that the fundamental \textit{d}-wave nature of the superconducting gap is unchanged by calcium doping. This is corroborated by the temperature dependence of the VL form factor which also shows the same \textit{d}-wave behaviour as observed in other cuprates. We also find evidence of Pauli paramagnetic effects in the field dependence of the VL form factor.

cond-mat.supr-con↗
arXiv2022

Deviations from the extended London model at high magnetic fields in YBa$_2$Cu$_3$O$_7$

We report on the evolution with magnetic field and temperature of the vortex lattice (VL) in fully-oxygenated YBa2Cu3O7 as studied by time-of-flight small angle neutron scattering. Using the HFM/EXED beamline, we have obtained data up to 25.9 T - much higher than that available previously. Our VL structure results indicate the progressive suppression by field of the superconductivity along the crystallographic b (CuO chain) direction. The intensity of the diffracted signal reveals the spatial variation of magnetization caused by the VL (the "form factor"). Instead of a rapid fall-off with field, as seen in superconductors with smaller upper critical fields, we find that the form factor is almost constant with field above about 12 T. We speculate that this is due to Pauli paramagnetic moments, which increase at high fields due to alignment of the spins of quasiparticles in the vortex cores.

cond-mat.supr-con↗
arXiv2022

Inhomogeneous spin excitations in weakly coupled spin-1/2 chains

We present a systematic inelastic neutron scattering and neutron diffraction study of the magnetic structure of the quasi-1D spin-1/2 magnet SrCo2V2O8, where the interchain coupling in the Neel-type antiferromagnetic ground state breaks the static spin lattice into two independent domains. At zero magnetic field, we observe two new spin excitations with small spectral weights inside the gapped region defined by the spinon bound states. In an external magnetic field along the chain axis, the Neel order is partially destabilized above 2 T and completely suppressed at 3.9 T, above which a quantum disordered Tomonaga-Luttinger liquid (TLL) prevails. We propose that the two new modes at zero field are spinon excitations inside the domain walls. Since they have a smaller gap than those excited in the Neel domains, the underlying spin chains enter the TLL state via a local quantum phase transition at 2 T, making a stable Neel / TLL coexistence until the excitation gap closes in the Neel state at 3.9 T.

cond-mat.str-el↗
arXiv2021

A Snapshot Review -- Fluctuations in Quantum Materials: From Skyrmions to Superconductivity

By measuring a linear response function directly, such as the dynamic susceptibility, one can understand fundamental material properties. However, a fresh perspective can be offered by studying fluctuations. This can be related back to the dynamic susceptibility through the fluctuation-dissipation theorem, which relates the fluctuations in a system to its response, an alternate route to access the physics of a material. Here, we describe a new x-ray tool for material characterization that will offer an opportunity to uncover new physics in quantum materials using this theorem. We provide details of the method and discuss the requisite analysis techniques in order to capitalize on the potential to explore an uncharted region of phase space. This is followed by recent results on a topological chiral magnet, together with a discussion of current work in progress. We provide a perspective on future measurements planned for work in unconventional superconductivity.

cond-mat.str-el↗
arXiv2020

Spatially Inhomogeneous Competition between Superconductivity and the Charge Density Wave in YBa$_2$Cu$_3$O$_{6.67}$

The charge density wave in the high-temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) is now known to have two different ordering tendencies differentiated by their $c$-axis correlations. These correspond to ferro- (F-CDW) and antiferro- (AF-CDW) couplings between CDW in neighbouring CuO$_2$ bilayers. This discovery has prompted a number of fundamental questions. For example, how does superconductivity adjust to two competing orders and are either of these orders responsible for the electronic reconstruction? Here we use high-energy x-ray diffraction to study YBa$_2$Cu$_3$O$_{6.67}$ as a function of magnetic field and temperature. We show that regions of the sample with F-CDW correlations suppress superconductivity more strongly than those with AF-CDW correlations. This implies that an inhomogeneous superconducting state exists, in which some regions show a weak or fragile form of superconductivity. By comparison of F-CDW and AF-CDW correlation lengths, it is furthermore concluded that F-CDW ordering is sufficiently long-range to modify the electronic structure. Our study thus suggests that F-CDW correlations have an important impact on superconducting and normal state properties of underdoped YBCO.

cond-mat.supr-con↗
arXiv2019

Magnetic Microphase Inhomogeneity as a Thermodynamic Precursor of Ground State Phase Separation in Weakly Coupled Spin-$\frac{3}{2}$ Chains

$γ$-CoV$_{2}$O$_{6}$ is a quasi one-dimensional spin-$\frac{3}{2}$ magnet that possesses two distinct magnetic orders in the ground state with modulation vectors $k_\mathrm{1}$ = ($\frac{1}{2}$, 0, 0) and $k_\mathrm{2}$ = ($\frac{1}{4}$, 0, -$\frac{1}{4}$), respectively. Here, we use muon spin relaxation and rotation to reveal the thermodynamics of the magnetic phase separation in this compound. In the paramagnetic (PM) region, short-range correlated spin clusters emerge at $T_\mathrm{m}$ $\simeq$ 26 K at the $\it{partial}$ expense of the PM volume. Upon further cooling, we show that these emergent clusters become spatially coherent at $T_\mathrm{N2}$ = 7.5 K and eventually form the $k_\mathrm{2}$ order at $T^{\star}$ = 5.6 K, while the remaining PM spins are driven into the $k_\mathrm{1}$ state at $T_\mathrm{N1}$ = 6.6 K. These results stress magnetic microphase inhomogeneity as a thermodynamic precursor for the ground state phase separation in weakly coupled spin-$\frac{3}{2}$ chains.

cond-mat.str-el↗
arXiv2019

Magnetic Guinier law

Small-angle scattering of x-rays and neutrons is a routine method for the determination of nanoparticle sizes. The so-called Guinier law represents the low-q approximation for the small-angle scattering curve from an assembly of particles. The Guinier law has originally been derived for nonmagnetic particle-matrix-type systems, and it is successfully employed for the estimation of particle sizes in various scientific domains (e.g., soft matter physics, biology, colloidal chemistry, materials science). An important prerequisite for it to apply is the presence of a discontinuous interface separating particles and matrix. Here, we introduce the Guinier law for the case of magnetic small-angle neutron scattering (SANS) and experimentally demonstrate its applicability for the example of nanocrystalline cobalt. It is well-known that the magnetic microstructure of nanocrystalline ferromagnets is highly nonuniform on the nanometer length scale and characterized by a spectrum of continuously varying long-wavelength magnetization fluctuations, i.e., these systems do not manifest sharp interfaces in their magnetization profile. The magnetic Guinier radius depends on the applied magnetic field, on the magnetic interactions (exchange, magnetostatics), and on the magnetic anisotropy-field radius, which characterizes the size over which the magnetic anisotropy field is coherently aligned into the same direction. In contrast to the nonmagnetic conventional Guinier law, the magnetic version can be applied to fully dense random-anisotropy-type ferromagnets.

cond-mat.mes-hall↗
arXiv2019

Magnetic phase diagram of the quantum spin chain compound SrCo$_{2}$V$_{2}$O$_{8}$: a single-crystal neutron diffraction study in magnetic field

We explore the spin states in the quantum spin chain compound SrCo$_{2}$V$_{2}$O$_{8}$ up to 14.9 T and down to 50 mK, using single-crystal neutron diffraction. Upon cooling in zero-field, antiferromagnetic (AFM) order of Néel type develops at $T_\mathrm{N}$ $\simeq$ 5.0 K. Applying an external magnetic field ($H$ $\parallel$ $c$-axis) destabilizes the Néel order, leading to an order-disorder transition when applying a field between $T_\mathrm{N}$ and $\sim$ 1.5 K. Below 1.5 K, we observe a Néel to longitudinal spin density wave (LSDW) order transition at 3.9 T, and a LSDW to emergent AFM order transition at 7.0 T. Our results also reveal several unique signatures for the states of the spins that are not present in the isostructural counterpart BaCo$_{2}$V$_{2}$O$_{8}$.

cond-mat.str-el↗
arXiv2018

Quantitative characterization of the nanoscale local lattice strain induced by Sr dopants in La$_{1.92}$Sr$_{0.08}$CuO$_4$

The nanometer scale lattice deformation brought about by the dopants in high temperature superconducting cuprate La$_{2-x}$Sr$_x$CuO$_4$(x=0.08) was investigated by measuring the associated X-ray diffuse scattering around multiple Bragg peaks. A characteristic diffuse scattering pattern was observed, which can be well described by continuum elastic theory. With the fitted dipole force parameters, the acoustic type lattice deformation pattern was re-constructed and found to be of similar size to lattice thermal vibration at 7 K. Our results address the long-term concern of dopant introduced local lattice inhomogeneity, and show that the associated nanometer scale lattice deformation is marginal and cannot, alone, be responsible for the patched variation in the spectral gaps observed with scanning tunneling microscopy in the cuprates.

cond-mat.str-el↗
arXiv2017

No Evidence for Orbital Loop Currents in Charge Ordered YBa$_2$Cu$_3$O$_{6+x}$ from Polarized Neutron Diffraction

It has been proposed that the pseudogap state of underdoped cuprate superconductors may be due to a transition to a phase which has circulating currents within each unit cell. Here, we use polarized neutron diffraction to search for the corresponding orbital moments in two samples of underdoped YBa$_2$Cu$_3$O$_{6+x}$ with doping levels $p=0.104$ and 0.123. In contrast to some other reports using polarized neutrons, but in agreement with nuclear magnetic resonance and muon spin rotation measurements, we find no evidence for the appearance of magnetic order below 300 K. Thus, our experiment suggests that such order is not an intrinsic property of high-quality cuprate superconductor single crystals. Our results provide an upper bound for a possible orbital loop moment which depends on the pattern of currents within the unit cell. For example, for the CC-$θ_{II}$ pattern proposed by Varma, we find that the ordered moment per current loop is less than 0.013 $μ_B$ for $p=0.104$.

cond-mat.supr-con↗
arXiv2017

Synchrotron x-ray scattering study of charge-density-wave order in HgBa$_2$CuO$_{4+δ}$

We present a detailed synchrotron x-ray scattering study of the charge-density-wave (CDW) order in simple tetragonal HgBa$_2$CuO$_{4+δ}$ (Hg1201). Resonant soft x-ray scattering measurements reveal that short-range order appears at a temperature that is distinctly lower than the pseudogap temperature and in excellent agreement with a prior transient reflectivity result. Despite considerable structural differences between Hg1201 and YBa$_2$Cu$_3$O$_{6+δ}$, the CDW correlations exhibit similar doping dependencies, and we demonstrate a universal relationship between the CDW wave vector and the size of the reconstructed Fermi pocket observed in quantum oscillation experiments. The CDW correlations in Hg1201 vanish already below optimal doping, once the correlation length is comparable to the CDW modulation period, and they appear to be limited by the disorder potential from unit cells hosting two interstitial oxygen atoms. A complementary hard x-ray diffraction measurement, performed on an underdoped Hg1201 sample in magnetic fields along the crystallographic $c$ axis of up to 16 T, provides information about the form factor of the CDW order. As expected from the single-CuO$_2$-layer structure of Hg1201, the CDW correlations vanish at half-integer values of $L$ and appear to be peaked at integer $L$. We conclude that the atomic displacements associated with the short-range CDW order are mainly planar, within the CuO$_2$ layers.

cond-mat.supr-con↗
arXiv2017

Unconventional magnetic phase separation in $γ$-CoV$_2$O$_6$

We have explored the magnetism in the non-geometrically frustrated spin-chain system $γ$-CoV$_{2}$O$_{6}$ which possesses a complex magnetic exchange network. Our neutron diffraction patterns at low temperatures ($T$ $\leqslant$ $T_{\mathrm{N}}$ = 6.6 K) are best described by a model in which two magnetic phases coexist in a volume ratio 65(1) : 35(1), with each phase consisting of a single spin modulation. This model fits previous studies and our observations better than the model proposed by Lenertz $et$ $al$ in J. Phys. Chem. C 118, 13981 (2014), which consisted of one phase with two spin modulations. By decreasing the temperature from $T_{\mathrm{N}}$, the minority phase of our model undergoes an incommensurate-commensurate lock-in transition at $T^{*}$ = 5.6 K. Based on these results, we propose that phase separation is an alternative approach for degeneracy-lifting in frustrated magnets.

cond-mat.str-el↗