# Publications

## Phase-sensitive determination of nodal d-wave order parameter in single-band and multiband superconductors

PHYSICAL REVIEW B 101 (2020) ARTN 214505

J Boeker, MA Sulangi, A Akbari, JCS Davis, PJ Hirschfeld, IM Eremin

## Enhancing easy-plane anisotropy in bespoke Ni(II) quantum magnets

Polyhedron 180 (2020)

JL Manson, ZE Manson, A Sargent, DY Villa, NL Etten, WJA Blackmore, SPM Curley, RC Williams, J Brambleby, PA Goddard, A Ozarowski, MN Wilson, BM Huddart, T Lancaster, RD Johnson, SJ Blundell, J Bendix, KA Wheeler, SH Lapidus, F Xiao, S Birnbaum, J Singleton

© 2020 The Authors We examine the crystal structures and magnetic properties of several S = 1 Ni(II) coordination compounds, molecules and polymers, that include the bridging ligands HF2−, AF62− (A = Ti, Zr) and pyrazine or non-bridging ligands F−, SiF62−, glycine, H2O, 1-vinylimidazole, 4-methylpyrazole and 3-hydroxypyridine. Pseudo-octahedral NiN4F2, NiN4O2 or NiN4OF cores consist of equatorial Ni-N bonds that are equal to or slightly longer than the axial Ni-Lax bonds. By design, the zero-field splitting (D) is large in these systems and, in the presence of substantial exchange interactions (J), can be difficult to discriminate from magnetometry measurements on powder samples. Thus, we relied on pulsed-field magnetization in those cases and employed electron-spin resonance (ESR) to confirm D when J ≪ D. The anisotropy of each compound was found to be easy-plane (D > 0) and range from ≈ 8–25 K. This work reveals a linear correlation between the ratio d(Ni-Lax)/d(Ni-Neq) and D although the ligand spectrochemical properties may play an important role. We assert that this relationship allows us to predict the type of magnetocrystalline anisotropy in tailored Ni(II) quantum magnets.

## Atomic-scale electronic structure of the cuprate pair density wave state coexisting with superconductivity.

Proceedings of the National Academy of Sciences of the United States of America (2020)

P Choubey, SH Joo, K Fujita, Z Du, SD Edkins, MH Hamidian, H Eisaki, S Uchida, AP Mackenzie, J Lee, JCS Davis, PJ Hirschfeld

The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states [Formula: see text] is predicted at the terminal BiO surface of Bi2Sr2CaCu2O8 and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of [Formula: see text], the modulations of the coherence peak energy [Formula: see text] and the characteristics of Bogoliubov quasiparticle interference in scattering-wavevector space [Formula: see text] Consistency between all these predictions and the corresponding experiments indicates that lightly hole-doped Bi2Sr2CaCu2O8 does contain a PDW + DSC state. Moreover, in the model the PDW + DSC state becomes unstable to a pure DSC state at a critical hole density p*, with empirically equivalent phenomena occurring in the experiments. All these results are consistent with a picture in which the cuprate translational symmetry-breaking state is a PDW, the observed charge modulations are its consequence, the antinodal pseudogap is that of the PDW state, and the cuprate critical point at p* ≈ 19% occurs due to disappearance of this PDW.

## Imaging the energy gap modulations of the cuprate pair-density-wave state.

Nature 580 (2020) 65-70

Z Du, H Li, SH Joo, EP Donoway, J Lee, JCS Davis, G Gu, PD Johnson, K Fujita

The defining characteristic1,2 of Cooper pairs with finite centre-of-mass momentum is a spatially modulating superconducting energy gap Δ(r), where r is a position. Recently, this concept has been generalized to the pair-density-wave (PDW) state predicted to exist in copper oxides (cuprates)3,4. Although the signature of a cuprate PDW has been detected in Cooper-pair tunnelling5, the distinctive signature in single-electron tunnelling of a periodic Δ(r) modulation has not been observed. Here, using a spectroscopic technique based on scanning tunnelling microscopy, we find strong Δ(r) modulations in the canonical cuprate Bi2Sr2CaCu2O8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a0)(1/8, 0) and Q ≈ (2π/a0)(0, 1/8) (where a0 is the distance between neighbouring Cu atoms). Simultaneous imaging of the local density of states N(r, E) (where E is the energy) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we find them to be concentrated in areas where the PDW spatial phase changes by π, as predicted by the theory of half-vortices in a PDW state6,7. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in Bi2Sr2CaCu2O8+δ.

## Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging.

Proceedings of the National Academy of Sciences of the United States of America 117 (2020) 5222-5227

R Sharma, SD Edkins, Z Wang, A Kostin, C Sow, Y Maeno, AP Mackenzie, JCS Davis, V Madhavan

Sr2RuO4 has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap [Formula: see text] on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the [Formula: see text] of Sr2RuO4 Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband [Formula: see text] At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors [Formula: see text] consistent with eight gap nodes/minima that are all closely aligned to the [Formula: see text] crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al., Nature 574, 72-75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al., Phys. Rev B, 100, 094530 (2019)], and theory [A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr2RuO4 appears most consistent with [Formula: see text] having [Formula: see text] [Formula: see text] symmetry.

## The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond

ANNUAL REVIEW OF CONDENSED MATTER PHYSICS, VOL 11, 2020 11 (2020) 231-270

DF Agterberg, JCS Davis, SD Edkins, E Fradkin, DJ Van Harlingen, SA Kivelson, PA Lee, L Radzihovsky, JM Tranquada, Y Wang

## Phase transitions for beginners

CONTEMPORARY PHYSICS (2020)

SJ Blundell

## Group theory for physicists, 2nd edition

CONTEMPORARY PHYSICS (2020)

SJ Blundell

## Optimization of superconducting properties of the stoichiometric CaKFe4As4

Superconductor Science and Technology IOP Press 33 (2019) 025003

SJ Singh, SJ Cassidy, M Bristow, S Blundell, SJ Clarke, A Coldea

CaKFe4As4 (1144) is a unique stoichiometric iron-based superconductor which harbours high upper critical fields and large critical current densities. In this work, we describe a study to optimize the synthesis conditions of stoichiometric polycrystalline samples of CaKFe4As4 and asses their structural, magnetic and transport properties. The samples were prepared over a wide temperature range (900-1100°C) and the pure phase formation is centered around 955°C. Outside this temperature region, impurity phases of KFe2As2 and CaFe2As2 can also form. Magnetic susceptibility and resistivity measurements establish that the critical temperature reaches ~34 K for the optimum synthesis conditions and the critical current reaches 2 × 104 A-cm−2. The post-annealing process demonstrates the stability of the 1144 phase up to 500°C, however, under higher temperature annealing, phase degradation occurs. Our study indicates that the formation of phase-pure 1144 occurs over a much narrower window and its highly prone to multi-phase formation as compared with the 122 family. As a result, the superconducting properties are enhanced for the pure 1144 phase but they are likely to be affected by the inter and intra-granular behaviour originating from the microstructural nature of polycrystalline CaKFe4As4, similar to other iron-based superconductors. Based on our study, we construct the phase diagram for polycrystalline 1144 and compared it with that reported for 1144 single crystal.

## Probing magnetic order and disorder in the one-dimensional molecular spin chains CuF2(pyz) and [Ln(hfac)3(boaDTDA)] n (Ln  =  Sm, La) using implanted muons.

Journal of physics. Condensed matter : an Institute of Physics journal 31 (2019) 394002-394002

T Lancaster, BM Huddart, RC Williams, F Xiao, KJA Franke, PJ Baker, FL Pratt, SJ Blundell, JA Schlueter, MB Mills, AC Maahs, KE Preuss

We present the results of muon-spin relaxation ([Formula: see text]SR) measurements on antiferromagnetic and ferromagnetic spin chains. In antiferromagnetic CuF2(pyz) we identify a transition to long range magnetic order taking place at [Formula: see text] K, allowing us to estimate a ratio with the intrachain exchange of [Formula: see text] and the ratio of interchain to intrachain exchange coupling as [Formula: see text]. The ferromagnetic chain [Sm(hfac)3(boaDTDA)] n undergoes an ordering transition at [Formula: see text] K, seen via a broad freezing of dynamic fluctuations on the muon (microsecond) timescale and implying [Formula: see text]. The ordered radical moment continues to fluctuate on this timescale down to 0.3 K, while the Sm moments remain disordered. In contrast, the radical spins in [La(hfac)3(boaDTDA)] n remain magnetically disordered down to T  =  0.1 K suggesting [Formula: see text].

## Mott polaritons in cavity-coupled quantum materials

New Journal of Physics IOP Publishing 21 (2019) 073066

M Kiffner, J Coulthard, F Schlawin, A Ardavan, D Jaksch

We show that strong electron-electron interactions in quantum materials can give rise to electronic transitions that couple strongly to cavity fields, and collective enhancement of these interactions can result in ultrastrong effective coupling strengths. As a paradigmatic example we consider a Fermi-Hubbard model coupled to a single-mode cavity and find that resonant electron-cavity interactions result in the formation of a quasi-continuum of polariton branches. The vacuum Rabi splitting of the two outermost branches is collectively enhanced and scales with USD g_{\text{eff}}\propto\sqrt{2L} USD, where USD L USD is the number of electronic sites, and the maximal achievable value for USD g_{\text{eff}} USD is determined by the volume of the unit cell of the crystal. We find that USD g_{\text{eff}} USD for existing quantum materials can by far exceed the width of the first excited Hubbard band. This effect can be experimentally observed via measurements of the optical conductivity and does not require ultrastrong coupling on the single-electron level. Quantum correlations in the electronic ground state as well as the microscopic nature of the light-matter interaction enhance the collective light-matter interaction compared to an ensemble of independent two-level atoms interacting with a cavity mode.

## Local magnetism, magnetic order and spin freezing in the 'nonmetallic metal' FeCrAs.

Journal of physics. Condensed matter : an Institute of Physics journal 31 (2019) 285803-285803

BM Huddart, MT Birch, FL Pratt, SJ Blundell, DG Porter, SJ Clark, W Wu, SR Julian, PD Hatton, T Lancaster

We present the results of x-ray scattering and muon-spin relaxation ([Formula: see text]SR) measurements on the iron-pnictide compound FeCrAs. Polarized non-resonant magnetic x-ray scattering results reveal the 120° periodicity expected from the suggested three-fold symmetric, non-collinear antiferromagnetic structure. [Formula: see text]SR measurements indicate a magnetically ordered phase throughout the bulk of the material below [Formula: see text] K. There are signs of fluctuating magnetism in a narrow range of temperatures above [Formula: see text] involving low-energy excitations, while at temperatures well below [Formula: see text] behaviour characteristic of freezing of dynamics is observed, likely reflecting the effect of disorder in our polycrystalline sample. Using density functional theory we propose a distinct muon stopping site in this compound and assess the degree of distortion induced by the implanted muon.

## Determining the anisotropy and exchange parameters of polycrystalline spin-1 magnets

NEW JOURNAL OF PHYSICS 21 (2019) 93025

W Blackmore, J Brambleby, T Lancaster, S Clark, J Schlueter, J Singleton, A Ozarowski, R Johnson, Y-S Chen, R Williams, S Lapidus, A Arif, F Xiao, S Blundell, M Pearce, P Manuel, M Lees, P Goddard, J Manson, D Villa, J Villa

© 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. Although low-dimensional S = 1 antiferromagnets remain of great interest, difficulty in obtaining high-quality single crystals of the newest materials hinders experimental research in this area. Polycrystalline samples are more readily produced, but there are inherent problems in extracting the magnetic properties of anisotropic systems from powder data. Following a discussion of the effect of powder-Averaging on various measurement techniques, we present a methodology to overcome this issue using thermodynamic measurements. In particular we focus on whether it is possible to characterise the magnetic properties of polycrystalline, anisotropic samples using readily available laboratory equipment. We test the efficacy of our method using the magnets [Ni(H2O)2(3,5-lutidine)4](BF4)2 and Ni(H2O)2(acetate)2(4-picoline)2, which have negligible exchange interactions, as well as the antiferromagnet [Ni(H2O)2(pyrazine)2](BF4)2, and show that we are able to extract the anisotropy parameters in each case. The results obtained from the thermodynamic measurements are checked against electron-spin resonance and neutron diffraction. We also present a density functional method, which incorporates spin-orbit coupling to estimate the size of the anisotropy in [Ni(H2O)2(pyrazine)2](BF4)2.

## Coherent spin manipulation of individual atoms on a surface

Science American Association for the Advancement of Science 366 (2019) 509-512

K Yang, W Paul, S-H Phark, P Willke, Y Bae, T Choi, T Esat, A Ardavan, A Heinrich, C Lutz

Achieving time-domain control of quantum states with atomic-scale spatial resolution in nanostructures is a long-term goal in quantum nanoscience and spintronics. Here, we demonstrate coherent spin rotations of individual atoms on a surface at the nanosecond time scale, using an all-electric scheme in a scanning tunneling microscope (STM). By modulating the atomically confined magnetic interaction between the STM tip and surface atoms, we drive quantum Rabi oscillations between spin-up and spin-down states in as little as ~20 nanoseconds. Ramsey fringes and spin echo signals allow us to understand and improve quantum coherence. We further demonstrate coherent operations on engineered atomic dimers. The coherent control of spins arranged with atomic precision provides a solid-state platform for quantum-state engineering and simulation of many-body systems.

## Fractionalized pair density wave in the pseudogap phase of cuprate superconductors

PHYSICAL REVIEW B 100 (2019) ARTN 224511

D Chakraborty, M Grandadam, MH Hamidian, JCS Davis, Y Sidis, C Pepin

## FeTi$_2$O$_5$: a spin Jahn-Teller transition tuned by cation substitution

Physical Review B American Physical Society (0)

F Lang, L Jowitt, D Prabhakaran, RD Johnson, SJ Blundell

We have used muon-spin rotation, heat capacity and x-ray diffraction measurements in combination with density functional theory and dipole field calculations to investigate the crystal and magnetic structure of FeTi$_2$O$_5$. We observe a long range ordered state below 41.8(5) K with indications of significant correlations existing above this temperature. We determine candidate muon stopping sites in this compound, and find that our data are consistent with the spin Jahn-Teller driven antiferromagnetic ground state with $\boldsymbol{k}$=(1/2,1/2,0) reported for CoTi$_2$O$_5$. By comparing our data with calculated dipolar fields we can restrict the possible moment size and directions of the Fe$^{2+}$ ions.

## Robustness of superconducting properties to transition metal substitution and impurity phases in Fe1-xVxSe

PHYSICAL REVIEW B 100 (2019) 94527

SJ Blundell, SJ Clarke, PJ Baker, FKK Kirschner, DN Woodruff, MJ Bristow, F Lang

© 2019 American Physical Society. We have performed transverse- and zero-field muon spin rotation/relaxation experiments, as well as magnetometry measurements, on samples of Fe1-xVxSe and their Li+NH3 intercalates Li0.6(NH2)0.2(NH3)0.8Fe1-xVxSe. We examine the low vanadium substitution regime: x=0.005, 0.01, and 0.02. The intercalation reaction significantly increases the critical temperature (Tc) and the superfluid stiffness for all x. The nonintercalated samples all exhibit Tc≈8.5 K while the intercalated samples all show an enhanced Tc&gt;40 K. Vanadium substitution has a negligible effect on Tc, but seems to suppress the superfluid stiffness for the nonintercalated samples and weakly enhance it for the intercalated materials. The optimal substitution level for the intercalated samples is found to be x=0.01, with Tc≈41K and λab(0)≈0.18μm. The nonintercalated samples can be modeled with either a single d-wave superconducting gap or with an anisotropic gap function based on recent quasiparticle imaging experiments, whereas the intercalates display multigap nodal behavior which can be fitted using s+d- or d+d-wave models. Magnetism, likely from iron impurities, appears after the intercalation reaction and coexists and competes with the superconductivity. However, it appears that the superconductivity is remarkably robust to the impurity phase, providing an avenue to stably improve the superconducting properties of transition metal substituted FeSe.

## Exsolution of SrO during the topochemical conversion of LaSr3CoRuO8 to the oxyhydride LaSr3CoRuO4H4

Inorganic Chemistry American Chemical Society (2019)

L Jin, M Batuk, FKK Kirschner, F Lang, SJ Blundell, J Hadermann, M Hayward

Reaction of the n = 1 Ruddlesden-Popper oxide LaSr3CoRuO8 with CaH2 yields the oxyhydride phase LaSr3CoRuO4H4 via a topochemical anion exchange. Close inspection of the X-ray and neutron powder diffraction data in combination with HAADF-STEM images reveals that the nanoparticles of SrO are exsolved from the system during the reaction, with the change in cation stoichiometry accommodated by the inclusion of n &gt; 1 (Co/Ru)nOn+1H2n "perovskite" layers into the Ruddlesden-Popper stacking sequence. This novel pseudotopochemical process offers a new route for the formation of n &gt; 1 Ruddlesden-Popper structured materials. Magnetization data are consistent with a LaSr3Co+Ru2+O4H4 (Co+, d8, S = 1; Ru2+, d6, S = 0) oxidation/spin state combination. Neutron diffraction and μ+SR data show no evidence for long-range magnetic order down to 2 K, suggesting the diamagnetic Ru2+ centers impede the Co-Co magnetic-exchange interactions.

## Muon-spin relaxation and AC magnetometry study of the ferrimagnet LaSr2Cr2SbO9

Journal of Solid State Chemistry Elsevier 279 (2019) 120935

EC Hunter, P Battle, S Blundell, E al.

AC susceptibility and muon spin relaxation data have been collected from a polycrystalline sample of LaSr2Cr2SbO9, a perovskite-like compound wherein the unequal distribution of Cr3+ and Sb5+ cations over two crystallographically-distinct six-coordinate B sites results in the onset of ferrimagnetism at ∼150 K. The data are used to elucidate the dynamics of the ferrimagnetic domain walls, thought to lie in Sb-rich regions, and suggest an energy barrier of ∼0.13 eV to their motion. The muon data confirm that the ferrimagnetic order is a true bulk phenomenon. The behaviour of this material is briefly compared to that of Ni2+- based relaxor ferromagnets.

## Magnetic monopole noise

Nature Springer Nature 571 (2019) 234-239

R Dusad, F Kirschner, JC Hoke, BR Roberts, A Eyal, F Flicker, GM Luke, S Blundell, J Davis

Magnetic monopoles1-3 are hypothetical elementary particles with quantized magnetic charge. In principle, a magnetic monopole can be detected by the quantized jump in magnetic flux that it generates upon passage through a superconducting quantum interference device (SQUID)4. Following the theoretical prediction that emergent magnetic monopoles should exist in several lanthanide pyrochlore magnetic insulators5,6, including Dy2Ti2O7, the SQUID technique has been proposed for their direct detection6. However, this approach has been hindered by the high number density and the generation-recombination fluctuations expected of such thermally generated monopoles. Recently, theoretical advances have enabled the prediction of the spectral density of magnetic-flux noise from monopole generation-recombination fluctuations in these materials7,8. Here we report the development of a SQUID-based flux noise spectrometer and measurements of the frequency and temperature dependence of magnetic-flux noise generated by Dy2Ti2O7 crystals. We detect almost all of the features of magnetic-flux noise predicted for magnetic monopole plasmas7,8, including the existence of intense magnetization noise and its characteristic frequency and temperature dependence. Moreover, comparisons of simulated and measured correlation functions of the magnetic-flux noise indicate that the motions of magnetic charges are strongly correlated. Intriguingly, because the generation-recombination time constant for Dy2Ti2O7 is in the millisecond range, magnetic monopole flux noise amplified by SQUID is audible to humans.