The poster sessions take place on**Tuesday, 1st August 19:30 - 21:30 CET** with focus on odd poster numbers AND**Thursday, 3rd August , 19:30-21:30 CET** with focus on even poster numbers.

The poster numbers can be found here.

For each poster contribution there will be one poster wall (width: 97 cm, height: 250 cm) available. Please do not feel obliged to fill the whole space. Posters can be put up for the full duration of the event.

Agarmani, Yassine

Recent thermodynamic measurements on the Mott insulator $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Cl ($\kappa$-Cl) have shed new light on understanding the coupling of electronic and lattice degrees of freedom at the Mott transition. While previous descriptions of the Mott transition focused primarily on electronic scenarios, the observation of strong nonlinearities in the stress-strain relationship in $\kappa$-Cl points to the importance of the coupling of the critical electronic system to the elastic degrees of freedom [1], in agreement with the concept of critical elasticity [2]. \newline In this contribution, we aim to enhance the understanding of critical elasticity in the $\kappa$-(ET)$_2$X family by providing a comprehensive and quantitative determination of the extension of the range of critical elasticity. To this end, we will compare the extension of critical elasticity of $\kappa$-Cl [1] with that of a related system, the fully deuterated $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br, which is positioned differently in the generic \textit{T-p} phase diagram of the $\kappa$-(ET)$_2$X family and therefore enables us to cover a larger \textit{T-p} range. To carry out this investigation, we use an advanced setup [3] allowing us to fine-tune the He-gas pressure while performing high-resolution measurements of relative length changes. [1] E. Gati \textit{et al.}, Science Advances \textbf{2}, 1601646 (2016) [2] M. Zacharias \textit{et al.}, Phys. Rev. Lett. \textbf{109}, 176401 (2012) [3] Y. Agarmani \textit{et al.}, Rev. Sci. Instrum. \textbf{93}, 113902 (2022)

Aggarwal, Deepanshu

In single-layer graphene, a superlattice potential provides the additional Dirac points in the energy spectrum, bringing the Van Hove singularities (VHS) closer to the Fermi level. However, the moir\'{e} superlattice potential formed by twisting the two superimposed graphene layers not only pushes the VHS but also provides a tunable parameter to control their locations [1]. Magic-angle twisted bilayer graphene (MATBLG) is the structure for which the two lowest bands flatten out and the VHS and Fermi level coincides at the twist-angle of 1.05 degrees. The curvature of either the conduction or the valence band can be altered by applying a periodic external potential to the MATBLG. We investigate the MATBLG in such external periodic potentials and show how it amplifies the strong correlation effect, further narrowing the bandwidth while improving the flatness of the conduction and valence bands [2]. References: [1] D. Aggarwal, R. Narula, and S. Ghosh J. Phys.: Condens. Matter 35 143001 [2] D. Aggarwal, R. Narula, and S. Ghosh (Work in progress)

Arora, Disha

By first explicitly involving the optical matrix elements, we calculate the polarisation-controlled Rayleigh scattering response of twisted bilayer graphene (TBLG) for a wide range of twist angles, including the magic angle. The dominant regions of the moir\'{e} Brillouin zone (MBZ) contributing to the Rayleigh scattering process are identified, and we describe their evolution in detail with the variation in the twist angle and the incoming laser energy. Remarkably, for various twist angles, the dominant wave vectors often emanate instead from the $\Gamma$ point of the MBZ in contrast to single-layer graphene (SLG) and AB-stacked bilayer graphene (AB-BLG), where the significant contributions always stem from the vicinity of the K point. Compared to SLG, the integrated Rayleigh intensity is strongly enhanced for small twist angles ( e.g., at twist angle $\theta=1.2^{\circ}$, the integrated Rayleigh intensity at laser energy $E_l=2eV $ is observed to enhance by a factor of $\approx$ 80 for the case of parallel polarisation). Interestingly for cross-polarisation, it exhibits a markedly complex behaviour suggestive of strong interference effects mediated by the optical matrix elements. The ratio $R_A$ = $\frac{integrated Rayleigh intensity for parallel polarisation} {integrated Rayleigh intensity for cross polarisation}$ for small twist angles (e.g., at $\theta=1.5^{\circ}$ ) is found to be enhanced $\approx$ 300 times viz a viz SLG or AB-BLG. Our calculations also show that the integrated Rayleigh intensity is isotropic w.r.t the polariser-analyser orientation when kept in phase. $R_A$ (measured as a function of the incoming laser energy) exhibits a characteristic evolution as the twist angle reduces, thus providing a unique fingerprint capable of serving as an experimental identification of the prevailing twist angle of the TBLG sample under study.

Battistoni, Paolo

Authors: Paolo Battistoni1, Yi Yao1, Amir-Abbas Haghighirad1, Sofia Michaela Souliou1, Mehdi Frachet1, Michael Merz1, Kristin Willa1, Matthieu Le Tacon1 1Institute for Quantum Materials and Technologies The transition-metal monopnictide CrAs features a complex phase diagram reminiscent of unconventional superconductors. A remarkable property of this material is the giant coupling between the structural and electronic degrees of freedom. In particular, at TN ~ 265 K a first-order magnetic transition is observed, from a paramagnetic state to a noncollinear helimagnetic state. In parallel, a dramatic isostructural transition takes place, with the b-axis expanding by almost 4% and the unit-cell volume by 2%. Upon the application of hydrostatic pressure, the magnetic phase transition temperature TN is suppressed although, strangely, the expansion of the unit-cell enhanced. This anomalous behavior echoes with possible evidences for quantum criticality [1]. Chemical pressure via substitution of arsenic with phosphorus in CrAs1-xPx seems to yield a suppression of the magnetic phase analogous to that of physical pressure, but superconductivity has not been reported in this case so far. We successfully grew CrAs and CrAs1-xPx single crystals, the latter up to x=4% doping, and subsequently characterized their properties using magnetometry, specific heat and powder x-ray diffraction experiments. Following our initial Raman scattering investigation of phonon excitations in CrAs [2], we extended the Raman scattering study on CrAs, under the application of hydrostatic pressure, as well on CrAs1-xPx at ambient pressure, as a function of temperature. Our results suggest a very narrow coexistence region of the magnetic and non-magnetic phase and thereby rapid variation of the local strain in this system. [1] M. Matsuda et al. Phys. Rev. X 8, 031017 (2018) [2] K. Sen et al. Phys. Rev. B 100, 104301 (2019)

Chakraborty, Nilotpal

We introduce a model to study magnon scattering in skyrmion crystals, sandwiched between ferromagnets which act as the source of magnons. Skyrmions are topological objects while skyrmion crystals break internal and translational symmetries, thus our setup allows us to study the interplay of topology and symmetry breaking. Starting from a basis of holomorphic theta functions, we construct an analytical ansatz for such a junction with finite spatially modulating topological charge density in the central region and vanishing in the leads. We then construct a suitably defined energy functional for the junction and derive the resulting equations of motion, which resemble a Bogoliubov-de Gennes-like equation. Using analytical techniques, field theory, heuristic models and microscopic recursive transfer-matrix numerics, we calculate the spectra and magnon transmission properties of the skyrmion crystal. We find that magnon transmission can be understood via a combination of low-energy Goldstone modes and effective emergent Landau levels at higher energies. The former manifests in discrete low-energy peaks in the transmission spectrum which reflect the nature of the Goldstone modes arising from symmetry breaking. The latter, which reflect the topology, lead to band-like transmission features, from the structure of which further details of the excitation spectrum of the skyrmion crystal can be inferred. Such characteristic transmission features are absent in competing phases of the quantum Hall phase diagram, and hence provide direct signatures of skyrmion crystal phases and their spectra. Our results directly apply to quantum Hall heterojunction experiments in monolayer graphene with the central region doped slightly away from unit filling, a ν=1:1±δν:1 junction and are also relevant to junctions formed by metallic magnets or in junctions with artificial gauge fields.

Chatterjee, Shouvik

Rare-earth monopnictide (RE-V) semimetal crystals subject to hydrostatic pressure have shown interesting trends in magnetoresistance, magnetic ordering, and superconductivity, with theory predicting pressure-induced band inversion. Yet, thus far, there have been no direct experimental reports of interchanged band order in RE-Vs due to strain. Here I will present our results on the evolution of band topology in biaxial strained GdSb (001) epitaxial films using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT). We find that biaxial strain continuously tunes the electronic structure from topologically trivial to nontrivial. Compressive biaxial strain eliminates the gap between the hole and the electron bands dispersing along the [001] direction. Using a simple tight-binding model accounting for the orbital symmetry of each band, we reproduce trends seen in DFT calculations and ARPES measurements and elucidate the origin of conduction and valence band shifts. If time permits, I will also show how dimensional confinement can lift the carrier compensation in these otherwise compensated semimetals and affects the magnetotransport properties in the ultra-thin limit.

Cichutek, Niklas

We use the functional renormalization group to calculate the global renormalization group flow of the Yukawa-SYK model describing N fermions on a quantum dot which are coupled to M phonons by a disorder-induced Yukawa coupling.

Ferrari, Francesco

The Hubbard model on the kagome lattice is often considered as a minimal model to describe the rich low-temperature behavior of AV3Sb5 compounds (with A=K, Rb, Cs) [1], featuring charge-density waves (CDWs), superconductivity (SC), and possibly broken time-reversal symmetry. We investigate its ground-state properties when both onsite and nearest-neighbor Coulomb repulsions are considered at the van Hove filling. Our study is based on variational Jastrow-Slater wave functions which are capable of describing both CDW and SC phases and account for the effects of electronic correlation beyond the mean-field level. We reveal the presence of different repulsion-driven CDWs and, contrary to previous studies, the absence of ferromagnetism and charge- or spin-bond order. No signatures of chiral phases are detected. Remarkably, the CDWs triggered by the Coulomb repulsion possess charge disproportionations that are not compatible with the ones observed in AV3Sb5. As an alternative mechanism to stabilize charge order, we consider the electron-phonon interaction, modeled by coupling the hopping amplitudes to quantum phonons, as in the Su-Schrieffer-Heeger model. Our results show the instability towards a tri-hexagonal distortion with 2x2 periodicity, in a closer agreement with experimental findings [2]. [1] B. R. Ortiz, L. C. Gomes, J. R. Morey et al., Phys. Rev. Materials 3, 094407 (2019) [2] F. Ferrari, F. Becca, R. Valentí, Phys. Rev. B 106, L081107 (2022)

Franke, Lars

It is a long standing result in the theory of classical criticality that a second order phase transition when coupled to a compressible lattice will become first order if the Larkin-Pikin criterion[1] is satisfied. More recently the extension of these results to quantum criticality has sparked the interest of the community[2,3]. However, until now a detailed analysis of a microscopic theory describing a quantum phase transition on a compressible lattice and its implications for the nature of the phase transition as well as the consequences for the lattice has been missing. Here we provide this calculation for a Lorentz-invariant $\phi^4$-theory with quadratic coupling to strain and analyze it using renormalization group (RG) methods to one-loop order. We find that both critical and phonon velocity flow with RG leading to an additional fixed point where the phonons have a renormalized dynamical exponent. Furthermore, our results show that the quantum version of the Larkin-Pikin criterion[2] holds, but even when the criterion is not satisfied a structural instability can still occur, if the coupling is large enough. [1] A. Larkin and S. Pikin, Sov. Phys. JETP 29, 891 (1969) [2] P. Chandra, P. Coleman, M. A. Continentino, and G. G. Lonzarich, Phys. Rev. Res. 2, 043440 (2020) [3] A. Samanta, E. Shimshoni, and D. Podolsky, Phys. Rev. B 106, 035154 (2022)

Gaa, Jonas

Garcia-Gassull Areitio, Laura

We look into the Van Hoove singularity in the Fermi surface of $Sr_2RuO_4$ when uniaxial strain along the c-axis is applied. We do so using DFT and DMFT. We also study the d-wave Pomeranchuk instability for the antiferromagnetic $RuO_2$. Here, the strain is uniaxial along the c-axis.

Haddad, Sonia

Marwa Mannaï 1 and Sonia Haddad 1,2 1 LPMC, Faculté des Sciences de Tunis, Université Tunis El Manar, Tunisia 2 Max Planck Institute for the Physics of Complex Systems, Dresden Germany Several numerical studies have shown that the electronic properties of twisted bilayers of graphene (TBLG) and transition metal dichalcogenides (TMDs) are tunable by strain engineering of the stacking layers. In particular, the flatness of the low-energy moiré bands of the rigid and the relaxed TBLG was found to be, substantially, sensitive to the strain. However, to the best of our knowledge, there are no full analytical calculations of the effect of strain on such bands. We derive, based on the continuum model of moiré flat bands, the low-energy Hamiltonian of twisted homobilayers of graphene and TMDs under strain at small twist angles. We obtain the analytical expressions of the strain-renormalized Dirac velocities and explain the role of strain in the emergence of the flat bands. We discuss how strain could correct the twist angles and bring them closer to the magic angle of TBLG and how it may reduce the widths of the lowest-energy bands at charge neutrality of the twisted homobilayer of TMDs. The analytical results are compared with numerical and experimental findings and also with our numerical calculations based on the continuum model.

Hameed, Sajna

The properties of quantum materials are commonly tuned using experimental variables such as pressure, magnetic field and doping. Here we explore a different approach using irreversible, plastic deformation of single crystals. We show that compressive plastic deformation induces low-dimensional superconductivity well above the superconducting transition temperature (Tc) of undeformed SrTiO3, with evidence of possible superconducting correlations at temperatures two orders of magnitude above the bulk Tc. The enhanced superconductivity is correlated with the appearance of self-organized dislocation structures, as revealed by diffuse neutron and X-ray scattering. We also observe deformation-induced signatures of quantum-critical ferroelectric fluctuations and inhomogeneous ferroelectric order using Raman scattering. Our results suggest that strain surrounding the self-organized dislocation structures induces local ferroelectricity and quantum-critical dynamics that strongly influence Tc, consistent with a theory of superconductivity enhanced by soft polar fluctuations. Our results demonstrate the potential of plastic deformation and dislocation engineering for the manipulation of electronic properties of quantum materials.

Hansen, Max Oberon

We re-examine the effect of long-range Coulomb interactions on the collective amplitude and phase modes in the incommensurate charge-density wave ground state of quasi-one-dimensional conductors. Using an effective action approach we show that the longitudinal acoustic phonon protects the gapless linear dispersion of the lowest phase mode in the presence of long-range Coulomb interactions. Moreover, in Gaussian approximation amplitude fluctuations are not affected by long- range Coulomb interactions. We also calculate the collective mode dispersions at finite temperatures and compare our results with the measured energies of amplitude and phase modes in K$_{0.3}$MoO$_3$. With the exception of the lowest phase mode, the temperature dependence of the measured mode energies can be quantitatively described within a multi-phonon Fr ̈ohlich model neglecting long-range Coulomb interactions.

Henßler, Fabian

Our goal is to investigate the effects of tensile out-of-plane strain on layered quantum materials in order to drive them towards the two-dimensional (2D) limit where emergent exotic physical properties can be induced. To this aim, we developed a comprehensive approach combining microstructure design, strain simulation, focused ion beam (FIB) techniques to microfabicate cantilevers out of the material of interest. We selectively choose materials with weak interlayer coupling, such as delafossites and pnictides and we explore, with a micrometer resolution, the spatially varying properties of the strained material by mean of microRaman spectroscopy. This enables us to probe locally the lattice dynamics, which is highly sensitive to strain, and can in principle allow us to detect strain-induced structural and electronic phase transitions (e.g. charge density wave (CDW) phases). To illustrate the methodology, we present preliminary results on delafossite materials renowned for their exceptional purity [1]. By subjecting PdCoO2 to controlled strain, our aim is to probe its low-temperature physics and evaluate the potential for inducing exotic phases. [1] Mackenzie, A.P., The properties of ultrapure delafossite metals. Reports on Progress in Physics, 2017. 80(3): p. 032501

Hsu, Hsiu-Chuan

We investigate the one-dimensional quantum ring constructed by the spin-orbit coupled material, in which the quantum spin-Hall Bernevig-Zhang (BZ) Hamiltonian and Rashba-Dirac (RD) type spin-orbit coupling are taken into account (called RD-BZ Hamiltonian in this paper).The BZ coupling could be realized by applying strain to Zinc-Blende semiconductors. It is known that the curvature of the ring generates an out-of-plane effective magnetic field, acting as an internal Zeeman field. We find that the BZ coupling can change the strength of the internal Zeeman field, which enables us to detect the effect of the internal Zeeman field by changing BZ coupling. The conductance without leads is discussed. The cancellation of the internal Zeeman field due to the BZ coupling can be detected by using specific fractional magnetic flux. Moreover,we find that the persistent spin and charge currents as a function of the magnetic flux exhibit nodelike lines, which amazingly are perpendicular to each other. As a consequence, the persistent spin current could be nonzero even when the charge current vanishes at nonzero magnetic flux. The result suggests a pure spin current in quantum rings, and its direction can be reversed by changing the magnetic flux. The increase in the BZ coupling would exhibit the plateaulike pure spin current.

Jibuti, Luka

Following the experimental observation of the Frude-Ferrel-Larnik-Ovchinnikov (FFLO) state in heavily hole-doped KFe2As2, we develop a microscopic theory of multi-orbital FFLO phase in this system, based on the microscopic low-energy model consisting of two $\Gamma$-centered hole pockets created by $d_{xz}$ and $d_{yz}$ orbitals and the sizeable spin-orbit coupling between them. We use the leading angular harmonics approximation (LAHA) to write down the general form of the interaction, that involves both s-wave and d-wave channels. By decomposing the interaction into s- and d-wave channels, employing the mean-field approximation and solving the self-consistent equations for the order parameters, we analyse the creation of the FFLO phase, with the appearance of the non-zero, symmetry preserving $\bold{q}$ vector for the nodal d-wave state and s-wave with accidental nodes. We also discuss the role of spin-orbit coupling and possible orbital FFLO state, discussed recently in the context of Ising superconductors.

Kaib, David

Recent experimental studies on the Kitaev candidate material $\alpha$-RuCl$_3$ have pointed to the presence of significant magnetoelastic coupling. For example, the longitudinal thermal conductivity, which is expected to be dominated by phonons, shows a strong dependence on magnetic field strength. In this study we present first-principles-based numerical results on magnetoelastic effects in $\alpha$-RuCl$_3$, modelling field-dependent magnetostriction, Grüneisen parameter and thermal conductivity with good agreement to experiment. We show that strains lead to a strong reorganization of the strongly anisotropic magnetic Hamiltonian and propose uniaxial pressure experiments to suppress the zigzag antiferromagnetic order.

Konieczna, Amanda

The Hubbard model describes the behaviour of electrons in a solid through two processes: the hopping between sites which is described by the kinetic term and the Coulomb interaction in the potential term. Usually one approximates the Coulomb interaction through the diagonal Hubbard interaction term and, additionally, Hund's coupling as the only off-diagonal contribution.The aim of our work is to show the non-negligible influence of other off-diagonal parts of the Coulomb interaction on the properties of a crystal. We work with a toy model that considers three and four orbitals on two sites, with hoppings and interaction strenght as input parameters and analyse results, e.g. energy bands and gaps in depencence of the newly added terms.

Kopp, Marvin

The colossal magnetoresistance (CMR) effect has inspired extensive studies for decades and is still the subject of intense research due to its central place in the physics of correlated electron systems as well as its potential relevance for applications. Unlike the prototypical CMR compounds based on mixed valence and double exchange in manganites or a structural Jahn-Teller distortion and ferromagnetic ordering, we focus on Europium based systems (Eu$_5$In$_2$Sb$_6$; EuCd$_2$P$_2$), exhibiting strikingly large ($10^4\,$\%) negative magnetoresistances in the vicinity of their antiferromagnetic ordering temperatures. Initial reports suggest that strong magnetic fluctuations within the layered structure could be responsible for the drastic change of resistance in the presence of magnetic fields. In this work, we aim to investigate these fluctuations using higher harmonic resistance and resistance fluctuation (noise) spectroscopy. Higher harmonic measurements are sensitive to the small changes in magneto-electric coupling caused by the postulated formation of magnetic clusters (polarons), that often remain undetected in standard resistance measurements. The dynamics of these magnetic clusters are studied using resistance noise spectroscopy as a function of temperature, magnetic field and pressure (strain). We also apply micro-Hall-magnetometry in order to further understand the origin of the onset of interactions between these polarons. Our results provide an outlook to use our techniques to study Eu-based systems which can be considered as model systems for CMR effects and polaron formation.

Krebber, Sarah

The interplay of topology and magnetism has been of great interest in the last few years. The coexistence of both phenomena can be realized in europium based compounds with the 122 stoichiometry and a trigonal crystal structure (P-3m1). Recently, a spin fluctuation induced Weyl semimetal state in the paramagnetic phase of EuCd$_{2}$As$_{2}$ [1,2] and its tunability by pressure [3] was discovered. Furthermore, EuCd$_{2}$P$_{2}$ has been explored due to its colossal magnetoresistance [4], where the origin of the effect was explained by the formation of ferromagnetic clusters [5]. With the aim of studying the Cd compound in detail and finding similar effects in EuZn$_{2}$P$_{2}$, both systems were studied. Here, we present the successful single crystal growth and characterization of EuCd$_{2}$P$_{2}$ and EuZn$_{2}$P$_{2}$ via magnetization, electrical transport, heat capacity and spectroscopy. [1] Ma et al., Science Adv. 5, eaaw4718 (2019). [2] Jo et al., Phys. Rev. B 101, 140402(R) (2020). [3] Gati et al., Phys. Rev. B 104, 155124 (2021). [4] Wang et al., Adv.Mater., 33, 2005755 (2021). [5] Sunko et al., arXiv:2208.05499, (2022).

Kumar, Sanjeev

Jahn-Teller effect and spin-orbit coupling are two of the very well known concepts in atomic physics. It becomes essential to invoke these concepts to understand a number of phenomena observed in condensed matter system, and more specifically in transition-metal oxides. We attempt to understand, in an unbiased approach, the interplay of these two effects in a three-orbital model for $t_{2g}$ bands relevant for $4d$ and $5d$ transition metal oxides. The atomic limit of this problem is thoroughly discussed by Streltsov and Khomskii in PRX 10, 031043 (2020). We set up a Monte-Carlo method to study the lattice version of the problem. The method relies on the approximation of treating the distortion variables classically. Within this approximation one can perform a Markov Chain Monte Carlo that is hybrid in nature, {\it i.e. }, Monte Carlo steps require solutions to the Fermion problem. In this talk, I will share some of the initial findings of our numerical analysis. We try to identify scenarios where spin-orbit coupling can enhance the Jahn-Teller effect and hence orbital ordering. Possibility of finding emergent topological phases in such models will also be discussed.

Lacmann, Tom

Authors: Tom Lacmann, Amir-Abbas Haghighirad, Sofia Michaela Souliou, Rolf Heid, Mehdi Frachet, Fabian Henßler, Mai Ye, Philippa McGuinness, Michael Merz, Kristin Willa, Tomasz Poreba, Konstantin Glazyrin, Gaston Garbarino, Matthieu Le Tacon Hydrostatic and uniaxial pressure have proven to be good tools for tuning competing orders, including superconductivity and charge density waves (CDW), in a wide variety of materials [1-2]. These techniques allow to gain new insights into the origin of the different orders and their interplay. The superconductor $BaNi_2As_2$ ($T_c$≈0.6 K) is isostructural with the Fe-based superconductor BaFe2As2 at ambient conditions but does not exhibit long-range magnetic order [3]. In analogy to the spin density wave in BaFe2As2, a degenerate incommensurate CDW is observed, and has been shown to be unconventional in nature [4-5]. Consequently, $BaNi_2As_2$ is a potential candidate system for charge driven nematicity, and recent Raman study further unveiled an unusual coupling of nematic fluctuations to the lattice, forming a nematic liquid [6]. Nematicity enhanced Cooper pairing has also been proposed in the Sr-substituted system [7], yet overall the interplay between lattice, charge density waves and superconductivity remains unclear. To better understand their relation, we present high-resolution X-ray diffraction studies of pure and P-substituted BaNi2As2 single crystals under hydrostatic and uniaxial pressure. Pressure was applied using a diamond anvil cell and a piezoelectric strain cell, respectively. We found a strong dependence of the charge density waves and the underlying lattice under applied pressure. Our DFT calculations find a phonon instability for all observed CDWs under hydrostatic pressure with similar wave vectors to the experimental one. The calculations suggest an unconventional nature of the CDWs. [1] T. Yamazak et al. Phys. Rev. B 79, 094508 [2] H.-H. Kim et al. Phys. Rev. Lett. 126, 037002 [3] A. S. Sefat et al. Phys. Rev. B 79, 094508 [4] S. M. Souliou et al. Phys. Rev. Lett. 129, 247602 [5] A. R. Pokharel et al. Commun Phys 5, 141 (2022). [6] Y. Yao et al. Nat Commun 13, 4535 (2022) [7] C. Eckberg et al Nat. Phys. 16, 346–350 (2020)

Lang, Michael

P. Eibisch$^{1}$, C. Thurn$^{1}$, A. Ata$^{1}$, Y. Saito$^{1}$, S. Hartmann$^{1}$, U. Tutsch$^{1}$, B. Wolf$^{1}$, A. T. M. Nazmul Islam$^{2}$, S. Chillal$^{2}$, A. R. N. Hanna$^{2,3}$, B. Lake$^{2,3}$, and M. Lang$^{1}$ $^{1}$Physikalisches Institut, Goethe-Universität, 60438 Frankfurt (M), Germany $^{2}$Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany $^{3}$Institut für Festkörperforschung, Technische Universität Berlin, 10623 Berlin, Germany PbCuTe$_2$O$_6$ is considered as one of the rare candidate materials for a three-dimensional quantum spin liquid (QSL). This assessment was based on the results of various magnetic investigations, performed mainly on poly-crystalline material [1-3]. More recently, thanks to the availability of high-quality single crystals [4], an even more exotic behavior was observed, yielding ferroelectric order below $T_{FE} \approx$ 1 K, accompanied by distinct lattice distortions, and a somewhat modified magnetic response which is still consistent with a QSL [5]. Here we report on low-temperature measurements of various thermodynamic, magnetic and dielectric properties of single crystalline PbCuTe$_2$O$_6$ in magnetic fields $B \leq$ 14.5 T [6]. The combination of these probes allows us to construct a detailed $B-T$ phase diagram featuring a ferroelectric phase for $B \leq$ 8 T and a $B$-induced magnetic phase at $B \geq$ 11 T. These phases are preceded by or coincide with a structural transition from a cubic high-temperature phase into a distorted non-cubic low-temperature state. The phase diagram discloses two quantum critical points (QCPs) in the accessible field range, a ferroelectric QCP at $B_{c1}$ = 7.9 T and a magnetic QCP at $B_{c2}$ = 11 T. Field-induced lattice distortions, observed in the state at $T >$ 1 K and which are assigned to the effect of spin-orbit interaction of the Cu$^{2+}$-ions, are considered as the key mechanism by which the magnetic field couples to the dielectric degrees of freedom in this material. References [1] B. Koteswararao et al., Phys. Rev. B 90, 035141 (2014) [2] P. Khuntia et al., Phys. Rev. Lett. 116, 107203 (2016) [3] S. Chilla et al., Nat. Commun. 11, 2348 (2020) [4] A. R. N. Hanna et al., Phys. Rev. Mater. 5, 113401 (2021) [5] Ch. Thurn et al., npj – Quantum Materials 6, 95 (2021) [6] P. Eibisch et al., arXiv:2302.13774

Mojarro Ramirez, Miguel

We study the effects of a uniform strain on the electronic and topological properties of the 2D kagome lattice using a tight-binding formalism that includes intrinsic and Rashba spin-orbit coupling (SOC). The degeneracy at the $\Gamma$ point, where a flat-band-parabolic-band touching occurs, evolves into a pair of (tilted) type-I Dirac cones owing to a uniform strain, as shown by effective Hamiltonians, where the anisotropy and tilting of the bands depend in a nontrivial way on the magnitude and direction of the strain field. Interestingly, we find that the Dirac cones become type-III (including flat dispersions) when the strain is applied along the sawtooth direction. As expected, the inclusion of SOC opens a gap at the emergent Dirac points, making the strained flat band to become topological, as characterized by a nontrivial $\mathbb{Z}_2$ index. We show that the strain drives the systems into a trivial phase for strains of a few percent (with Grüneisen parameter and Poisson ratio values taken as in graphene), allowing topological transitions via uniform deformations. These findings suggest an alternative way of engineering anisotropic tilted Dirac bands with tunable topological properties in strained kagome lattices.

Möller, Marius

The honeycomb Kitaev material $\alpha$-RuCl$_3$ is widely investigated due to its originally suspected proximity to a spin liquid state suggested by unusual neutron scattering results. The magnetic Hamiltonian was initially formulated as a generalized Kitaev model $K_1$-$J_1$-$\Gamma_1$-$\Gamma^{'}_1$-$J_3$ in a cubic spin reference orientated along the Ru-Cl bonds. Recent studies, however, suggest that a crystallographic parametrization of the Hamiltonian in a spin-ice-like language $J(XY)$-$\Delta$-$J_{\pm\pm}$-$J_{z\pm}$-$J_3$ could lead to significant reduction of the parameter space, hinting towards a potential minimal model of $\alpha$-RuCl$_3$. We present the classical and quantum phase diagram of this $J(XY)$-$J_{z\pm}$-$J_3$ minimal model candidate obtained by Luttinger-Tisza method (LT), Exact Diagonalization (ED) and Density Matrix Renormalization Group (DMRG). Further, we present the phase diagrams of three interesting parameter regions with constrained anisotropic exchanges $K_1$,$\Gamma_1$,$\Gamma^{'}_1$ leading to effective $J_1$-$J_3$ models which possibly capture the relevant region to describe the essential physics of $\alpha$-RuCl$_3$.

Müller, Jens

Thanks to the powerful toolkit of organic chemistry, quasi-two-dimensional molecular metals $\kappa$-(ET)$_2$X and related compounds are highly tunable and constitute a playground for studying rich phase diagrams with novel quantum phases and interesting ground states of strongly interacting electrons residing in a relatively soft lattice. Electronic ferroelectricity, where electrons play the role of the ions in conventional displacive ferroelectrics, has recently become an active area of research, where it has been suggested that in certain dimerized systems the electric dipoles originate from charge order, i.e., a charge disproportionation within the (ET)$_2$ dimers, indicating a breakdown of the dimer-Mott model. In such a scenario, one expects characteristic and large changes of the low-frequency dynamics of the charge carriers coupled to the electronic, magnetic and lattice degrees of freedom. In this talk we will discuss such dynamical measurements employing fluctuation (noise) spectroscopy in the mHz – kHz regime. The method is complementary to dielectric spectroscopy and allows to extract spectroscopic information in conductive systems from electronic transport measurements, i.e.\ without injecting additional charge carriers. In this talk we aim to give an overview of the systematics of charge fluctuations in the dimer- Mott and charge-ordered states of various different materials. We compare various compounds with different anion X and discuss in detail the recently synthesized system $\kappa$-(BETS)$_2$Mn[N(CN)$_2$]$_3$. Among these different compounds, we will discuss remarkable similarities as, e.g., the formation of nano-scale polarized clusters and strong out-of-equilibrium kinetic processes upon approaching and inside the ordered phase, respectively, as well as electric-field tuning of the charge dynamics. Finally, we will comment on the controversial relationship of structural and electronic glassiness in the non-dimerized compounds $\theta$-phase compounds, where a charge-ordered state can be kinetically avoided in favor of a novel charge-glass state.

Nediadath Sathyanadhan, Sangeetha

O'Neil, Caitlin

Sr$_2$RuO$_4$ under uniaxial pressure undergoes a Lifshitz transition [1]. It has recently been shown that the electronic Lifshitz transition results in a pronounced lattice softening which can be observed through measurements of the Young's Modulus [2]. The Young's Modulus has previously been measured using both force and displacement capacitors on the uniaxial pressure cell [3]. We present a new technique using AC stresses and strains which allows for the direct measurement of the Young's Modulus. In addition, the AC stress-strain measurements also allow to determine imaginary part of the Young’s modulus, which can be indicative of slow lattice relaxations. Through these experiments on Sr$_2$RuO$_4$ we prove the viability of this technique. [1] Sunko et al., npj Quantum Mater. 4, 46 (2019) [2] Noad et al., submitted (2023). [3] Barber et al., Review of Scientific Instruments 90, 023904 (2019)

Ocker, Michelle

At ambient pressure the compound YbInCu4 undergoes a 1$^{st}$ order valence transition at T$_v$ = 42 K by changing the temperature [1]. Thus, ytterbium in the compound is present in the Yb$^{2.9+}$ state at high temperatures and as Yb$^{2.7+}$ at low temperatures [2]. In analogy to Eu compounds, the line of first order valence transitions might end in a second order critical endpoint [3]. In order to study the nature of the phase transition in more detail, single crystal samples can be prepared in In-Cu flux which are substituted with silver and gold [4]. With increasing substitution level, negative chemical pressure within the crystal is increased and the characteristics of the valence transition changes significantly. Here, we report on the single crystal growth with different substitution levels and the results of our structural, chemical and physical characterization.\\ [1] I. Felner et al., Physical Review B 35, (1987) 6956.\\ [2] H. Sato et al., Physica B 351, (2004) 298.\\ [3] Y. Onuki et al., Journal of the Physical Society of Japan 89, (2020) - 102001.\\ [4] J. L. Sarrao et al., Physical Review B 54, (1996) 12207.

Palan, Yash

Schindler, Paul Manuel

Periodic driving has become an essential tool for controlling quantum systems. Besides it utmost importance in engineering Hamiltonians otherwise not experimentally accesible, periodic driving opens the possibility to realise novel, non-equilibrium phases of matter without analog in static systems. While much advance has been made in engineering desired Hamiltonians, studying the actual states of interest of these periodically driven systems still mainly relies on adiabatic state preparation. However, ideal adiabatic processes require very slow dynamics, leading to a compromise in time scales of heating and decoherence processes. In order to allow for faster state preparation, we extent the framework of counter-diabatic driving to the non-equilibrium regime. In particular, we introduce a variational principle allowing us to compute experimentally accesible approximate counter-diabatic protocols in complex quantum systems. We apply our scheme to speed up the state preparation in a Floquet topological pump, a system recently realised in experiments.

Sharma, Vishal Kumar

The study of coupling between electron-phonon is of fundamental importance to understand the transport and thermodynamic properties of materials. It is posited to play an important role in material properties optical, magnetic and transport properties. The study of e-p coupling is essential to understand the role of electron-phonon coupling in high critical temperature superconducting materials such as Cuperates. Here we present a new approach to detecting the strength of electron-phonon coupling, which is complementary to the usual resonant inelastic x-ray scattering (RIXS), Angle-Resolved Photoemission (ARPES) and methods which uses the emission line broadening with temperature to infer about the electron-phonon coupling strength. First, we will suggest a theoretical explanation of the method which combines 2D pump-probe technique with the Two photon absorption to measure the momentum dependent electron phonon coupling in materials. Then we discuss the experimental results on the mode resolved, momentum-dependent electron-phonon coupling the methyl ammonium lead iodide and it's evolution with temperature.

Song, Young-Joon

In this presentation, using ab initio calculations and photoemission spectroscopy techniques, we will address the valence transition in tetragonal EuPd$_2$Si$_2$ in the context of a microscopic point of view. EuPd$_2$Si$_2$ is a well-known material to show the valence transition from Eu$^{2+}$ to Eu$^{3+}$ when a decrease(increase) in temperature(pressure). We found out that Eu's valence state is strongly related to two bond lengths, Eu-Pd and Eu-Si. What is more, our results reveal how an excess electron from Eu is redistributed by applying volume reduction, which is good in agreement with our recent HAXPES measurements.

Stangier, Veronika

Critical phases can be found through a wide range of materials, often accompanied by a superconducting phase emerging around the quantum critical point. However, the theoretical description of the pairing mechanism remains challenging due to the absence of quasi-particles in the critical phase. One promising approach to describe critical phases is the class of SYK models. While previous works have found superconductivity from incoherent electrons through a Yukawa-SYK interaction, this model is only applicable in zero dimensions. Extensions of this model have found critical phases in finite spatial dimensions without addressing superconductivity. In this work we present a model for the emergence of superconductivity from a critical phase that is exactly solvable in the large N limit and holds in both one and two spatial dimensions.

Steward, Charles

The combined rotational and time-reversal symmetry breakings that define an altermagnet lead to an unusual d-wave (or g-wave) magnetization order parameter, which in turn can be modeled in terms of multipolar magnetic moments. Here, we show that such an altermagnetic order parameter couples to the dynamics of the lattice even in the absence of an external magnetic field. This coupling is analogous to the non-dissipative Hall viscosity and describes the stress generated by a time-varying strain under broken time-reversal symmetry. We demonstrate that this effect generates a hybridized paramagnon-polaron mode, which allows one to assess altermagnetic excitations directly from the phonon spectrum. Using a scaling analysis, we also demonstrate that the dynamic strain coupling strongly affects the altermagnetic phase boundary, but in different ways in the thermal and quantum regimes. In the ground state, we find that a hardening of the altermagnon mode leads to an extended altermagnetic ordered regime, whereas for non-zero temperatures, the softening of the phonon modes leads to increased fluctuations that lower the altermagnetic transition temperature. We also discuss the application of these results to standard ferromagnetic systems.

Stilkerich, Nina

PdCrO$_2$ is a triangular antiferromagnet that undergoes a transition from a double-q to single-q magnetic structure under moderate uniaxial stress [1]. When pushing the lattice towards a square-like lattice, another transition from spin-spiral order to a linear antiferromagnetic structure is predicted for high stress of about 1 GPa [1]. On PdCrO$_2$, we performed stress-strain measurements and XRD measurements under strain. With both techniques, we were not only able to identify the double- to single-q transition, but we also discovered an additional transition under higher stress. This might be the predicted spin-spiral to Néel transition. [1] D. Sun et al., New J. Phys. 23, 123050 (2021)

Thomas, Teslin Rose

Thomson, Mark

Thyzel, Tim

To study the Mott metal-insulator transition, quasi-two-dimensional organic charge-transfer salts are ideal model systems, because the transition is accessible in a convenient temperature-pressure region. Specifically, in the material family $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Z, where Z is Br or Cl, the Mott transition occurs below 30 MPa of hydrostatic pressure and above 30 K. Of particular interest is the critical endpoint of the transition, where a breakdown of Hooke's law of elasticity has been observed [1], as well as indications of ergodicity breaking [2]. In order to explore the extent of these effects, as well as the carrier dynamics near the bandwidth-controlled finite-temperature Mott transition line, we employ resistance noise spectroscopy as a probe for very slow fluctuations in transport. Using this technique in an automated fashion allows us to scan the phase diagram for signs of critical slowing-down and non-stationarity of the fluctuations, which hint at critical behaviour. [1] E. Gati, Sci. Adv. 2, e1601646, 2016 [2] B. Hartmann, Phys. Rev. Lett. 114, 216403, 2015

Valadkhani, Adrian

Recently, it was discovered that SrNi$_2$P$_2$ has a high recoverable strain rate of approx. $14\%$, which is very stable against repetition[1]. Common values for such strain rates are less than one percent and limited by plastic deformation or fracture. For SrNi$_2$P$_2$, a double lattice collapse was proposed as the underlying mechanism. We perform ab initio density functional theory calculations for AT$_2$X$_2$ (A = (earth) alkaline, T = transition metal, X = atom of the C or N group) under various strain conditions and find that the strain-free ground state exists in an orthorhombic unit cell in which both collapsed and uncollapsed P-bonds are present. Upon strain, a structural transition to a tetragonal unit cell of the ThCr2Si2 family occurs. Furthermore, we investigate the strain effect one tetragonal 1144 systems as well. [1] S. Xiao et al. Nano Lett. 2021, 21, 19, 7913–7920

Walther, Franziska

The ternary europium-based intermetallic compounds with the ThCr$_{2}$Si$_{2}$-type structure show a variety of intriguing physical properties due to the coupling between lattice and electronic degrees of freedom. Eu ions can be present in a magnetic divalent or non-magnetic trivalent state. Under variation of temperature and pressure, it's possible to enforce a valence transition associated with a change of the unit cell volume [1]. At ambient pressure, EuRh$_{2}$Si$_{2}$ orders antiferromagnetically below T$_N$= 24 K in a stable divalent state [2], whereas the isoelectronic related compound EuCo$_{2}$Si$_{2}$ is nearly trivalent und indicates no magnetic ordering [1]. EuRh$_{2}$Si$_{2}$ undergoes a pressure-induced first order valence transition [3]. We expect the second order critical endpoint in the pressure range from 1.7 to 2.1 GPa, where the first-order phase transition terminates and critical elasticity may occur. We want to approach the critical endpoint by applying chemical pressure through substituting Rh in EuRh$_{2}$Si$_{2}$ with Co. We report on the growth of samples of the Eu(Rh$_{1-x}$Co$_x$)$_{2}$Si$_{2}$ -system and the characterization of their physical and chemical properties. \newline [1] Y. Onuki et al., J. Phys. Soc. Japan \textbf{89}, 102001 (2020) \newline [2] S. Seiro, C. Geibel, J. Phys.: Condens. Matter \textbf{26}, 046002, (2014) \newline [3] F. Honda et al J. Phys. Soc. Japan \textbf{85}, 063701 (2016)

Warawa, Konstantin

Weber, Manuel

The study of competing orders in strongly correlated quantum systems is motivated by the rich phase diagrams of real materials, but also by proposals of exotic phase transitions beyond the Landau paradigm. Different orders can arise either from different interactions or from local and nonlocal components of the same Coulomb interaction. In this talk, we will discuss how competing orders can arise from retardation effects originating from a coupling to quantum phonons. To this end, we will consider the one-dimensional Su-Schrieffer-Heeger model at half-filling, where the electronic hopping is modulated by a coupling to bond phonons. For this model, the Peierls instability predicts a transition towards a single dimerized phase. Using a recently developed quantum Monte Carlo method for retarded interactions, we show that the coupling to bond phonons instead leads to two dimerized phases originating from the same retarded interaction upon variation of the phonon frequency. Our numerics provides evidence for a non-Landau continuous quantum phase transition between the two orders, that is consistent with a field theory previously predicted for frustrated spin chains. Motivated by these results, we also study the phase diagram of a spin-Peierls model on the honeycomb lattice. We find that a coupling to phonons can destroy the antiferromagnetic ground state and induce a valence-bond solid with Kekule pattern. While the transition is strongly first order in the adiabatic phonon limit, we find that quantum lattice fluctuations tune the transition towards weakly first order. Our results motivate future studies of retarded effects in strongly correlated systems.

Wolf, Bernd

Tuning the ground state of EuPd$_2$(Si$_{1−x}$Ge$_x$)$_2$ using He-gas pressure B. Wolf, T. Lundbeck, M. Peters, K. Kliemt, C. Krellner, M. Lang Physikalisches Institut, Goethe University, 60438 Frankfurt/Main, Germany The strongly correlated intermetallic compound EuPd$_2$Si$_2$ is one of the rare examples exhibiting a temperature-induced valence-change crossover centered around $T'_{\text{V}}$, the cross-crossover temperature. Pronounced lattice effects together with significant changes in the magnetic properties accompany the valence change in a narrow temperature interval. In the general $p-T$ phase diagram of Eu-based valence fluctuating compounds [1] EuPd$_2$Si$_2$ is located on the high-pressure side (crossover range) of the second-order critical endpoint (CEP) where novel collective phenomena originating from a particularly strong coupling between electronic-, magnetic- and lattice degrees of freedom can be expected [2]. We present magnetic susceptibility data taken on high-quality single crystals of EuPd$_2$(Si$_{1−x}$Ge$_x$)$_2$ for Ge-concentrations 0 ≤ x ≤ 0.105 in the temperature range 2 K $≤$ T $≤$ 300 K and He-gas pressure up to 0.5 GPa. For x = 0 at ambient pressure, we observe a pronounced valence crossover around $T'_{\text{V}}$ ∼ 160 K. As expected, $T'_{\text{V}}$ shifts to lower temperatures with increasing Ge-concentration, reaching $T'_{\text{V}}$ ∼ 90 K for x = 0.058, while still showing a non-magnetic ground state. In contrast, for x = 0.105 we observe long-range antiferromagnetic (afm) order setting in below $T_{\text{N}}$ = 47.3 K [3]. The valence-change-crossover temperature T’V shows an extraordinarily strong pressure dependence of d$T'_{\text{V}}$ /d$p = + (80 ± 10)$ K/GPa. On the other hand, only a very small pressure dependence of d$T_{\text{N}}$/d$p ≤ + (1 ± 0.5)$ K/GPa is found for the afm order upon pressurizing the x = 0.105 crystal from $p$ = 0 to 0.05 GPa. The important finding of the present study is that for x = 0.105 a further mild increase in pressure to 0.1 GPa can induce a drastic change in the material’s ground state from afm order to valence change crossover. Estimates of the entropy as a function of temperature for varying pressure indicate a first-order phase transition separating the afm order from the valence change crossover [4]. Our results imply the existence of particular type of second-order critical endpoint terminating this first-order transition line at $p_{\text{cr}}$ ≈ 0.06 GPa and $T_{\text{cr}}$ ≈ 45 K. [1] A. Onuki, et.al, Philosophical Magazine 97, 3399 (2017) [2] B. Wolf, F. Spathelf, J. Zimmermann, T. Lundbeck, M. Peters, K. Kliemt, C. Krellner, M. Lang, SciPost 202207-00023v2 (2022) [3] M. Peters, K. Kliemt, B. Wolf, M. Lang, and C. Krellner, http://arxiv.org/2303.07472v1 [4] B. Wolf, T. Lundbeck, J. Zimmermann, M. Peters, K.Kliemt, C. Krellner, M.Lang, http://arxiv.org/2303.0776v1

Ye, Mai

We study the strain dependence of the lattice parameters and diffuse scattering of high-temperature superconductor HgBa$_2$CuO$_{4+\delta}$ with T$_c$=78K . At European Synchrotron Radiation Facility, we apply a-axis compressive strain at T$_c$, and find that the lattice becomes orthorhombic and broad features of diffuse scattering develops around (h+0.5, 0, l) in which h is integer. We further investigate the temperature dependence of the diffuse scattering under strain. The results are interpreted in terms of shifts of atomic positions, and possible formation of charge density waves.

Ye, Mengxing

The search for fractionalization in quantum spin liquids largely relies on their decoupling with the environment. However, the spin-lattice interaction is inevitable in a real setting. While the Majorana fermion evades a strong decay due to the gradient form of spin-lattice coupling, the study of the phonon dynamics may serve as an indirect probe of fractionalization in a quantum spin liquid. First, we show that the Marajoana fermion edge and bulk phonon coupling plays an important role in the quantization of the thermal Hall conductivity in a chiral spin liquid [1]. Second, we show that the signatures of fractionalization of the Kitaev spin liquid can be seen in the sound attenuation and the Hall viscosity [2,3]: the former describes the phonon decay into the fractionalized excitations, and the latter is the leading order time-reversal symmetry breaking effect on the acoustic phonon. Indeed, a recent ultrasound experiment in $\alpha$-RuCl$_3$ [4] demonstrates the potential of phonon dynamics as a promising probe for uncovering fractionalized excitations in $\alpha$-RuCl$_3$. This poster is based on four papers: [1] Quantization of the thermal Hall conductivity at small Hall angles, Phys. Rev. Lett. 121, 147201 (2018) [2] Phonon dynamics in the Kitaev spin liquid,” Phys. Rev. Research 2, 033180 (2020) [3] Temperature evolution of the phonon dynamics in the Kitaev spin liquid,” Phys. Rev. B. 103, 214416 (2021) [4] Fractionalized Excitations Probed by Ultrasound, arXiv: 2303.09288

Zimmermann, Jan Niklas

Probing the electron-lattice coupling near the valence transition in $YbIn_{1−x}Ag_{x}Cu_{4}$ — Jan Zimmermann, Bernd Wolf, Michelle Ocker, Kristin Kliemt, Cornelius Krellner, and Michael Lang — PI, SFB/TR288, Goethe Univ., Frankfurt/M,. Deutschland The recently proposed phenomenon of \textit{critical elasticity} is linked to a non-perturbatively strong coupling between lattice- and critical electronic degrees of freedom [1]. Intermetallic compounds that show various types of phase transitions such as valence- or structural instabilities, that make it possible to study such collective phenomena, are currently a field of high interest. It has been shown that substitution can be used in $EuPd_{2}(Si_{1−x}Ge_{x})_{2}$ to generate chemical pressure which may open up the possibility to experimentally access directly the area around the critical endpoint [2]. It is expected to find similar effects for the valence transition in the intermetallic compound $YbIn_{1−x}Ag_{x}Cu_{4}$ [3]. We are investigating the elasticity of $YbIn_{1−x}Ag_{x}Cu_{4}$ using ultrasound-wave-propagation. In addition to measurements performed under variable temperature, we have developed a new setup that allows ultrasonic measurements to be performed under variable He-gas pressure. We will discuss first results on the elasticity, in comparison with data on the magnetic susceptibility, and highlight the additional experimental possibilities the new setup offers. [1] E. Gati \textit{et al.}, Sci. Adv. \textbf{2}, e1601646 (2016) [2] B. Wolf \textit{et al.}, arXiv:2210.12227, (2022) [3] S. Zherlitsyn \textit{et al.}, Phys. Rev. B, \textbf{60}, 5, (1999)