Christian Pfleiderer

Topology of Correlated Systems

Technical University of Munich

Department of Physics

James-Franck-Str. 1

85748 Garching


Group Webpage


Research focus: quantum phase transitions, electronic order, topology of correlated systems

The systematic search for quantum order in bulk materials, comprising the synthesis of high-purity single crystals, the experimental exploration of their thermodynamic and transport properties under extreme conditions, as well as microscopic studies using advance neutron and x-ray scattering form the basis for harvesting quantum phenomena in real materials.

Quantum phase transitions

The notion of particle-like elementary excitations represents a cornerstone of present day condensed matter physics. The putative breakdown of this concept in the vicinity of so-called quantum phase transitions, driven by quantum rather than thermal fluctuations, has been attracting tremendous interest for many decades. In turn the materials properties in the vicinity of quantum phase transitions offer an important starting point for an understanding of a wide range of materials with anomalous normal state properties, as well as emergent novel electronic phases such as magnetically mediated superconductivity or partial spin and charge order.

Selected publications

- Formation of a Topological Non-Fermi Liquid in MnSi; Nature, 497, 231 (2013)

- Spin Dynamics and Spin Freezing at Ferromagnetic Quantum Phase Transitions, European Journal of Physics: Special Topics, 224, 1041 (2015)

Complex forms of electronic order

Complex forms of electronic order are intimately connected with the electronic structure and the topological character of the Fermi surface as well as their modification in the presence of strong quantum correlations. The experimental investigation of the electronic structure of materials with complex forms of electronic order permits to track the effects of many body quantum effects and their relationship with thermodynamic and transport properties close to and far from equilibrium.

Selected publications

- Spin-resolved Fermi surface of the localized ferromagnetic Heusler compound Cu2MnAl measured with spin-polarized positron annihilation, Phys. Rev. Lett., 115, 206404 (2015)

- Parasitic small-moment-antiferromagnetism and non-linear coupling of hidden order and antiferromagnetism in URu2Si2 observed by Larmor diffraction, Phys. Rev. Lett., 104, 106406 (2010)

- Superconducting phases of f-electron compounds, Rev. Mod. Phys., 81, 1551 (2009)

Topological phenomena

The notions of symmetry breaking and generalized rigidities have let to a remarkably comprehensive account of complex forms of magnetic order in condensed matter systems. In recent years a new facet of magnetism research receives increasing attention that concerns the topological character of magnetically ordered systems, notably those properties that remain unchanged under elastic deformations. Important examples include skyrmions, vortices and monopoles in chiral or frustrated magnets. These topological aspects of magnetic order are not only appealing from an esthetical and conceptual point of view, but offer strikingly simple explanations for materials properties that may seem to be surprising and hideously complicated at first sight.

Selected publications

- Universal Helimagnon and Skyrmion Excitations in Metallic, Semiconducting, and Insulating Chiral Magnets, Nature Materials 14, 478 (2015)

- Unwinding of a Skyrmion Lattice by Magnetic Monopoles, Science 340, 1076 (2013)

- First Order Metamagnetic Transition in Ho2Ti2O7 observed by Vibrating Coil Magnetometery at Milli- Kelvin Temperatures, Phys. Rev. Lett. 108, 257204 (2012)

- Spin Transfer Torques in MnSi at Ultra-low Current Densities, Science 330, 1648 (2010)

- Skyrmion Lattice in a Chiral Magnet, Science 323, 915 (2009)


Tunable cooperativity in coupled spin-cavity systems

L. Liensberger, F.X. Haslbeck, A. Bauer, H. Berger, R. Gross, H. Huebl, C. Pfleiderer, M. Weiler

Physical Review B 104, L100415 (2021).

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We experimentally study the tunability of the cooperativity in coupled spin-cavity systems by changing the magnetic state of the spin system via an external control parameter. As a model system, we use the skyrmion host material Cu2OSeO3 coupled to a microwave cavity resonator. We measure a dispersive coupling between the resonator and magnon modes in different magnetic phases of the material and model our results by using the input-output formalism. Our results show a strong tunability of the normalized coupling rate by magnetic field, allowing us to change the magnon-photon cooperativity from 1 to 60 at the phase boundaries of the skyrmion lattice state.

DOI: 10.1103/PhysRevB.104.L100415

Compositional Studies of Metals with Complex Order by means of the Optical Floating-Zone Technique

A. Bauer, G. Benka, A. Neubauer, A. Regnat, A. Engelhardt, C. Resch, S. Wurmehl, C.G.F. Blum, T. Adams, A. Chacon, R. Jungwirth, R. Georgii, A. Senyshyn, B. Pedersen, M. Meven, C. Pfleiderer

Physica Status Solidi B-Basic Solid State Physics 2100159 (2021).

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The availability of large high-quality single crystals is an important prerequisite for many studies in solid-state research. The optical floating-zone technique is an elegant method to grow such crystals, offering potential to prepare samples that may be hardly accessible with other techniques. As elaborated in this report, examples include single crystals with intentional compositional gradients, deliberate off-stoichiometry, or complex metallurgy. For the cubic chiral magnets Mn1–xFexSi and Fe1–xCoxSi, single crystals are prepared in which the composition is varied during growth from x = 0 to 0.15 and from x = 0.1 to 0.3, respectively. Such samples allow us to efficiently study the evolution of the magnetic properties as a function of composition, as demonstrated by means of neutron scattering. For the archetypical chiral magnet MnSi and the itinerant antiferromagnet CrB2, single crystals with varying initial manganese (0.99–1.04) and boron (1.95–2.1) content are grown. Measurements of the low-temperature properties address the correlation between magnetic transition temperature and sample quality. Furthermore, single crystals of the diborides ErB2, MnB2, and VB2 are prepared. In addition to high vapor pressures, these materials suffer from peritectic formation, potential decomposition, and high melting temperature, respectively.

DOI: 10.1002/pssb.202100159

Confined dipole and exchange spin waves in a bulk chiral magnet with Dzyaloshinskii-Moriya interaction

P. Che, I. Stasinopoulos, A. Mucchietto, J. Li, H. Berger, A. Bauer, C. Pfleiderer, D. Grundler

Physical Review Research 3, 33104 (2021).

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The Dzyaloshinskii-Moriya interaction (DMI) has an impact on excited spin waves in the chiral magnet Cu2OSeO3 by means of introducing asymmetry in their dispersion relations. The confined eigenmodes of a chiral magnet are hence no longer the conventional standing spin waves. Here we report a combined experimental and micromagnetic modeling study by broadband microwave spectroscopy, and we observe confined spin waves up to eleventh order in bulk Cu2OSeO3 in the field-polarized state. In micromagnetic simulations we find similarly rich spectra. They indicate the simultaneous excitation of both dipole- and exchange-dominated spin waves with wavelengths down to (47.2±0.05) nm attributed to the exchange interaction modulation. Our results suggest the DMI to be effective in creating exchange spin waves in a bulk sample without the challenging nanofabrication and thereby in exploring their scattering with noncollinear spin textures.

DOI: 10.1103/PhysRevResearch.3.033104

Symmetry-enforced topological nodal planes in a chiral magnet

M.A. Wilde, M. Dodenhöft, A. Niedermayr, A. Bauer, M.M. Hirschmann, K. Alpin, A.P. Schnyder, C. Pfleiderer

Nature 594, 374 (2021).

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Despite recent efforts to advance spintronics devices and quantum information technology using materials with non-trivial topological properties, three key challenges are still unresolved. First, the identification of topological band degeneracies that are generically rather than accidentally located at the Fermi level. Second, the ability to easily control such topological degeneracies. And third, the identification of generic topological degeneracies in large, multisheeted Fermi surfaces. By combining de Haas–van Alphen spectroscopy with density functional theory and band-topology calculations, here we show that the non-symmorphic symmetries in chiral, ferromagnetic manganese silicide (MnSi) generate nodal planes (NPs), which enforce topological protectorates (TPs) with substantial Berry curvatures at the intersection of the NPs with the Fermi surface (FS) regardless of the complexity of the FS. We predict that these TPs will be accompanied by sizeable Fermi arcs subject to the direction of the magnetization. Deriving the symmetry conditions underlying topological NPs, we show that the 1,651 magnetic space groups comprise 7 grey groups and 26 black-and-white groups with topological NPs, including the space group of ferromagnetic MnSi. Thus, the identification of symmetry-enforced TPs, which can be controlled with a magnetic field, on the FS of MnSi suggests the existence of similar properties—amenable for technological exploitation—in a large number of materials.

DOI: 10.1038/s41586-021-03543-x

Atomistic investigation of surface characteristics and electronic features at high-purity FeSi(110) presenting interfacial metallicity

B. Yang, M. Uphoff, Y.-Q. Zhang, J. Reichert, A.P. Seitsonen, A. Bauer, C. Pfleiderer, J.V. Barth

PNAS 118 , e2021203118 (2021).

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Iron silicide (FeSi) provides multiple fascinating features whereby intriguing functional properties bearing significant application prospects were recognized. FeSi is understood notably as a correlated d-electron narrow-gap semiconductor and a putative Kondo insulator, hosting unconventional quasiparticles. Recently, metallic surface conduction channels were identified at cryogenic conditions and suggested to play a key role in the resistivity of high-quality single-crystalline specimens. Motivated by these findings, we prepared and closely examined a FeSi(110) surface with atomistically defined termination and topography. In the low-temperature regime, where surface metallicity emerges, the electronic band gap undergoes a subtle evolution. The pertaining key features, asymmetrization of the gap shape and formation of in-gap states, underscore the similarity of FeSi to unequivocal topological Kondo insulator materials.

DOI: 10.1073/pnas.2021203118

Microwave Spectroscopy of the Low-Temperature Skyrmion State in Cu2OSeO3

A. Aqeel, J. Sahliger, T. Taniguchi, S. Maendl, D. Mettus, H. Berger, A. Bauer, M. Garst, C. Pfleiderer, C.H. Back.

Physical Review Letters 126 (1), 017202 (2021).

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In the cubic chiral magnet Cu2OSeO3 a low-temperature skyrmion state (LTS) and a concomitant tilted conical state are observed for magnetic fields parallel to h100i. Here, we report on the dynamic resonances of these novel magnetic states. After promoting the nucleation of the LTS by means of field cycling, we apply broadband microwave spectroscopy in two experimental geometries that provide either predominantly in-plane or out-of-plane excitation. By comparing the results to linear spin-wave theory, we clearly identify resonant modes associated with the tilted conical state, the gyrational and breathing modes associated with the LTS, as well as the hybridization of the breathing mode with a dark octupole gyration mode mediated by the magnetocrystalline anisotropies. Most intriguingly, our findings suggest that under decreasing fields the hexagonal skyrmion lattice becomes unstable with respect to an oblique deformation, reflected in the formation of elongated skyrmions.

DOI: 10.1103/PhysRevLett.126.017202

Field-induced reorientation of helimagnetic order in Cu2OSeO3 probed by magnetic force microscopy

P. Milde, L. Koehler, E. Neuber, P. Ritzinger, M. Garst, A. Bauer, C. Pfleiderer, H. Berger, L.M. Eng

Physical Review B 102 (2), 024426 (2020).

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Cu2OSeO3 is an insulating skyrmion-host material with a magnetoelectric coupling giving rise to an electric polarization with a characteristic dependence on the magnetic-field (H) over right arrow. We report a magnetic force microscopy imaging of the helical real-space spin structure on the surface of a bulk single crystal of Cu2OSeO3. In the presence of a magnetic field, the helimagnetic order, in general, reorients and acquires a homogeneous component of the magnetization, resulting in a conical arrangement at larger fields. We investigate this reorientation process at a temperature of 10 K for fields close to the crystallographic < 110 > direction that involves a phase transition at H-c1. Experimental evidence is presented for the formation of magnetic domains in real space as well as for the microscopic origin of relaxation events that accompany the reorientation process. In addition, the electric polarization is measured by means of Kelvin-probe force microscopy. We show that the characteristic field dependency of the electric polarization originates in this helimagnetic reorientation process. Our experimental results are well described by an effective Landau theory previously invoked for MnSi, that captures the competition between magnetocrystalline anisotropies and Zeeman energy.

DOI: 10.1103/PhysRevB.102.024426

The 2020 Skyrmionics roadmap

C.H. Back, V. Cros, H. Ebert, K. Everschor-Sitte, A. Fert, M. Garst, Tianping Ma, S. Mankovsky, T. L. Monchesky, M. Mostovoy, N. Nagaosa, S.S.P. Parkin, C. Pfleiderer, N. Reyren, A. Rosch, Y. Taguchi, Y. Tokura, K. von Bergmann, J. Zang

Journal of Physics D: Applied Physics 53, 363001 (2020).

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The notion of non-trivial topological winding in condensed matter systems represents a major area of present-day theoretical and experimental research. Magnetic materials offer a versatile platform that is particularly amenable for the exploration of topological spin solitons in real space such as skyrmions. First identified in non-centrosymmetric bulk materials, the rapidly growing zoology of materials systems hosting skyrmions and related topological spin solitons includes bulk compounds, surfaces, thin films, heterostructures, nano-wires and nano-dots. This underscores an exceptional potential for major breakthroughs ranging from fundamental questions to applications as driven by an interdisciplinary exchange of ideas between areas in magnetism which traditionally have been pursued rather independently. The skyrmionics Roadmap provides a review of the present state of the art and the wide range of research directions and strategies currently under way. These are, for instance, motivated by the identification of the fundamental structural properties of skyrmions and related textures, processes of nucleation and annihilation in the presence of non-trivial topological winding, an exceptionally efficient coupling to spin currents generating spin transfer torques at tiny current densities, as well as the capability to purpose-design broad-band spin dynamic and logic devices.

DOI: 10.1088/1361-6463/ab8418

Orientation dependence of the magnetic phase diagram of Yb2Ti2O7

S. Säubert, A. Scheie, C. Duvinage, J. Kindervater, S. Zhang, H.J. Changlani, G. Xu, S.M. Kohpayeh, O. Tchernyshyov, C.L. Broholm, C. Pfleiderer

Physical Review B 101, 174434 (2020).

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In the quest to realize a quantum spin liquid (QSL), magnetic long-range order is hardly welcome. Yet it can offer deep insights into a complex world of strong correlations and fluctuations. Much hope was placed in the cubic pyrochlore Yb2Ti2O7 as a putative U(1) QSL but a new class of ultrapure single crystals make it abundantly clear that the stoichiometric compound is a ferromagnet. Here we present a detailed experimental and theoretical study of the corresponding field-temperature phase diagram. We find it to be richly anisotropic with a critical endpoint for B∥⟨100⟩, while a field parallel to ⟨110⟩ or ⟨111⟩ enhances the critical temperature by up to a factor of two and shifts the onset of the field-polarized state to finite fields. Landau theory shows that Yb2Ti2O7 in some ways is remarkably similar to pure iron. However, it also pinpoints anomalies that cannot be accounted for at the classical mean-field level including a dramatic enhancement of TC and a reentrant phase boundary under applied magnetic fields with a component transverse to the easy axes, as well as the anisotropy of the upper critical field in the quantum limit.

DOI: 10.1103/PhysRevB.101.174434

Evolution of magnetocrystalline anisotropies in Mn1-xFexSi and Mn1-xCoxSi as inferred from small-angle neutron scattering and bulk properties

J. Kindervater, T. Adams, A. Bauer, F.X. Haslbeck, A. Chacon, S. Muehlbauer, F. Jonietz, A. Neubauer, U. Gasser, G. Nagy, N. Martin, W. Haeussler, R. Georgii, M. Garst, C. Pfleiderer

Physical Review B 101 (10), 104406 (2020).

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We report a comprehensive small-angle neutron scattering (SANS) study of magnetic correlations in Mn1-xFexSi at zero magnetic field. To delineate changes of magnetocrystalline anisotropies (MCAs) from effects due to defects and disorder, we recorded complementary susceptibility and high-resolution specific heat data and investigated selected compositions of Mn1-xCoxSi. For all systems studied, the helimagnetic transition temperature and magnetic phase diagrams evolve monotonically with composition consistent with literature. The SANS intensity patterns of the spontaneous magnetic order recorded under zero-field cooling, which were systematically tracked over forty angular positions, display strong changes of the directions of the intensity maxima and smeared out intensity distributions as a function of composition. We show that cubic MCAs account for the complex evolution of the SANS patterns, where for increasing x the character of the MCAs shifts from terms that are fourth order to terms that are sixth order in spin-orbit coupling. The magnetic field dependence of the susceptibility and SANS establishes that the helix reorientation as a function of magnetic field for Fe- or Co-doped MnSi is dominated by pinning due to defects and disorder. The presence of well-defined thermodynamic anomalies of the specific heat at the phase boundaries of the skyrmion lattice phase in the doped samples and properties observed in Mn1-xCoxSi establishes that the pinning due to defects and disorder remains, however, weak and comparable to the field scale of the helix reorientation. The observation that MCAs, which are sixth order in spin-orbit coupling, play an important role for the spontaneous order in Mn1-xFexSi and Mn1-xCoxSi offers a fresh perspective for a wide range of topics in cubic chiral magnets such as the generic magnetic phase diagram, the morphology of topological spin textures, the paramagnetic-to-helical transition, and quantum phase transitions.

DOI: 10.1103/PhysRevB.101.104406

Weak crystallization of fluctuating skyrmion textures

J. Kindervater, I. Stasinopoulos, A. Bauer, F. Haslbeck, F. Rucker, A. Chacon, S. Mühlbauer, C. Franz, M. Garst, D. Grundler, C. Pfleiderer

Physical Review X 9 , 41059 (2019).

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We report an experimental study of the emergence of nontrivial topological winding and long-range order across the paramagnetic-to-skyrmion lattice transition in the transition metal helimagnet MnSi. Combining measurements of the susceptibility with small-angle neutron scattering, neutron-resonance spin-echo spectroscopy, and all-electrical microwave spectroscopy, we find evidence of skyrmion textures in the paramagnetic state exceeding 103 Å, with lifetimes above several 10−9 s. Our experimental findings establish that the paramagnetic-to-skyrmion lattice transition in MnSi is well described by the Landau soft-mode mechanism of weak crystallization, originally proposed in the context of the liquid-to-crystal transition. As a key aspect of this theoretical model, the modulation vectors of periodic small-amplitude components of the magnetization form triangles that add to zero. In excellent agreement with our experimental findings, these triangles of the modulation vectors entail the presence of the nontrivial topological winding of skyrmions already in the paramagnetic state of MnSi when approaching the skyrmion lattice transition.

DOI: 10.1103/PhysRevX.9.041059

Ferromagnetic Resonance with Magnetic Phase Selectivity by Means of Resonant Elastic X-Ray Scattering on a Chiral Magnet

S. Pollath, A. Aqeel, A. Bauer, C. Luo, H. Ryll, F. Radu, C. Pfleiderer, G. Woltersdorf, C.H. Back

Physical Review Letters 123 (16), 167201 (2019).

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Cubic chiral magnets, such as Cu2OSeO3, exhibit a variety of noncollinear spin textures, including a trigonal lattice of spin whirls, the so-called skyrmions. Using magnetic resonant elastic x-ray scattering (REXS) on a crystalline Bragg peak and its magnetic satellites while exciting the sample with magnetic fields at gigahertz frequencies, we probe the ferromagnetic resonance (FMR) modes of these spin textures by means of the scattered intensity. Most notably, the three eigenmodes of the skyrmion lattice are detected with large sensitivity. As this novel technique, which we label REXS FMR, is carried out at distinct positions in reciprocal space, it allows us to distinguish contributions originating from different magnetic states, providing information on the precise character, weight, and mode mixing as a prerequisite of tailored excitations for applications.

DOI: 10.1103/PhysRevLett.123.167201

MIEZE Neutron Spin-Echo Spectroscopy of Strongly Correlated Electron Systems

C. Franz, S. Saubert, A. Wendl, F.X. Haslbeck, O. Soltwedel, J.K. Jochum, L. SPitz, J. Kindervater, A. Bauer, P. Boni, C. Pfleiderer

Journal of the Physical Society of Japan 88 (8), 081002 (2019).

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Recent progress in neutron spin-echo spectroscopy by means of longitudinal Modulation of IntEnsity with Zero Effort (MIEZE) is reviewed. Key technical characteristics are summarized which highlight that the parameter range accessible in momentum and energy, as well as its limitations, are extremely well understood and controlled. Typical experimental data comprising quasi-elastic and inelastic scattering are presented, featuring magneto-elastic coupling and crystal field excitations in Ho2Ti2O7, the skyrmion lattice to paramagnetic transition under applied magnetic field in MnSi, ferromagnetic criticality and spin waves in Fe. In addition bench marking studies of the molecular dynamics in H2O are reported. Taken together. the advantages of MIEZE spectroscopy in studies at small and intermediate momentum transfers comprise an exceptionally wide dynamic range of over seven orders of magnitude, the capability to perform straight forward studies on depolarizing samples or under depolarizing sample environments, as well as on incoherently scattering materials.

DOI: 10.7566/JPSJ.88.081002

Surface pinning and triggered unwinding of skyrmions in a cubic chiral magnet

P. Milde, E. Neuber, A. Bauer, C. Pfleiderer, L.M. Eng

Physical Review B 100, 24408 (2019).

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In the cubic chiral magnet Fe1−xCoxSi a metastable state comprising topologically nontrivial spin whirls, so-called skyrmions, may be preserved down to low temperatures by means of field cooling the sample. This metastable skyrmion state is energetically separated from the topologically trivial ground state by a considerable potential barrier, a phenomenon also referred to as topological protection. Using magnetic force microscopy on the surface of a bulk crystal, we show that certain positions are preferentially and reproducibly decorated with metastable skyrmions, indicating that surface pinning plays a crucial role. Increasing the magnetic field allows an increasing number of skyrmions to overcome the potential barrier and hence to transform into the ground state. Most notably, we find that the unwinding of individual skyrmions may be triggered by the magnetic tip sample interaction itself, however, only when its magnetization is aligned parallel to the external field. This implies that the stray field of the tip is key for locally overcoming the topological protection. Both the control of the position of topologically nontrivial states and their creation and annihilation on demand pose important challenges in the context of potential skyrmionic applications.

DOI: 10.1103/PhysRevB.100.024408

Putative spin-nematic phase in BaCdVO(PO4)(2)

K. Skoulatos, F. Rucker, G.J. Nilsen, A. Bertin, E. Pomjakushina, J. Olliver, A. Schneidewind, R. Georgii, O. Zaharko, L. Keller, C. Ruegg, C. Pfleiderer, B. Schmidt, N. Shannon, A. Kriele, A. Senyshyn, A. Smerald

Physical Review B 100 (1), 014405 (2019).

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We report neutron-scattering and ac magnetic susceptibility measurements of the two-dimensional spin-1/2 frustrated magnet BaCdVO(PO4)(2). At temperatures well below T-N approximate to 1 K, we show that only 34% of the spin moment orders in an up-up-down-down stripe structure. Dominant magnetic diffuse scattering and comparison to published muon-spin-rotation measurements indicates that the remaining 66% is fluctuating. This demonstrates the presence of strong frustration, associated with competing ferromagnetic and antiferromagnetic interactions, and points to a subtle ordering mechanism driven by magnon interactions. On applying magnetic field, we find that at T = 0.1 K the magnetic order vanishes at 3.8 T, whereas magnetic saturation is reached only above 4.5 T. We argue that the putative high-field phase is a realization of the long-sought bond-spin-nematic state.

DOI: 10.1103/PhysRevB.100.014405

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