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## The physics of local and global frustration: From disorder-induced multiferroicity to quantum topology

 English title The physics of local and global frustration: From disorder-induced multiferroicity to quantum topology Mudry Christopher 184637 Project funding Paul Scherrer Institut Paul Scherrer Institute - PSI Condensed Matter Physics 01.09.2019 - 31.08.2023 234'964.00
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### Keywords (5)

Crystalline topological semimetals; Strong correlations; Semimetals; Multiferroism; Itinerant magnetism

### Lay Summary (French)

Titre: La physique de la frustration locale et globaleLe jeu de mots "physique de la frustration"a pour but de communiquer la notion que des phénomènes collectifs surprenantspeuvent emerge de la physique à un grand nombre de corps.Cette possibilité est due à des interactions qui ne peuvent pas toutes êtreoptimisées simultanément (le phénomène de la frustration).Ce projet explore la physique de la frustration dans deux cadres;celui de la frustration locale en magnétisme classiqueet celui de la frustration globale en physique quantique.Les deux projets sont motivé par des expériences conduitesà l'institut Paul Scherrer (PSI).
Lay summary

Le premier projet est intitulé "multiferroism induit par le désordre".
Le but de ce projet est d'expliquer l'observation faite au PSI que le cristal
YBaCuFeO5 supporte un ordre magnétique du type antiferromagnétique en dessous
de 440K est un ordre magnétique du type spiral en dessous d'une température
qui augmente de 180K à 310K si on augmente la densité des imperfections
de ce cristal.

Le deusieme projet est intitulé "topologie quantique".
Le cristal EuCd2 As2 est un exemple d'un semi-métal magnétique.
Le magnétisme du type antiferromagnétique est présent en dessous de 10K.
Des nodes du type Weyl sont observés entre 10K et 100K
par une technique spectroscopique au PSI qui indique
que les états quantiques de Bloch des électrons itinerants
ont un caractère topologique associé à une frustration dans
l'espace de Brillouin (une frustration globale).
Expliquer l'observation des nodes de Weyl est le but de ce second projet.
 Direct link to Lay Summary Last update: 18.12.2019

### Responsible applicant and co-applicants

Name Institute
 Mudry Christopher Paul Scherrer Institut

### Employees

Name Institute
 Aksoy Ömer Mert Paul Scherrer Institute

### Abstract

The play of words physics of frustration''aims at conveying that many-body physics and, more generally, complex systems display a plethora of unanticipated phenomena arising from many competing interactions that cannot be optimized simultaneously. This proposal seeks the funding of two PhD students for two distinct projects, the first one exploring the physics of local frustration in classical magnetism, the second one exploring the physics of global frustration in many-body quantum physics. Both projects are motivated by experiments done at the Paul Scherrer Institute.Project I: Disorder-induced multiferroicity Emergent phenomena by which high-temperature multiferroicity becomes possible are interesting in their own right and could deliver important applications to the field of spintronics.The material YBaCuFeO${}^{\,}_{5}$is a magnetic insulator with a magnetic transition from a paramagnetic phase to an antiferromagnetic phase with the ordering temperature$T^{\,}_{\mathrm{AF}}\sim 440\,$K and a second magnetic transition to a spiral phase with an ordering temperature that range from $T^{\,}_{\mathrm{spi}}\sim 180\,$K to $T^{\,}_{\mathrm{spi}}\sim 310\,$K depending on the rate at which the material is annealed from high- to low-temperatures. [1] It was shown in Ref. [2] that the dependence of the spiral ordering temperature on annealing is captured by modeling annealing with a unidirectional and dilute concentration of magnetic exchange couplings with the wrong'' sign (the so-called impurity bonds). This wrong'' sign is an example of local frustration.What was not explained in Ref. [2] is the observation in Ref.[1] that the plane in which the spins rotate around the wave vector of the spiral is tilted away from the crystallographic axis, thereby opening the remarkable possibility that YBaCuFeO${}^{\,}_{5}$ is multiferroic at room temperature.The task of the first PhD will be (i) to explain theoretically the tilting of the plane in which the spin are rotating in the spiral phase,(ii) to extend the theory from Ref. [2] away from the dilute limit of impurity bonds, and(iii) to export this disorder-driven physics to other physical platforms such as quantum spin-1/2 models on geometrically frustrated lattices or arrays of superconducting metallic grains coupled by Josephson couplings. The methods to be used will combine microscopic calculations to establish the size of the Dzyaloshinskii-Moriya interactions inYBaCuFeO${}^{\,}_{5}$ with a construction of an effective theory that captures the tilting of the plane.Project II: Quantum topologyBloch bands are endowed with a quantum topology when their Berry connections cannot be defined in a smooth fashion over the entire Brillouin zone. By combining symmetries and topology, there follows the existence of crystalline topological insulators and crystalline semimetals.A canonical example of a Dirac semimetal in two-dimensional space is graphene.A canonical example of a Dirac semimetal in three-dimensional space is Cd${\,}_{3}$As${\,}_{2}$. The material EuCd${}_{2}$As${}_{2}$ is closely related to Cd${\,}_{3}$As${\,}_{2}$ in that the orbitals Cd $5s$ and As $4p$deliver in each compound Dirac crossings. However, Eu is a magnetic ion that provides a bath of localized magnetic degrees of freedom. These interact with the itinerant electrons stemming from the Cd $5s$ and As $4p$orbitals. In fact, upon lowering temperature,EuCd${}_{2}$As${}_{2}$ undergoes a phase transition from a paramagnetic to a $A$-type antiferromagnetic phase at around $T^{\,}_{\mathrm{A-AF}}\sim9.5\,$K that gaps the Dirac crossing originating from the Kramers' degenerate bands of Cd $5s$ and As $4p$ orbital character. All together,transport, muon spin relaxation, electron spin resonance, and angle-resolved photoemission spectroscopy experiments reveal Weyl, instead of Dirac, crossings in the paramagnetic phase of EuCd${}_{2}$As${}_{2}$up to the much larger temperature of order $T^{*}\sim100\,$K.%~\cite{Ma18} The first task of the second PhD will be to explain theoretically by what mechanism the Kramers' degeneracy of the bands with aa Dirac-like dispersion below $T^{\,}_{A\mathrm{-AF}}\sim9.5\,$K is split and replaced by two Weyl-like dispersions when\$T^{\,}_{A\mathrm{-AF}}
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## Contact

Swiss National Science Foundation (SNSF)

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CH-3001 Bern
Phone +41 31 308 22 22

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