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Publication# Order and dynamics in Kagome like compound Cu2OSO4 and other quantum magnets

Résumé

This thesis presents results of studies of novel compounds modeling complex fundamental physics phenomena. Cu2OSO4 is a copper based magnetic Mott Insulator system, where spin half magnetic moments form a new type of lattice. These intrinsically quantum pins are exhibiting atypical magnetic order and spin dynamics. The recent success in the growth of large single crystals of Cu2OSO4 enabled to perform measurements probing its static and fluctuating properties. The peculiarity of this sample is that its atoms are forming layers, with a geometry close to the intensively studied Kagomé lattice, but with a third of its spins replaced by dimers. This quantum magnetism system has been probed in its bulk, by the means of heat capacity and DC-susceptibility measurements, revealing a transition to a magnetically long range ordered state upon cooling, the details of which are revealed by neutron scattering. Single crystal inelastic neutron scattering shed light on the spin-dynamics in the system, with clear spin waves appearing as fluctuations around the peculiar ground state of the system: a 120 degrees spin configuration where the magnetic moment of the spin-dimer causes the sample to be globally ferrimagnetic. The presented results indicate that Cu2OSO4 represents a new type of model lattice with frustrated interactions where interplay between magnetic order, thermal and quantum fluctuations can be explored. The magnetic excitations of the compound can be modeled by a yet-to-be-understood internal effective mean-field that no simple magnetic coupling seems to reproduce. K2Ni2(SO4)3 is another compound that allows for the existence of non-trivial topological phases. This thesis presents results of the study of the unusual magnetic behavior of K2Ni2(SO4)3. No clear sign of well-established magnetic long range order has been observed down to dilution temperatures. Neutron scattering reveals the details of the competition between frustration and fluctuations that prevent order from settling in. Low temperature spin excitations take the form of a continuum at 500 mK, but also of broad, energy independent continua at higher temperatures. Bulk and neutron scattering measurements are put in perspective and linked together with a view to building up a better understanding of how quantum spin liquids can be stabilized in general, and in particular in this model compound. Finally, the last contribution of this thesis to the field of condensed matter physics regards the establishment of a state-of-the-art technique to fit heat capacity and unit cell volume of samples to try and make the extraction of magnetic information from specific heat measurements more robust. This newly-developed technique consists in modeling lattice contributions with better accuracy by using data from multiple experimentally accessible quantities to consolidate the fitting scheme. This method has been cautiously applied to several compounds at the forefront of research in experimental physics.

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Moment magnétique

En physique, le moment magnétique est une grandeur vectorielle qui permet de caractériser l'intensité d'une source magnétique. Cette source peut être un courant électrique, ou bien un objet aimanté.

Ferrimagnétisme

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This thesis is devoted to the investigation of static and dynamic properties of
two different sets of quantum magnets with neutron scattering techniques and
the help of linear spin wave theory.
Both systems are copper-based with spin-1/2, which makes them ideal to
study the interplay between purely quantum and semi-classical effects.
I start with the analysis of the antiferromagnet SeCuO3, which has a canted spins
structure. Through careful
inelastic neutron scattering experiments on thermal and cold triple-axis spectrometers,
I demonstrate that this compound exhibits three primary types of excitations that are
intrinsically opposite : spin waves (magnons), singlet to triplet excitations
(triplons), and fractional spins excitations (spinons).
Such a strong coexistence and interdependence of these collective excitations has not
been observed yet, thereby the quantification and description of the excitations in
SeCuO3 leads the way to further theoretical work on multi-excitation spin systems,
as well as the existence of quantum effects in high dimensional systems.\
My second project is on the extraction of the magnetic structure of three members of the
A(BO)Cu4(PO4)4 chiral family, namely (A; B) = (Ba; Ti), (Sr; Ti) and (Pb; Ti),
from spherical neutron polarimetry measurements. I prove that the first two compounds exhibit
a highly non-collinear magnetic structure, with the Cu spins forming clusters of 'two-in--two-out'
arrangements on each structural unit. This structure is stabilised by the presence of a strong
Dzyaloshinskii-Moriya interaction, and explains the observation of magnetoelectric effects as
emerging from quadrupole moments. The analysis of the latter compound did not lead to the confirmation
of its magnetic structure due to strong nuclear-magnetic interference.
I conclude this thesis by the investigation of the magnetic excitation spectrum of some members
of the (A; B) family, probed by inelastic neutron scattering measurements. Indeed, its particular
crystallographic structure makes it an ideal playground to study tetramerisation effects on the
two dimensional square lattice.
Additionally, the aforementioned Dzyaloshinskii-Moriya interaction ensures the presence of a structural
gap, which competes with the quantum one emerging from tetramerisation effects. Using linear spin wave
theory, I describe (Ba; Ti) as a chequerboard system with almost equal intra- and inter-plaquette
couplings, with weak quantum effects. I also provide a qualitative description of (Pb; Ti), which exhibits
similar physics, and conclude by presenting the first results on the highly symmetric compound (K; Nb),
which shows hints of a strong quantum behaviour.

This thesis reports results on magnetic properties of supported cobalt nanostructures. The nanostructures were grown on single crystal metal surface by Molecular Beam Epitaxy in an Ultra High Vacuum chamber. Our experimental setup is based on two in situ measurement techniques. The first is the Scanning Tunneling Microscope (STM) allowing to investigate the nanostructure morphology. The second, called Surface Magneto-Optical Kerr Effect (SMOKE), probes the magnetism of the nanostructures. By combining the data obtained with both techniques we were able to investigate the magnetism of 2D nanoparticles down to the atomic level. The first aim of the thesis consisted in disclosing the role played by the differently coordinated atoms in determining the Magnetic Energy Anisotropy in 2D nanostructures. To this purpose, we performed experiments on the Co/Pt(111) system, chosen as a model system since the Pt surface is well known to increase the out-of-plane uniaxial anisotropy as well as the magnetic moment of the Co islands. A preliminary work has been devoted to the growth of the Co islands as a function of the deposition and annealing temperatures. As a result, we learned to grow three different island's shapes : ramified, compact and double-layer islands. We then concentrated on the magnetism of these islands. Due to the nonlinear relationship between perimeter length and surface area, we were able to distinguish the different contributions to the anisotropy energy of surface and perimeter atoms. We found that the magnetic anisotropy in 2D Co nanostructures is predominantly due to the low-coordinated edge atoms, for which the anisotropy energy can be as large as 20 times the bulk value. This finding opens new possibilities to separately tune the anisotropy and moment of nanostructures. To exemplify this, and to illustrate once more the role of perimeter atoms, we produced Co island with a non-magnetic Pt core. As expected, these bimetallic islands have identical anisotropy and lower magnetic moment to their equally shaped pure Co counterpart. The second aim we focused on was the investigation of the magnetic properties of ultra-high density arrays of nanostructures created by self-assembly. We chose Co/Au(788) as a model system since the nanoscopic Co dots were found to have a very narrow size distribution and to be placed onto a lattice which is phase coherent on a macroscopic length scale. Moreover, the array has a density of 26 Tdot/in2 which allows the investigation of inter-particle interaction in ultra high density arrays. We showed that the narrow size distribution of the dots corresponds to an unprecedented narrow Magnetic Anisotropy Energy distribution with 35% width at half of the maximum. Moreover, we demonstrated the weak magnetic coupling between the Co dots despite their high density. In parallel to these fundamental researches, we developed a new experimental setup that will replace the current one. We designed a UHV chamber equipped with a homemade variable temperature STM combined with a SMOKE experiment. A quadrupole, focused on the sample, generates a 0.35 T magnetic field. This field is one order of magnitude larger than the present one and can be uniformly rotated in the plane of the quadrupole. Furthermore, the design of the new chamber allows STM imaging in this magnetic field. In this report, we present the adopted solutions as well as the first tests of the components (STM, SMOKE, cryostat).

Collective magnetic excitations are a fascinating aspect of condensed matter physics, where neutron scattering can provide valuable insight into the magnetic properties of physical realisations of model systems. This thesis focuses on the excitation spectra of layered quantum magnets in the case of the frustrated quantum magnet SrCu$_2$(BO$_3$)$_2$ and the family of quasi-2D antiferromagnets MPS$_3$, with M a transition metal. \begin{itemize}[topsep=2pt,itemsep=-0.7ex] \item SrCu$_2$(BO$_3$)$_2$ is a physical realisation of the two-dimensional Shastry-Sutherland theoretical model, constructed as orthogonal dimers with the product of singlets on the strong antiferromagnetic $J$ bond as an exact ground state. The spin interactions for such a particular geometry induces strong frustration which leads to unconventional magnetism and exotic phases of matter. This work is concerned with a series of aspects of the magnetic excitations in this compound. The excitation spectra as a function of field, temperature and pressure are measured using neutron time-of-flight spectroscopy. The experimental results show that correlations, bound magnons and finite temperature properties are highly unconventional and these results are compared with existing theories on frustrated model systems. In addition, predicted topological properties of SrCu$_2$(BO$_3$)$_2$ in an applied field are confirmed experimentally. \item The transition metal phosphorus trisulfides (MPS$_3$) are a family of quasi two-dimensional materials on a honeycomb lattice with weakly bound magnetic planes. This work focuses mainly on the exchange interactions and critical properties of FePS$_3$, which is largely anisotropic with the S=2 Fe$^{2+}$ moments pointing normal to the $(a,b)$ plane. Inelastic neutron scattering on single crystals is used to measure the spin wave dispersion, providing new insight on the strength of the coupling interactions and anisotropies and showing that FePS$_3$ is a good two-dimensional model antiferromagnet. Similar experiments on powdered samples of NiPS$_3$ show low-Q dispersive spin waves with a small spin-gap. Critical properties of FePS$_3$ close to the Néel temperature are further discussed, as the magnetic nature of the measured quasi-elastic scattering is confirmed. Based on magnetization measurements in high pulsed fields, a possible tricritical point in the 40-50T range is proposed. \end{itemize} The work presented in this thesis has been carried out in a collaboration between the Institut Laue Langevin in Grenoble and the Laboratory for Quantum Magnetism of the EPFL.