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Publication# Magnetic structures and quadratic magnetoelectric effect in LiNiPO4 beyond 30 T

Abstract

Neutron diffraction with static and pulsed magnetic fields is used to directly probe the magnetic structures in LiNiPO4 up to 25 T and 42 T, respectively. By combining these results with magnetometry and electric polarization measurements under pulsed fields, the magnetic and magnetoelectric phases are investigated up to 56 T applied along the easy c axis. In addition to the already known transitions at lower fields, three new ones are reported at 37.6, 39.4, and 54 T. Ordering vectors are identified with Q(VI) = (0, 1/3, 0) in the interval 37.6 - 39.4 T and Q(VII) = (0, 0, 0) in the interval 39.4 - 54 T. A quadratic magnetoelectric effect is discovered in the Q(VII) = (0, 0, 0) phase and the field dependence of the induced electric polarization is described using a simple mean-field model. The observed magnetic structure and magnetoelectric tensor elements point to a change in the lattice symmetry in this phase. We speculate on the possible physical mechanism responsible for the magnetoelectric effect in LiNiPO4.

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Magnetism

Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, magnetism is one of two aspects of electromagnetism. The most familiar effects occur in ferromagnetic materials, which are strongly attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves.

Neutron diffraction

Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a diffraction pattern that provides information of the structure of the material. The technique is similar to X-ray diffraction but due to their different scattering properties, neutrons and X-rays provide complementary information: X-Rays are suited for superficial analysis, strong x-rays from synchrotron radiation are suited for shallow depths or thin specimens, while neutrons having high penetration depth are suited for bulk samples.

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Quantum magnetism remains a hot topic in condensed matter physics due to its complexity and possible powerful and significant applications in data storage and memory. To understand how the materials can achieve these goals, one should have a clear idea about the fundamentals behind it. In this thesis, we focus on three examples that can help us deepen the knowledge in many-body effects, which stand to be crucial for quantum magnetism.(1) The well-known \textbf{CuSO$_4\cdot$5D$_2$O} material has already demonstrated the model behaviour as one-dimensional Heisenberg antiferromagnet in zero and high ($H>H_{sat}$) fields. The fully-polarized magnetic ground state is described by linear spin-wave theory with magnons, whereas at zero field, the excitations are pairs of topological excitations called spinons. In an intermediate field, the dynamic properties are even more complicated. The inelastic spectrum cannot be reproduced without considering exotic elementary excitations and bound states such as psinons and Bethe strings. Although Bethe in 1931 provided an exact solution for 1D Heisenberg systems, there is still no quantitative comparison between theory and experiment.(2) The magnetic ground state and hence the dynamic properties of the gemstone mineral green dioptase, \textbf{Cu$_6[$Si$_6$O$_{18}]\cdot6$H$_2$O} are under debate: starting from controversial theories and continuing with non-explained experimental observations. Dioptase is a quasi-one-dimensional spin chain with dominant antiferromagnetic interactions. Recent studies claim the classical spin chain behaviour and absence of any quantum fluctuations in the system. In contrast, our experimental findings indicate the presence of continuous excitations above and below T$_N$.(3) Newly synthesized material \textbf{CuSb$_2$O$_6$} of rosiaite-type structure tends to become a quantum spin-liquid (QSL) candidate since the magnetic cations Cu$^{2+}$ are arranged in trigonal layers, and no long-range order is observed down to 2~K. The idea of QSL on the triangular lattice was proposed by P. Anderson in 1973. Since his work, a lot of efforts have been made to explore deeper, both theoretically and experimentally, this state. As for now, there are several requirements needed to be met -- small spin number, absence of long-range order or spin freezing, long-range entanglement, and the associated fractional spin excitations. We aim to establish whether or not CuSb$_2$O$_6$ can be considered as a potential quantum spin-liquid candidate employing different techniques suitable for a powder sample.

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 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.