"Bust my buffers" - neutrons disentangle the quantum nature of matter

“Because that is the way it is” I finally answered to our son’s favorite word “Why?”. He had discovered – like most kids his age – that his wooden train with magnetic buffers would pull one end of the wagon, but repel the other end. His first “why” was easily rewarded: “because they are magnetic”. But another 3-4 “why”s sliced through our entire physics education: “Magnets have 2 poles (north and south), we call them dipole magnetic moments. The magnet is made of many tiny (atomic) magnetic moments. The atomic magnetic moment comes from …”. Suddenly he had me cornered with only two possible routes of escape: Maxwell’s laws for electromagnetism, which is the consequence of Einstein’s theory of relativity for moving electrons, or Quantum Mechanics, which cause particles to have intrinsic magnetic moments called a ‘spin’

Aspects of Quantum Magnetism in One, Two and Three dimensions

The study of \emph{quantum magnetism} remains at the forefront of condensed matter physics. Spin models provide a large class of many-body systems, in which cooperative quantum phenomena can be studied in a controlled way. In addition, the \emph{neutron scattering} technique offers a near-ideal tool to probe the state of magnetic materials. This thesis presents neutron scattering studies of three selected materials, each representing an important aspect of quantum magnetism. \begin{itemize} \item CuGeO$_3$ is a quasi one-dimensional $S=1/2$ spin--Peierls material. This is an example of a system that has a \emph{quantum ground state} with no classical analogue. The spins dimerize to form a coherent non-magnetic singlet, where the expectation value of each individual spin is zero, as if they were `hidden'. As a consequence, the \emph{excitations} (called solitons) are different from the spin waves of a classical system. In a high magnetic field, the solitons can be condensed to form a periodic lattice. Through neutron scattering measurements, the structure of this soliton lattice has been determined, and the excitations in the soliton phase have been identified. \item Cu(DCOO)$_2 \cdot$4D$_2$O is a two-dimensional $S=1/2$ Heisenberg antiferromagnet on a square lattice. The $T=0$ ground state of this system has long range order similar to the classical system. But the order parameter is reduced by \emph{quantum fluctuations}, and the physical observables are \emph{renormalized}. In particular, it was found that the spin wave dispersion is non-uniformly renormalized. At finite temperatures long range order is destroyed by thermal and quantum fluctuations, which act together. Still, there are strong \emph{correlations}, which on short length and time scales resembles the long range order. The temperature dependence of the correlation length and the excitation spectrum has been measured using two specialized neutron scattering methods. \item LiHoF$_4$ is a three- dimensional Ising ferromagnet, in which the magnetic order can be destroyed even at $T=0$ by applying a large magnetic field transverse to the Ising axis. Ordinary phase transitions occur as a function of temperature, when the thermal fluctuations become strong enough to destroy the order. At $T=0$ there are no thermal fluctuations and the transition is driven by quantum fluctuations, which are controlled by some external parameter,in this case the magnetic field. It is important to understand the universal behaviour of such \emph{quantum phase transitions}, as several novel phenomena in solid state physics may be related to the proximity of a \emph{quantum critical point}. Using inelastic neutron scattering the behaviour of the excitations around the quantum critical point in LiHoF$_4$ has been investigated. \end{itemize} This thesis was submitted in partial fulfillment of the requirements for a Ph.D.\ in physics at the University of Copenhagen. The work presented was carried out in the Department of Condensed Matter Physics and Chemistry at Ris\o{} National Laboratory, Denmark. The supervisors were Des McMowrrow from Ris\o{} and Jens Jensen from the University of Copenhagen

Quantum Magnetism - a strange fish

De skabninger, der bebor de dybe verdenshave, er væsensforskellige fra dem fiskehandleren sælger. De ekstreme betingelser, der hersker i 10 kilometers dybde kræver andre overlevelsesstrategier, end dem de lettere tilgængelige overfladefisk anvender. Inden for magnetisme kan ekstreme betingelser – nærmere beskrevet nedenfor – tilsvarende give anledning til fænomener, der adskiller sig kraftigt fra den klassiske ferromagnetisme, der blandt andet tillader os at sætte huskesedlen fast p°a køleskabsdøren. Man taler løst om kvantemagnetisme. I denne artikel vil vi kort introducere nogle af de fisk, man kan fange, hvis man smider fiskesnøren i det kvantemagnetiske hav

Cavity-Magnon-Polariton spectroscopy of strongly hybridized electro-nuclear spin excitations in LiHoF4

We first present a formalism that incorporates the input-output formalism and the linear response theory to employ cavity-magnon-polariton coupling as a spectroscopic tool for investigating strongly hybridized electro-nuclear spin excitations. A microscopic relation between the generalized susceptibility and the scattering parameter |S11| in strongly hybridized cavity-magnon-polariton systems has been derived without resorting to semi-classical approximations. The formalism is then applied to both analyze and simulate a specific systems comprising a model quantum Ising magnet (LiHoF4) and a high-finesse 3D re-entrant cavity resonator. Quantitative information on the electro-nuclear spin states in LiHoF4 is extracted, and the experimental observations across a broad parameter range were numerically reproduced, including an external magnetic field titraversing a quantum critical point. The method potentially opens a new avenue not only for further studies on the quantum phase transition in LiHoF4 but also for a wide range of complex magnetic systems.Comment: 16 pages, 8 figure

Revisiting the magnetic and crystal structure of multiferroic KNiPO4_4

The magnetic, dielectric and structural properties of type-I multiferroic KNiPO$_4$ have been investigated by neutron powder diffraction, magnetization, dielectric and high temperature synchrotron-XRD measurements. Below the N\'{e}el transition of $T_\mathrm{N}$ = 25 K, KNiPO$_4$ displays a weakly non-collinear antiferromagnetic (AFM) structure with the orientation of the Ni$^{2+}$ magnetic moments mainly along $a$ axis. The compound crystallizes in the polar orthorhombic $Pna2_1$ space group at room temperature. A second-order structural phase transition corresponding to the onset ferroelectricity is observed at around $T_\mathrm{C}\sim$ 594(3)$^\circ$C, above which the crystal structure of KNiPO$_4$ adopts the centrosymmetric $Pnma$ space group. The compound also displays another structural phase transition at $T_\mathrm{0}\sim$ 469 -- 488$^\circ$C, with a first-order character, which is attributed to the rearrangement of oxygen ligands, resulting in a change in the nickel ion co-ordination from four to five

Unravelling the origin of the peculiar transition in the magnetically ordered phase of the Weyl semimetal Co3Sn2S2

Recent discovery of topologically non-trivial behavior in Co3Sn2S2 stimulated a notable interest in this itinerant ferromagnet (Tc = 174 K). The exact magnetic state remains ambiguous, with several reports indicating the existence of a second transition in the range 125 -- 130 K, with antiferromagnetic and glassy phases proposed to coexist with the ferromagnetic phase. Using detailed angle-dependent DC and AC magnetization measurements on large, high-quality single crystals we reveal a highly anisotropic behavior of both static and dynamic response of Co3Sn2S2. It is established that many observations related to sharp magnetization changes when B || c are influenced by the demagnetization factor of a sample. On the other hand, a genuine transition has been found at Tp = 128 K, with the magnetic response being strictly perpendicular to the c-axis and several orders of magnitude smaller than for B || c. Calculations using density-functional theory indicate that the ground state magnetic structure consist of magnetic moments canted away from the c-axis by a small angle (~ 1.5deg). We argue that the second transition originates from a small additional canting of moments within the kagome plane, with two equivalent orientations for each spin.Comment: accepted as a Letter in PR

Triplons, Magnons, and Spinons in a Single Quantum Spin System: SeCuO3

Quantum spin systems exhibit an enormous range of collective excitations, but their spin waves, gapped triplons, fractional spinons, or yet other modes are generally held to be mutually exclusive. Here we show by neutron spectroscopy on SeCuO$_3$ that magnons, triplons, and spinons are present simultaneously. We demonstrate that this is a consequence of a structure consisting of two coupled subsystems and identify all the interactions of a minimal magnetic model. Our results serve qualitatively to open the field of multi-excitation spin systems and quantitatively to constrain the complete theoretical description of one member of this class of materials.Comment: 8 pages, 5 figure

Determining the Short-Range Spin Correlations in Cuprate Chain Materials with Resonant Inelastic X-ray Scattering

We report a high-resolution resonant inelastic soft x-ray scattering study of the quantum magnetic spin-chain materials Li2CuO2 and CuGeO3. By tuning the incoming photon energy to the oxygen K-edge, a strong excitation around 3.5 eV energy loss is clearly resolved for both materials. Comparing the experimental data to many-body calculations, we identify this excitation as a Zhang-Rice singlet exciton on neighboring CuO4-plaquettes. We demonstrate that the strong temperature dependence of the inelastic scattering related to this high-energy exciton enables to probe short-range spin correlations on the 1 meV scale with outstanding sensitivity.Comment: 5 pages, 4 figure