Magnetic Monopole Noise

It has long been known that a magnet cannot be broken down to its simplest constituents—the north and south poles. This is reflected in the asymmetry of Maxwell’s equations with respect to electric and magnetic fields. While the electric monopole is very much present and is the foundational basis of modern electronics, the magnetic monopole charge is conspicuous by its absence. The search for the fundamental magnetic monopole has proven to be quite elusive till date, but condensed matter physics has provided a few candidates. This chapter reviews one such class of candidate materials, namely the Dipolar Spin Ices: Dysprosium Titanate and Holmium Titanate.

The simplest excitations out of the lowest energy 2-in-2-out configuration of the Dy spins in Dy₂Ti₂O₇ are not the typically expected spin waves. In fact, individual spin flips breaking the ice rules are the elementary excitations in this compound. These individual flips may be generated by temperature fluctuations, or applied magnetic fields of the order of a few Tesla. Since the pyrochlore lattice is comprised of interconnected tetrahedra, a single spin flip would result in a 3-out-1-in and 3-in-1-out spin configuration on two adjoining tetrahedra (Fig. 2.1 left). The center of a tetrahedron for these positive (negative) defects can be thought of as a source(sink) of magnetic flux and was thus termed as magnetic monopole (anti-monopole) for this solid state system. In this chapter, I discuss the energetics of these monopoles, how they are predicted to interact with each other, as well as some of the past searches for these elusive particles in Dysprosium Titanate. Towards the end of the chapter, a new technique employing a Superconducting QUantum Interference Device is proposed to look for magnetic monopoles.

The objective of the experiment presented in this thesis is to perform direct detection of magnetic monopoles in Dy₂Ti₂O₇. This could be achieved by optimizing the sensitivity of detector to flux noise from a plethora of monopoles anticipated to be present in mm-sized samples of Dy₂Ti₂O₇ in the temperature range of 1K-4K. To be able to detect noise coming from monopole motion alone, it was important to eliminate all other sources of noise from entering the detector. To that effect, a custom cryostat was built to house the spectrometer. This chapter details the design of a 1K cryostat and the apparatus that houses the Dysprosium Titanate sample that comprise the Spin Noise Spectrometer. Initial observations of flux noise observed in our experiment and the premise for Monte Carlo simulations of spin fluctuations in Dysprosium Titanate are also presented. Finally, a new paradigm for understanding magnetic monopoles: generation recombination noise is introduced.

In the past decade of trying to understand how potential magnetic monopoles would behave in this material, the focus was on the ’free’/independent motion of this magnetic charge. However, it was important to keep in mind and realize that these charges come in pairs of opposite signs. A system similar to this has been in existence for over half a century and is the basis of modern electronics. To understand the temperature and frequency dependence of noise from a magnetic monopole system consisting of equal and opposite charges, it could be instructive to look to its electronic cousin—the semiconductor with electrons and holes. In an intrinsic semiconductor, electric charges ± q that are subject to Coulomb interactions may also undergo spontaneous generation and recombination processes (Fig. 4.1a) that are well understood. Here, thermal generation and recombination (GR) of ± q pairs generates a spectral density of voltage noise \(S_V (\omega ,T)=V^2 S_N (\omega ,T)/N_0^2\), where S _N(ω, T) is the spectral density of GR fluctuations in the number of ± q pairs. In this chapter the formalism for magnetic monopole antimonopole generation and recombination is developed. The predictions coming out of this formalism for the analytic form of magnetic monopole noise are layed out. Finally, Monte Carlo simulations for Dysprosium Titanate in the temperature range of 1.2K-4K are compared with the aforementioned predictions.

The experiment we conduct is based on the premise that monopoles traversing the pickup coil of a SQUID will thread flux Φ_∗ through it, proportional to their charge ± m _∗. Instead of step function jumps in the SQUID signal (Fig. 2.​7), a magnetic noise Φ(t) (Fig. 2.​8) is expected to be detected by the highly sensitive flux noise spectrometer developed for this experiment. This noise originates from a thermally stimulated dense plasma of monopoles that get generated and may recombine in the temperature range 1.2K ≤ T ≤ 4K. In this chapter, the experimental results of Spin Noise Spectroscopy of Dysprosium Titanate are presented and analyzed. These results are then compared to the predictions made by the analytic formulation of generation recombination noise as well as Monte Carlo simulations of spin noise coming from a Dy₂Ti₂O₇ sample.

To understand the correlations in ± m _∗ GR noise, we compare our experimental knowledge to \(S_{B_z}(\omega )\) MC predictions made by three different spin interaction hamiltonians for spin ices as explained in Sect. 5.​4. By varying certain parameters like dipolar coupling D or constraints on ± m _∗ motion, we learn about how the magnetic monopole noise is more complex than that of a free plasma of ± m _∗ charges.

In our experiment, we have measured spin noise spectrum of a Dysprosium Titanate sample at equilibrium, from 1.2K to 4K using a DC-SQUID. From the Fluctuation Dissipation (FD) theorem, we know that statistical fluctuations in a physical variable of a system are related to the linear response to a small force applied to the system. In this chapter our experimental results of flux noise coming from a sample of Dy₂Ti₂O₇ are discussed in the context of previous boundary-free AC susceptibility measurements of Dysprosium Titanate.

Noise is an entity that most scientists attempt to sideline in their measurements. There may however be some benefits to examining the characteristics of noise intrinsic to a black box that one is studying. A famous example of the usefulness of such a study is the discovery of the Cosmic Microwave Background that stemmed from an unprecedented measurement. In this thesis, the intrinsic noise coming from a single crystal of Dy₂Ti₂O₇ was studied and a microscopic understanding of the inner workings of this material were developed. In conclusion we observe that virtually all the elements of S _Φ(ω, T) predicted for a magnetic monopole plasma, including the existence of intense magnetization noise and its characteristic frequency and temperature dependence, are detected. Moreover, comparisons of simulated and measured correlation functions C _Φ(t) of the magnetic-flux noise Φ(t) imply that the motion of magnetic charges is strongly correlated. At the end of the chapter, directions for some future experiments are presented.