Spin Ice

An ultra-low field SQUID magnetometer for measuring antiferromagnetic and weakly remanent magnetic materials at low temperatures

A novel setup for measuring magnetic fields of antiferromagnets (i.e., quadrupolar or higher-order magnetic fields) and generally weakly remanent magnetic materials is presented. The setup features a highly sensitive superconducting quantum interference device magnetometer with a magnetic field resolution of ∼ 10 fT and non-electric temperature control of the sample space for a temperature range of 1.5-65 K with a non-electric sample movement drive and optical position encoding. To minimize magnetic susceptibility effects, the setup components are degaussed and realized with plastic materials in sample proximity. Running the setup in magnetically shielded rooms allows for a well-defined ultra-low magnetic background field well below 150 nT in situ. The setup enables studies of inherently weak magnetic materials, which cannot be measured with high field susceptibility setups, optical methods, or neutron scattering techniques, giving new opportunities for the research on, e.g., spin-spiral multiferroics, skyrmion materials, and spin ices.

Magnetic properties of monoclinic lanthanide metaborates, Ln(BO2)3, Ln = Pr, Nd, Gd, Tb

The bulk magnetic properties of the lanthanide metaborates, Ln(BO₂)₃, Ln  =  Pr, Nd, Gd, Tb are studied using magnetic susceptibility, heat capacity and isothermal magnetisation measurements. They are found to crystallise in a monoclinic structure containing chains of magnetic Ln ³⁺ and could therefore exhibit features of low-dimensional magnetism and frustration. Pr(BO₂)₃ is found to have a non-magnetic singlet ground state. No magnetic ordering is observed down to 0.4 K for Nd(BO₂)₃. Gd(BO₂)₃ exhibits a sharp magnetic transition at 1.1 K, corresponding to 3D magnetic ordering. Tb(BO₂)₃ shows two magnetic ordering features at 1.05 K and 1.95 K. A magnetisation plateau at a third of the saturation magnetisation is seen at 2 K for both Nd(BO₂)₃ and Tb(BO₂)₃, which persists in an applied field of 14 T. This is proposed to be a signature of quasi 1D behaviour in Nd(BO₂)₃ and Tb(BO₂)₃.

Quantum spin liquids: a review

Quantum spin liquids may be considered 'quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.

Intermediate magnetization state and competing orders in Dy2Ti2O7 and Ho2Ti2O7

Among the frustrated magnetic materials, spin-ice stands out as a particularly interesting system. Residual entropy, freezing and glassiness, Kasteleyn transitions and fractionalization of excitations in three dimensions all stem from a simple classical Hamiltonian. But is the usual spin-ice Hamiltonian a correct description of the experimental systems? Here we address this issue by measuring magnetic susceptibility in the two most studied spin-ice compounds, Dy₂Ti₂O₇ and Ho₂Ti₂O₇, using a vector magnet. Using these results, and guided by a theoretical analysis of possible distortions to the pyrochlore lattice, we construct an effective Hamiltonian and explore it using Monte Carlo simulations. We show how this Hamiltonian reproduces the experimental results, including the formation of a phase of intermediate polarization, and gives important information about the possible ground state of real spin-ice systems. Our work suggests an unusual situation in which distortions might contribute to the preservation rather than relief of the effects of frustration.

A classical Hamiltonian captures key properties of spin ice materials such as residual entropy and fractionalized excitations. Here, the authors present experimental results of the polarization transition that motivate a Hamiltonian with lattice distortions, which predicts an intermediate magnetization state and competing ground state orders.

Spin jam induced by quantum fluctuations in a frustrated magnet

Since the discovery of spin glasses in dilute magnetic systems, their study has been largely focused on understanding randomness and defects as the driving mechanism. The same paradigm has also been applied to explain glassy states found in dense frustrated systems. Recently, however, it has been theoretically suggested that different mechanisms, such as quantum fluctuations and topological features, may induce glassy states in defect-free spin systems, far from the conventional dilute limit. Here we report experimental evidence for existence of a glassy state, which we call a spin jam, in the vicinity of the clean limit of a frustrated magnet, which is insensitive to a low concentration of defects. We have studied the effect of impurities on SrCr9pGa12-9pO19 [SCGO(p)], a highly frustrated magnet, in which the magnetic Cr(3+) (s = 3/2) ions form a quasi-2D triangular system of bipyramids. Our experimental data show that as the nonmagnetic Ga(3+) impurity concentration is changed, there are two distinct phases of glassiness: an exotic glassy state, which we call a spin jam, for the high magnetic concentration region (p > 0.8) and a cluster spin glass for lower magnetic concentration (p < 0.8). This observation indicates that a spin jam is a unique vantage point from which the class of glassy states of dense frustrated magnets can be understood.

Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets

The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare-earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Spin ices provide one of very few experimentally realized examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the classical spin ice state characterized by emergent photon-like excitations. Whereas in classical spin ices the excitations are akin to electrostatic charges with a mutual Coulomb interaction, in the quantum spin liquid these charges interact through a dynamic and emergent electromagnetic field. In this review, we describe the latest developments in the study of such a quantum spin ice, focusing on the spin liquid phenomenology and the kinds of materials where such a phase might be found.

Random site dilution properties of frustrated magnets on a hierarchical lattice

We present a method to analyze the magnetic properties of frustrated Ising spin models on specific hierarchical lattices with random dilution. Disorder is induced by dilution and geometrical frustration rather than randomness in the internal couplings of the original Hamiltonian. The two-dimensional model presented here possesses a macroscopic entropy at zero temperature in the large size limit, very close to the Pauling estimate for spin-ice on the pyrochlore lattice, and a crossover towards a paramagnetic phase. The disorder due to dilution is taken into account by considering a replicated version of the recursion equations between partition functions at different lattice sizes. An analysis to first order in replica number allows a systematic reorganization of the disorder configurations, leading to a recurrence scheme. This method is numerically implemented to evaluate thermodynamical quantities such as specific heat and susceptibility in an external field.