Sources of magnetic fields-magnetic monopoles-have so far proven elusive as elementary particles. Condensed-matter physicists have recently proposed several scenarios of emergent quasiparticles resembling monopoles. A particularly simple proposition pertains to spin ice on the highly frustrated pyrochlore lattice. The spin-ice state is argued to be well described by networks of aligned dipoles resembling solenoidal tubes-classical, and observable, versions of a Dirac string. Where these tubes end, the resulting defects look like magnetic monopoles. We demonstrated, by diffuse neutron scattering, the presence of such strings in the spin ice dysprosium titanate (Dy2Ti2O7). This is achieved by applying a symmetry-breaking magnetic field with which we can manipulate the density and orientation of the strings. In turn, heat capacity is described by a gas of magnetic monopoles interacting via a magnetic Coulomb interaction.

We present a specific heat and inelastic neutron scattering study in magnetic fields up into the 1/3 magnetization plateau phase of the diamond chain compound azurite Cu3(CO3)2(OH)2. We establish that the magnetization plateau is a dimer-monomer state, i.e., consisting of a chain of S = 1/2 monomers, which are separated by S = 0 dimers on the diamond chain backbone. The effective spin couplings Jmono/kB = 10.1(2) K and J dimer /kB = 1.8(1) K are derived from the monomer and dimer dispersions. They are associated to microscopic couplings J1/kB = 1(2) K, J2/kB = 55(5) K and a ferromagnetic J3/kB = −20(5) K, possibly as result of d z 2 orbitals in the Cu-O bonds providing the superexchange pathways.PACS numbers: 75.30. Et, 75.10.Pq, 75.45.+j Great interest has surrounded the observation of a 1/3 magnetization plateau in azurite CuThis material, famous as a painting pigment of deepblue colour, has been proposed as a realisation of the exotic diamond-chain Hamiltonian of coupled spin-1/2 moments, written aŝHere, J 2 is the magnetic coupling of the diamond backbone, while J 1 and J 3 represent the coupling of the monomers along the chain [3, 4, 5] (Fig. 3). Depending on the relative coupling strengths J 1 , J 2 , J 3 , this model affords a host of exotic phases and quantum phase transitions, including possibly M = 1/3 fractionalisation [6] or exotic dimer phases [4]. However, determining the magnetic exchange couplings in azurite has proved difficult, yielding controversial results. While a susceptibility χ study claims, subsequent numerical studies of χ dispute this claim, proposing a ferromagnetic (FM) J 3 , and thus a non-frustrated scenario [2]. The general issue underlying these starkly contrasting interpretations of the same experimental data is that of the nature of magnetic coupling in low-dimensional (low-D) quantum magnets. In azurite Cu 3 (CO 3 ) 2 (OH) 2 , the Cu 2+ ions (S = 1/2) are in a square-planar coordination on two inequivalent sites [7]. The system has a monoclinic crystal structure (space group P2 1 /c, lattice parameters a = 5.

Neutron scattering from single crystals has been used to determine the magnetic structure and magnon dynamics of FePS 3 , an S = 2 Ising-like quasi-two-dimensional antiferromagnet with a honeycomb lattice. The magnetic structure has been confirmed to have a magnetic propagation vector of k M = [ 01 1 2 ] and the moments are collinear with the normal to the ab planes. The magnon data could be modeled using a Heisenberg Hamiltonian with a single-ion anisotropy. Magnetic interactions up to the third in-plane nearest neighbor needed to be included for a suitable fit. The best fit parameters for the in-plane exchange interactions were J 1 = 1.46, J 2 = −0.04, and J 3 = −0.96 meV. The single-ion anisotropy is large, = 2.66 meV, explaining the Ising-like behavior of the magnetism in the compound. The interlayer exchange is very small, J = −0.0073 meV, proving that FePS 3 is a very good approximation to a two-dimensional magnet.

The recent discovery of 2D magnetic order in van der Waals materials has stimulated a renaissance in the field of atomically thin magnets. This has led to promising demonstrations of spintronic functionality such as tunneling magnetoresistance. The frantic pace of this emerging research, however, has also led to some confusion surrounding the underlying phenomena of phase transitions in 2D magnets. In fact, there is a rich history of experimental precedents beginning in the 1960s with quasi-2D bulk magnets and progressing to the 1980s using atomically thin sheets of elemental metals. This review provides a holistic discussion of the current state of knowledge on the three distinct families of low-dimensional magnets: quasi-2D, ultrathin films, and van der Waals crystals. It highlights the unique opportunities presented by the latest implementation in van der Waals materials. By revisiting the fundamental insights from the field of low-dimensional magnetism, this review highlights factors that can be used to enhance material performance. For example, the limits imposed on the critical temperature by the Mermin-Wagner theorem can be escaped in three separate ways: magnetocrystalline anisotropy, long-range interactions, and shape anisotropy. Several recent experimental reports of atomically thin magnets with Curie temperatures above room temperature are highlighted.