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 combined neutron diffraction and bulk thermodynamic study of the natural mineral linarite PbCuSO4(OH)2, this way establishing the nature of the ground-state magnetic order. An incommensurate magnetic ordering with a propagation vector k=(0,0.186,1/2) was found below T(N)=2.8 K in a zero magnetic field. The analysis of the neutron diffraction data yields an elliptical helical structure, where one component (0.638μ(B)) is in the monoclinic ac plane forming an angle with the a axis of 27(2)°, while the other component (0.833μ(B)) points along the b axis. From a detailed thermodynamic study of bulk linarite in magnetic fields up to 12 T, applied along the chain direction, a very rich magnetic phase diagram is established, with multiple field-induced phases, and possibly short-range-order effects occurring in high fields. Our data establish linarite as a model compound of the frustrated one-dimensional spin chain, with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. Long-range magnetic order is brought about by interchain coupling 1 order of magnitude smaller than the intrachain coupling.

The complex interplay between the 3d and 4 f moments in hexagonal ErMnO 3 is investigated by magnetization, optical second harmonic generation, and neutron-diffraction measurements. We revise the phase diagram and provide a microscopic model for the emergent spin structures with a special focus on the intermediary phase transitions. Our measurements reveal that the 3d exchange between Mn 3+ ions dominates the magnetic symmetry at 10 K < T < T N with Mn 3+ order according to the Γ 4 representation triggering 4 f ordering according to the same representation on the Er 3+ (4b) site. Below 10 K the magnetic order is governed by 4 f exchange interactions of Er 3+ ions on the 2a site. The magnetic Er 3+ (2a) order according to the representation Γ 2 induces a magnetic reorientation (Γ 4 → Γ 2 ) at the Er 3+ (4b) and the Mn 3+ sites. Our findings highlight the fundamentally different roles the Mn 3+ , R 3+ (2a), and R 3+ (4b) magnetism play in establishing the magnetic phase diagram of the hexagonal RMnO 3 system.

We present a comprehensive macroscopic thermodynamic study of the quasi-one-dimensional (1D) s = 1 2 frustrated spin-chain system linarite. Susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements were performed to characterize the magnetic phase diagram. In particular, for magnetic fields along the b axis five different magnetic regions have been detected, some of them exhibiting short-range-order effects. The experimental magnetic entropy and magnetization are compared to a theoretical modelling of these quantities using DMRG and TMRG approaches. Within the framework of a purely 1D isotropic model Hamiltonian, only a qualitative agreement between theory and the experimental data can be achieved. Instead, it is demonstrated that a significant symmetric anisotropic exchange of about 10 % is necessary to account for the basic experimental observations, including the 3D saturation field, and which in turn might stabilize a triatic (three-magnon) multipolar phase.