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.

Single-crystal magnetic susceptibility and specific heat studies of the one-dimensional copper complex [PM·Cu(NO3)2·(H2O)2]n (PM = pyrimidine) show that it behaves like a uniform S = 1/2 antiferromagnetic Heisenberg chain, characterized by the exchange parameter J/kB = 36 K. Specific heat measurements in the applied magnetic field, however, reveal the formation of a field-induced spin excitation gap, whose magnitude depends on the magnitude and direction of the field. This behaviour is inconsistent with the ideal S = 1/2 Heisenberg chain. In the low-temperature region, a contribution to the susceptibility, approximately proportional to 1/T, is observed which varies strongly with the varying direction of the magnetic field. The field-induced gap and the 1/T contribution are largest for the same field direction. Previous observations of a field-induced gap in the related compounds copper benzoate and Yb4As3 have been explained by the alternating g tensor and alternating Dzyaloshinkii-Moriya interaction, producing an effective staggered magnetic field at the Cu and Yb ions. We apply this model to [PM·Cu(NO3)2·(H2O)2]n and obtain a consistent quantitative explanation of the low-temperature susceptibility, the field-induced gap and their dependence on the magnetic-field direction.

Neutrons are highly sensitive to magnetic fields owing to their magnetic moment, whereas their charge neutrality enables them to penetrate even massive samples. The combination of these properties with radiographic and tomographic imaging [1][2][3][4] enables a technique that is unique for investigations of macroscopic magnetic phenomena inside solid materials. Here, we introduce a new experimental method yielding twoand three-dimensional images that represent changes of the quantum-mechanical spin state of neutrons caused by magnetic fields in and around bulk objects. It opens up a way to the detection and imaging of previously inaccessible magnetic field distributions, hence closing the gap between high-resolution two-dimensional techniques for surface magnetism 5,6 and scattering techniques for the investigation of bulk magnetism 7-9 . The technique was used to investigate quantum effects inside a massive sample of lead (a type-I superconductor).The specific interaction of neutrons with matter enables neutron radiography to complement X-ray imaging methods for analysing materials 1 . Conventional radiography is a geometrical projection technique based on the attenuation of a beam by a sample along a given ray. Quantum mechanically, neutrons are described by de Broglie wave packets 10 whose spatial extent may be large enough to produce interference effects similar to those known from visible laser light or highly brilliant synchrotron X-rays. Measurements of the neutron wave packet's phase shift induced by the interaction with matter have a long and distinguished history [11][12][13][14] and were recently combined with neutron imaging approaches, where two-and three-dimensionally resolved spatial information about the quantum mechanical interactions of neutrons with matter was obtained 2,3,15 . In addition, neutrons, which from the particle-physicist's point of view are small massive particles with a confinement radius of about 0.7 fm, possess another outstanding property: a magnetic moment µ (µ = −9.66 × 10 −27 J T −1 ). The magnetic moment is antiparallel to the internal angular momentum of the neutron described by a spin S with the quantum number s = 1/2. Consequently, the high sensitivity of neutrons to magnetic interactions has extensively been and is still being exploited in numerous experiments to study fundamental magnetic properties and to understand basic phenomena in condensed matter 7-9 . Here, we present an experimental method that combines spin analysis with neutron imaging and yields a new contrast mechanism for neutron radiography that enables two-and three-dimensional investigations of magnetic fields in matter. This method is unique not only in that it provides spatial information about the interaction of the spin with magnetic fields but also in its ability to measure these fields within the bulk of materials, which is not possible by any other conventional technique.Our concept is based on the fact that any spin wavefunction corresponds to a definite spin direction and by using the Schrödin...

The field induced magnetic phase transitions of Cs 2 CuBr 4 were investigated by means of magnetization process and neutron scattering experiments. This system undergoes magnetic phase transition at Neél temperature T N = 1.4 K at zero field, and exhibits the magnetization plateau at approximately one third of the saturation magnetization for the field directions H b and H c. In the present study, additional symptom of the two-third magnetization plateau was found in the field derivative of the magnetization process. The magnetic structure was found to be incommensurate with the ordering vector Q = (0, 0.575, 0) at zero field. With increasing magnetic field parallel to the c-axis, the ordering vector increases continuously and is locked at Q = (0, 0.662, 0) in the plateau field range 13.1 T < H < 14.4 T. This indicates that the collinear up-up-down spin structure is stabilized by quantum fluctuation at the magnetization plateau. a c b Figure 2. Antiferromagnetic interactions J 1 and J 2 within the bc-plane. The open circles denote Cu 2+ -ions.

Cs2CuBr4 is an S = 1/2 quasi-two-dimensional frustrated antiferromagnet with a distorted triangular lattice parallel to the bc-plane. Cs2CuBr4 undergoes magnetic ordering at TN = 1.4 K at zero magnetic field. In the ordered phase below TN, spins lie in a plane that is almost parallel to the bc-plane and form a helical incommensurate structure with ordering vector Õ 0 = (0, 0.575, 0). The incommensurate spin structure arises from the spin frustration on the distorted triangular lattice. The magnetization curve has a plateau at approximately one-third of the saturation magnetization for magnetic field H parallel to the b-and c-axes, while no plateau is observed for H a. The ordering vector Õ 0 increases with increasing magnetic field parallel to the c-axis, and is locked at Õ 0 (0, 2/3, 0) in the plateau region, which indicates that the up-up-down spin structure is realized in the plateau state. The magnetization plateau should be attributed to quantum fluctuation. For H b and H c, the second anomaly suggestive of tiny plateau is observed at roughly two-third of the saturation magnetization. The magnetic field versus temperature diagram is presented. Small amount of Cl − substitution for Br − produces drastic suppression of TN. With increasing Cl − concentration x, the magnetic ordering disappears at x 0.17. It is also observed that in Cs2Cu(Br1−xClx)4 phase transition smears with increasing external field and disappears, irrespective of field direction. This should be attributed to the random field effect.KEYWORDS: Cs2CuBr4, Cs2CuCl4, Cs2Cu(Br1−xClx)4, spin frustration, triangular antiferromagnet, quantum fluctuation, helical magnetic ordering, magnetization plateaus, disorder, random field effect IntroductionTriangular antiferromagnets (TAF) have been of great interest from the viewpoint of the interplay of spin frustration and quantum fluctuation. In most of conventional antiferromagnets, which are described by two-sublattice model, the ground state is determined by the classical energy, and the quantum fluctuation gives only small correction to the ground state energy. On the other hand, in Heisenberg TAF, spins form the 120• structure in the ground state due to the spin frustration. However, in a magnetic field, spin structure of the ground state cannot be uniquely determined by the classical energy only, and thus, the ground state has continuous degeneracy in the magnetic field. No phase transition occurs up to saturation, so that the magnetization curve is monotonic. For quantum Heisenberg TAF with small spin S, the quantum fluctuation plays an important role in determining the ground state, because the quantum fluctuation can remove the continuous degeneracy of the classical ground state. The quantum fluctuation in TAF was discussed using the spin wave theory, which describes the spin system