Bose–Einstein Condensation of Magnons in NiCl 2 -4SC (NH 2 ) 2

Abstract

A Bose-Einstein condensation (BEC) has been observed in magnetic insulators in the last decade. The bosons that condensed are magnons, associated with an ordered magnetic phase induced by a magnetic field. We review the experiments in the spin-gap compound NiCl 2 -4SC(NH 2 ) 2 , in which the formation of BEC occurs by applying a magnetic field at low temperatures. This is a contribution to the celebration for the 50th anniversary of the Solid State and Low Temperature Laboratory of the University of São Paulo, where this compound was first magnetically characterized.PACS numbers: 75.50.Tt, 75.50.Gg, 75.30.Ds, Macroscopic systems governed by quantum mechanics of interacting particles attract a great deal of interest. Cold atoms and quantum magnets, whose total spin is an integer, have interesting similarities that show the common physics of these two seemingly different realizations 1-11 . All atoms with an even number of neutrons satisfy Bose statistics, which accounts for about 75 per cent of the atoms in the periodic table. Based on the Bose-Einstein statistics a gas of non-interacting massive bosons condenses below a certain temperature T BEC , in which the Bose-Einstein condensation (BEC) occurs. This is a macroscopic quantum phenomenon characterized by spontaneous quantum coherence persisting over macroscopic length and time scales. In dilute atomic gases this phenomenon was realized experimentally for cold atoms. Several quantum spin systems in solids, which show a magnetic-field induced transition, are expected to also show condensation above or below a certain critical field 2,7,12 . Studies have shown that the magnetic system can be mapped non-locally onto a set of weakly interacting bosons on a lattice.The sorting phase can be described as a BEC of bosonic quasi-particles, in which the magnetic field acts to preserve the number of bosons. Therefore, the tuning parameter to induce condensation in spin-ordered systems is not the temperature, but the magnetic field. For particles as well as magnons, a macroscopic number of bosons condense into a single quantum state-the state of lowest energy. The quantum coherence of Bose-Einstein condensation dates back to the prediction of Einstein, based on Bose's work, in 1924.In the diluted BEC the macroscopic wave function is directly connected with the microscopic energy levels, providing a complete description of these phenomena in terms of the Gross-Pitaevskii equation. The concept of a coherent macroscopic matter wave in interacting many-body systems is independent of a detailed microscopic understanding of particles. The intricacies of the many-body problem with interactions that lead to non-separable Hamiltonians are solved by this equation, which introduces effective potentials that are sim-pler than the original interactions, which in turn renders the physical problem more tractable.Experimental evidence of the BEC in confined weakly interacting gases was produced by E. A. Cornell, W. Ketterle, and C. E. Wieman in 1995, leading to a Nobel Prize in 2001. That...

A New Technique for Measuring the Chemical Potential of Magnons Confined in Nanostructures

“…Also, Bennett, et al [1] discusses that BEC is always in an open system and exhibits metastability that can be treated as a thermodynamic equilibrium for a finite time window. The observed upturn signature has also been recorded in some metallic ferromagnetic nanomaterials within the 10 to 50 K [25] and in some ladder compounds [26,27]. This observation reinforces the presence of a phase transition attributed to magnons BEC.…”

Temperature dependence of the NMR relaxation rate1/T1for quantum spin chains

“…We also discuss a quasi-1d magnetic insulator compound NiCl 2 -4SC(NH 2 ) 2 , also called DTN, whose relevant 3d structure consists of weakly coupled S = 1 chains in the two other transverse (with respect to the chain axis) directions. Its experimental interest comes from the appearance of a Bose-Einstein condensation (BEC) phase when applying a magnetic field at low temperature [26,27]. More recently, Br-doped (disordered) DTN was suggested to be a good experimental candidate for observing a Bose glass phase [28][29][30].…”

First-Principles study of an S = 1 quasi-1D quantum molecular magnetic material

“…The organic quantum magnetic system NiCl 2 -4SC(NH 2 ) 2 (DTN) 17 , which has been studied in experiments and by quantum Monte-Carlo simulations based on model Hamiltonians 2,[21][22][23][26][27][28] , is the subject of this work. The molecular unit of this system (Figure 1) has a central magnetic cation Ni surrounded by four electrically polar ligands, SC(NH 2 ) (thiourea).…”