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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.'
author:
- 'Armando Paduan-Filho'
title: 'Bose-Einstein Condensation of Magnons in NiCl$_{2}$-4SC(NH$_{2}$)$_{2}$'
---

I. INTRODUCTION
===============

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; @2; @3; @4; @5; @6; @7; @8; @9; @10; @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 