Session W8: Bose-Einstein Condensation of Magnons and Related Phenomena

Spin Dimers: from BEC to Luttinger liquids

Localized spin systems, and in particular dimer systems, provide a fantastic laboratory to study the interplay between quantum effects and the interaction between excitations. Magnetic field and temperature allow an excellent control on the density of excitations and various very efficient probes such as neutrons and NMR are available. They can thus be used as ``quantum simulators'' to tackle with great success questions that one would normally search in itinerant interacting quantum systems. In particular they have provided excellent realizations of Bose-Einstein condensates [1,2]. This allowed not only to probe the properties of interacting bosons in a variety of dimensions but also to study in a controlled way additional effects such as disorder. If the dimensionality is reduced they also allow to test in a quantitative way Luttinger liquid physics [3,4,5]. I will discuss these various cases, and show that we have now good theoretical tools [6] to make quantitative comparisons with the experiments. Finally, how to go from this low dimensional case where the spins behave essentially as fermions, to the higher dimensional case where they behave as (essentially free) bosons, is a very challenging, and experimentally relevant issue.\\[4pt] [1] T. Giamarchi and A. Tsvelik, Phys. Rev. B {\bf 59} 11398 (1999).\\[0pt] [2] T. Giamarchi, C. R\"uegg and O. Tchernyshyov, Nat. Phys. {\bf 4} 198 (2008).\\[0pt] [3] M. Klanjsek et al., Phys. Rev. Lett. {\bf 101} 137207 (2008).\\[0pt] [4] C. R\"uegg et al., Phys. Rev. Lett. {\bf 101} 247202 (2008).\\[0pt] [5] B. Thielemann et al., Phys. Rev. B {\bf 79} 020408(R) (2009).\\[0pt] [6] P. Bouillot et al., arXiv:1009.0840 (2010).   

Luttinger--liquid and BEC physics in spin ladders

Spin ladder materials serve as model systems in which the fundamental phases, exotic order, and elementary excitations of low-dimensional quantum magnets can be studied experimentally and compared quantitatively to predictions by theory. We have utilised the optimal energy scale of the exchange interactions and excellent low dimensionality of the metal--organic spin ladder material (C$_{5}$H$_{12}$N)$_{2}$CuBr$_{4}$ to study spin Luttinger--liquid (LL) and magnon Bose--Einstein Condensate (BEC) physics realized at low temperatures and in high magnetic fields in this magnetic insulator. Furthermore, the inherent chemical flexibility and the structural tunability of such metal--organic compounds enable studies of the effects of bond randomness and of non--magnetic and magnetic dopants on the spin LL and magnon BEC. Bose glass phases form and the localized impurities dominate the physics near the intrinsic quantum critical points of the ladder. Measurements of the elementary excitations, phase diagrams, and thermodynamic and magnetic properties of the LL and BEC have also been extended recently to BiCu$_{2}$PO$_{6}$ in which these phenomena are combined intriguingly with frustration of the magnetic exchange interactions.   

Bose-Einstein Condensation and Asymmetry induced by Quantum Fluctuations in NiCl$_{2}$-4SC(NH$_{2})_{2}$

I will review Bose-Einstein condensation (BEC) in quantum magnets, in particular the compound NiCl$_{2}$-4SC(NH$_{2})_{2}$. This compound exhibits field-induced XY antiferromagnetism of the S = 1 Ni system for magnetic fields along the tetragonal c-axis between H$_{c1}$ = 2.1 and H$_{c2}$ = 12.6 T, and the axial symmetry of the spin environment allows us to understand the quantum phase transitions at H$_{c1}$ and H$_{c2}$ in terms of BEC of the spin system. Here the tuning parameter for the BEC transition is the magnetic field and not the temperature. It turns out that mass of the bosons that condense can be strongly suppressed by quantum fluctuations, resulting in a remarkable asymmetry between the properties at H$_{c1}$ and H$_{c2}$. Here I will present magnetization, thermal conductivity and specific heat data to probe BEC and in particular the effect of quantum fluctuations on the boson mass.   

Spin Superfluidity and Magnone BEC in He-3

The spin superfluidity -- superfluidity in the magnetic subsystem of a condensed matter -- is manifested as the spontaneous phase-coherent precession of spins first discovered in 1984 in $^3$He-B. This superfluid current of spins -- spin supercurrent -- is one more representative of superfluid currents known or discussed in other systems, such as the superfluid current of mass and atoms in superfluid $^4$He; superfluid current of electric charge in superconductors; superfluid current of hypercharge in Standard Model of particle physics; superfluid baryonic current and current of chiral charge in quark matter; etc. Spin superfluidity can be described in terms of the Bose condensation of spin waves -- magnons. We discuss different states of magnon superfluidity with different types of spin-orbit coupling: in bulk $^3$He-B; magnetically traped ``$Q$-balls'' at very low temperatures; in $^3$He-A and $^3$He-B immerged in deformed aerogel; etc. Some effects in normal $^3$He can also be treated as a magnetic BEC of fermi liquid. A very similar phenomena can be observed also in a magnetic systems with dinamical frequensy shift, like $MnC0_3$. We will discuss the main experimental signatures of magnons superfluidity: (i) spin supercurrent, which transports the magnetization on a macroscopic distance more than 1 cm long; (ii) spin current Josephson effect which shows interference between two condensates; (iii) spin current vortex -- a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; (iv) Goldstone modes related to the broken $U(1)$ symmetry -- phonons in the spin-superfluid magnon gas; etc. For recent review see Yu. M. Bunkov and G. E. Volovik J. Phys. Cond. Matter. {\bf 22}, 164210 (2010)   

Bose-Einstein condensation of magnons at room temperature

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