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arXiv:cond-mat/0610536 · Physical Review B

Bose-Einstein condensation of magnons in magnets with predominant ferromagnetic interactions

A. V. Syromyatnikov

Published Apr 25, 2007• 22 citations
arXivHTMLPDF

Abstract

We discuss Bose-Einstein condensation (BEC) of magnons in magnets with predominant ferromagnetic (FM) interaction in a magnetic field $H$ near saturation $({H}_{c})$. Because ${H}_{c}$ is independent of FM couplings, magnetic materials of this type can have small ${H}_{c}$ which makes them promising candidates for experimental investigation of BECs. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe a small effective interaction between magnons near the quantum critical point in such magnets, in contrast to the AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature ${T}_{c}(H)\ensuremath{\propto}{({H}_{c}\ensuremath{-}H)}^{1∕\ensuremath{\phi}}$ from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}=1$ in quasi-one-dimensional magnets, and from $\ensuremath{\phi}=3∕2$ to $\ensuremath{\phi}\ensuremath{\approx}1$ $({T}_{c}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{T}_{c}\ensuremath{\propto}{H}_{c}\ensuremath{-}H)$ in quasi-two-dimensional ones.

DOI
10.1103/physrevb.75.134421

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We discuss Bose-Einstein condensation (BEC) of magnons in magnets with predominant ferromagnetic (FM) interaction in a magnetic field HHH near saturation (Hc)({H}_{c})(Hc​). Because Hc{H}_{c}Hc​ is independent of FM couplings, magnetic materials of this type can have small Hc{H}_{c}Hc​ which makes them promising candidates for experimental investigation of BECs. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe a small effective interaction between magnons near the quantum critical point in such magnets, in contrast to the AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature Tc(H)\ensuremath∝(Hc\ensuremath−H)1∕\ensuremathϕ{T}_{c}(H)\ensuremath{\propto}{({H}_{c}\ensuremath{-}H)}^{1∕\ensuremath{\phi}}Tc​(H)\ensuremath∝(Hc​\ensuremath−H)1∕\ensuremathϕ from \ensuremathϕ=3∕2\ensuremath{\phi}=3∕2\ensuremathϕ=3∕2 to \ensuremathϕ=1\ensuremath{\phi}=1\ensuremathϕ=1 in quasi-one-dimensional magnets, and from \ensuremathϕ=3∕2\ensuremath{\phi}=3∕2\ensuremathϕ=3∕2 to \ensuremathϕ\ensuremath≈1\ensuremath{\phi}\ensuremath{\approx}1\ensuremathϕ\ensuremath≈1 (TclnTc\ensuremath∝Hc\ensuremath−H)({T}_{c}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}\phantom{\rule{0.2em}{0ex}}{T}_{c}\ensuremath{\propto}{H}_{c}\ensuremath{-}H)(Tc​lnTc​\ensuremath∝Hc​\ensuremath−H) in quasi-two-dimensional ones.
The Bose-Einstein condensation (BEC) was predicted by Einstein in 1925 and this effect is characterized by the formation of a collective quantum state, when macroscopic number of particles is governed by a single wave function. The BEC of magnons was discovered experimentally in superfluid phase of 3 He. In the present work we report our progress on the BEC of magnons investigations in solid antiferromagnets at low temperatures by magnetic resonance methods. The duration of the FID signal in two samples of easy-plane antiferromagnets CsMnF 3 has been studied. Obtained data confirm the formation of magnon BEC in antiferromagnet CsMnF 3 .
Abstract Bose–Einstein condensation (BEC) is a quantum phenomenon in which a macroscopic number of bosons occupy the lowest energy state and acquire coherence at low temperatures. In three-dimensional antiferromagnets, a magnetic-field-induced transition has been successfully described as a magnon BEC. For a strictly two-dimensional (2D) system, it is known that BEC cannot take place due to the presence of a finite density of states at zero energy. However, in a realistic quasi-2D magnet consisting of stacked magnetic layers, a small but finite interlayer coupling stabilizes marginal BEC but such that 2D physics is still expected to dominate. This 2D-limit BEC behaviour has been reported in a few materials but only at very high magnetic fields that are difficult to access. The honeycomb S = 1/2 Heisenberg antiferromagnet YbCl3 exhibits a transition to a fully polarized state at a relatively low in-plane magnetic field. Here, we demonstrate the formation of a quantum critical 2D Bose gas at the transition field, which, with lowering the field, experiences a BEC marginally stabilized by an extremely small interlayer coupling. Our observations establish YbCl3, previously a Kitaev quantum spin liquid material, as a realization of a quantum critical BEC in the 2D limit.
We propose a mechanism for destabilizing or stabilizing Bose-Einstein condensation (BEC) of interacting magnons in an antiferromagnet. We study how the interaction between magnons affects the magnon BEC in a two-sublattice antiferromagnet without and with an external magnetic field. We show that in the absence of the magnetic field the magnon BEC is destabilized by the attractive interband interaction, which is larger than the repulsive intraband interaction. We also show that in the presence of the magnetic field the magnon BEC is stabilized only if the magnetic field is large enough to make the intraband interaction larger than the interband interaction. Our results provide the first step for understanding the interaction effects on the magnon BEC in antiferromagnets and may open interaction physics of multicomponent BEC of magnons in magnets.
Phase transitions in spinor Bose gases with ferromagnetic (FM) couplings are studied via mean-field theory. We show that an infinitesimal value of the coupling can induce a FM phase transition at a finite temperature always above the critical temperature of Bose-Einstein condensation. This contrasts sharply with the case of Fermi gases, in which the Stoner coupling Is{I}_{s}Is​ cannot lead to a FM phase transition unless it is larger than a threshold value I0.{I}_{0}.I0​. The FM coupling also increases the critical temperatures of both the ferromagnetic transition and the Bose-Einstein condensation.
A quantised spin wave – magnon – in magnetic films can undergo Bose-Einstein condensation (BEC) into two energetically degenerate lowest-energy quantum states with nonzero wave vectors ±k BEC . This corresponds to two interfering condensates forming spontaneously in momentum space. Brillouin Light Scattering studies for a microwavepumped film with submicrometer spatial resolution experimentally confirm the existence of the two wavefunctions and show that their interference results in a nonuniform ground state of the condensate with the density oscillating in space. Moreover, fork dislocations in the density fringes provide direct experimental evidence for the formation of pinned half-quantum vortices in the magnon condensate. The measured amplitude of the density oscillation implies the formation of a nonsymmetric state that corresponds to nonequal occupation of two energy minima. We discuss the experimental findings and consider the theory of magnon condensates, which includes, to leading order, the contribution from the noncondensed magnons. The effect of the noncondensed magnon cloud is to increase the contrast of the asymmetric state and to bring about the experimental measurements. Introduction Magnons are quasiparticles corresponding to quantised spin waves that describe the collective motion of spins [1]. In recent years, it has become possible to realise a BEC of magnons in two remarkably different systems: in superfluid phases of an isotope of helium – Helium-3 at ultralow temperatures [2, 3] and in ferrimagnetic insulators [4, 5, 6, 7]. In the normal, noncondensed state, these magnetic materials exhibit a magnetically ordered state with a gas of magnons whose phases are not correlated. However, once condensation occurs, spins develop phase coherence resulting in a common global frequency and phase of precession. At room temperature, ferrimagnetic insulators, such as yttrium-iron garnet (YIG) films, together with a combination of an in-plane magnetic field and microwave radiation, are required for the magnon condensation [4, 5, 6, 7]. Therefore, in analogy with exciton– polariton condensates, this provides yet another example of a BEC of quasiparticle excitations in a solid-state system. Experimental Realisation of a Bose-Einstein Condensate of Magnons in an Epitaxial YIG-film A room-temperature Bose-Einstein condensate of magnons was created in an epitaxial YIG-film using an experimental setup shown in Fig. 25.1a, which, in general, is similar to that used in our previous studies [4, 5]. Given that magnons are quasiparticle excitations, their number is not conserved and, therefore, the chemical potential is zero.
In the first part we discuss how the BEC picture for magnons is modified by anisotropies induced by spin-orbit coupling. In particular, we focus on the effects of antisymmetric spin interactions and/or a staggered component of the g (gyromagnetic) tensor. Such terms lead to a gapped quasiparticle spectrum and a non-zero condensate density for all temperatures so that no phase transition occurs. We contrast this to the effect of crystal field anisotropies which are also induced by spin-orbit coupling. In the second part, we study the field-induced magnetic ordering in TlCuCl 3 on a quantitative level. We show that the usual BEC picture does not allow for a good description of the experimental magnetisation data and argue that antisymmetric spin interactions and/or a staggered g tensor component are still crucial, although both are expected to be tiny in this compound due to crystal symmetries. Including this type of interaction, we obtain excellent agreement with experimental data.