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Physical Review Letters

New Non-Goldstone Collective Mode of BEC of Magnons in Superfluid He3−B

Marcel Človečko, Emil Gažo, Martin Kupka, Peter Skyba

Published Apr 17, 2008• 18 citations
Publisher

Abstract

Bose-Einstein condensation of magnons in superfluid 3He-B is experimentally manifested by various states where coherent spin precession is established spontaneously, even in nonhomogeneous magnetic fields. Once such a condensate with coherent spin precession is created, it occupies the state with minimal energy, the ground state. The application of an additional magnetic field to that condensate may cause its deflection from the energy minimum and the condensate responds by creating collective gapless oscillations known as Goldstone modes. This Letter reports the experimental observation of a new (non-)Goldstone mode, which can be viewed as an additional NMR mode of condensed magnons in a rotating frame of reference.

DOI
10.1103/physrevlett.100.155301

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Bose-Einstein condensation of magnons in superfluid 3He-B is experimentally manifested by various states where coherent spin precession is established spontaneously, even in nonhomogeneous magnetic fields. Once such a condensate with coherent spin precession is created, it occupies the state with minimal energy, the ground state. The application of an additional magnetic field to that condensate may cause its deflection from the energy minimum and the condensate responds by creating collective gapless oscillations known as Goldstone modes. This Letter reports the experimental observation of a new (non-)Goldstone mode, which can be viewed as an additional NMR mode of condensed magnons in a rotating frame of reference.
States with a coherent precession of magnetization such as a homogeneously precessing domain or a persistently precessing domain created in the superfluid 3{}^{3}3He-BBB represent the macroscopic examples of the Bose-Einstein condensates of magnons. Once the magnons form one of these states, this many-magnon coherent quantum state is described by a ``single-magnon wave function'' (or an order parameter). A suitable external perturbation may cause the condensate to oscillate around the state of coherent precession, which demonstrates a collective rigidity of the condensate against scattering a single magnon out of it. The states corresponding to a free coherent precession of magnetization are degenerate in the phase of precession, so there exist oscillations around such states with a gapless dispersion relation, known as the Goldstone modes. Here, we present both experimental and theoretical results of the study of the spin density oscillations superposed on a homogeneously precessing domain in superfluid 3{}^{3}3He-BBB in the presence of a high-frequency excitation field Brf{B}_{\text{rf}}Brf​. We show that the presence of this field lifts the degeneracy of the precessing state with respect to the phase of precession, that is, it violates the symmetry of the magnon condensate, and former Goldstone modes become non-Goldstone ones, as they acquire the energy gap in their spectrum.
Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of the collective quantum state, in which the macroscopic number of particles occupies the lowest energy state and thus is governed by a single wave function. Here we highlight the BEC in a magnetic subsystem -- the BEC of magnons, elementary magnetic excitations. Magnon BEC is manifested as the spontaneously emerging state of the precessing spins, in which all spins precess with the same frequency and phase even in the inhomogeneous magnetic field. We consider this phenomenon on example of spin precession in superfluid phases of 3^33He. The magnon BEC in these phases has all the properties of spin superfluidity. The states of the phase-coherent precession belong to the class of the coherent quantum states, which manifest themselves by superfluidity, superconductivity, quantum Hall effect, Josephson effect and many other macroscopic quantum phenomena.
Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of a collective quantum state in which a macroscopic number of particles occupy the lowest energy state and thus is governed by a single wavefunction. Here we highlight the BEC in a magnetic subsystem--the BEC of magnons, elementary magnetic excitations. The magnon BEC is manifested as the spontaneously emerging state of the precessing spins, in which all spins precess with the same frequency and phase even in an inhomogeneous magnetic field. The coherent spin precession was observed first in superfluid (3)He-B and this domain was called the homogeneously precessing domain (HPD). The main feature of the HPD is the induction decay signal, which ranges over many orders of magnitude longer than is prescribed by the inhomogeneity of magnetic field. This means that spins precess not with a local Larmor frequency, but coherently with a common frequency and phase. This BEC can also be created and stabilized by continuous NMR pumping. In this case the NMR frequency plays the role of a magnon chemical potential, which determines the density of the magnon condensate. The interference between two condensates has also been demonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. The main property is the existence of a spin supercurrent. This spin supercurrent flows separately from the mass current. Transfer of magnetization by the spin supercurrent by a distance of more than 1 cm has been observed. Also related phenomena have been observed: the spin current Josephson effect; the phase-slip processes at the critical current; and the spin current vortex--a topological defect which is the analog of a quantized vortex in superfluids and of an Abrikosov vortex in superconductors; and so on. It is important to mention that the spin supercurrent is a magnetic phenomenon, which is not directly related to the mass superfluidity of (3)He: it is the consequence of a specific antiferromagnetic ordering in superfluid (3)He. Several different states of coherent precession have been observed in (3)He-B: the homogeneously precessing domain (HPD); a persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of coherent precession in compressed aerogel. In compressed aerogel the coherent precession has been also found in (3)He-A. We demonstrate that the coherent precession of magnetization is a true BEC of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by spin-orbit coupling which is different for different states of the magnon BEC.
The Bose–Einstein condensation (BEC) corresponds to the formation of a collective quantum state in which macroscopic number of particles is governed by a single wave function. The magnon BEC forms by excited non-equilibrium magnons and manifests itself by coherent precession of magnetization even in an inhomogeneous magnetic field. The magnon BEC is very similar to an atomic BEC, but the potential of the interaction between magnons may variate very significantly. The superfluid phases of 3He are the best antiferromagnetic system for investigations of magnon BEC and spin superfluidity. The 6 different states of magon BEC were observed in 3He. Recently magnon BEC was observed in antiferromagnets with Suhl–Nakamura interaction and ferrites. Here we review for the first time the switch off NMR method, when magnon BEC forms during a long radiofrequency pulse. The new experimental results are discussed.
Long-lived coherent spin precession of 3He-B at low temperatures around 0.2 Tc is a manifestation of Bose-Einstein condensation of spin-wave excitations or magnons in a magnetic trap which is formed by the order-parameter texture and can be manipulated experimentally. When the number of magnons increases, the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons. This is the first experimental example of Bose condensation in a box. By selective rf pumping the trap can be populated with a ground-state condensate or one at any of the excited energy levels. In the latter case the ground state is simultaneously populated by relaxation from the exited level, forming a system of two coexisting condensates.
The polar phase of ^{3}He, which is topological spin-triplet superfluid with the Dirac nodal line in the spectrum of Bogoliubov quasiparticles, has been recently stabilized in a nanoconfined geometry. We pump magnetic excitations (magnons) into the sample of polar phase and observe how they form a Bose-Einstein condensate, revealed by coherent precession of the magnetization of the sample. Spin superfluidity, which supports this coherence, is associated with the spontaneous breaking of U(1) symmetry by the phase of precession. We observe the corresponding Nambu-Goldstone boson and measure its mass emerging when applied rf field violates the U(1) symmetry explicitly. We suggest that the magnon BEC in the polar phase is a powerful probe for topological objects such as vortices and solitons and topological nodes in the fermionic spectrum.