Starting from a phenomenological standard energy functional to describe the condensation of a dilute gas of bosonic quasiparticles in magnetic insulators, we find that the inclusion of a perturbation term that explicitly violates the axial symmetry significantly modifies the details of the resulting Bose Einstein condensation. Systems with an originally axial symmetry must show an intrinsic tendency to spontaneously violate this symmetry as soon as the condensation sets in, and the phase transition at the respective critical field may even become of first order. We can explain a number of features in the experimental data of various insulating spin systems, such as a slightly nonlinear magnetization near the critical field as well as hysteresis effects and peculiarities in the energy-level scheme of TlCuCl3. We also offer a consistent explanation for certain anomalies in the magnetocaloric effect and in the magnetization of BaCuSi2O6 by assuming a spontaneous violation of axial symmetry at the magnetic phase transition on an energy scale of about 1 micro-eV. The resulting anisotropy gap in the magnetic excitation spectrum, that inevitably forms at the critical field of all such systems, lifts the linear Goldstone mode and is therefore seriously limiting the lifetime of magnetic condensates to a few nanoseconds at most.
Starting from a phenomenological standard energy functional to describe the condensation of a dilute gas of bosonic quasiparticles in magnetic insulators, we find that the inclusion of a perturbation term that explicitly violates the axial symmetry significantly modifies the details of the resulting Bose Einstein condensation. Systems with an originally axial symmetry must show an intrinsic tendency to spontaneously violate this symmetry as soon as the condensation sets in, and the phase transition at the respective critical field may even become of first order. We can explain a number of features in the experimental data of various insulating spin systems, such as a slightly nonlinear magnetization near the critical field as well as hysteresis effects and peculiarities in the energy-level scheme of TlCuCl3. We also offer a consistent explanation for certain anomalies in the magnetocaloric effect and in the magnetization of BaCuSi2O6 by assuming a spontaneous violation of axial symmetry at the magnetic phase transition on an energy scale of about 1 micro-eV. The resulting anisotropy gap in the magnetic excitation spectrum, that inevitably forms at the critical field of all such systems, lifts the linear Goldstone mode and is therefore seriously limiting the lifetime of magnetic condensates to a few nanoseconds at most.
We describe the Bose-Einstein condensate of magnetic bosonic quasiparticles in insulating spin systems using a phenomenological standard functional method for T=0. We show that results that are already known from advanced computational techniques immediately follow. The inclusion of a perturbative anisotropy term that violates the axial symmetry allows us to remarkably well explain a number of experimental features of the dimerized spin-1/2 system TlCuCl3. Based on an energetic argument we predict a general intrinsic instability of an axially symmetric magnetic condensate toward a violation of this symmetry, which leads to the spontaneous formation of an anisotropy gap in the energy spectrum above the critical field. We, therefore, expect that a true Goldstone mode in insulating spin systems, i.e., a strictly linear energy-dispersion relation down to arbitrarily small excitations energies, cannot be observed in any real material.
The low-temperature properties of certain quantum magnets can be described in terms of a Bose–Einstein condensation (BEC) of magnetic quasiparticles (triplons). Some mean-field approaches (MFA) to describe these systems, based on the standard grand canonical ensemble, do not take the anomalous density into account and leads to an internal inconsistency, as it has been shown by Hohenberg and Martin, and may therefore produce unphysical results. Moreover, an explicit breaking of the U(1) symmetry as observed, for example, in TlCuCl 3 makes the application of MFA more complicated. In the present work, we develop a self-consistent MFA approach, similar to the Hartree–Fock–Bogolyubov approximation in the notion of representative statistical ensembles, including the effect of a weakly broken U(1) symmetry. We apply our results on experimental data of the quantum magnet TlCuCl 3 and show that magnetization curves and the energy dispersion can be well described within this approximation assuming that the BEC scenario is still valid. We predict that the shift of the critical temperature T c due to a finite exchange anisotropy is rather substantial even when the anisotropy parameter γ is small, e.g., of T c in H = 6 T and for .
Due to the coexistence of phase coherence and magnetic order, Bose-Einstein condensates with internal degrees of freedom, i.e., spinor BECs, are considered to serve as an ideal table-top playground for the studies of various phenomena in different fields of physics.They have been widely used in studying spin textures and topological defects, coherent spin dynamics, quantum symmetry breaking, quantum phase transitions, etc.However, the theoretical framework used in these works is based on the mean-field theory in which the effects of quantum fluctuations are ignored.Despite the success of the mean-field theory in the description of spinor BECs, there are particular features whose account must rely on a beyond-mean-field theory as the effects of quantum fluctuations become significant.In this thesis, we develop the Beliaev theory, which is a Green's function approach beyond the Bogoliubov theory, for spinor BECs to study the effects of quantum fluctuations on the condensates' phase structures, elementary excitations, stabilities, and phase transitions.First, we point out that the Bogoliubov theory fails to capture the metastable states associated with first-order quantum phase transitions in spin-2 BECs.In fact, we show that these metastable states are induced by quantum fluctuations, and only by going to the next-order approximation, i.e., the Beliaev theory, can we show that they indeed appear around the phase boundaries.Besides the fluctuation-induced metastability, we find another important class of first-order quantum phase transitions in both spin-1 and spin-2 BECs.In this class, there is no metastable state to all orders of approximation since it is prohibited by a high symmetry of the Hamiltonian at the phase boundary, resulting in a characteristic flat energy landscape.Despite being first-order phase transitions, the flat energy landscape leads to the criticality in the dynamics of the condensate through these transitions in a manner similar to second-order phase transitions.Second, we succeed in deriving the analytic expression for the energy gap of the so-called quasi-Nambu-Goldstone (quasi-NG) modes, which are excitations not generated by spontaneous symmetry breaking, in the nematic phase of spin-2 BECs.Although quasi-NG modes are gapless at the mean-field level, we prove that with quantum corrections they acquire a nonzero energy gap.From the obtained magnitude of the energy gap, we can evaluate the critical temperature above which a topological defect such as a vortex of spin nematicity would decay by emitting thermally excited quasi-NG modes.We also study how the propagation of quasi-NG modes in space is affected by the particle-number density fluctuations of the condensate.Third, we calculate the damping rates of various types of quasiparticles in a spin-2 BEC including phonons, magnons, and quasi-NG modes.They actually have finite lifetime and decay via numerous channels of collision with the condensate atoms.Using either the Fermi's golden rule or the spinor Beliaev theory, we obtain the analytic expressions for the damping rates of phonons and magnons, from which the power-law dependence of the damping rates on the momentum is deduced.In contrast, the damping of quasi-NG modes is suppressed due to the energy conservation.
States with a coherent precession of magnetization such as a homogeneously precessing domain or a persistently precessing domain created in the superfluid 3He-B 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 3He-B in the presence of a high-frequency excitation field 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.
The quasiparticle excitations and dynamical stability of an atomic Bose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms at zero temperature is studied. The Fermi gas is assumed to be either in the normal state or to have undergone a phase transition to a superfluid state by forming Cooper pairs. The quasiparticle excitations of the Bose-Einstein condensate exhibit a dynamical instability due to a resonant exchange of energy and momentum with quasiparticle excitations of the Fermi gas. The stability regime for the bosons depends on whether the Fermi gas is in the normal state or in the superfluid state. We show that the energy gap in the quasiparticle spectrum for the superfluid state stabilizes the low-energy excitations of the condensate. In the stable regime, we calculate the boson quasiparticle spectrum, which is modified by the fluctuations in the density of the Fermi gas.
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.