Magnetic properties and spin waves of bilayer magnets in a uniform field

Sommer, Torsten; Vojta, Matthias; Becker, K. W.

doi:10.1007/s100510170052

Cited by 82 publications

(109 citation statements)

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Section: Formalismmentioning

confidence: 99%

“…In the Zeeman energy term, g is the g-factor, µ B the Bohr magneton, and H the external magnetic field. For treating the spin system, we can adopt the bond operator formalism [17][18][19], in which the four spin states (one singlet and three triplet) in a dimer are described by four bosonic operators, s and t, asHere |0, 0 and |1, α (α = ±, 0) stand for singlet and triplet states, respectively, while |vac denotes the vacuum of s, t. The transformation becomes exact when a constraint, s † s + α=±,0 t † α t α = 1, is imposed. With the bond operators, the Hamiltonian (1) is expressed as…”

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Supersolid states in a spin system: Phase diagram and collective excitations

2013

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Phases analogous to supersolids can be realized in spin systems. Here we obtain the phase diagram of a frustrated dimer spin-1/2 system on a square lattice and study the collective excitation spectra, focusing on the supersolid state (SS). In the phase diagram on a parameter space of the exchange interaction and magnetic field, we find, on top of the SS phase, a phase that has no counterpart in the Bose Hubbard model and this state becomes dominant at the region where the enhancement of SS occurs in the bose Hubbard model. We then investigate the excitation spectrum and spinspin correlation, which can be detected by neutron scattering experiments. We obtain an analytic expression for the spin wave velocity, which agrees with hydrodynamic relations. The intensity of excitation modes in the spin-spin correlation function is calculated and their change in the supersolid and superfluid states is discussed.PACS numbers: 75.10. Jm, 75.40.Gb, 64.70.Tg, 03.75. Kk INTRODUCTIONSupersolid (SS) state is a phase where both offdiagonal long-range order and diagonal-long range order coexist. After the non-classical rotational inertia experiment in He 4 suggested an SS phase, the SS state attracted considerable interest [1]. However, the interpretation of the result is still controversial [2], and efforts to find SS continue. Lattice systems are other candidates to find SS than He 4 . Cold atoms on optical lattices are one of them. A proposal [3] was made based on the fact that the extended bose Hubbard model with a nearest neighbor interaction shows SS [4,5]. Dipole-dipole interaction is also suggested to help realizing SS [6].Another, entirely different avenue to find SS in lattice systems is to consider quantum magnets. This is because certain spin systems can be effectively regarded as bose systems [7][8][9]. After a theoretical proposal of SS in a dimer spin system [10], spin systems are attracting much attention as a promising candidate to find SS phases [10][11][12][13][14][15]. One example is the spin-1 Heisenberg model with an anisotropy, which is effectively obtained from a spin-1 frustrated dimer model [11]. Another example is the spin-1/2 dimer model with large Ising-like exchange anisotropy [10,12]. The anisotropy can be effectively realized in a lattice with large frustration. Ref. [13] has investigated a frustrated spin-1/2 spin-dimer Heisenberg model with spin-isotropic couplings on square lattice( Fig.1), and shown that the model actually exhibits a SS state. However, the study was concentrated on a specific choice of parameters, while the phase diagram in a wider parameter space has yet to be determined. In addition, experimentally relevant properties of the SS phase have not been fully understood, either.These have motivated us, in the present work, to investigate the phase diagram and dynamical properties of the frustrated spin-1/2 dimer Heisenberg model on square lattice. There, we employ the bond operator method as well as the generalized spin wave theory. In the phase diagram on a parameter space of t...

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Section: Formalismmentioning

confidence: 99%

mentioning

confidence: 99%

Supersolid states in a spin system: Phase diagram and collective excitations

2013

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“…[38,39,51] to describe the BEC and perform the local transformation |s r = u |s r + ve iQ0r (f |t +,r + g |t −,r ) (7a) t +,r = u (f |t…”

Section: P-1mentioning

confidence: 99%

Microscopic model for Bose-Einstein condensation and quasiparticle decay

Fischer¹,

Duffe²,

Uhrig³

2011

EPL

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Abstract. -Sufficiently dimerized quantum antiferromagnets display elementary S = 1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J1 ≈ −2.3 meV, J2 ≈ 1.2 meV, J3 ≈ 2.9 meV and J4 ≈ −0.3 meV. These couplings determine IPA-CuCl3 as system of coupled asymmetric S = 1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.Low-dimensional antiferromagnetic quantum spin systems display various fascinating properties, e.g., spinPeierls transition [1, 2], appearance of a Haldane gap for integer spins [3,4], high-temperature superconductivity upon doping [5], and the Bose-Einstein condensation (BEC) in spin-dimer systems [6][7][8][9], where the latter one is characterized by a phase transition from a non-magnetic phase to a long-range antiferromagnetically ordered gapless phase at a critical magnetic field H c1 .Another fascinating phenomenon recently observed in low-dimensional antiferromagnets is the decay of their elementary S = 1 excitations, triplons [10], at higher energies so that the triplons exist only in a restricted part of the Brillouin zone [11,12]. Theoretically as well, there is rising interest in the understanding and quantitative description of this phenomenon for gapped triplons [13][14][15][16] as well as for gapless magnons [17][18][19].The description of quasiparticle decay faces an intrinsic difficulty. The merging of the long-lived, infinitely sharp elementary triplon with a multitriplon continuum requires to describe the resulting resonance and its edges precisely. This is still a challenge for numerical approaches such as exact diagonalization or dynamic density-matrix (a) fischer@fkt.physik.tu-dortmund.de (b) goetz.uhrig@tu-dortmund.de renormalization [20]. Diagrammatic approaches are able to capture the qualitative features but may encounter difficulties in the quantitative description in the regime of strong merging where the sharp mode dissolves completely in the continuum because this is a strong coupling phenomenon [13,14]. Unitary transformations also face difficulties when modes of finite life-time occur [16].A crucial step in the understanding of both phenomena is to identify a suitable experimental system. The best studied candidate for the BEC in coupled spin-dimer systems is TlCuCl 3 . Unfortunately, recent research suggests that the high field spectrum remains gapped [21,22] in contrast to what is expected from a phase where a continuous s...

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“…In this limit, the ground state is non-magnetic with zero total angular momentum, and therefore a QCP separating it from a magnetically ordered phase is expected as a matter of principle. Although this QCP can be pre-empted by an insulator-metal transition 17,18 or rendered first-order by coupling to the lattice or other extraneous factors, it is sufficient that the system is reasonably close to the hypothetical QCP.To assess the proximity to the QCP and the possibility of finding the Higgs mode, we first reproduce the observed transverse spin-wave modes by applying the spin-wave theory 19,20 to the following phenomenological Hamiltonian dictated by general symmetry considerations:Here,S denotes a pseudospin-1 operator describing the entangled spin and orbital degrees of freedom. This model includes single-ion terms (E and ) of tetragonal (z c) and orthorhombic (x a) symmetries, correspondingly, as well as an XY-type exchange anisotropy (α > 0) and the bond-directional pseudodipolar interaction (A); note that its sign depends on the bond.…”

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confidence: 99%

“…To assess the proximity to the QCP and the possibility of finding the Higgs mode, we first reproduce the observed transverse spin-wave modes by applying the spin-wave theory 19,20 to the following phenomenological Hamiltonian dictated by general symmetry considerations:…”

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confidence: 99%

Higgs mode and its decay in a two-dimensional antiferromagnet

et al. 2017

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Condensed-matter analogues of the Higgs boson in particle physics allow insights into its behaviour in di erent symmetries and dimensionalities 1 . Evidence for the Higgs mode has been reported in a number of di erent settings, including ultracold atomic gases 2 , disordered superconductors 3 , and dimerized quantum magnets 4 . However, decay processes of the Higgs mode (which are eminently important in particle physics)have not yet been studied in condensed matter due to the lack of a suitable material system coupled to a direct experimental probe. A quantitative understanding of these processes is particularly important for low-dimensional systems, where the Higgs mode decays rapidly and has remained elusive to most experimental probes. Here, we discover and study the Higgs mode in a two-dimensional antiferromagnet using spin-polarized inelastic neutron scattering. Our spin-wave spectra of Ca 2 RuO 4 directly reveal a well-defined, dispersive Higgs mode, which quickly decays into transverse Goldstone modes at the antiferromagnetic ordering wavevector. Through a complete mapping of the transverse modes in the reciprocal space, we uniquely specify the minimal model Hamiltonian and describe the decay process. We thus establish a novel condensed-matter platform for research on the dynamics of the Higgs mode.For a system of interacting spins, amplitude fluctuations of the local magnetization-the Higgs mode-can exist as well-defined collective excitations near a quantum critical point (QCP). We consider here a magnetic instability driven by the intra-ionic spinorbit coupling, which tends towards a non-magnetic state through complete cancellation of orbital (L) and spin (S) moments when they are antiparallel and of equal magnitude 5,6 . This mechanism should be broadly relevant for d 4 compounds of such ions as Ir(V), Ru(IV), Os(IV) and Re(III) with sizable spin-orbit coupling but remains little explored. We investigate the magnetic insulator Ca 2 RuO 4 , a quasi-two-dimensional antiferromagnet 7 with nominally L = 1 and S = 1 (Fig. 1). Because the local symmetry around the Ru(IV) ion is very low 8,9 (having only inversion symmetry), it is widely believed that the orbital moment is completely quenched by the crystalline electric field 10-13 , which is dominated by the compressive distortion of the RuO 6 octahedra along the c-axis (Fig. 1). In the absence of an orbital moment, the nearest-neighbour magnetic exchange interaction is necessarily isotropic. Deviations from this behaviour are a sensitive indicator of an unquenched orbital moment. If this moment is sufficiently strong, it can drive Ca 2 RuO 4 close to a QCP with novel Higgs physics.Our comprehensive set of time-of-flight (TOF) inelastic neutron scattering (INS) data over the full Brillouin zone (Fig. 2a) indeed reveal qualitative deviations of the transverse spin-wave dispersion from those of a Heisenberg antiferromagnet. In particular, the global maximum of the dispersion is found at q = (0,0), in sharp contrast to a Heisenberg antiferromagnet, which has a...

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Magnetic properties and spin waves of bilayer magnets in a uniform field

Cited by 82 publications

References 28 publications

Supersolid states in a spin system: Phase diagram and collective excitations

Supersolid states in a spin system: Phase diagram and collective excitations

Microscopic model for Bose-Einstein condensation and quasiparticle decay

Higgs mode and its decay in a two-dimensional antiferromagnet

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