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

Abstract

We discuss Bose-Einstein condensation of magnons (BEC) in magnets with predominant ferromagnetic (FM) interaction in magnetic field H near saturation (Hc). Because Hc is independent of FM couplings, magnetic materials of this type can have small Hc that makes them promising candidates for experimental investigation of BEC. Ferromagnets with easy-plane anisotropy and antiferromagnets (AFs) containing weakly coupled FM planes or chains are discussed in detail. We observe small effective interaction between magnons near the QCP in such magnets, in contrast to AFs with strong AF coupling previously discussed. In particular, this smallness allows us to find crossovers in the critical temperature Tc(H) ∝ (Hc − H) 1/φ from φ = 3/2 to φ = 1 in quasi-1D magnets, and from φ = 3/2 to φ ≈ 1 (Tc ln Tc ∝ Hc − H) in quasi-2D ones.

Quasi-two-dimensional Bose-Einstein condensation of lattice bosons in the spin- 12 XXZ ferromagnet K2CuF4

“…Figure 4(a) shows the phase diagram for temperature vs internal magnetic field for K 2 CuF 4 with H c. The transition points determined from the temperature and magnetic field dependences of the magnetization are consistent with each other. We can see that the phase boundary is linear in a wide temperature range below 5 K in accordance with the theory [21]. The solid line in Fig.…”

“…The phase boundary between the polarized paramagnetic and ordered phases is described by the power law in Eq. (1) with exponent φ ≈ 1.0 in a wide temperature range below 5 K. This result is in agreement with the theory of quasi-2D BEC universality [21].…”

“…In this paper we present a phase diagram for temperature vs the magnetic field applied parallel to the c axis in K 2 CuF 4 and show that the phase boundary is described by the power law with exponent φ ≈ 1.0 in a wide temperature range, as predicted by the theory [21].…”

“…In a three-dimensional (3D) system, the critical exponent is given by φ BEC = 3/2 [1,3,4], which has been confirmed for several gapped quantum magnets, such as TlCuCl 3 [18,19], DTN [13,14] and (CH 3 ) 2 CHNH 3 CuCl 3 [20]. On the other hand, for a quasi-2D system, the theory [21] predicts that the phase boundary is described with φ ≈ 1.0 in a wide temperature range except at sufficiently low temperatures that are lower than the magnitude of the interlayer interaction. However, this prediction has not been sufficiently verified experimentally.…”

Secondary Phase Transition of Ising Model

“…In addition, we notice that the lattice-spin phonons can be regarded as ideal Bose gas, its special property at low temperature should be reviewed. Since Bose-Einstein condensation (BEC) in dilute atomic gases has produced by experimental groups in 1995 [2][3][4][5], the experimental observations and relevant theoretical explanations for BEC phenomena in diverse physical systems have successively been reported [6][7][8][9][10][11][12][13][14], among them the interesting issues for us are that refer to BEC of magnons [8][9][10][11][12]. The similarity between magnons and lattice-spin phonons enable us to believe that an Ising model, as an example of ferromagnet, may experience a BEC phase transition at ultralow temperature, which will determine a characteristic of magnetic saturation.…”