Low temperature properties of the triangular-lattice antiferromagnet: a bosonic spinon theory

Abstract

We study the low temperature properties of the triangular-lattice Heisenberg antiferromagnet with a mean field Schwinger spin-1 2 boson scheme that reproduces quantitatively the zero temperature energy spectrum derived previously using series expansions. By analyzing the spin-spin and the boson density-density dynamical structure factors, we identify the unphysical spin excitations that come from the relaxation of the local constraint on bosons. This allows us to reconstruct a free energy based on the physical excitations only, whose predictions for entropy and uniform susceptibility seem to be reliable within the temperature range 0 T 0.3J , which is difficult to access by other methods. The high values of entropy, also found in high temperature expansion studies, can be attributed to the roton-like narrowed dispersion at finite temperatures. of several numerical techniques [3][4][5][6][7][8][9][10][11] was crucial to elucidate that the zero point quantum fluctuations in this particular system are not enough to destroy the classical 120 • Néel order, lending support to a simple semiclassical description at low temperatures such as that provided by linear spin wave theory (LSWT) [12].Nonetheless, early high temperature expansion (HTE) studies [6] performed down to low temperatures showed no evidence of a renormalized classical behavior as predicted by the nonlinear sigma model (NLσ M) [13,14]. For instance, around T = 0.25J , the correlation length calculated by HTE is only ξ ∼ 1.5 lattice constants, in contrast to the value ξ ∼ 12 predicted by NLσ M [6,10]. Consistent with these values, the entropy calculated by HTE was one order of magnitude larger than that of the NLσ M. These early results were interpreted as a probable crossover between renormalized classical and quantum critical regimes [15].Unexpectedly, series expansion (SE) studies [10,16] performed at zero temperature also showed a strong downward renormalization of the high energy part of the spectrum with respect to LSWT, along with the appearance of roton-like minima at the midpoints of the edges of the hexagonal Brillouin zone (BZ). Originally, the presence of such roton-like excitations were proposed to be related to possible fermionic spinon excitations which in turn would lead to the anomalous low temperature properties of the THM [10]. However, subsequent works showed that nontrivial 1/S corrections, arising from the noncollinearity of the 120 • Néel order, accurately recovers the T = 0 SE results [17][18][19]. This gave support to an interacting magnon picture for the spectrum, although it was found that the magnon-quasiparticles are not well defined for a significant part of the BZ [18,19]. Nevertheless, by assuming a bosonic character for the SE dispersion relation, the high values of entropy found at low temperature was attributed to the thermal excitation of rotons, even at temperatures below the roton gap [10].Here we explore the low temperature properties of THM from an alternative viewpoint: a bosonic spinon perspective, based on the Sch...

Spin-liquid phase in a spatially anisotropic frustrated antiferromagnet: A Schwinger boson mean-field approach

“…The SB-MF approach can describe spin-liquid states with short-range spin correlations. However, at temperatures T 0.4J , we find that variational parameters A δ ,B δ vanish (see also [27]). This indicates that SB-MF is unable to describe paramagnetic phases occurring, for instance, in the experimental phase diagram of Cs 2 CuCl 4 .…”

“…The SB-MF approach can be extended trivially to finite temperatures by minimizing the total free energy of the system leading to the set of self-consistent equations [27] …”

“…Since these interactions can be generated by fourth-order processes that also lead to ring exchange as discussed above, our work contributes to the general understanding of ring-exchange effects on frustrated antiferromagnets [23]. We use Schwinger boson mean-field theory (SB-MF) [25] expressed in terms of antiferromagnetic and ferromagnetic bonds which are treated as variational parameters [26][27][28]. The Schwinger boson approach is particularly useful since it can describe ordered and disordered phases on equal footing; the magnetically ordered phases resulting from the condensation of the bosons at particular order wave vectors of the system.…”

Large- S limit of the large- N theory for the triangular antiferromagnet

“…The RPA propagator of the fluctuation fields can be expressed as is the polarization operator and Π 0 is a diagonal matrix containing the exchange couplings J ij along the diagonal except for the entries corresponding to λ − λ derivatives, which are zero. Replacing the Green function (40) in the polarization operator (46) and by applying the power counting rule shown in Fig. 3, we obtain Π αβ (q, iω n ) ∼ S 0 in the large S limit (the dominant contribution arises from a loop containing one condensed and one non-condensed spinon propagator).…”

Static and Dynamical Properties of the Spin-1/2Equilateral Triangular-Lattice AntiferromagnetBa3CoSbMa1, Kamiya2, Hong3 et al. 2016Phys. Rev. Lett.136201454View full textAdd to dashboardCite

“…Introduction.-The S = 1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) is the paradigmatic example of a two-dimensional (2D) frustrated quantum magnet [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. The combination of frustration, strong quantum fluctuations and low dimensionality is anticipated to produce strong deviations from semiclassical theories.…”