Research
My research point of view.........
Figure 1 : (a) The J1 -J2 model on the HTLA. (b) Phase diagram of J1 -J2 model
Geometrically frustrated Heisenberg triangular lattice antiferromagnets (HTLA) have attracted tremendous attention due to numerous quantum phenomena that they exhibit at low temperatures. In such systems, the combined effects of magnetic frustration, reduced dimensionality, and low spin value have a vast implication on the ground state and low-temperature properties. All these effects bring about the enhanced quantum fluctuations leading to the emergence of exotic quantum phases in magnetic materials. One of the most striking examples is the formation of a quantum spin-liquid (QSL), a uniquely disordered (no magnetic long-range-order) ground state but with strong correlations. Anderson in 1973 predicted that the spin-1/2 HTLAs have a resonating-valance-bond (RVB) ground state, one kind of the QSL . Subsequently, several triangular antiferromagnets have been discovered which do not show long-range magnetic order (LRO) and are even established as QSL candidates . On the other hand, the majority of triangular antiferromagnets entail subtle deviations from the ideal regime that may reduce the frustration and stabilize the LRO. In fact, even the idealized case of the quantum Heisenberg model on the triangular lattice features LRO with the 120° spin structure and thus lacks the QSL phase.
The extent of frustration can be enhanced further by introducing the NNN antiferromagnetic (AFM) interaction (J2 ) which can compete with AFM J1 , known as Heisenberg J1 -J2 model on a triangular lattice. A rich phase diagram has been proposed theoretically for spin-1/2 HTLA, based on the ratio J2 /J1. This model has three distinct phases. The precise boundary and nature of these phases are still under debate. Recent theoretical studies proposed that the QSL phase is stabilized for 0.08< J2 /J1 < 0.16.
Figure 2 : (a) Spin-1/2 anisotropic HTLA. (b) Phase diagram of anisotropic HTLA
The above phase diagram is modified significantly when anisotropic exchange interactions are introduced in the triangular unit. Theoretical and numerical studies have found evidence for two QSL regimes in the phase diagram . A gapless QSL phase is reported for small values of the ratio J’/J ~ 0.65. The second one is a more conventional QSL with a small spin gap and is favoured in the region 0.65 ≤ J’/J ≤ 0.8.
On the experimental side, Ba3CoSb2O9 is a good example of spin-1/2 HTLA with a very small spatial distortion. It undergoes an AFM ordering at TN ≈ 3.9 K and exhibits a magnetization plateau at 1/3 of the saturation magnetization, where the system evolves from a 120° magnetic ordering phase to an up-up-down (uud) phase in a finite field. The compounds Cs2CuCl4 , Cs2CuBr4 , and κ-(BEDT-TTF)2 Cu2 (CN)3 are also extensively studied as spin-1/2 distorted triangular lattices with spatially anisotropic exchange interactions. For κ-(BEDT-TTF)2 Cu2 (CN)3 , no indication of magnetic LRO is reported down to 32 mK and the ratio J’/J ≈ 0.8, placing the compound close to the QSL regime in the phase diagram.[8] Similarly, Cs2CuCl4 has a weak anisotropic exchange interaction with J’/J ≈ 0.34. Inelastic neutron scattering experiments revealed fractional QSL type ground state in Cs2CuCl4 . The Bose-Einstein condensation (BEC) of magnons is also reported in this compound.[10] Another compound Cs2CuBr4 is isostructural to Cs2CuCl4 in which the ratio J’/J ≈ 0.74 is somewhat larger compared to Cs2CuCl4 . It exhibits a magnetic LRO at TN ≈ 1.4 K in zero magnetic field and a magnetization plateau at 1/3 of the saturation magnetization.
Broadly speaking, my research interest is inclined towards two-dimensional (2-D) Heisenberg lattices, especially triangular lattices. But due to the lack of structurally perfect triangle lattice compounds, the QSL ground state still remains a theoretical construct and an experimental challenge. So, to overcome this experimental difficulty, inducing spatial anisotropies in the lattice will induce the quantum fluctuation leading to unusual ground states featuring an anisotropic triangular lattices (ATL). Even though extensive theoretical studies have been performed on these ATL systems, a complete and rich phase diagram of these materials is still elusive. Thus, my primary aim is to find interesting ATL systems and tune these spatial anisotropies such that incommensurate properties appear, which will give me non-thermal parameters to push these towards a quantum critical point and to precisely understand their phase diagram.