Quantum spin dynamics studied by the nuclear magnetic relaxation of protons in the Haldane-gap system(CH3)4NNi(NO2)3

Abstract

The nuclear spin-lattice relaxation time T 1 of 1 H in the Haldane-gap system ͑CH 3 ͒ 4 NNi͑NO 2 ͒ 3 has been measured at the temperatures down to 50 mK in the gapped and gapless phases with an external field H up to 8.5 T. In the gapless phase for H Ͼ H C1 = 2.7 T, the relaxation rate T 1 −1 exhibited, below about 3 K, a divergent behavior with decreasing temperature. Such a feature is described by an equation, such as T 1 −1 ϳ T −␣ with ␣ =1−, where is the exponent of the power-law decay for the staggered mode of transverse correlation with respect to the distance in the one-dimensional chain. It has been found that the exponent ␣ takes the values around 0.6, which are consistent with the numerical evaluation for S = 1 Heisenberg antiferromagnetic linear chain ͑HALC͒. This yields evidence for the realization of Tomonaga-Luttinger liquid phase. At very low temperatures, T 1 −1 changes into a remarkable decrease after taking a round peak, accompanying an appreciable broadening in the NMR spectrum, and the temperature for such a peak has a trend to increase with increasing field. In the gapped phase for H Ͻ H C1 , T 1 −1 showed an exponential decrease with decreasing temperature. The experimental results were well interpreted in terms of the intrabranch process associated with the scattering of the magnons within each of S z = −1 and +1 branches of the first excited state. Anomalous hump of T 1 −1 appeared at low fields below 1 T and at low temperatures below 1 K. This was reasonably explained considering the fractional-spin effect in the S = 1 HALC.−1 ϳ T −1/2 for H C1 ͑=7.5 T͒ Ͻ H Ͻ H C2 ͑=13.5 T͒. 9 Such a behavior is consistent with the theoretical prediction presented in Refs. 6 and 7, thus yielding evidence for the realization of the TL liquid phase.Recently, Haga and Suga investigated theoretically the nuclear spin-lattice relaxation for the TL liquid phases in gapped systems, such as S =1/2 two-leg ladder with a diagonal interaction, which corresponds to the exchange Hamiltonian for CuHpCl, and the S =1/2 two-leg ladder, by mapping the corresponding Hamiltonians onto the S =1/2 XXZ chain. 10 By evaluating the Luttinger parameters and z , PHYSICAL REVIEW B 73, 214406 ͑2006͒

Temperature dependence of the NMR relaxation rate1/T1for quantum spin chains

“…For gapless Heisenberg chain systems, the low-energy critical behavior has been studied [9][10][11][12] for Sr 2 CuO 3 which is an almost ideal realization with a large J 1d ∼ 2000 K and much smaller 3d couplings so that Néel temperature is pushed down to T N 5 K. For such an SU(2) symmetric material, a careful comparison of experimental and numerical NMR data has shown the prominent role of logarithmic corrections [13]. Another route to TLL behavior is to apply an external magnetic field on gapped materials such as spin-1 Haldane gap compound [14] (CH 3 ) 4 NNi(NO 2 ) 3 or dimerized spin-1/2 chains [15]. For such systems, a theoretical analysis of the 1/T 1 behavior has been performed in Refs.…”

Significant Inverse Magnetocaloric Effect induced by Quantum Criticality

“…( 1)] besides J. In this work, we are particularly interested in the compounds TMNIN [29][30][31][32] and DTN [23,[33][34][35][36][37], due to their very moderate critical fields B c ≤ 3 T (cf. Tab.…”

Review of NMR studies of nanoscale molecular magnets composed of geometrically frustrated antiferromagnetic triangles

“…In the case of TLL state, 1/T 1 is expected to follow the relation of 1/T 1 ∼ 1/T α with α = 0.5 − 0.66. 68 Goto et al reported a observation of 1/T 1 ∼ 1/T 0.6 behavior in one dimensional s = 1 quantum spin system (CH 3 ) 4 NNi(NO 2 ) 3 in a gapless state under magnetic fields, suggesting the realization of TLL state in that system. 68 In the present system, 1/T 1 does not show such a behavior expected for the TLL states.…”

“…68 Goto et al reported a observation of 1/T 1 ∼ 1/T 0.6 behavior in one dimensional s = 1 quantum spin system (CH 3 ) 4 NNi(NO 2 ) 3 in a gapless state under magnetic fields, suggesting the realization of TLL state in that system. 68 In the present system, 1/T 1 does not show such a behavior expected for the TLL states. Thus it seems to be difficult to explain the anomalous behavior of 1/T 1 observed in the twisted Heisenberg triangular spin tube by the conventional explanations described above.…”