Quantum critical scaling for a Heisenberg spin-12chain around saturation

Abstract

We demonstrate quantum critical scaling for an S = 1/2 Heisenberg antiferromagnetic chain compound Cu(C 4 H 4 N 2 )(NO 3 ) 2 in a magnetic field around saturation, by analyzing previously reported magnetization [Y. Kono et al., Phys. Rev. Lett. 114, 037202 (2015)], thermal expansion [J. Rohrkamp et al., J. Phys.: Conf. Ser. 200, 012169 (2010)], and NMR relaxation data [H. Kühne et al., Phys. Rev. B 80, 045110 (2009)]. The scaling of magnetization is demonstrated through collapsing the data for a range of both temperature and field onto a single curve without making any assumption for a theoretical form. The data collapse is subsequently shown to closely follow the theoretically predicted scaling function without any adjustable parameters. Experimental boundaries for the quantum critical region could be drawn from the variable range beyond which the scaled data deviate from the theoretical function. Similarly to the magnetization, quantum critical scaling of the thermal expansion is also demonstrated. Further, the spin dynamics probed via NMR relaxation rate 1/T 1 close to the saturation is shown to follow the theoretically predicted quantum critical behavior as 1/T 1 ∝ T −0.5 persisting up to temperatures as high as k B T J , where J is the exchange coupling constant. A quantum critical point (QCP) is a zero-temperature singularity in the phase diagram of matter forming the border between two competing ground states [1]. It is driven by a nonthermal parameter such as a magnetic field, pressure, or chemical substitution, and characterized by strong quantum fluctuations. While a QCP is defined strictly at zero temperature, the interplay between quantum and thermal fluctuations gives rise to a so-called quantum critical region at finite temperatures in an extended parameter space (illustrated by the yellow fan-out area in Fig. 1). This intriguing region is characterized by the absence of energy scales other than temperature as well as the corresponding critical properties of physical observables, e.g., correlation or response functions, which culminate into scaling behavior and universality [1][2][3][4]. Such quantum criticality has been experimentally observed or inferred in diverse systems including magnetic insulators [5][6][7], organic conductors [8], heavy fermions [9,10], cuprates [11], pnictides [12], and cold atoms [13], and is widely believed to underpin exotic phenomena like unconventional superconductivity. However, understanding quantum criticality through connecting microscopics to experimental observation largely remains challenging [1,[8][9][10][11][12]14].Quantum magnets are an ideal playground in that respect owing to their simple and well-defined Hamiltonian [15]. In particular, one-dimensional (1D) spin systems for which exact solutions are available may serve as a test bed for quantitative comparison between theories and experiments [16][17][18][19]. Indeed, quite a few excellent quasi-1D quantum magnets having accessible critical field strength, i.e., relatively small exchange coupling strengt...

Thermodynamics of a frustrated quantum magnet on a square lattice

“…at saturation in the AF spin chains [20,21]. This feature -square root cusp at the saturation magnetization…”

Temperature dependence of the NMR spin-lattice relaxation rate for spin-12chains

“…In addition, in Fig. 7 we offer a comparison between our magnetization data, computed at finite temperature, and the scaling function close to (or on) a field-induced quantum critical point, which have been calculated and used in the literature [45,49,50]. At h = 2J = h c , from Eqs.…”

“…At h = 2J = h c , from Eqs. (2) and (3) in [49], we know that the magnetization per site should behave as…”

“…[48] and discussed in Ref. [49]. In this situation the prefactor is not easily extracted and therefore we fit the expected algebraic behavior J (1/T 1 ) +− / = a(k B T /J ) −0.5 with a free fit parameter a.…”

Finite-temperature correlations in a quantum spin chain near saturation

“…In spin chains near saturation, recent studies addressed the universality of thermodynamic properties [14][15][16] and quasistatic (low-frequency limit) correlation functions [15,17,18]. Unfortunately, the much-anticipated universality of finitetemperature dynamic spin correlations remained elusive to date due to unique technical challenges.…”