Home >  About ISSP >  Publications > Activity Report 2018 > Xxxx Group

Field-Induced Quantum Criticality and Universal Temperature Dependence of the Magnetization of a Spin-1/2 Heisenberg Chain

Sakakibara Group

The spin-1/2 Heisenberg antiferromagnet in one dimension is one of the few exactly solvable models of strongly interacting systems [1]. By now, we have complete understanding of its static properties, and much progress has been made in elucidating its dynamics and excited states. Yet experimental verifications of theoretical predictions on these properties are still limited. There has been a total lack of systematic experiments, in particular, near the magnetic-field-induced quantum critical point, at which the system undergoes a quantum phase transition from a quantum disordered Tomonaga-Luttinger liquid (TLL) to a gapped ferromagnet [1]. We have made precise dc magnetization measurements of Cu(C4H4N2)(NO3)2, CuPzN, an ideal one-dimensional spin-1/2 Heisenberg antiferromagnet, near the critical field Hs [2]. The power-law dependences of the magnetization on temperature and magnetic field determined by this experiment are in excellent agreement with theory.

Fig. 1. Field dependence of the magnetization of CuPzN at 0.08 K (dots), along with the result of exact QTM calculations (open squares) for the 1D spin-1/2 Heisenberg antiferromagnet at 0.08 K. Temperature dependence of M/H at various fields.

Fig. 2. T vs H phase diagram of CuPzN. Open circles denote the position of Tp. The dotted line is the universal crossover line for the free-fermion limit.

Figure 1(a) shows the magnetization M of CuPzN at 0.08 K as a function of the magnetic field up to 14.7 T. M(H) shows a strong upturn as Hs (=13.97 T) is approached, and saturates to the value Ms=1.15 μB/Cu. The relation Hs=J/Ms yields the intrachain interaction J=10.8 K. Theory predicts that M(H) close to Hs exhibits a singularity 1-M/Ms = D(1-H/Hs)1/δ, where D is a constant (=4/π) and the exponent δ=2 [3]. Fitting the expression to the data between 13.6 and 13.9 T yields D=1.24 and δ=1.98, in agreement with the predicted values. Open squares in Fig. 1(a) indicate the exact curve for 0.08 K calculated by the quantum transfer-matrix (QTM) method [4], in close agreement with our experimental data in the whole field range.

The temperature dependence of M/H is shown in Fig. 1(b) for several magnetic fields. In the limit of H→0, M/H is expected to reach a maximum at Tp~0.641J [3]. This relation, combined with the experimental value of Tp=6.89 K at 1 T, yields J=10.8 K, in perfect agreement with the value determined from the M(H) data. As the field increases, Tp gradually decreases, and at 13.9 T the magnetization peak eventually vanishes into a temperature region well below 0.08 K. At H=Hs, excitations (magnons) from the ferromagnetic state can be described exactly as free fermions, and M(T) is predicted to exhibit a square-root singularity Ms-M=bMs(kBT/J)1/2 [5] with the coefficient b=0.48264. This equation can be fitted very well to the 14 T data with b=0.460, in good agreement with theory.

The magnetic phase diagram of CuPzN is presented in Fig. 2 on the basis of d(M/H)/dT, with Tp superposed to indicate the crossover to the TLL phase. The free-fermion description gives a parameter-free expression for Tp, kBTp=1.52476Ms(Hs-H) [5]. This universal relation, shown as a dotted line with Ms and Hs obtained from the M(H) data, with no fitting parameter, agrees excellently with the data near Hs. As the magnetic field decreases, Tp deviates downward from the straight line, owing to the repulsion between magnons.

The quantum critical behavior of the magnetization of CuPzN withstands quantitative tests against theory [2], demonstrating that the material is a practically perfect one-dimensional spin-1/2 Heisenberg amtiferromagnet.


References
  • [1] T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, Oxford, England, 2004).
  • [2] Y. Kono, T. Sakakibara, C. P. Aoyama, C. Hotta, M. M. Turnbull, C. P. Landee, and Y. Takano, Phys. Rev. Lett. 114, 037202 (2015).
  • [3] J. C. Bonner and M. E. Fisher, Phys. Rev. 135, A640 (1964).
  • [4] A. Klümper, Z. Phys. B 91, 507 (1993).
  • [5] Y. Maeda, C. Hotta, and M. Oshikawa, Phys. Rev. Lett. 99, 057205 (2007).
Authors
  • Y. Kono, T. Sakakibara, C. P. Aoyamaa, C. Hottab, M.M. Turnbullc, C. P. Landeec, and Y. Takanoa
  • aUniversity of Florida
  • bThe University of Tokyo
  • cClark University