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Physical review. B, Condensed matter

Observation of S=1 fractional spins in the S=2 finite linear-chain Heisenberg antiferromagnet CsCr1−xMgxCl3

Hiroki Yamazaki, K. Katsumata

Published Sep 1, 1996• 19 citations
Publisher

Abstract

The magnetic properties of $\mathrm{Cs}{\mathrm{Cr}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{Cl}}_{3} (x=0.073)$ are studied by electron-spin-resonance (ESR), magnetic-susceptibility, and heat-capacity measurements to elucidate the edge state in the finite chains of the $S=2$ quasi-one-dimensional Heisenberg antiferromagnet CsCr${\mathrm{Cl}}_{3}$. The results of the ESR measurements in the temperature range 14-40 K are well explained by an effective $S=1$ fractional spin. A crossover between different Curie constants observed in the susceptibility measurements is also explained by assuming $S=1$ free spins at the ends of the finite chains below 40 K. The appearance of the $S=1$ fractional spin can be understood by the valence-bond-solid model.

DOI
10.1103/physrevb.54.r6831

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Physical review. B, Condensed matter•Feb 1, 1996•36 citations
The magnetic properties of CsCr1\ensuremath−xMgxCl3(x=0.073)\mathrm{Cs}{\mathrm{Cr}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{Cl}}_{3} (x=0.073)CsCr1\ensuremath−x​Mgx​Cl3​(x=0.073) are studied by electron-spin-resonance (ESR), magnetic-susceptibility, and heat-capacity measurements to elucidate the edge state in the finite chains of the S=2S=2S=2 quasi-one-dimensional Heisenberg antiferromagnet CsCrCl3{\mathrm{Cl}}_{3}Cl3​. The results of the ESR measurements in the temperature range 14-40 K are well explained by an effective S=1S=1S=1 fractional spin. A crossover between different Curie constants observed in the susceptibility measurements is also explained by assuming S=1S=1S=1 free spins at the ends of the finite chains below 40 K. The appearance of the S=1S=1S=1 fractional spin can be understood by the valence-bond-solid model.
The phenomenological expression $\ensuremath{\chi}T∕(N{g}^{2}{\ensuremath{\mu}}_{B}^{2}∕k)={C}_{1n}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(\ensuremath{-}{W}_{1n}∕T)+{C}_{2n}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(\ensuremath{-}{W}_{2n}∕T)$ describes very accurately the temperature dependence of the magnetic susceptibility computed for antiferromagnetic rings of Heisenberg spins S=1S=1S=1, whose size nnn is even and ranges from 6 to 20. This expression has been obtained through a strategy justified by scaling considerations together with finite size numerical calculations. For nnn large, the coefficients of the expression converge towards C1=0.125{C}_{1}=0.125C1​=0.125, W1=0.451J{W}_{1}=0.451JW1​=0.451J, C2=0.564{C}_{2}=0.564C2​=0.564, W2=1.793J{W}_{2}=1.793JW2​=1.793J (JJJ is the exchange constant), which are appropriate for describing the susceptibility of the spin-1 Haldane chain. The Curie constant, the paramagnetic Curie--Weiss temperature, the correlation length at T=0T=0T=0 and the Haldane gap are found to be closely related to these coefficients. With this expression, a very good description of the magnetic behavior of Y2BaNiO5{\mathrm{Y}}_{2}\mathrm{Ba}\mathrm{Ni}{\mathrm{O}}_{5}Y2​BaNiO5​ and of Ni(C2H8N2)2NO2ClO4\mathrm{Ni}{({\mathrm{C}}_{2}{\mathrm{H}}_{8}{\mathrm{N}}_{2})}_{2}\mathrm{N}{\mathrm{O}}_{2}\mathrm{Cl}{\mathrm{O}}_{4}Ni(C2​H8​N2​)2​NO2​ClO4​ (NENP), the archetype of the Haldane gap systems, is achieved over the whole temperature range.
Thermodynamic properties of S=1 antiferromagnetic Heisenberg chains with free and periodic boundaries are investigated by a quantum Monte Carlo method. In particular, temperature dependences of the specific heat, the magnetic susceptibility, and the hidden order parameter, which are inherent to the Haldane phase, are investigated. The specific heat turns out to have a peak at a temperature Tpeak{\mathit{T}}_{\mathrm{peak}}Tpeak​\ensuremath{\sim}2\ensuremath{\Delta}, where \ensuremath{\Delta} is the energy gap of the present model, although the temperature dependence of the specific heat is very similar to the Schottky type. In open chains, due to the fourfold degeneracy of the ground state, the magnetic susceptibility shows a Curie-like divergence regardless of the number of spins in the chain. The amplitude of the Curie-like divergence is consistent with the edge moments (S=1/2). On the other hand, it is confirmed that the long-range hidden order exists only in the ground state. How the hidden order grows as the temperature goes to zero (T\ensuremath{\rightarrow}0) is investigated by introducing an intrinsic correlation length ${\ensuremath{\xi}}_{\mathit{D}}$ of the ordering, which diverges as T\ensuremath{\rightarrow}0. A qualitative difference in fluctuations between the ground state and the finite-temperature states is discussed making use of snapshots of the transformed two-dimensional Ising system on which a Monte Carlo simulation is being performed.
High-field electron spin resonance (ESR) measurements were performed on the S = 1/2 Ising-like antiferromagnetic chain CsCoCl3 in the frequency range up to 4.4 THz and magnetic fields for H || c up to 53 T. We observed softening of the spinon excitation, which drives the spin chain into the quantum critical state at the critical field Hc = 33.0 T. Above Hc, we observed the string excitation at the wave number q = π, which is characteristic of the S = 1/2 spin chain in the quantum critical state in the magnetic fields. We also observed a crossover of the string excitation to the magnon bound state above the saturation field Hs = 43.9 T upon increasing the magnetic fields. Finally, we discuss how the string excitation and magnon bound state can be excited by the electric dipole transition due to spin quadrupolar resonance.
Thermodynamic properties of a tetrameric bond-alternating Heisenberg spin chain with ferromagnetic-ferromagnetic-antiferromagnetic-antiferromagnetic exchange interactions are studied using the transfer-matrix renormalization group and compared to experimental measurements. The temperature dependence of the uniform susceptibility exhibits typical ferrimagnetic features. Both the uniform and staggered magnetic susceptibilities diverge in the limit $T\ensuremath{\rightarrow}0$, indicating that the ground state has both ferromagnetic and antiferromagnetic long-range orders. A double-peak structure appears in the temperature dependence of the specific heat. Our numerical calculation gives a good account for the temperature and field dependence of the susceptibility, the magnetization, and the specific heat for $\mathrm{Cu}{(3\text{\ensuremath{-}}\mathrm{Clpy})}_{2}{({\mathrm{N}}_{3})}_{2}$ $(3\text{\ensuremath{-}}\mathrm{Clpy}=3\text{\ensuremath{-}}\text{Chloroyridine})$.
Finite-size effects in a spin-1/21/21/2 one-dimensional (1D) Heisenberg antiferromagnet (HAF) are studied experimentally and theoretically. The calculated susceptibility is compared with that observed in the quasi-1D HAF ${\mathrm{SrCu}}_{1\ensuremath{-}x}{\mathrm{Mg}}_{x}{\mathrm{O}}_{2}$. Excellent agreement between theory and experiment is obtained without any adjustable parameters above about 0.02J0.02J0.02J, where JJJ is the dominant exchange interaction constant.
Thermodynamic properties of S=2 antiferromagnetic Heisenberg chains are studied not only under the periodic boundary condition but also under the open one employing a quantum Monte Carlo method. Temperature and size dependences of the energy, the specific heat, and the magnetic susceptibility are calculated and edge effects on them are investigated in detail. The specific heat shows a well-pronounced Schottky anomaly but the maximum is located at a temperature much larger than the Haldane gap of the system. As temperature goes to zero, the magnetic susceptibility vanishes for the periodic chains, while it diverges for the open chains. The edge contribution in the open-chain susceptibility is attributed to the two S=1 effective spins localized at the chain ends at low temperatures, while to an S=2 free spin at high temperatures. This is a visualization of a quantum-classical crossover and an evidence that the present model is a Haldane system. High-temperature behaviors of the thermodynamic quantities are also discussed with the help of a series-expansion method. \textcopyright{} 1996 The American Physical Society.