Review/Synthèse: Triangular antiferromagnets

We study the phase diagram ofS=1 antiferromagnetic chains with particular emphasis on the Haldane phase. The hidden symmetry breaking measured by the string order parameter of den Nijs and Rommelse can be transformed into an explicit breaking of aZ2×Z2 symmetry by a nonlocal unitary transformation of the chain. For a particular class of Hamiltonians which includes the usual Heisenberg Hamiltonian, we prove that the usual Neel order parameter is always less than or equal to the string order parameter. We give a general treatment of rigorous perturbation theory for the ground state of quantum spin systems which are small perturbations of diagonal Hamiltonians. We then extend this rigorous perturbation theory to a class of “diagonally dominant” Hamiltonians. Using this theory we prove the existence of the Haldane phase in an open subset of the parameter space of a particular class of Hamiltonians by showing that the string order parameter does not vanish and the hiddenZ2×Z2 symmetry is completely broken. While this open subset does not include the usual Heisenberg Hamiltonian, it does include models other than VBS models.

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Hidden symmetry breaking and the Haldane phase in S=1 quantum spin chains

The magnetic structure and magnetization dynamics of systems of plane frustrated Ising chain lattices are reviewed for three groups of compounds: , , and . The available experimental data are analyzed and compared in detail. It is shown that a high-temperature magnetic phase on a triangle lattice is normally and universally a partially disordered antiferromagnetic (PDA) structure. The diversity of low-temperature phases results from weak interactions that lift the degeneracy of a 2D antiferromagnetic Ising model on the triangle lattice. Mean-field models, Monte Carlo simulation results on the static magnetization curve, and results on slow magnetization dynamics obtained with Glauber's theory are discussed in detail.

Frustrated lattices of Ising chains

Heavy rare earth chromites of the formula LnCrO3 with Ln = Ho, Er, Yb, Lu and Y are shown to be multiferroic, exhibiting canted antiferromagnetism at low temperatures (TN = 113–140 K) and a ferroelectric transition in the 472–516 K range.

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Rare earth chromites: a new family of multiferroics

We present an up-to-date survey of theoretical concepts and results in the field of one-dimensional magnetism and of their relevance to experiments and real materials. Main emphasis of the chapter is on quantum phenomena in models of localized spins with isotropic exchange and additional interactions from anisotropy and external magnetic fields.

One-dimensional magnetism

Magnetization measurements in strong pulsed magnetic fields on single-crystal samples of the S=1 linear-chain Heisenberg antiferromagnet Ni(${\mathrm{C}}_{2}$${\mathrm{H}}_{8}$${\mathrm{H}}_{2}$${)}_{2}$${\mathrm{NO}}_{2}$(${\mathrm{ClO}}_{4}$) are reported. The magnetization is very small at the low-field region and begins to increase sharply at a finite field for all of the three principal axes. This is evidence for the existence of the Haldane gap in this compound.

Magnetization process of an S=1 linear-chain Heisenberg antiferromagnet

Magnetization measurements have been performed on the single crystal samples of Ni(C 2 H 8 N 2 ) 2 NO 2 (ClO 4 ), NENP, and Ni(C 3 H 10 N 2 ) 2 NO 2 (ClO 4 ), NINO in pulsed high magnetic fields. No magnetization appears up to about 10 T reflecting the presence of the Haldane gap and the linear magnetization appears in both compounds above this field. The observed anisotropy of the transition field is explained by the Haldane gap energy E g and the crystalline field constants D and E in the lowest excited triplet. The parameters are estimated as E g =16.8 K, D =-16.1 K, and E =-1.3 K and E g =14.2 K, D =-11.5 K and E =2.1 K for NENP and NINO, respectively.

Magnetization Measurement of NENP and NINO in High Magnetic Field

Magnetization measurements have been performed on the Haldane gap materials (CH 3 ) 4 NNi(NO 2 ) 3 (TMNIN) and Ni(C 3 H 10 N 2 ) 2 N 3 (ClO 4 ) (NINAZ) in pulsed high magnetic fields. TMNIN shows a typical magnetization profile of the Haldane material with the gap energy of 4.1 K. Quenching of the gap appears around 2.7 Tesla(T) and magnetic saturation is obtained above 30 T. In NINAZ, however, the quenching appears at around 30 T reflecting a large Haldane gap energy with the magnitude of 44.3 K.

Magnetization Process of Haldane Materials TMNIN and NINAZ

Magnetization of quasi one dimensional Ising antiferromagnet CsCoCl 3 is measured at liquid 4 He temperatures in pulsed high magnetic fields. In the case of an applied field H parallel to the Ising c -axis, the magnetization M at liq. 4 He temperatures shows a metamagnetic transition which is characterized by the sharp double peaks of the field derivative of the magnetization d M /d H at 33.0 T and 43.9 T, respectively. The results are qualitatively explained by the Ising-like linear chain model with small antiferromagnetic inter-chain exchange interaction. The role of the inter-chain interaction is discussed within the framework of molecular field approximation. The temperature dependence and the transverse case of the magnetization process are also studied.

High Field Magnetization of Quasi One Dimensional Ising Antiferromagnet CsCoCl 3

The Zeeman effect of R-absorption lines in ruby was observed in a high pulsed magnetic field up to 520 kOe using an optical multichannel analyzer. The experiment was done under a thermal equilibrium condition ( T =130 K) and the Zeeman line intensity is satisfactorily explained. When a magnetic field is applied perpendicular to the C 3 -axis, the excited \barE and 2\barA states show a level mixing and the observed pattern indicates a clear Paschen-Back effect The observed g // -values of the excited states are -2.49±0.05 and 1.49±0.05 for \barE and 2\barA, respectively. g ⊥ -values for these levels were estimated to be smaller than 0.1 at 500 kOe.

Hidenobu Hori

Papers

Magnetization process of an S=1 linear-chain Heisenberg antiferromagnet

Magnetization Measurement of NENP and NINO in High Magnetic Field

Magnetization Process of Haldane Materials TMNIN and NINAZ

High Field Magnetization of Quasi One Dimensional Ising Antiferromagnet CsCoCl 3

Zeeman Effect of R-lines in Ruby under a High Magnetic Field