Field-induced Long-range Order Research Articles

Two types of alternating spin- 12 chains and their field-induced transitions in ɛ−LiVOPO4

Thermodynamic properties, $^{31}$P nuclear magnetic resonance (NMR) measurements, and density-functional band-structure calculations for $\varepsilon$-LiVOPO$_4$ are reported. This quantum magnet features a singlet ground state and comprises two types of alternating spin-$\frac12$ chains that manifest themselves by the double maxima in the susceptibility and magnetic specific heat, and by the two-step magnetization process with an intermediate $\frac12$-plateau. From thermodynamic data and band-structure calculations, we estimate the leading couplings of $J_1\simeq 20$ K and $J_2\simeq 60$ K and the alternation ratios of $\alpha_1=J_1'/J_1\simeq 0.6$ and $\alpha_2=J_2'/J_2\simeq 0.3$ within the two chains, respectively. The zero-field spin gap $\Delta_0/k_{\rm B}\simeq 7.3$ K probed by thermodynamic and NMR measurements is caused by the $J_1$-$J_1'$ spin chains and can be closed in the applied field of $\mu_{0}H_{\rm c1}\simeq 5.6$ T, giving rise to a field-induced long-range order. The NMR data reveal predominant three-dimensional spin-spin correlations at low temperatures. Field-induced magnetic ordering transition observed above $H_{c1}$ is attributed to the Bose-Einstein condensation of triplons in the sublattice formed by the $J_1$-$J_1'$ chains with weaker exchange couplings.

Quantum phase transitions and Bose–Einstein condensation of magnons in hexagonal spinsystems

We study the S = 1 Heisenberg antiferromagnet with single-ion anisotropy in the hexagonal latticeusing the bond-operator theory. The quantum phase transition from the spinsinglet state to the ordered one and the field-induced long-range order inthe perpendicular plane are shown to be described by the condensationof magnons. The results are compared with those from experiments usingAFeX3 (A = Cs, Rb andX = Cl, Br). The criticalexponent α nearHc1 is found to beabout 1.144 in CsFeCl3 and 1.599 in CsFeBr3, which provides another route to study the dimensional crossover behavior inlow-dimensional spin systems.

FIELD-INDUCED TOMONAGA–LUTTINGER LIQUID OF A QUASI-ONE-DIMENSIONAL S = 1 ANTIFERROMAGNET

We review the results of specific-heat experiments on the S = 1 quasi-one-dimensional (quasi-1D) bond-alternating antiferromagnet Ni(C 9 H 24 N 4)( NO 2) ClO 4, alias NTENP. At low temperatures above the transition temperature of a field-induced long-range order, the magnetic specific heat (C mag ) of this compound becomes proportional to temperature (T), when a magnetic field along the spin chains exceeds the critical field H c at which the energy gap vanishes. The ratio C mag /T, which increases as the magnetic field approaches H c from above, is in good quantitative agreement with a prediction of conformal field theory combined with the field-dependent velocity of the excitations calculated by the Lanczos method. This result is the first conclusive evidence for a Tomonaga–Luttinger liquid in a gapped quasi-1D antiferromagnet.

Electric-field-induced redistribution of polar nano-regions in a relaxor ferroelectric

Relaxor ferroelectrics, with their strong dependence of polarization on the applied electric field, are of considerable technological importance. On a microscopic scale, however, there exists competition as well as coexistence between short-range and long-range polar order. The conventional picture is that the polar nano-regions (PNRs) that appear at high temperatures beyond the Curie transition, form nuclei for the field-induced long-range order at low temperatures. Here, we report high-energy X-ray diffuse-scattering measurements on the relaxor Pb(Zn(1/3)Nb(2/3))O(3) (PZN) to study the short-range polar order under an electric field applied along the [111] direction. In contrast to conventional expectations, the overall diffuse-scattering intensity is not suppressed. On the other hand, the field induces a marked change on the shape of the three-dimensional diffuse-scattering intensity pattern, corresponding to a redistribution of PNRs in real space. We show that these surprising results are consistent with a model in which the PNRs with [110]-type polarizations, orthogonal to that of the surrounding environment, are embedded and persist in the [111]-polarized ferroelectric order of the bulk.

Magnetic properties of S=1 spin chains with alternating interactions

Magnetic properties of S =1 antiferromagnetic spin chains with alternating nearest-neighbor and competing next-nearest-neighbor interactions are studied, using the strong coupling expansion as well as numerical methods . Characteristic features of this system such as magnetization plateau, field-induced long-range ordering and incommensurate behavior are discussed in connection with the dimer gap, focusing on a novel role of the anisotropy.

Observation of field-induced long-range order in disordered Sr14Cu24O41

Abstract Field-induced magnetic order in a structural disordered single-crystal Sr 14 Cu 24 O 41 (Sr 14 -B) has been observed in the Cu-nuclear magnetic resonance (NMR) measurements for the ladder sites below 20 K under the magnetic field H ∼11 T. For the Zhang Rice (ZR) sites in the chains, the spectrum splits below 20 K due to an appearance of the internal field, whereas that of less disordered Sr 14 -A does not. This gives an evidence of three-dimensional (3D) long-range (LR) ordering in Sr 14 -B below T N ∼20 K under H ∼11 T.

NDMAP: the best material to study the Haldane's prediction

As predicted by Haldane, spin, S=1 one-dimensional (1D) Heisenberg antiferromagnet (HAF) has an energy gap between the singlet ground state and first excited triplet. On application of magnetic field, the triplet state Zeeman splits and the energy of one of the triplet state becomes zero at a critical field, H c. Above H c the system recovers magnetism. Then, we expect that a quasi-1D HAF will show a magnetic long-range ordering (LRO) at low temperatures due to the inter-chain coupling. This field-induced LRO has not been observed before due to complication of the crystal structure in the materials studied so far and/or technical difficulty. From a heat capacity measurement on a single crystal of an S=1 quasi-Q1D HAF, Ni(C 5H 14N 2) 2N 3(PF 6), we found an anomaly at a temperature in finite fields indicating a field-induced phase transition. A magnetic LRO is confirmed by a neutron diffraction measurement on the same sample. The temperature versus magnetic field phase diagram of this compound is constructed and discussed.

Field-induced long-range ordering in a quasi-one-dimensional Haldane system

Quantum S=1 spin chain with single-ion anisotropy in the presence of an external magnetic field is investigated by means of the finite-temperature density-matrix renormalization group. Emphasis is laid on the point that the underlying physics differs significantly with respect to magnetic-field directions. There appear various phases, which are absent in the classical counterpart studied extensively in the past. We argue possible implications of our numerical results in the field-induced magnetic long-range ordering observed experimentally in NDMAP.

Neutron scattering study of linear-chain Haldane compounds NDMAZ and NDMAP

Neutron scattering experiments were carried out for the new Haldane compounds Ni(C 5H 14N 2) 2N 3(ClO 4) (NDMAZ) and Ni(C 5H 14N 2) 2N 3(PF 6) (NDMAP) in the magnetic field up to 10 T in order to investigate the field-induced long-range ordering and the spin excitation. For NDMAZ, the triplet excited state (1.61, 1.76, and 3.2 meV) and field dependence of these levels were observed at Q=(0 0 0.5). From these data, the intra-chain coupling constant≈4.3 meV and the anisotropic parameters D≈0.76 meV and | E|≈0.038 meV were estimated. For NDMAP the gap was observed at about 0.48 and 0.64 meV at Q=(0 0 0.5). By applying the field of 5 T, the first excited state shifted below the resolution less than 0.13 meV. Above the critical field H C, the intensities of singlet–triplet excitation becomes very weak. This work is the first neutron scattering study on a Haldane system above the critical fields.

Proton NMR study of the field-induced long-range ordering in Haldane gap system NDMAP

Appearance of the field-induced long-range ordering was observed directly by a proton NMR measurement in Haldane gap system, Ni(C 5H 14N 2) 2N 3(PF 6) (NDMAP). A sudden splitting of the spectrum due to the appearance of the transverse staggered moment was observed just below T N. The transverse staggered moment is estimated as 1.1 μ B in the external field of 10.9 T parallel to the ab-plane.

Field-Induced Long-Range Ordering in Haldane Gap System NDMAZ

Field-induced long-range ordering is investigated by heat capacity and high-field magnetization measurements in Haldane gap system Ni(C 5 H 14 N 2 ) 2 N 3 (ClO 4 ) (NDMAZ). In the high-field magnet...

Low-temperature high-field magnetization measurement on a quantum spin chain

We report the result of magnetization ( M) measurements at low temperatures down to 80 mK and high magnetic fields ( H) up to 60 T on the S=1 quasi-one-dimensional Heisenberg antiferromagnetic compound Ni(C 5H 14N 2) 2N 3(PF 6) which shows a field-induced long-range ordering (LRO) at low temperatures. The experimental M– H curve is in reasonably good agreement with theoretical one. No indication of field-induced LRO is detected in the magnetization measurement.

Study of the low temperature thermal properties of the geometrically frustrated magnet: Gadolinium gallium garnet

Gadolinium gallium garnet, Gd3Ga5O12 (GGG) has an extraordinary low temperature phase diagram. Although the Curie–Weiss temperature of GGG is about −2 K, GGG shows no long-range order down to T∼0.4 K. At low temperatures GGG has a spin glass phase at low fields (⩽0.1 T) and a field-induced long-range order antiferromagnetic state at fields of between 0.7 and 1.3 T [P. Schiffer et al., Phys. Rev. Lett. 73, 2500 (1994), S. Hov, H. Bratsberg, and A. T. Skjeltorp, J. Magn. Magn. Mater. 15–18, 455 (1980); S. Hov, Ph.D. thesis, University of Oslo, 1979 (unpublished), A. P. Ramirez and R. N. Kleiman, J. Appl. Phys. 69, 5252 (1991)]. However, the nature of the ground state at intermediate fields is still unknown, and has been hypothesized to be a three-dimensional spin liquid. We have measured the thermal conductivity (κ) and heat capacity (C) of a high-quality single crystal of GGG in the low temperature regime in order to study the nature of this state. The field dependence of κ shows that phonons are the predominant heat carriers and are scattered by spin fluctuations. We observe indications in κ(H) and C(H) of both the field induced ordering and the spin glass phase at low temperatures (T⩽200 mK).