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Observation of a quantum spin liquid (QSL) state is one of the most important goals in condensed-matter physics, as well as the development of new spintronic devices that support next-generation industries. The QSL in two dimensional quantum spin systems is expected to be due to geometrical magnetic frustration, and thus a kagome-based lattice is the most probable playground for QSL. Here, we report the first experimental results of the QSL state on a square-kagome quantum antiferromagnet, KCu6AlBiO4(SO4)5Cl. Comprehensive experimental studies via magnetic susceptibility, magnetisation, heat capacity, muon spin relaxation (μSR), and inelastic neutron scattering (INS) measurements reveal the formation of a gapless QSL at very low temperatures close to the ground state. The QSL behavior cannot be explained fully by a frustrated Heisenberg model with nearest-neighbor exchange interactions, providing a theoretical challenge to unveil the nature of the QSL state., There exist many theoretical models of frustrated quantum magnetism, most of which lack convincing experimental realisations. Here the authors combine several experimental methods to argue that KCu6AlBiO4(SO4)5Cl behaves as a square-kagome-lattice quantum Heisenberg antiferromagnet.

Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin-1/2 kagome-strip chain, which is one of the frustrated one-dimensional spin systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using the density matrix renormalization group method. We find fifteen magnetization-plateau phases, one of which is equivalent to the spin-1 Haldane phase.

For the spin-1/2 spherical kagomé cluster, as well as for the 2D kagomé lattice, many low-energy singlet excitations have been expected to exist in the energy region below the spin gap, which has been actually confirmed by Kihara et al. in their specific heat measurements up to 10 K in {W72V30}, for which the exchange interaction was estimated as J = 115 K. However, the experimental result of the specific heat cannot be reproduced by the theoretical result in the Heisenberg model. Although the theoretical result has a peak around 2 K, the experimental one does not. To elucidate this difference, we incorporate Dzyaloshinskii–Moriya (DM) interactions and bond-randomness into the model Hamiltonian for {W72V30} and calculate the density of states, entropy, and specific heat at low temperatures by using the Lanczos method. We find that DM interactions do not significantly affect the energy distribution of about 10 singlet states above the ground state, which are involved in the peak structure of the specific heat around 2 K, while even 10% bond-randomness disperses this distribution to collapse the 2 K peak. Kihara et al. also reported experimental specific heats under magnetic fields up to 15 T (= 0.17J), and found that the specific heats show almost no magnetic field dependence, which strongly suggests that the bond-randomness is much stronger than the magnetic fields. For example, our calculated specific heats with 50% randomness reproduce the experimental ones up to about 5 K.

In this study, we investigate the magnetic susceptibility, entropy, and isothermal magnetization curve of the spin-1/2 Heisenberg model on an anisotropic triangular lattice using the orthogonalized finite-temperature Lanczos method. In addition, we investigate the adiabatic magnetization curve and magnetocaloric effect. We estimate these physical quantities with sufficient accuracy in the thermodynamic limit, except at low temperatures. We observe a 1/3 magnetization plateau in the isothermal magnetization process, whereas the plateau is observed to have a slope in the adiabatic process. We show that the magnetocaloric effect can be used to detect the signature of phase transitions. We believe that these results will be useful for understanding the magnetism of anisotropic triangular lattice compounds through a comparison with experimental results in the future.

Highly frustrated spin systems such as the kagome lattice are a treasure trove of new quantum states with large entanglements. Herein, we study the spin-$$\frac{1}{2}$$ 1 2 Heisenberg model on a kagome-strip chain, which is a one-dimensional kagome lattice, using the density matrix renormalization group method. Calculating the central charge and entanglement spectrum for the kagome-strip chain, we find a gapless spin liquid state with doubly degenerate entanglement spectra in a 1/5 magnetization plateau. We also obtain a gapless low-lying continuum in the dynamic spin structure calculated using the dynamical density matrix renormalization group method. We then propose a resonating dimer–monomer liquid state that meets these features.

We present numerical results for finite-temperature $T>0$ thermodynamic quantities, entropy $s(T)$, uniform susceptibility $\chi_0(T)$ and the Wilson ratio $R(T)$, for several isotropic $S=1/2$ extended Heisenberg models which are prototype models for planar quantum spin liquids. We consider in this context the frustrated $J_1$-$J_2$ model on kagome, triangular, and square lattice, as well as the Heisenberg model on triangular lattice with the ring exchange. Our analysis reveals that typically in the spin-liquid parameter regimes the low-temperature $s(T)$ remains considerable, while $\chi_0(T)$ is reduced consistent mostly with a triplet gap. This leads to vanishing $R(T \to 0)$, being the indication of macroscopic number of singlets lying below triplet excitations. This is in contrast to $J_1$-$J_2$ Heisenberg chain, where $R(T \to 0)$ either remains finite in the gapless regime, or the singlet and triplet gap are equal in the dimerized regime.

Recent experimental study on Tsai-type quasicrystalline approximant Au-Al-Gd has revealed the presence of magnetic orders and phase transitions with changing the Au/Al concentration. Motivated by the experiment, we theoretically investigate whether a successive change of magnetic orders occurs in a minimal magnetic model including the RKKY interaction only. We find that the model induces multifarious magnetic orders depending on the Fermi wavenumber and gives a good starting point for understanding the experimental observation. In addition, we predict the presence of an undiscovered novel magnetic order called cuboc order at large Fermi wavenumber region., 6 pages, 4 figures

The Heisenberg model on a face center cubic (fcc) lattice is a typical three-dimensional frustrated spin system expected to have magnetization plateaus and supersolid phases. There are model compounds ${A}_{2}{\mathrm{CoTeO}}_{6}$ ($A=\text{Ca}$, Sr, Pb) for the fcc lattice but with lattice distortions. Motivated by the presence of the compounds, we investigate the ground state of the spin-1/2 antiferromagnetic Heisenberg model on a tetragonally distorted fcc lattice in the magnetic field using a large-size cluster mean-field method for the sake of finding new supersolid phases. We find five supersolid phases in the model, indicating the possibility to observe supersolid phases in these compounds. We also find that one of the supersolid phases is similar to the nonclassical coplanar phase obtained in the $XXZ$ model on the triangular lattice.

Frustrated quantum spin systems such as the Heisenberg and Kitaev models on various lattices, have been known to exhibit various exotic properties not only at zero temperature but also for finite temperatures. Inspired by the remarkable development of the quantum frustrated spin systems in recent years, we investigate the finite-temperature properties of the $S=1/2$ Kitaev-Heisenberg models on kagome and triangular lattices by means of finite-temperature Lanczos methods with improved accuracy. In both lattices, multiple peaks are confirmed in the specific heat. To find the origin of the multiple peaks, we calculate the static spin structure factor. The origin of the high-temperature peak of the specific heat is attributed to a crossover from the paramagnetic state to a short-range ordered state whose static spin structure factor has zigzag or linear intensity distributions in momentum space. In the triangular Kitaev model, the "order by disorder" due to quantum fluctuation occurs. On the other hand, in the kagome Kitaev model it does not occur even with both quantum and thermal fluctuations.

The Kitaev-Heisenberg model defined on both honeycomb and triangular lattices has been studied intensively in recent years as a possible model to describe spin-orbital physics in iridium oxides. In the model, there are many phases characteristic for each lattice. However, there is no study of how the phases in the two lattices merge with each other when geometry changes from the honeycomb lattice to triangular lattice. We investigate the ground state of the Kitaev-Heisenberg model defined on the system connecting the honeycomb and triangular lattices, named a honeycomb-triangular lattice. We obtain a ground state phase diagram of this model with classical spins by using the Luttinger-Tisza method and classical Monte Carlo simulation. In addition to known phases in the honeycomb and triangular lattices, we find coexisting phases consisting of the known phases. From the exact diagonalization and density-matrix renormalization-group calculations for the model with quantum spins, we find phases similar to the classical results, implying a small effect of quantum fluctuation on the phase diagram.

The Kitaev-Heisenberg model on the honeycomb lattice has been studied for the purpose of finding exotic states such as quantum spin liquid and topological orders. On the kagome lattice, in spite of a spin-liquid ground state in the Heisenberg model, the stability of the spin-liquid state has hardly been studied in the presence of the Kitaev interaction. Therefore, we investigate the ground state of the classical and quantum spin systems of the kagome Kitaev-Heisenberg model. In the classical system, we obtain an exact phase diagram that has an eightfold degenerated canted ferromagnetic phase and a subextensive degenerated Kitaev antiferromagnetic phase. In the quantum system, using Lanczos-type exact diagonalization and cluster mean-field methods, we obtain two quantum spin-liquid phases, an eightfold degenerated canted ferromagnetic phase similar to the classical spin system, and an eightfold degenerated, $\mathbf{q}=\mathbf{0},{120}^{\ensuremath{\circ}}$ ordered phase induced by quantum fluctuation. These results may provide a crucial clue to recently observed magnetic structures of the rare-earth-based kagome lattice compounds ${A}_{2}{\mathrm{RE}}_{3}{\mathrm{Sb}}_{3}{\mathrm{O}}_{14}\phantom{\rule{4pt}{0ex}}(A=\text{Mg}$, Zn; $\text{RE}=\text{Pr}$, Nd, Gd, Tb, Dy, Ho, Er, Yb).

K3Cu3AlO2(SO4)4 is a highly one-dimensional spin-1/2 inequilateral diamond-chain antiferromagnet. Spinon continuum and spin-singlet dimer excitations are observed in the inelastic neutron scattering spectra, which is in excellent agreement with a theoretical prediction: a dimer-monomer composite structure, where the dimer is caused by strong antiferromagnetic (AFM) coupling and the monomer forms an almost isolated quantum AFM chain controlling low-energy excitations. Moreover, muon spin rotation/relaxation spectroscopy shows no long-range ordering down to 90 mK, which is roughly three orders of magnitude lower than the exchange interaction of the quantum AFM chain. K3Cu3AlO2(SO4)4 is, thus, regarded as a compound that exhibits a Tomonaga-Luttinger spin liquid behavior at low temperatures close to the ground state.

The spin-$\frac{1}{2}$ Heisenberg model on a kagome lattice is a typical frustrated quantum spin system. The basic structure of a kagome lattice is also present in the kagome-strip lattice in one dimension, where a similar type of frustration is expected. We thus study the magnetization plateaus of the spin-$\frac{1}{2}$ Heisenberg model on a kagome-strip chain with three-independent antiferromagnetic exchange interactions using the density-matrix renormalization-group method. In a certain range of exchange parameters, we find twelve kinds of magnetization plateaus, nine of which have magnetic structures breaking translational and/or reflection symmetry spontaneously. The structures are classified by an array of five-site unit cells with specific bond-spin correlations. In a case with a nontrivial plateau, namely a 3/10 plateau, we find long-period magnetic structure with a period of four unit cells.

Spin-$\frac{1}{2}$ compounds ${A}_{3}{\mathrm{Cu}}_{3}{\mathrm{AlO}}_{2}{({\mathrm{SO}}_{4})}_{4}\phantom{\rule{0.28em}{0ex}}(A=\mathrm{K},\phantom{\rule{0.28em}{0ex}}\mathrm{Rb},\phantom{\rule{0.28em}{0ex}}\mathrm{and}\phantom{\rule{0.28em}{0ex}}\mathrm{Cs})$ have one-dimensional (1D) inequilateral diamond chains. We analyze the temperature dependence of the magnetic susceptibility and determine the magnetic exchange interactions. In contrast to azurite, a dimer is formed on one of the sides of the diamond. From numerical analyses of the proposed model, we find that the dimer together with a nearly isolated 1D Heisenberg chain characterize magnetic properties including magnetization curve and magnetic excitations. This implies that a dimer-monomer composite chain without frustration is a good starting point for describing these compounds.

We study the ground state of the $S=\frac{1}{2}$ Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group method with the sine-square deformation. We obtain magnetization plateaus at $M/{M}_{\mathrm{sat}}=0,\frac{1}{4},\frac{3}{8},\frac{1}{2}$, and $\frac{3}{4}$, where ${M}_{\mathrm{sat}}$ is the saturated magnetization. The obtained $\frac{3}{4}$ plateau state is consistent with the exact result, and the $\frac{1}{2}$ plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the $\frac{1}{3}$ plateau of the kagome lattice. Different four-spin loop structures are obtained in the $\frac{1}{4}$ and $\frac{3}{8}$ plateaus but no corresponding states exist in the kagome lattice. The $\frac{3}{8}$ plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\ifmmode\times\else\texttimes\fi{}2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.

We study the magnetic field dependence of the ground state of the S = 1/2 J1–J2 Heisenberg model on the square lattice by the density matrix renormalization group (DMRG) method. With the use of the sine-square deformation, we obtain eight different ground states including plaquette valence-bond crystal with a finite spin gap, transverse Neel, transverse stripe, 1/2 magnetization plateau with up–up–up–down (uuud), and three new states we named the Y-like, V-like, and Ψ states around J2/J1 = 0.55–0.6. The phase transitions from the transverse Neel (at J2/J1 = 0.55) and stripe (at J2/J1 = 0.6) states to the uuud and Y-like states, respectively, are discontinuous, as in the case of a spin flop.

We have studied a hot-wall heating system to produce GdBa 2 Cu 3 O y (GdBCO) films with large critical currents ( I c ) at a high production rate by a pulsed-laser-deposition (PLD) method. GdBCO films fabricated at a production rate of 30 m/h under the optimized conditions, especially a distance of 95 mm between the target and the substrate (T–S), exhibited high critical current densities ( J c ) of about 3 MA/cm 2 and I c over 300 A at a thickness of 1–2 μm. Furthermore, long GdBCO tapes prepared by repeated depositions at each tape-passing speed of 80 m/h showed uniform I c distribution along the longitudinal direction, because the hot-wall system enabled to stabilize temperature within a few degrees at 800 °C. A 170 m long tape with I c over 600 A was successfully fabricated at a production rate of 16 m/h using a laser power of 360 W.

Single crystals of a two-dimensional quantum spin system with geometric frustration lead to the observation of a ‘pinwheel’ valence-bond ground state. In this case, the distortion of the ideal kagome lattice structure helps to stabilize the quantum spin state. Determining ground states of correlated electron systems is fundamental to understanding unusual phenomena in condensed-matter physics. A difficulty, however, arises in a geometrically frustrated system in which the incompatibility between the global topology of an underlying lattice and local spin interactions gives rise to macroscopically degenerate ground states1, potentially prompting the emergence of quantum spin states, such as resonating valence bond2,3,4,5,6,7 and valence-bond solid8,9,10,11 (VBS). Although theoretically proposed to exist in a kagome lattice—one of the most highly frustrated lattices in two dimensions being comprised of corner-sharing triangles—such quantum-fluctuation-induced states have not been observed experimentally. Here we report the first realization of the ‘pinwheel’ VBS ground state in the S=1/2 deformed kagome lattice antiferromagnet Rb2Cu3SnF12 (refs 12, 13). In this system, a lattice distortion breaks the translational symmetry of the ideal kagome lattice and stabilizes the VBS state.

Magnetization plateaus in quantum spin systems emerge in two-dimensional frustrated systems such as a kagome lattice. The spin-1/2 antiferromagnetic Heisenberg model on a square-kagome lattice is also appropriate for the study of the magnetization plateau. Motivated by recent experimental findings of such a square kagome lattice with three nonequivalent bonds, we investigate the phase diagrams and magnetization plateaus of the lattice using the exact diagonalization method. In addition to the previously reported 1/3 and 2/3 plateaus in the model with two equivalent bonds, we find a new 2/3 plateau whose magnetic structure is characterized by spontaneously broken four-fold rotational symmetry. The plateau appears only in the case of three nonequivalent bonds. We propose the possibility of finding plateaus including the new one.

Exactly solvable frustrated quantum spin models consisting of a diamond unit structure are presented. The ground states are characterized by tetramer-dimer states with a macroscopic degeneracy in a certain range of isotropic exchange interaction. The lower bound of the excitation gap is exactly calculated to be finite and the bulk entropy in the limit of zero temperature remains finite depending on the shape of the boundary of system. Residual entropy is in a range of 0~6.1% of the entropy at high temperature for hexagonal diamond lattice and 0~8.4% for square diamond lattice. These diamond lattices are generalized to any dimensions and it is likely to be synthesized experimentally., Comment: 4 pages, 5 figures

In Fujikura, a large-scale ion-beam-assisted deposition (IBAD) system with a large ion source has been employed to fabricate biaxially textured MgO films. The large-scale IBAD system has multiple deposition lanes where substrate tapes move, and therefore we have to optimize experimental conditions at each lane. We selected an appropriate deposition area and, finally, we successfully fabricated a 1 km-length IBAD-MgO film at a production rate of 1 km/h. We also studied pulsed-laser-deposited (PLD) CeO 2 films directly on the IBAD-MgO films in spite of a large lattice mismatch between CeO 2 and MgO. From transmission electron microscope (TEM) observations at an interface between MgO and CeO 2 films, it is revealed that there is domain-matching-epitaxy relationship between MgO and CeO 2 films. We also fabricated thin (1.0 μm) and thick (3.7 μm) PLD – GdBa 2 Cu 3 O 7− x (GdBCO) film on the long-length CeO 2 /MgO substrate (over 150 m). Critical currents ( I c ) and current density ( J c ) were over 300 A and 3 MA/cm 2 respectively for the thin GdBCO film and were about 645 A and 1.7 MA/cm 2 for the thick GdBCO film at 77 K in self-field.

We report the crystal structure and unconventional magnetic ordering of ${\text{Cs}}_{2}{\text{Cu}}_{3}{\text{CeF}}_{12}$, which is composed of buckled kagome lattice of ${\text{Cu}}^{2+}$ ions. The exchange network in the buckled kagome lattice is fairly anisotropic, so that the present spin system can be divided into two subsystems: alternating Heisenberg chains with strong antiferromagnetic exchange interactions and dangling spins. Although the direct exchange interactions between neighboring spins were found to be all antiferromagnetic, ferromagnetic magnetic ordering of the dangling spins was observed. Magnetization exhibits a plateau at one-third of the saturation magnetization. These observations can be understood in terms of the indirect interaction between dangling spins mediated by the chain spin.

Hexagonal antiferromagnets ${\text{Cs}}_{2}{\text{Cu}}_{3}M{\text{F}}_{12}$ ($M=\text{Zr}$, Hf, and Sn) have uniform kagome lattices of ${\text{Cu}}^{2+}$ with $S=1/2$, whereas ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ has a $2a\ifmmode\times\else\texttimes\fi{}2a$ enlarged cell as compared to the uniform kagome lattice. The crystal data of ${\text{Cs}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ synthesized in the present work are reported. We performed magnetic-susceptibility measurements on this family of kagome antiferromagnet using single crystals. In the ${\text{Cs}}_{2}{\text{Cu}}_{3}M{\text{F}}_{12}$ systems, structural phase transitions were observed at ${T}_{t}=225$, 172, and 185 K for $M=\text{Zr}$, Hf, and Sn, respectively. The magnetic susceptibilities observed for $Tg{T}_{t}$ are almost perfectly described using theoretical results obtained by exact diagonalization for the 24-site kagome cluster with $J/{k}_{B}=244$, 266, and 240 K, respectively. Magnetic ordering accompanied by the weak ferromagnetic moment occurs at ${T}_{N}=23.5$, 24.5, and 20.0 K, respectively. The origins of the weak ferromagnetic moment should be ascribed to the lattice distortion that breaks the hexagonal symmetry of the exchange network for $Tl{T}_{t}$ and the Dzyaloshinsky-Moriya interaction. ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ is magnetically described as a modified kagome antiferromagnet with four types of neighboring exchange interactions. Neither structural nor magnetic phase transition was observed in ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$. Its magnetic ground state was found to be a spin singlet with a triplet gap. Using exact diagonalization for a 12-site kagome cluster, we analyzed the magnetic susceptibility and evaluated individual exchange interactions. The causes leading to the different ground states in ${\text{Cs}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ and ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ are discussed.

We synthesized single crystals of the new hexagonal compounds A$_2$Cu$_3$SnF$_{12}$ with A=Cs and Rb, and investigated their magnetic properties. These compounds are composed of Kagom\'{e} layers of corner-sharing CuF$_6$-octahedra. Cs$_2$Cu$_3$SnF$_{12}$ has the proper Kagom\'{e} layer at room temperature, and undergoes structural phase transition at $T_\mathrm{t}\simeq 185$ K. The temperature dependence of the magnetic susceptibility in Cs$_2$Cu$_3$SnF$_{12}$ agrees well with the result of the numerical calculation for $S=1/2$ two-dimensional Heisenberg Kagom\'{e} antiferromagnet down to $T_\mathrm{t}$ with the nearest exchange interaction $J/k_\mathrm{B}\simeq 240$ K. Although the magnetic susceptibility deviates from the calculated result below $T, Comment: 6 pages, 4 figures, to appear in the Proceedings of International Conference on Highly Frustrated Magnetism 2008

A large-scale IBAD system with the world largest ion source was employed to fabricate ion beam-assisted deposition (IBAD) MgO films. Finally, we successfully fabricated a 1 km-length IBAD-MgO film at a production rate of 1 km/h. We also studied pulsed laser deposited (PLD) CeO 2 films directly on IBAD-MgO films. An observation at the interface between MgO and CeO 2 films by a transmission electron microscope (TEM), showed that a CeO 2 film was finely textured on an IBAD-MgO film though a lattice mismatch was large (28.5%). Then we fabricated PLD–GdBa 2 Cu 3 O 7− x (GdBCO) film on the CeO 2 /MgO substrate. Critical currents ( I c ) and critical current density ( J c ) of the films were over 300 A and 3 MA/cm 2 at 77 K, self-field.

Increase of production rate and improvement of quality for RE123 coated conductors have been tried. In-plane texturing of MgO was attempted by the IBAD system with the world largest ion source. As a result of optimizing condition in large deposition area, the dramatically high throughput of 1000 m / h was realized to obtain the IBAD-MgO with Δ 600 A except some locations was obtained at the throughput of 15 m / h. In addition to the speed-up, the very high Ic of 1040 A was also achieved by the hot-wall heating PLD system.

We have studied the ion-beam-assisted deposition (IBAD)-MgO process using a large IBAD system with a large ion source. Using the large IBAD system, we successfully fabricated a long-length IBAD-MgO tape (1 km) at a production rate of 1 km h−1. We have also studied a process to deposit CeO2 films directly on IBAD-MgO tapes. It is revealed that the CeO2 film is fully textured at about 100 nm. GdBa2Cu3O7−x (GdBCO) film was fabricated on a 180 m-long CeO2 /IBAD-MgO film. Its critical current (Ic) and current density (Jc) were over 300 A and 3 MA cm−2 at 77 K, self-field.

We have studied the use of a hot-wall heating system for producing GdBa2Cu3O7?X (Gd123) films with large critical current (Ic), stably, at high speed, by a pulsed laser deposition (PLD) method. We achieved a material yield from the PLD system with hot-wall heating of about 50% through optimization of the evaporation conditions. With the PLD system, we were able to fabricate a Gd123 film about 20?cm long with a high Ic of 997?A (77?K, self-field) at about 6??m thickness. The maximum Ic that we achieved for a Gd123 film about 2?cm long was 1040?A (77?K, self-field) at about 6? ?m thickness. Furthermore, we were able to form a Gd123 film about 1? ?m thick and 20?cm long with an Ic of 352?A (77?K, self-field) at a high speed of 60? m?h?1 using high laser power. For the production of long conductors coated with RE123 (REBa2Cu3O7?X, where RE stands for rare earth) using hot-wall heating, it was found that RE123 coated conductors over 100?m long with Ic of over 200?A had uniform Ic distributions with ? 2% variations in the direction of the length.

In the usual moire method and the multiplication method, the sensitivity to deformation is not sufficient at present. Then, how to increase the sensitivity is studied. In the measurement of a usual sheet metal specimen, moire fringes with large mis-match is photographed on a film at first. Such fringes are equivalent to grating lines on the specimen, as thy displace corresponding to strain, and they can be amplified by applying the multiplication method to that film. When strain is expressed by two beam interference fringes, one of the beams is tilted by a small amount, then fine fringes are obtained. They are equivalent to moire fringes with large mis-match and the multiplication method can be applied. Applications in various conditions have been shown. Consequently, concerning a sheet metal, measurement of elastic-plastic strain (eb 0.001) becomes possible and in the special condition that the surface of a specimen has been finished mirror-like, elastic strain (eb 0.001) can be measured.