Multiple Spin Exchange Research Articles

Sound velocity measurements of nuclear-spin ordered BCC solid 3He

We measured sound velocity, v ( T , B ) , in the two nuclear-spin ordered phases (the low field phase (U2D2) and the high field phase (CNAF)) of single crystal of BCC solid 3He below 1 mK along the melting curve ( P m ≃ 34 bar ) . The change in sound velocity, Δ v ( T , B ) ( ≡ v ( T , B ) - v ( 0 , 0 ) ) , arises from the nuclear-spin parts of the internal energy. In the U2D2, the measured Δ v ( T , 0.06 T ) was proportional to T 4 and Δ v ( 0.5 mK , B ) was proportional to B 2 . In the CNAF, the measured Δ v ( T , 0.50 T ) was proportional to T 4 and Δ v ( 0.5 mK , B ) was proportional to B - B c 1 ( T ) , where B c 1 ( T ) is the lower critical field. From Δ v for different crystal orientations, we determined the nuclear-spin elastic-stiffness tensors Δ c ij ℓ , h ( T , B ) , six components for U2D2 and three components for CNAF as a function of T and B. We obtained the generalized Grüneisen constants Γ ij 1 / χ for the magnetic susceptibility χ from Δ c ij ℓ (0.5 mK, B) and Γ ij c for the spin wave velocity c from Δ c ij ℓ ( T, 0.06 T) in the U2D2 by using the nuclear-spin part of the internal energy U ( T , B ) . In particular, the obtained Γ ij c and Γ ij 1 / χ are compared with the theoretical estimation based on the multiple-spin exchange model (MSE) with three parameters. The validity of the MSE with three parameters is quantitatively discussed.

Spin-Wave Theory of the Multiple-Spin Exchange Model on a Triangular Lattice in a Magnetic Field: 3-Sublattice Structures

We study the spin wave in the S =1/2 multiple-spin exchange model on a triangular lattice in a magnetic field within the linear spin-wave theory. We take only two-, three-, and four-spin exchange interactions into account and restrict ourselves to the region where a coplanar three-sublattice state is the mean-field ground state. We found that the Y-shape ground state survives quantum fluctuations and the phase transition to a phase with a 6-sublattice structure occurs with softening of the spin wave. We estimated the quantum corrections to the ground state sublattice magnetizations due to zero-point spin-wave fluctuations.

Ferromagnetic nanoclusters in two-dimensionalHe3

$^{3}\mathrm{He}$ adsorbed on graphite is an almost ideal two-dimensional (2D) fermionic system. The 2D solid, where the interaction between the nuclear spins $S=\frac{1}{2}$ is due to multiple spin exchange, has been extensively studied as a model system for strongly interacting fermions in 2D. At high densities in the second layer, three-body exchange dominates and leads to Heisenberg ferromagnetism. We report on nuclear magnetic resonance measurements at ultralow temperatures and low magnetic fields of the second layer of $^{3}\mathrm{He}$ on graphite preplated by one layer of $^{4}\mathrm{He}$. By adding controlled amounts of $^{4}\mathrm{He}$, $^{3}\mathrm{He}$ atoms are pushed out from the ferromagnetic domains, which become smaller and denser. We can evaluate the properties of these clusters, and control their size from a few tens to a few hundreds of atoms. These sizes are comparable to today's computing capabilities for exact numerical calculations on small clusters, and should lead to direct comparison between measurements on this model Heisenberg system and theory.

Exactly solvable quantum spin model with alternating and multiple spin exchange interactions

We propose an exactly solvable quantum spin model, in which the alternation of the exchange interactions between neighboring spins is accompanied by the multiple spin exchange. The model permits us to obtain exactly thermodynamic characteristics of the considered quantum spin chain. In the ground state, depending on the strength of the three-spin coupling, the model manifests either the spin-gapped behavior of low-lying excitations at low magnetic fields, or the ferrimagnetic ordering with the spontaneous magnetization and with gapless low-lying excitations. The system undergoes second order or first order quantum phase transitions, governed by an external magnetic field and the multiple spin exchange coupling strength. Our exactly solvable quantum spin model demonstrates that multispin interactions in a dimerized quantum spin chain can produce a spontaneous magnetization. On the other hand, for quantum spin chains with a spontaneous magnetization, caused by multispin couplings, the alternation of nearest neighbor exchange interactions can be the reason for destroying of that magnetization and the onset of a spin gap for low-lying excitations.

Quest for the ground state in two-dimensional antiferromagnetic solid 3He

A low-density solid 3He film adsorbed on graphite surface forms an ideal two-dimensional (2D) quantum spin system with nuclear spin S=1/2 on a triangular lattice. In the antiferromagnetic region called the 4/7 phase, the existence of the competing higher order multiple spin exchange (MSE) interactions in addition to a geometrical frustration, makes the system strongly frustrated. The ground state has been investigated both theoretically and experimentally, but it is still an open question. The NMR measurements for the 4/7 phase adsorbed on both one layer of 4He and two layers of HD preplated graphite have been made down to the temperatures of 10 μK which is by a factor of 10 lower than the previous. The observed susceptibility shows a gradual increase with no abrupt change. This fact strongly suggests that the triangular antiferromagnet with the higher order multiple exchanges has a gapless spin liquid ground state.

Anomalous heat capacities in submonolayer solid 3He films commensurate to graphite substrate

The heat capacities ( C) of submonolayer solid 3He films adsorbed on a graphite surface are measured down to 100 μK at areal densities between 6.6 and 7.5 nm −2, where 3He film is expected to be commensurate to the corrugation of the adsorption potential of the graphite substrate and some novel adsorption structures have been predicted. In this areal density regime there has been no previous measurement below 2 mK. The temperature ( T) variation of C shows almost single power law behavior, C∝ T α , in a wide temperature range. And the exponent α is much smaller than −2, an expected exponent for localized spins in the high temperature limit. These behaviors should imply that the competition of multiple spin exchange interactions is strong at this density range.

Multiple-spin exchange models on the checkerboard lattice with an exact two-fold degenerate Shastry-Sutherland ground state

Two quantum spin models with bilinear-biquadratic exchange interactions are constructed on the checkerboard lattice. It is proved that, under certain sufficient conditions on the exchange parameters, their ground states consist of two degenerate Shastry-Sutherland singlet configurations. The constructions are studied for arbitrary spin-S. The sufficient conditions for the existence of ferromagnetic ground state are also found exactly. The approximate quantum phase diagrams are presented using the exact results, together with a variational estimate for the N\'eel antiferromagnetic phase. A two-leg spin-1/2 ladder model, based on one of the above constructions, is considered which admits exact solution for a large number of eigenstates. The ladder model is shown to have exact level-crossing between the rung-singlet state and the AKLT state in the singlet ground state. Also introduced is the notion of perpendicularity for quantum spin vectors, which appears in the discussion on one of the two checkerboard models, and is discussed in the Appendix.

Heat Capacities of Submonolayer Solid 3He Films on Graphite at Highly Frustrated Density Regime

The heat capacities (C) of submonolayer solid films adsorbed on a graphite surface are measured down to 100 μK at areal densities between 6.6 and 7.5 nm−2, where there has been no previous measurement below 2 mK. The temperature (T) variation of C shows almost single power low behavior, C ∝ Tα, in a wide temperature range. And the exponent α is much smaller than −2, an expected exponent for localized spins in the high temperature limit. These behaviors should imply that the competition of multiple spin exchange interactions is strong at this density range.

Detection of Exotic Order Parameters of Quantum Antiferromagnets through Reduced Density Matrices

We propose a new method based on reduced density matrices for determining order parameters of quantum spin systems. Our method can extract the order parameter directly from ground-state wave functions without prior knowledge, and thus has a potential for detecting unknown exotic orders. We numerically apply our method to the multiple-spin exchange model on the ladder and detect the staggered dimer and the scalar chiral orders which have been found in previous studies. We also consider the resonating valence bond liquid in a solvable quantum dimer model and demonstrate through reduced density matrices that its ground states cannot be characterized by any local order parameter. Frustrated quantum antiferromagnets often exhibit exotic orders which are difficult to preconceive from the type of interactions or lattice structures. To determine the order parameters characterizing them, usually, we examine correlation functions of candidate order parameters or look for characteristic spectral properties. Such methods, however, rely on our knowledge about previously-found orders and do not work if the order is beyond our experiences. To overcome this difficulty, in this paper, we propose a new method which can determine the order parameter without prior knowledge. Suppose that we have obtained the low-energy spectrum and eigenstates of the finite-size systems by exact diagonalization, for instance. In a phase which breaks a discrete symmetry in the thermodynamic limit, we find a finite number of nearly-degenerate ground states which become asymptotically degenerate as the size of the system increases. The symmetry-breaking ground states jΨii (i = 1, 2,¢¢¢ ) in the thermodynamic limit can be constructed as the linear combinations of these nearly-degenerate ground states. An order parameter can be identified with an operator which distinguishes the symmetry-breaking ground states. The order parameter is local, if the corresponding operator can be defined on a finite local area in the entire system, even when the system size is taken to infinity. The central idea of our method is to search the order parameter by comparing the reduced density matrices (RDMs) ρ i = Tr ¯ A jΨiihΨij (i = 1, 2,¢¢¢ ), where A is an area of the system and ¯ A is its complement. If these RDMs are different (identical) in an area, an order parameter can (cannot) be defined in that area. In this way, we can elucidate in what area order parameters can be defined. In x2, we give the detailed formulation of our method. In x3, we demonstrate our method in a ladder model with the dimer and scalar chiral orders. In x4, we exploit the relation between RDMs and order parameters to prove that the resonating

Nematic Order in the Multiple-Spin Exchange Model on the Triangular Lattice

We discuss the possibility of finding n-type nematic order in the vicinity of a FM phase in the multiple--spin exchange model on the triangular lattice. We study this problem both from S=\infty (classical) and S=1/2 (quantum) limits.

On the spin-liquid phase of two-dimensional3He

Multiple spin exchange processes lead to strong quantum frustration in low density solid phases of3He. It has been predicted theoretically that the4/7 phase of thesecond layer of 3He adsorbed on graphite is a two-dimensional RVB magnet with a spin-liquid groundstate. We have measured the nuclear magnetization of the second layer of3He adsorbed on a Papyex substrate preplated by a monolayer of4He, using cw-NMR techniques, for a large temperature range (0.1–400 mK). Special attentionhas been devoted to carefully eliminating from our sample spurious phases andparamagnetic defects. The analysis of the data provides us with information on thepresence of a spin gap in the excitation spectrum and on the density of states of themagnetic excitations of this phase.

Neutron scattering from solid [formula omitted

Multiple spin exchange leads, according to present understanding, to a variety of magnetically ordered states in solid 3 He , depending on pressure and applied magnetic field. We report the status of experiments to directly determine these structures by neutron scattering. The large neutron absorption cross section, and associated sample heating, impose severe experimental demands on the design of the sample cell. We report on our proposed solution, including details of the sintered heat exchanger necessary to cool the sample, as well as the PrNi 5 nuclear demagnetization stage. The use of nmr in parallel experiments to characterise growth of the solid sample within the sinter is also discussed.

Evidence for ferromagnetic ordering of [formula omitted] films on graphite

Recent experiments at USC have shown that two-dimensional films of 3 He on graphite order ferromagnetically at finite temperatures ( T>0) for densities above 20 atoms/ nm 2 . These results, obtained by measuring NMR on these films in the zero field limit, appear to contradict several studies which concluded that there is no spontaneous order by measuring magnetic susceptibility through conventional NMR in finite magnetic fields, and heat capacity in zero field. The low field limit is important in understanding these two-dimensional magnetic systems. At higher temperatures and/or fields, these films have been described in terms of the multiple spin exchange model. However, two-dimensional systems are extremely sensitive to anisotropies such as nuclear dipole interactions, even when they are several orders of magnitude less than the dominant exchange mechanism.

Striped-honeycomb transition of domain wall structure of [formula omitted] submonolayer solid film on graphite

We predict the striped (superheavy)-honeycomb (heavy) structural phase transition of the domain wall structure of 3 He submonolayer solid film on a graphite surface at 6.8 nm −2 based on the adsorption energy calculation by the path integral Monte Carlo simulation. The experimentally observed sudden jump of the Weiss temperature at the same density can be explained by this transition within the multiple spin exchange model.

Magnetic ground-state phase diagram of a multiple-spin exchange model on the triangular lattice

We investigated the ground state of a multiple-spin exchange model, which may describe magnetism of the solid 3 He layers adsorbed on graphite. The model contains four-spin exchange terms together with the conventional Heisenberg ones. Using the mean-field theory we found numerous ground-state phases with large numbers (up to 144) of sublattices. These phases replace the previously reported infinitely degenerate phase. A novel phase with 6-sublattice non-coplanar spin structure, where both vector and scalar chiral orders exist, appears between the 120° Néel and tetrahedral phases. This phase is replaced by a novel 12-sublattice phase under the magnetic field.

Multisite-interaction Ising model approach to the solid3Hesystem on a triangular lattice

We consider the Ising model with multiple-spin interactions on a recursive lattice of special type (the Bethe lattice of square plaquettes with additional inner link) as some approximation to the two-dimensional multiple-spin exchange model with two-, three-, and four-spin exchanges. This statistical system can be regarded as an approach to solid 3 He films which have the structure of a regular triangular two-dimensional lattice. The corresponding recursion relations for the partition function and magnetization per site are obtained. Using the dynamical method, we plot the diagrams of magnetization versus the external magnetic field for various values of exchange parameters and finite temperatures. The system exhibits different magnetic behaviors, depending on the values of the exchange parameters. The plots, corresponding to a purely ferromagnetic situation as well as more complex plots containing magnetization plateaus at m=0 and m/m s a t = ½, are obtained. We also show that on some recursive lattices plateaus can appear with Ising pair interactions solely. A diagram with one bifurcation loop is also obtained. As usual, the bifurcation points are identified with second-order phase transitions. An attempt is made to elucidate the microscopic structure of the emerging novel ordered phases.

Anomalous nuclear-spin heat capacities in submonolayer solid3Headsorbed on graphite

Nuclear-spin heat capacities of submonolayer solid ${}^{3}\mathrm{He}$ adsorbed on a graphite surface are measured down to $100 \ensuremath{\mu}\mathrm{K},$ a factor of 20 lower temperature than in previous works. This system is one of the most ideal two-dimensional quantum spin systems $(S=1/2).$ In a wide areal density region $(6.1 {\mathrm{nm}}^{\ensuremath{-}2}<~\ensuremath{\rho}<~8.7 {\mathrm{nm}}^{\ensuremath{-}2}),$ anomalous temperature dependencies of the heat capacity, $C\ensuremath{\propto}{T}^{\ensuremath{\alpha}}(\ensuremath{-}1.6\ensuremath{\lesssim}\ensuremath{\alpha}\ensuremath{\lesssim}\ensuremath{-}0.7),$ are observed in a temperature range over two orders of magnitude $(0.1 \mathrm{mK}<~T<~20 \mathrm{mK})$ instead of the expected high-temperature behavior $(\ensuremath{\alpha}=\ensuremath{-}2)$ for localized spins. The $\ensuremath{\alpha}$ value shows a complicated density dependence which is accompanied by a density variation of a heat capacity isotherm at an extremely low temperature $(=0.2 \mathrm{mK}).$ This anomaly is similar to the previously observed high-temperature behavior $(\ensuremath{\alpha}\ensuremath{\approx}\ensuremath{-}1)$ of the lowest density solid in the second layer. Although quantitative explanations are lacking for these anomalies, they are likely due to the high frustration caused by competing ferromagnetic and antiferromagnetic multiple-spin exchange interactions at least up to the six-spin exchange. We find that the excess heat-capacity ${(C}_{\mathrm{ex}})$ due to the amorphous ${}^{3}\mathrm{He}$ adsorbed on substrate heterogeneities is certainly not an origin of the anomalous behavior in C of the uniform submonolayer. Only at and below the density for the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ commensurate phase $(\ensuremath{\rho}=6.4 {\mathrm{nm}}^{\ensuremath{-}2})$ heat capacity bumps at around 20 mK are observed. We suggest the possibility of spin-polaron effects caused by delocalized vacancies to explain this anomaly.

Search for spin liquid state in sub-monolayer 3He adsorbed on HD-preplated graphite

NMR studies of sub-monolayer solid 3He adsorbed on a bilayer of HD-preplated graphite have been made down to 100 µK, which is more than one order of magnitude smaller than the exchange energy (J). In the highly frustrated anti-ferromagnetic region, the magnetization obeys a Curie–Weiss law even at temperatures around J and then increases gradually down to 100 µK. Nevertheless, it does not show any anomalous behavior corresponding to the existence of the spin gap. The normalized magnetization versus the reduced temperature (T/J) is independent of the density just after solidification. This fact is consistent with the result in the high-temperature region where the main multiple spin exchanges have a similar density dependence in the present density region. PACS Nos.: 67.80Jd, 67.70+n, 75.10Jm

Multiple-spin exchange in a two-dimensional Wigner crystal

Multiple-spin exchange constants in a two-dimensional Wigner crystal calculated with the help of the WKB approximation. The result is compared with a recent experimental result and also with a recent path-integral Monte Carlo (PIMC) calculation.

Multiple-spin exchange in a two-dimensional Wigner crystal in a magnetic field

Multiple-spin exchange constants in a two-dimensional Wigner crystal, in a magnetic field perpendicular to the plane, is calculated with a semiclassical approximation. The field causes an Aharanov-Bohm oscillation in the exchange constants and can change a ferromagnetic exchange constant to an antiferromagnetic one and vice versa, in addition to reducing the magnitude of the exchange constants. The field can destabilize the ferromagnetic ground state and bring about a rich ground state phase diagram.