2D XY Research Articles

Domain state of the axial next-nearest-neighbor Ising model in two dimensions

We have examined the spin ordering of an axial next-nearest-neighbor Ising (ANNNI) model in two dimensions (2D) near above the antiphase ($\langle 2 \rangle$ phase). We considered an $N_R$-replica system and calculated an overlap function $q_m$ between different replicas having used a cluster heat bath (CHB) Monte Carlo method. We determined transition temperature between $\langle 2 \rangle$ phase and a floating incommensurate (IC) phase as $T_{C2}/J = 0.89 \pm 0.01$ with frustration ratio $\kappa (\equiv -J_2/J_1) = 0.6$. We found that the spin state at $T \gtrsim T_{C2}$ may be called as a domain state, because the spin structure is characterized by a sequentially arranged four types of domains with different $\langle 2 \rangle$ structures. In the domain state, the 2D XY symmetry of the spin correlation in the IC phase weakly breaks and the diversity of the spin arrangement increases as $T \rightarrow T_{C2}$. The Binder ratio $g_L$ exhibits a depression at $T \sim T_{C2}$ and the quasi-periodic spin structure, which is realized in the IC phase, becomes diverse at $T \gtrsim T_{C2}$. We discussed that the domain state is stable against the thermal fluctuation which brings a two-stage development of the spin structure at low temperatures.

Energy probability distribution zeros: A route to study phase transitions

In the study of phase transitions a very few models are accessible to exact solution. In most cases analytical simplifications have to be done or some numerical techniques have to be used to get insight about their critical properties. Numerically, the most common approaches are those based on Monte Carlo simulations together with finite size scaling analysis. The use of Monte Carlo techniques requires the estimation of quantities like the specific heat or susceptibilities in a wide range of temperaturesor the construction of the density of states in large intervals of energy. Although many of these techniques are well developed they may be very time consuming when the system size becomes large enough. It should be suitable to have a method that could surpass those difficulties. In this work we present an iterative method to study the critical behavior of a system based on the partial knowledge of the complex Fisher zeros set of the partition function. The method is general with advantages over most conventional techniques since it does not need to identify any order parameter a priori. The critical temperature and exponents can be obtained with great precision even in the most unamenable cases like the two dimensional XY model. To test the method and to show how it works we applied it to some selected models where the transitions are well known: The 2D Ising, Potts and XY models and to a homopolymer system. Our choices cover systems with first order, continuous and Berezinskii–Kosterlitz–Thouless transitions as well as the homopolymer that has two pseudo-transitions. The strategy can easily be adapted to any model, classical or quantum, once we are able to build the corresponding energy probability distribution.

Quantum and thermal phase transitions in a bosonic atom-molecule mixture in a two-dimensional optical lattice

We study the ground state and the thermal phase diagram of a two-species Bose-Hubbard model, with $U(1)\times \mathbb{Z}_2$ symmetry, describing atoms and molecules on a 2D optical lattice interacting via a Feshbach resonance. Using quantum Monte Carlo simulations and mean field theory, we show that the conversion between the two-species, coherently coupling the atomic and molecular states, has a crucial impact on the Mott-Superfluid transition and stabilizes an insulating phase with a gap controlled by the conversion term -- \textit{the Feshbach insulator} -- instead of a standard Mott insulating phase. Depending on the detuning between atoms and molecules, this model exhibits three phases: the Feshbach insulator, a molecular condensate coexisting with non condensed atoms and a mixed atomic-molecular condensate. Employing a finite-size scaling method, we observe 3D XY (3D Ising) transition when $U(1)$ ($ \mathbb{Z}_2$) is broken whereas the transition is first-order when both $U(1)$ and $ \mathbb{Z}_2$ symmetries are spontaneously broken. The finite temperature phase diagram is also discussed. The thermal disappearance of the molecular superfluid leads to a Berezinskii-Kosterlitz-Thouless transition with unusual universal jump in the superfluid density. The loss of the quasi-long-range coherence of the mixed atomic and molecular superfluid is more subtle since only atoms exhibit conventional Berezinskii-Kosterlitz-Thouless criticality. We also observe a classical first-order transition between the mixed superfluid and the normal Bose liquid at low temperature.

In English

Complex compounds of various types and nature have been widely applied in many fields of science and technology. Complex aggregates based on nanostructures such as nanotubes and other coordination compounds, for example, metallocenes, have unique properties, since a combination of their individual characteristics provides for further growing interest to the research in chemistry, physics, electronics, medicine, etc. The initial structure was a (5.5)@(10.10) nanotube (CNT) having 270 carbon atoms. Intercalation of this double-walled carbon nanotubes (DWCNT) assumes placing the intercalate inside the (5.5) CNT, into intertubular space, and its differently oriented sorption on the outer surface of the (10.10) CNT. By employing the methods of MM+, РМ3 and Monte-Carlo, the positioning has been studied of molecules of tricarbonyl(cyclopentadienyl)manganese, monocyclopentadienylferrum(ІІ), bis(cyclopentadienyl)nickel and bis(η 5 -cyclopentadienyl)cobalt in a double-walled (5,5)@(10,10) carbon nanotube depending on intercalate concentration and intercalation temperature. The temperature increase (over ~455–460 K) causes gradual bond ruining followed by extrusion of interwall intercalate. Further temperature increase up to 620–650 K is characterised with intercalate external surface desorption, stabilising the whole systems and keeping the interwall intercalate only. It is necessary to note that the suggested model variant allows to demonstrate the thermodynamic selectivity of physical and chemical sorption-desorption. At lower temperatures there appears physical sorption, its natural feature is most likely to overlap the non-hybridized orbital 3d xy of the metal ions with the π-system of the DWCNT side surface while chemisorption is observed at higher temperatures that is peculiar or π-π interactions of aromatic and quasiaromatic cyclic (heterocyclic) systems. Moreover, simultaneous presence of donor/acceptor feature of the DWCNT’s intertube space as a result of positive and negative Gaussian curvature, makes it possible to regulate orientation of intercalate donor and acceptor edges what allows us to view it as a potential molecular switch. There have been calculated the UV-spectra for (5,5)@(10,10) DWCNT depending on the intercalate concentration as well as an association constant of the systems which makes 26.45 l·mol –1 (for system with ferrocene); 36.2 l·mol –1 (for system with nickelocene); 76.8 l·mol –1 (for system with cobaltocene) and 6.745 l·mol –1 (for system with manganocene).

Thermodynamic and critical properties of the charge density wave system ErTe3

We present specific heat and ultrasonic measurements on the rare earth tritelluride ErTe3 compound. Thermodynamic anomalies are observed at the upper charge density wave (CDW) phase transition TCDW1=265K and the second one at TCDW2=155K. Similar critical behaviors are found at both CDW phase transitions and that we tentatively described in terms of the 3D XY model. Different anisotropic stress dependences ∂TCDW1/∂σii and ∂TCDW2/∂σii are found at the two successive CDW phase transitions. Magnitude of the elastic constant anomalies at TCDW2 is ten times smaller than that at TCDW1. Anomalies in the elastic constants at the upper CDW TCDW1 exhibit two dimensional features in the layer planes while in contrast a three dimensional behavior is observed at TCDW2.

Chemical pressure effects on crystal and magnetic structures of bilayer manganites PrA2Mn2O7 (A = Sr or Ca)

The crystal and magnetic structures of the bilayer manganites PrSr2Mn2O7 (PSMO) and PrCa2Mn2O7 (PCMO) have been studied by neutron powder diffraction. It was found that PSMO crystallizes in space group I4/mmm, while PCMO adopts space group Cmc21 at room temperature. The difference in the structure arises from chemical pressure induced by the Ca substitution for Sr on the A sites, which causes different Jahn-Teller distortions. In PSMO, the MnO6 octahedra suffer a small elongated distortion, while those in PCMO adopt strong compressed distortion along the axial direction. In addition, the octahedra in PCMO show a+b0c0 rotation and a0b+c+ tilting in the Glazer notation in comparison to PSMO. As a result, these two compounds adopt very different magnetic structures: The magnetic structure of PSMO is an A-type magnetic structure (Im'm'm) with propagation vector k = (0, 0, 1) and magnetic moments in the ab plane. In contrast, a C-type antiferromagnetic magnetic structure (Cm'c2′1) with the multiple propagation vectors (k = (0, 12, 12) and (0, 12, 0)) and magnetic moments mainly along the b axis is found in PCMO. The critical exponent of the magnetic phase transition is around 0.345 for PSMO and 0.235 for PCMO, indicating 3D and 2D XY transitions, respectively. The strong Jahn-Teller distortion induced by the chemical pressure is believed to suppress the double exchange and favour super-exchange in PCMO, leading to the dramatic difference in the magnetic structure.

Nature of the possible magnetic phases in a frustrated hyperkagome iridate

Based on Kitaev-Heisenberg model with Dzyaloshinskii-Moriya (DM) interactions, we studied nature of possible magnetic phases in frustrated hyperkagome iridate, Na$_4$Ir$_{3}$O$_8$ (Na-438). Using Monte-Carlo simulation, we showed that the phase diagram is mostly covered by two competing magnetic ordered phases; Z$_2$ symmetry breaking (SB) phase and Z$_6$ SB phase, latter of which is stabilized by the classical order by disorder. These two phases are separated by a first order phase transition line with Z$_8$-like symmetry. The critical nature at the Z$_6$ SB ordering temperature is characterized by the 3D XY universality class, below which U(1) to Z$_6$ crossover phenomena appears; the Z$_6$ spin anisotropy becomes irrelevant in a length scale shorter than a crossover length $\Lambda_*$ while becomes relevant otherwise. A possible phenomenology of polycrystalline Na-438 is discussed based on this crossover phenomena.

Magnetic critical properties and basal-plane anisotropy of Sr2IrO4

The anisotropic magnetic properties of Sr2IrO4 are investigated, using longitudinal and torque magnetometry. The critical scaling across of the longitudinal magnetization is that expected for the 2D XY universality class. Modeling the torque for a magnetic field in the basal plane, and taking into account all in-plane and out-of-plane magnetic couplings, we derive the effective fourfold anisotropy erg mol−1. Although larger than for the cuprates, it is found to be too small to account for a significant departure from the isotropic 2D XY model. The in-plane torque also allows us to set an upper bound for the anisotropy of a field-induced shift of the antiferromagnetic ordering temperature.

Magnetic States and Frustrations of Square Spin Ice in 2D XY Point Dipoles Model

In the discrete 2D XY model of finite number of point dipoles of square spin ice, the order parameter has been calculated exactly as the average size of the maximal cluster. The finite size and edge effects do not allow research the critical behavior of the phase transition for finite systems. It is found that frustrations in spin ice model with long-range interaction are possible only in presence of symmetry for the distribution of magnetic moments.

Non-self-averaging in Ising spin glasses and hyperuniversality.

Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized intersample variance) parameter U_{22}(T,L) for the spin glass susceptibility [and for higher moments U_{nn}(T,L)] is reported for dimensions 2,3,4,5, and 7. In each dimension d the non-self-averaging parameters in the paramagnetic regime vary with the sample size L and the correlation length ξ(T,L) as U_{nn}(β,L)=[K_{d}ξ(T,L)/L]^{d} and so follow a renormalization group law due to Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)PRLTAO0031-900710.1103/PhysRevLett.77.3700]. Empirically, it is found that the K_{d} values are independent of d to within the statistics. The maximum values [U_{nn}(T,L)]_{max} are almost independent of L in each dimension, and remarkably the estimated thermodynamic limit critical [U_{nn}(T,L)]_{max} peak values are also practically dimension-independent to within the statistics and so are "hyperuniversal." These results show that the form of the spin-spin correlation function distribution at criticality in the large L limit is independent of dimension within the ISG family. Inspection of published non-self-averaging data for three-dimensional Heisenberg and XY spin glasses the light of the Ising spin glass non-self-averaging results show behavior which appears to be compatible with that expected on a chiral-driven ordering interpretation but incompatible with a spin-driven ordering scenario.

Nonequilibrium behaviors of the three-dimensional Heisenberg model in the Swendsen-Wang algorithm.

Recently, it was shown [Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014)JUPSAU0031-901510.7566/JPSJ.83.113001] that the nonequilibrium critical relaxation of the two-dimensional (2D) Ising model from a perfectly ordered state in the Wolff algorithm is described by stretched-exponential decay, and a universal scaling scheme was found to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. To evaluate the critical temperature and critical exponents precisely using the above scaling scheme, we calculate nonequilibrium ordering from the perfectly disordered state in the Swendsen-Wang algorithm, and we find that the critical ordering process is described by stretched-exponential growth with a comparable exponent to that of the 3D XY model. The critical exponents evaluated in the present study are consistent with those in previous studies.

Observation of critical behavior of ultra-cold Bose gas in a magnetic trap

Quantum criticality emerges when the collective fluctuations of matter undergo a continuous phase transition at zero temperature and has been a research focus in conventional condensed-matter physics over the past several decades. In the quantum critical regime, the exotic and universal properties are expected. These properties are independent of the microscopic details of the system, but depend only on a few general properties of the system, such as its dimensionality and the symmetry of the order parameter. The research of quantum criticality can not only help us to understand quantum phase transitions, but also provide a novel route to new material design and discovery.Ultracold bosonic gases have provided a clean system for studying the quantum critical phenomena. The critical behavior of a weakly interacting three-dimensional (3D) Bose gas should be identical to that of 4He at the superfluid transition, which belongs to the 3D XY universality class. From the normal fluid to the superfluid, the system undergoes a phase transition from completely disorder to long-range order, while in the vicinity of the phase transition point, the system parameters will show some singularity characteristics. In this paper, we observe the critical behavior of 87Rb Bose gas in a quadrupole-Ioffe configuration (QUIC) trap near the phase transition temperature Tc. A novel singularity behavior of the full width at half maximum of momentum distribution (FWHMMD) of atomic gas is discovered in the experiment. Prior to our experiment, we prepare a sample with 7.8105 87Rb atoms in the 5S1/2 |F=2, mF=2 state. Then the sample is held in a QUIC trap for a presetting period of time to control the temperature of atom sample precisely. During the holding time, the sample is heated up due to background gas collisions or fluctuations of the trap potential. In our experiment, the heating rate is deduced to be 0.3480.078 nK/ms from the absorption image. For a bosonic gas in a harmonic trap, critical gas can only cover a finite-size region due to a spatially varying density. We define the finite-size region as a critical region determined by the Ginzburg criterion. Then the FWHMMDs of atomic gas in the critical region are measured for different temperatures near the critical point. To this aim, we first extract the momentum distribution of atomic gas from the absorption image of the atomic clouds released from the QIUC trap after free expansion. Thus momentum distribution of atomic gas in the critical region can be extracted from the absorption image by subtracting the momentum distribution of thermal gas outside the critical region. According to the statistical results of the FWHMMD at different temperatures, we find that the FWHMMD suddenly reduces, thus revealing a very notable singularity behavior when the temperature is very close to the phase transition temperature Tc.

Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the Berezinsky-Kosterlitz-Thouless and weak first-order phase transitions.

Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D q=5 Potts model and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the three- and four-dimensional XY models and in the 2D q-state Potts models for 2≤q≤4 and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D q=5 and 6 Potts models and propose a quantitative criterion on "weakness" of the first-order phase transition.

Improved CUDA programs for GPU computing of Swendsen–Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models

Improved CUDA programs for GPU computing of Swendsen–Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models

Phase transition and critical behavior of spin–orbital coupled spinel ZnV2O4**Project supported by the National Basic Research Program of China (Grant No. 2012CB821404), the National Natural Science Foundation of China (Grant Nos. 51172166 and 61106005), the National Science Fund for Talent Training in Basic Science, China (Grant No. J1210061), and the Doctoral Fund of Ministry of Education of China (Grant No.

We present the temperature-dependent susceptibility and specific heat measurement of spinel ZnV2O4. The structural transition with orbital ordering and the antiferromagnetic transition with spin ordering were observed at 50 K and 37 K, respectively. By analysis of the hysteresis behavior between the specific heat curves obtained in warming and cooling processes, the structural transition was confirmed to be the first-order transition, while the antiferromagnetic transition was found to be of the second-order type. At the structural transition, the latent heat and entropy change were calculated from the excess specific heat, and the derivative of pressure with respect to temperature was obtained using the Clausius–Clapayron equation. At the magnetic transition, the width of the critical fluctuation region was obtained to be about 0.5 K by comparing with Gaussian fluctuations. In the critical region, the critical behavior was analyzed by using renormalization-group theory. The critical amplitude ratio A+/A− = 1.46, which deviates from the 3D Heisenburg model; while the critical exponent α is −0.011, which is close to the 3D XY model. We proposed that these abnormal critical behaviors can be attributed to strong spin–orbital coupling accompanied with the antiferromagnetic transition. Moreover, in the low temperature range (2–5 K), the Fermi energy, the density of states near the Fermi surface, and the low limit of Debye temperature were estimated to be 2.42 eV, 2.48 eV−1, and 240 K, respectively.

Monte Carlo simulations of the site-diluted 3d XY model with superexchange interaction: Application to Fe[Se2CN(C2H5)2]2Cl–Zn[S2CN(C2H5)2]2 diluted magnets

A simple site-diluted classical XY model is proposed to study the magnetic properties of the ferromagnetic polycrystalline Fe[Se2CN(C2H5)2]2Cl diluted with diamagnetic Zn[S2CN(C2H5)2]2. An extra superexchange interaction is assumed between next-nearest-neighbors on a simple cubic lattice, which are induced by a diluted ion. The critical properties are obtained by Monte Carlo simulations using a hybrid algorithm, single histograms procedures and finite-size scaling techniques. Quite good fits to the experimental results of the ordering temperature are obtained, namely its much less rapidly decreasing with dilution than predicted by the standard diluted 3d XY model, and the change in curvature around 86% of the magnetic Fe[Se2CN(C2H5)2]2Cl compound.

New insight into the Berezinskii-Kosterlitz-Thouless phase transition

We investigate the 2d XY model by using the constraint angle action, which belongs to the class of topological lattice actions. These actions violate important features usually demanded for a lattice action, such as the correct classical continuum limit and the applicability of perturbation theory. Nevertheless, they still lead to the same universal quantum continuum limit and show excellent scaling behavior. By using the constraint angle action we gain new insight into the Berezinskii-Kosterlitz-Thouless phase transition of the 2d XY model. This phase transition is of special interest since it is one of the few examples of a phase transition beyond second order. It is of infinite order and therefore an essential phase transition. In particular, we observe an excellent scaling behavior of the helicity modulus, which characterizes this phase transition. We also observe that the mechanism of (un)binding vortex-anti-vortex pairs follows the usual pattern, although free vortices do not require any energy in the formulation of the 2d XY model using the constraint angle action.

OpenACC programs of the Swendsen–Wang multi-cluster spin flip algorithm

We present sample OpenACC programs of the Swendsen–Wang multi-cluster spin flip algorithm. OpenACC is a directive-based programming model for accelerators without requiring modification to the underlying CPU code itself. In this paper, we deal with the classical spin models as with the sample CUDA programs (Komura and Okabe, 2014), that is, two-dimensional (2D) Ising model, three-dimensional (3D) Ising model, 2D Potts model, 3D Potts model, 2D XY model and 3D XY model. We explain the details of sample OpenACC programs and compare the performance of the present OpenACC implementations with that of the CUDA implementations for the 2D and 3D Ising models and the 2D and 3D XY models. Program summaryProgram title: SWspin_OpenACCCatalogue identifier: AEXU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEXU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2898No. of bytes in distributed program, including test data, etc.: 9729Distribution format: tar.gzProgramming language: C, OpenACC.Computer: Any computer with an OpenACC-enabled accelerator (tested on NVIDIA GPU).Operating system: No limits (tested on Linux).RAM: About 1MiB for the parameters used in the sample programs.Classification: 23.Nature of problem: Monte Carlo simulation of classical spin systems. Ising model, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices.Solution method: Swendsen–Wang multi-cluster spin flip Monte Carlo method. The OpenACC implementation for the cluster-labeling is based on the work by Kalentev et al. [J. Parallel Distrib. Comput. 71 (2011) 615–620].Restrictions: The system size is limited depending on the memory of an accelerator.Running time: A few minutes per each program for the parameters used in the sample program.

Hydrogen bond donation to the heme distal ligand of Staphylococcus aureus IsdG tunes the electronic structure.

Staphylococcus aureus IsdG catalyzes the final step of staphylococcal iron acquisition from host hemoglobin, whereby host-derived heme is converted to iron and organic products. The Asn7 distal pocket residue is known to be critical for enzyme activity, but the influence of this residue on the substrate electronic structure was unknown prior to this work. Here, an optical spectroscopic and density functional theory characterization of azide- and cyanide-inhibited wild type and N7A IsdG is presented. Magnetic circular dichroism data demonstrate that Asn7 perturbs the electronic structure of azide-inhibited, but not cyanide-inhibited, IsdG. As the iron-ligating α-atom of azide, but not cyanide, can act as a hydrogen bond acceptor, these data indicate that the terminal amide of Asn7 is a hydrogen bond donor to the α-atom of a distal ligand to heme in IsdG. Circular dichroism characterization of azide- and cyanide-inhibited forms of WT and N7A IsdG strongly suggests that the Asn7···N3 hydrogen bond influences the orientation of a distal azide ligand with respect to the heme substrate. Specifically, density functional theory calculations suggest that Asn7···N3 hydrogen bond donation causes the azide ligand to rotate about an axis perpendicular to the porphyrin plane and weakens the π-donor strength of the azide ligand. This lowers the energies of the Fe 3d xz and 3d yz orbitals, mixes Fe 3d xy and porphyrin a 2u character into the singly-occupied molecular orbital, and results in spin delocalization onto the heme meso carbons. These discoveries have important implications for the mechanism of heme oxygenation catalyzed by IsdG.

Detailed Characterization of a Nanosecond-Lived Excited State: X-ray and Theoretical Investigation of the Quintet State in Photoexcited [Fe(terpy)2]2.

Theoretical predictions show that depending on the populations of the Fe 3dxy, 3dxz, and 3dyz orbitals two possible quintet states can exist for the high-spin state of the photoswitchable model system [Fe(terpy)2]2+. The differences in the structure and molecular properties of these 5B2 and 5E quintets are very small and pose a substantial challenge for experiments to resolve them. Yet for a better understanding of the physics of this system, which can lead to the design of novel molecules with enhanced photoswitching performance, it is vital to determine which high-spin state is reached in the transitions that follow the light excitation. The quintet state can be prepared with a short laser pulse and can be studied with cutting-edge time-resolved X-ray techniques. Here we report on the application of an extended set of X-ray spectroscopy and scattering techniques applied to investigate the quintet state of [Fe(terpy)2]2+ 80 ps after light excitation. High-quality X-ray absorption, nonresonant emission, and resonant emission spectra as well as X-ray diffuse scattering data clearly reflect the formation of the high-spin state of the [Fe(terpy)2]2+ molecule; moreover, extended X-ray absorption fine structure spectroscopy resolves the Fe–ligand bond-length variations with unprecedented bond-length accuracy in time-resolved experiments. With ab initio calculations we determine why, in contrast to most related systems, one configurational mode is insufficient for the description of the low-spin (LS)–high-spin (HS) transition. We identify the electronic structure origin of the differences between the two possible quintet modes, and finally, we unambiguously identify the formed quintet state as 5E, in agreement with our theoretical expectations.