Field-induced Quantum Phase Transition Research Articles

Pressure-Tuned Classical–Quantum Crossover in Magnetic Field-Induced Quantum Phase Transitions of a Triangular-Lattice Antiferromagnet

he correspondence principle states that as quantum numbers approach infinity, the nature of a system described by quantum mechanics should match that described by classical mechanics. Quantum phenomena, such as quantum superposition and quantum correlation, generally become unobservable when a system approaches this regime. Conversely, as quantum numbers decrease, classical descriptions give way to observable quantum effects. The external approach to classical–quantum crossover has attracted research interest. This study aims to demonstrate a method for achieving such control in materials.

Quantum spin dynamics of quasi-one-dimensional Heisenberg-Ising magnets in a transverse field: confined spinons, E 8 spectrum, and quantum phase transitions

We report on high-resolution terahertz spectroscopic studies of quantum spin dynamics in the quasi-one-dimensional Ising-like ferromagnet CoNb2O6 and antiferromagnet BaCo2V2O8 as a function of an applied transverse magnetic field. In the ordered phases stabilized by inter-chain couplings, we reveal characteristics for confined spinon excitations, E 8 dynamical spectrum, and field-induced quantum phase transitions. The connections between these characteristic dynamical features are found in the field-dependent evolution of the excitation spectra.

Investigating field-induced magnetic order in Han purple by neutron scattering up to 25.9 T

BaCuSi$_2$O$_6$ is a quasi-two-dimensional (2D) quantum antiferromagnet containing three different types of stacked, square-lattice bilayer hosting spin-1/2 dimers. Although this compound has been studied extensively over the last two decades, the critical applied magnetic field required to close the dimer spin gap and induce magnetic order, which exceeds 23 T, has to date precluded any kind of neutron scattering investigation. However, the HFM/EXED instrument at the Helmholtz-Zentrum Berlin made this possible at magnetic fields up to 25.9 T. Thus we have used HFM/EXED to investigate the field-induced ordered phase, in particular to look for quasi-2D physics arising from the layered structure and from the different bilayer types. From neutron diffraction data, we determined the global dependence of the magnetic order parameter on both magnetic field and temperature, finding a form consistent with 3D quantum critical scaling; from this we deduce that the quasi-2D interactions and nonuniform layering of BaCuSi$_2$O$_6$ are not anisotropic enough to induce hallmarks of 2D physics. From neutron spectroscopy data, we measured the dispersion of the strongly Zeeman-split magnetic excitations, finding good agreement with the zero-field interaction parameters of BaCuSi$_2$O$_6$. We conclude that HFM/EXED allowed a significant extension in the application of neutron scattering techniques to the field range above 20 T and in particular opened new horizons in the study of field-induced magnetic quantum phase transitions.

Possible coexistence of short-range resonating valence bond and long-range stripe correlations in the spatially anisotropic triangular-lattice quantum magnet Cu2 (OH) 3NO3

We show that short-range resonating valence bond correlations and long-range order can coexist in the ground state (GS) of a frustrated spin system. Our study comprises a comprehensive investigation of the quantum magnetism on the structurally disorder-free single crystal of ${\mathrm{Cu}}_{2}{(\mathrm{OH})}_{3}{\mathrm{NO}}_{3}$, which realizes the $s$ = 1/2 Heisenberg model on a spatially anisotropic triangular lattice. Competing exchange interactions determined by fitting the magnetization measured up to 55 T give rise to an exotic GS wave function with the coexistence of the dominant short-range resonating valence bond correlations and weak long-range stripe order (ordered moment ${M}_{0}=|\ensuremath{\langle}{s}_{i}^{z}\ensuremath{\rangle}|\ensuremath{\sim}0.02$). At low temperatures, a first-order spin-flop transition is visible at $\ensuremath{\sim}$1--3 T. As the applied field further increases, another two magnetic field induced quantum phase transitions are observed at $\ensuremath{\sim}$14--19 and $\ensuremath{\sim}$46--52 T, respectively. Simulations of the Heisenberg exchange model show semiquantitative agreement with the magnetic-field modulation of these unconventional phases, as well as the absence of visible magnetic reflections in neutron diffraction, thus supporting the GS of the spin system of ${\mathrm{Cu}}_{2}{(\mathrm{OH})}_{3}{\mathrm{NO}}_{3}$ may be approximate to a quantum spin liquid. Our study establishes structurally disorder-free magnetic materials with spatially anisotropic exchange interactions as a possible arena for spin liquids.

Field-induced multiple quantum phase transitions in the antiferromagnetic Kondo-lattice compound CeRhAl4Si2

We report a comprehensive phase diagram of the antiferromagnetic Kondo-lattice compound ${\mathrm{CeRhAl}}_{4}{\mathrm{Si}}_{2}$ down to 0.3 K by investigating electrical resistivity, magnetoresistivity, and Hall resistivity under the magnetic field along the $c$ axis. At zero field, ${\mathrm{CeRhAl}}_{4}{\mathrm{Si}}_{2}$ undergoes two successive antiferromagnetic transitions at ${T}_{\mathrm{N}1}=14.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{N}2}=8.4\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, respectively. Upon applying magnetic field, the first-order transition of ${T}_{\mathrm{N}2}$ is continuously suppressed at the critical field of 5.5 T. On the other hand, the smooth suppression of the second-order transition of ${T}_{\mathrm{N}1}$ terminates at a tricritical point of 6.6 T and 4.7 K, followed by a first-order transition line and an additional phase transition line, which are monotonically suppressed at 6.7 and 7.2 T, respectively, implying the field-induced multiple quantum phase transitions. Particularly, in the paramagnetic region before the Fermi liquid behavior is fully developed, a quantum critical phase with non-Fermi liquid behavior is revealed, indicating a potential spin liquid state that was predicted from the global quantum phase diagram. These results suggest that ${\mathrm{CeRhAl}}_{4}{\mathrm{Si}}_{2}$ is a promising candidate to study a quantum phase transition that occurs in electronic systems with high degree of frustration.

Critical dielectric susceptibility at a magnetic BEC quantum critical point

Magnetic-field-induced phase transitions are investigated in the frustrated gapped quantum paramagnet Rb$_{2}$Cu$_{2}$Mo$_3$O$_{12}$ through dielectric and calorimetric measurements on single-crystal samples. It is clarified that the previously reported dielectric anomaly at 8~K in powder samples is not due to a chiral spin liquid state as has been suggested, but rather to a tiny amount of a ferroelectric impurity phase. Two field-induced quantum phase transitions between paraelectric and paramagnetic and ferroelectric and magnetically ordered states are clearly observed. It is shown that the electric polarization is a secondary order parameter at the lower-field (gap closure) quantum critical point but a primary one at the saturation transition. Having clearly identified the magnetic Bose-Einstein condensation (BEC) nature of the latter, we use the dielectric channel to directly measure the critical divergence of BEC susceptibility. The observed power-law behavior is in very good agreement with theoretical expectations for three-dimensional BEC. Finally, dielectric data reveal magnetic presaturation phases in this compound that may feature exotic order with unconventional broken symmetries.

Absence of magnetic order in dichloro [1,2-bis (diphenylphosphino) ethane] nickel2+ single crystal* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0403502), the National Natural Science Foundation of China, and Youth Innovation Promotion Association of Chinese Academy of Sciences (Grant No. 2017483). A portion of this work was supported by the High Magnetic Field Laboratory

Dichloro [1,2-bis (diphenylphosphino) ethane] nickel2+ (NiCl2(dppe)) is an organic compound containing C26H24P2(dppe) molecules and Cl−, Ni2+ ions. The large-size NiCl2(dppe) single crystals with longest dimension of 4 mm were grown by the method of slow evaporation of organic solution. Single crystal x-ray diffraction spectrum indicates that the single crystal is of high quality. Magnetization results of the NiCl2(dppe) single crystals show an anisotropic paramagnetism behavior and diamagnetic background, which come from Ni2+ ions and benzene ring, respectively. However, according to the specific heat results with temperature down to 0.1 K and magnetic field up to 14 T, no expected field-induced quantum phase transition was observed in NiCl2(dppe) single crystals.

Capacitive detection of magnetic field induced quantum phase transitions in an imbalanced bilayer electron system

Ground states that appear in a quantizing magnetic field in an imbalanced bilayer electron system hosted by a dual-gated, wide GaAs quantum well are explored with a magnetocapacitance technique that enables detection of the compressibility of each layer separately, the characterization of the charge distribution, as well as the distinction of single- or double-layer-like behavior. Magnetic field induced reentrant quantum phase transitions are observed between a compressible double-layer ground state and a single-layer-like incompressible phase for both total fillings 1 and 2. The transitions are accompanied by a charge redistribution across the well. Our observations indicate for both incompressible states easy-plane pseudospin ferromagnetism as the origin.

High-field quantum disordered state in α−RuCl3 : Spin flips, bound states, and multiparticle continuum

Layered $\alpha$-RuCl3 has been discussed as a proximate Kitaev spin liquid compound. Raman and THz spectroscopy of magnetic excitations confirm that the low-temperature antiferromagnetic ordered phase features a broad Raman continuum, together with two magnon-like excitations at 2.7 and 3.6 meV, respectively. The continuum strength is maximized as long-range order is suppressed by an external magnetic field. The state above the field-induced quantum phase transition around 7.5 T is characterized by a gapped multi-particle continuum out of which a two-particle bound state emerges, together with a well-defined single-particle excitation at lower energy. Exact diagonalization calculations demonstrate that Kitaev and off-diagonal exchange terms in the Fleury-Loudon operator are crucial for the occurrence of these features in the Raman spectra. Our study firmly establishes the partially-polarized quantum disordered character of the high-field phase.

Microwave dynamics of the stoichiometric and bond-disordered anisotropic S=1 chain antiferromagnet NiCl2−4SC(NH2)2

We studied electron spin resonance in a quantum magnet NiCl2-4SC(NH2)2, demonstrating a field-induced quantum phase transition from a quantum-disordered phase to an antiferromagnet. We observe two branches of the antiferromagnetic resonance of the ordered phase, one of them has a gap and the other is a Goldstone mode with zero frequency at a magnetic field along the four-fold axis. This zero frequency mode acquires a gap at a small tilting of the magnetic field with respect to this direction. The upper gap was found to be reduced in the doped compound Ni(Cl(1-x)Br(x))2-4SC(NH2)2 with $x=0.21$. This reduction is unexpected because of the previously reported rise of the main exchange constant in a doped compound. Further, a nonresonant diamagnetic susceptibility $\chi^{\prime}$ was found for the ordered phase in a wide frequency range above the quasi-Goldstone mode. This dynamic diamagnetism is as large as the dynamic susceptibility of the paramagnetic resonance. We speculate that it originates from a two-magnon absorption band of low-frequency dispersive magnon branch.

Field-induced QCD3 -Chern-Simons quantum criticalities in Kitaev materials

Kitaev materials are promising for realizing exotic quantum spin liquid phases, such as a non-Abelian chiral spin liquid. Motivated by recent experiments in these materials, we theoretically study the novel field-induced quantum phase transitions from the non-Abelian chiral spin liquid to the symmetry-broken zigzag phase and to the trivial polarized state. Utilizing the recently developed dualities of gauge theories, we find these transitions can be described by critical bosons or gapless fermions coupled to emergent non-Abelian gauge fields, and the critical theories are of the type of a QCD$_3$-Chern-Simons theory. We propose that all these exotic quantum phase transitions can potentially be direct and continuous in Kitaev materials, and we present sound evidence for this proposal. Therefore, besides being systems with intriguing quantum magnetism, Kitaev materials may also serve as table-top experimental platforms to study the interesting dynamics of emergent strongly interacting quarks and gluons in $2+1$ dimensions.

Field-induced instability of the quantum spin liquid ground state in the Jeff=12 triangular-lattice compound NaYbO2

Polycrystalline samples of NaYbO$_2$ are investigated by bulk magnetization and specific-heat measurements, as well as by nuclear magnetic resonance (NMR) and electron spin resonance (ESR) as local probes. No signatures of long-range magnetic order are found down to 0.3~K, evidencing a highly frustrated spin-liquid-like ground state in zero field. Above 2\,T, signatures of magnetic order are observed in thermodynamic measurements, suggesting the possibility of a field-induced quantum phase transition. The $^{23}$Na NMR relaxation rates reveal the absence of magnetic order and persistent fluctuations down to 0.3~K at very low fields and confirm the bulk magnetic order above 2~T. The $H$-$T$ phase diagram is obtained and discussed along with the existing theoretical concepts for layered spin-$\frac{1}{2}$ triangular-lattice antiferromagnets

Field-induced ordering in a random-bond quantum spin ladder compound with weak anisotropy

The field induced quantum phase transitions in the disorder-free and disordered samples of the spin ladder material (CH_3)_2CHNH_3Cu(Cl_{1-x}Br_x)_3 are studied using magnetic calorimetry and magnetic neutron diffraction on single crystal samples. Drastically different critical indexes and correlation lengths in the high field phase are found for two different orientations of the applied field. It is argued that for a field applied along the crystallographic c axis, as in previous studies [1], the transition is best described as an Ising transition in random field and anisotropy, rather than as a magnetic Bose Glass to Bose Condensate transition. [1] Tao Hong, A. Zheludev, H. Manaka, and L.- P. Regnault, Phys. Rev. B 81, 060410 (2010).

Mermin-Wagner physics, (H,T) phase diagram, and candidate quantum spin-liquid phase in the spin- 12 triangular-lattice antiferromagnet Ba8CoNb6O24

Ba$_8$CoNb$_6$O$_{24}$ presents a system whose Co$^{2+}$ ions have an effective spin 1/2 and construct a regular triangular-lattice antiferromagnet (TLAFM) with a very large interlayer spacing, ensuring purely two-dimensional character. We exploit this ideal realization to perform a detailed experimental analysis of the $S = 1/2$ TLAFM, which is one of the keystone models in frustrated quantum magnetism. We find strong low-energy spin fluctuations and no magnetic ordering, but a diverging correlation length down to 0.1 K, indicating a Mermin-Wagner trend towards zero-temperature order. Below 0.1 K, however, our low-field measurements show an nexpected magnetically disordered state, which is a candidate quantum spin liquid. We establish the $(H,T)$ phase diagram, mapping in detail the quantum fluctuation corrections to the available theoretical analysis. These include a strong upshift in field of the maximum ordering temperature, qualitative changes to both low- and high-field phase boundaries, and an ordered regime apparently dominated by the collinear "up-up-down" state. Ba$_8$CoNb$_6$O$_{24}$ therefore offers fresh input for the development of theoretical approaches to the field-induced quantum phase transitions of the $S = 1/2$ Heisenberg TLAFM.

Dynamics of photogenerated carriers near magnetic field driven quantum phase transition in aperiodic multiple quantum wells

Time-resolved magneto-photoluminescence was employed to study the magnetic field induced quantum phase transition separating two phases with different distributions of electrons over quantum wells in an aperiodic multiple quantum well, embedded in a wide AlGaAs parabolic quantum well. Intensities, broadenings and recombination times attributed to the photoluminescence lines emitted from individual quantum wells of the multiple quantum well structure were measured as a function of the magnetic field near the transition. The presented data manifest themselves to the magnetic field driven migration of the free electrons between the quantum wells of the studied multiple quantum well structure. The observed charge transfer was found to influence the screening of the multiple quantum well and disorder potentials. Evidence of the localization of the electrons in the peripheral quantum wells in strong magnetic field is presented.

Reentrant behaviors in the phase diagram of spin-1 planar ferromagnet with single-ion anisotropy

We used the two-time Green function framework to investigate the role played by the easy-axis single-ion anisotropy on the phase diagram of (d>2)-dimensional spin-1planar ferromagnets, which exhibit a magnetic field induced quantum phase transition. We tackled the problem using two different kind of approximations: the Anderson-Callen decoupling scheme and the Devlin approach. In the latter scheme, the exchange anisotropy terms in the equations of motion are treated at the Tyablikov decoupling level while the crystal field anisotropy contribution is handled exactly. The emerging key result is a reentrant structure of the phase diagram close to the quantum critical point, for certain values of the single-ion anisotropy parameter. We compare the results obtained within the two approximation schemes. In particular, we recover the same qualitative behavior. We show the phase diagram, close to the field-induced quantum critical point and the behavior of the susceptibility for different values of the single-ion anisotropy parameter, enhancing the differences between the two different scenarios (i.e. with and without reentrant behavior).

Quantum critical scaling for field-induced quantum phase transition in a periodic Anderson-like model polymer chain

The quantum phase transition and thermodynamics of a periodic Anderson-like polymer chain in a magnetic field are investigated by Green’s function theory. The T-h phase diagram is explored, wherein a crossover temperature T∗ denoting the gapless phase crossover into quantum critical regimes, smoothly connects near the critical fields to the universal linear line T∗∼(h−hc,s), and ends at hc,s, providing a new route to capture quantum critical point (QCP). The quantum critical scaling around QCPs is demonstrated by analyzing magnetization, specific heat and Grüneisen parameter Γh, which provide direct access to distill the power-law critical exponents (β, δ and α) obeying the critical scaling relation α+β(1+δ)=2, analogous to the quantum spin system. Furthermore, scaling hypothesis equations are proposed to check the scaling analysis, for which all the data collapse onto a single curve or two independent branches for the plot against an appropriate scaling variable, indicating the self-consistency and reliability of the obtained critical exponents.

Multipartite non-locality and entanglement signatures of a field-induced quantum phase transition

Quantum correlation measures are limited in practice to a few number of parties, since no general theory is still capable of reaching the thermodynamic limit. In the present work we study entanglement and non-locality for a cluster of spins belonging to a compound that displays a magnetocaloric effect. A quantum phase transition (QPT) is induced by an external magnetic field B, in such a way that the corresponding quantum fluctuations are reproduced at a much smaller scale than the experimental outcomes, and then described by means of the aforementioned quantum measures.

Field-Induced Quantum Phase Transitions inS= 1/2J1–J2Heisenberg Model on Square Lattice

We study the magnetic field dependence of the ground state of $S=1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice by the DMRG method with the sine-square deformation. We obtain 8 different phases including plaquette valence-bond crystal with a finite spin gap, transverse N$\acute{\rm e}$el, transverse stripe, 1/2 magnetization plateau with up-up-up-down (uuud), and three new phases we named Y-like, V-like, and $\Psi$ phases around $J_2/J_1$ =0.55-0.6 depending on the magnetic field. The phase transitions to uuud and Y-like states from transverse N$\acute{\rm e}$el (at $J_2/J_1$ = 0.55) and stripe (at $J_2/J_1$ = 0.6) states are discontinuous, as in the case of spin-flop.

Magnetic quantum phase transitions and entropy in Van Vleck magnet

Field-induced magnetic quantum phase transitions in the Van Vleck paramagnet with easy-plane single-ion anisotropy and competing Ising exchange between ions with the spin S=1 have been studied theoretically. The description was made by minimizing the Lagrange function at zero temperature (Т=0) and the free energy at T≠0. Stable and unstable solutions of equations corresponding to the case ψ0=|0〉 asymptotically transform into those following from the Lagrange function at Т=0. First-order phase transitions from the Van Vleck paramagnet state into the ferromagnet one were found to take place at a sufficiently high single-ion anisotropy. The entropy of such a magnet was shown to grow with its magnetization, as it occurs for antiferromagnets. At the point of quantum phase transition, the entropy has a jump, which magnitude depends on the ratio between the Ising exchange and anisotropy constants, as well as on the temperature. The described magnetic phase transition was supposed to be accompanied by the magnetocaloric effect. In the case when the Ising exchange dominates over the single-ion anisotropy, the magnetization reversal of ferromagnetic state by an external field was shown to be a phase transition of the first kind, which does not belong to orientational ones and which should be regarded as a quantum order-order phase transition.