By combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising-like quantum antiferromagnet BaCo2V2O8 in a longitudinal magnetic field applied along the Ising anisotropy, which is also the chain direction. The external field closes the excitation gap due to the magnetic anisotropy, inducing a transition from the Neel ordered state to an incommensurate longitudinal spin density wave phase. If the field is increased further, another transition into a transverse antiferromagnetic phase takes place at 9 T due to the competition between longitudinal and transverse correlations. We numerically and experimentally show that the model of XXZ chains connected by a weak interchain interaction well reproduces this transition. We also calculate the dynamical susceptibility and demonstrate that it agrees quantitatively with inelastic neutron scattering measurements. In contrast to the abrupt change of magnetic ordering, the spectra do not change much at the transition at 9 T, and the spin dynamics can be described as a Tomonaga-Luttinger liquid. We also refine the modeling of BaCo2V2O8 by including a four-site periodic term arising from the crystal structure which enables one to account for an anomaly of the magnetic susceptibility appearing at 19.5 T, as well as for the anticrossing observed in the inelastic neutron scattering spectra.

We study the dynamics of the quasi-one-dimensional Ising-Heisenberg antiferromagnet BaCo2V2O8 under a transverse magnetic field. Combining inelastic neutron scattering experiments and theoretical analyses by field theories and numerical simulations, we mainly elucidate the structure of the spin excitation spectrum in the high field phase, appearing above the quantum phase transition point mu0Hc 10 T. We find that it is characterized by collective solitonic excitations superimposed on a continuum. These solitons are strongly bound in pairs due to the effective staggered field induced by the nondiagonal g tensor of the compound, and are topologically different from the fractionalized spinons in the weak field region. The dynamical susceptibility numerically calculated with the infinite time-evolving block decimation method shows an excellent agreement with the measured spectra, which enables us to identify the dispersion branches with elementary excitations. The lowest energy dispersion has an incommensurate nature and has a local minimum at an irrational wave number due to the applied transverse field.

Combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising anisotropic quantum antiferromagnet BaCo_{2}V_{2}O_{8} in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly, the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnetic chains.

a. Université Grenoble Alpes, INAC/MEM/MDN-CEA, Grenoble, France. b. DPMC-MaNEP, University of Geneva, Geneva, Switzerland. c. Institut Néel CNRS, Grenoble, France. d. Laboratoire Léon Brillouin, CEA, CNRS, Université Paris-Saclay, Gif-sur-Yvette, France. e. Paul Scherrer Institut, Villigen, Switzerland. f. KTH Royal Institute of Technology, Stockholm, Sweden. g. Materials Physics, KTH Royal Institute of Technology, Stockholm, Sweden h. II. Physikalisches Institut, Universitt zu Köln, Köln, Germany i. Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama, Japan

Since the seminal ideas of Berezinskii, Kosterlitz and Thouless, topological excitations have been at the heart of our understanding of a whole novel class of phase transitions. In most cases, those transitions are controlled by a single type of topological objects. There are, however, some situations, still poorly understood, where two dual topological excitations fight to control the phase diagram and the transition. Finding experimental realizations of such cases is thus of considerable interest. We show here that this situation occurs in BaCo 2 V 2 O 8 , a spin-1/2 Ising-like quasi-one-dimensional antiferromagnet, when subjected to a uniform magnetic field transverse to the Ising axis. Using neutron scattering experiments, we measure a drastic modification of the quantum excitations beyond a critical value of the magnetic field. This quantum phase transition is identified, through a comparison with theoretical calculations, to be a transition between two different types of solitonic topological object, which are captured by different components of the dynamical structure factor.

S. Guitteny, I. Mirebeau, P. Dalmas de Réotier, C. V. Colin, P. Bonville, F. Porcher, B. Grenier, C. Decorse and S. Petit 1 CEA, Centre de Saclay, DSM/IRAMIS/ Laboratoire Léon Brillouin, F-91191 Gif-sur-Yvette, France 2 Université Grenoble Alpes, INAC-SPSMS, 38000 Grenoble, France 3 CEA, INAC-SPSMS, 38000 Grenoble, France 4 Univ. Grenoble Alpes, Inst NEEL F-38000 Grenoble, France 5 CNRS, Inst NEEL, F-38000 Grenoble, France 6 CEA, Centre de Saclay, DSM/IRAMIS/ Service de Physique de l’Etat Condensé, F-91191 Gif-Sur-Yvette, France and 7 ICMMO, Université Paris-Sud, F-91400 Orsay France (Dated: November 6, 2018)

In the version of this Letter originally published, the year for ref. 30 was incorrectly listed as 2009; it should have been 2004. This has now been corrected.

We investigate magnetic properties of an $S$=1/2 quasi-one dimensional organic antiferromagnet, D-F$_{5}$PNN using magnetization measurements taken at temperatures as low as 0.5 K. Three distinct phases were observed consisting of uniform, dimerized (D), and incommensurate (I) spin structures in the magnetic field versus temperature plane, where a significant hysteresis appears between D-I transitions in the field scan measurements. A combination of magnon ($S$=1) and soliton ($S$=1/2) excitations have successfully reproduced the observed magnetic susceptibility. In addition, such excitations provide a reasonable interpretation of the temperature dependent electron spin resonance (ESR) spectra. By comparison with the theoretical study, we conclude that D-F$_{5}$PNN is an ideal compound for investigating the spin-Peierls transition.

We explore the spin dynamics emerging from the Néel phase of the chain compound antiferromagnet BaCo(2)V(2)O(8). Our inelastic neutron scattering study reveals unconventional discrete spin excitations, so-called Zeeman ladders, understood in terms of spinon confinement, due to the interchain attractive linear potential. These excitations consist of two interlaced series of modes, respectively, with transverse and longitudinal polarization. The latter, which correspond to a longitudinal fluctuation of the ordered moment, have no classical counterpart and are related to the zero-point fluctuations that weaken the ordered moment in weakly coupled quantum chains. Our analysis reveals that BaCo(2)V(2)O(8), with moderate Ising anisotropy and sizable interchain interactions, remarkably fulfills the conditions necessary for the observation of discrete long-lived longitudinal excitations.

We have studied the spin correlations with k = (1/2, 1/2, 1/2) propagation vector, which appear below 0.4 K in Tb2Ti2O7 spin liquid by combining powder neutron diffraction and specific heat on Tb2+xTi2-xO7+y samples with x = 0, 0.01, and -0.01. The k = (1/2, 1/2, 1/2) order clearly appears on all neutron patterns by subtracting a pattern at 1.2(1) K. Refining the subtracted patterns at 0.07 K yields two possible spin structures, with spin-ice-like and monopolelike correlations. Mesoscopic correlations involve Tb moments of 1 to 2 mu(B) ordered on a length scale of about 20 angstrom. In addition, long-range order involving a small spin component of 0.1 to 0.2 mu(B) is detected for the x = 0 and 0.01 samples showing a peak in the specific heat. Comparison with previous single-crystal data suggests that the (1/2, 1/2, 1/2) order settles in through nanometric spin textures with dominant spin-ice character and correlated orientations, analogous to nanomagnetic twins.

The quasi-one-dimensional antiferromagnetic Ising-like compound BaCo2V2O8 has been shown to be describable by the Tomonaga-Luttinger liquid theory in its gapless phase induced by a magnetic field applied along the Ising axis. Above 3.9 T, this leads to an exotic field-induced low-temperature magnetic order, made of a longitudinal incommensurate spin-density wave, stabilized by weak interchain interactions. By single-crystal neutron diffraction we explore the destabilization of this phase at a higher magnetic field. We evidence a transition at around 8.5 T towards a more conventional magnetic structure with antiferromagnetic components in the plane perpendicular to the magnetic field. The phase diagram boundaries and the nature of this second field-induced phase are discussed with respect to previous results obtained by means of nuclear magnetic resonance and electron spin resonance, and in the framework of the simple model based on the Tomonaga-Luttinger liquid theory, which obviously has to be refined in this complex system.

A comprehensive experimental investigation of a PrPtAl single crystal concludes that it displays modulated magnetic order driven by quantum critical phenomena. The transition between paramagnetism and ferromagnetism is the paradigm for a continuous phase transition at finite temperature. When such a transition is tuned to zero temperature in clean materials, the growth of low-energy zero-point fluctuations potentially drives an array of phenomena, including the formation of novel states such as non-conventional superconductivity. Experimentally, the growth of the fluctuations, however, is curtailed and the transition becomes discontinuous as its temperature is reduced. This is understood to arise from non-analytic corrections to the free energy that always occur1. In a recent theory2,3, changes of the excitation spectrum are self-consistently considered alongside the ground state. This analysis reveals that a transition to a new state may be an alternative outcome. As the excitation spectrum (the ‘disorder’) is pivotal to promoting the new ‘order’ this mechanism is referred to as ‘order by disorder’. Here, we report the discovery of modulated order in PrPtAl, consistent with complex spirals, at the boundary between paramagnetism and ferromagnetism, giving the first clear experimental realization of such a state.

We use nuclear magnetic resonance to map the complete low-temperature phase diagram of the antiferromagnetic Ising-like spin-chain system BaCo2V2O8 as a function of the magnetic field applied along the chains. In contrast to the predicted crossover from the longitudinal incommensurate to the transverse antiferromagnetic ordered phase, we find a sequence of three magnetically ordered phases between the critical fields 3.8 and 22.8 T. Their origin is traced to the giant magnetic field dependence of the total effective coupling between spin chains, found to vary by a factor of 24. We explain this interesting phenomenon as emerging from a combination of non-trivially coupled spin chains and incommensurate spin fluctuations in the chains treated as Tomonaga-Luttinger liquids.

We determine the low-field ordered magnetic phases of the S = 1 dimerized antiferromagnet Ba3Mn2O8 using single-crystal neutron diffraction. We find that for magnetic fields between mu H-0 = 8.80 T and 10.56 T applied along the [1 (1) over bar0] direction the system exhibits spin density wave order with incommensurate wave vectors of type (eta,eta,epsilon). For mu H-0 > 10.56 T, the magnetic order changes to a spiral phase with incommensurate wave vectors only along the [hh0] direction. For both field-induced ordered phases, the magnetic moments are lying in the plane perpendicular to the field direction. The nature of these two transitions is fundamentally different: the low-field transition is a second-order transition to a spin density wave ground state, while the one at higher field, toward the spiral phase, is of first order.

In the effective Ising spin-1/2 antiferromagnetic chain system BaCo$_2$V$_2$O$_8, the magnetic-field influence is highly anisotropic. For magnetic fields along the easy axis $c$, the Néel order is strongly suppressed already for low fields and an incommensurate order is entered above 4 T. We present a detailed study of the magnetic phase diagrams for different magnetic field directions, which are derived from magnetization data, high-resolution thermal expansion and magnetostriction measurements as well as from the thermal conductivity. Zero-field thermal expansion data reveal that the magnetic transition is accompanied by an orthorhombic distortion within the $ab$ plane. Under ambient conditions the crystals are heavily twinned, but the domain orientation can be influenced either by applying uniaxial pressure or a magnetic field along the [100] direction. In addition, our data reveal a pronounced in-plane magnetic anisotropy for fields applied within the $ab$ plane. For $H || [110]$, the magnetic field influence on T$_N$ is weak, whereas for magnetic fields applied along [100], T$_N$ vanishes at about 10 T and the zero-field Néel order is completely suppressed as is confirmed by neutron diffraction data. The second-order phase transition strongly suggests a quantum critical point being present at $H\simeq 10$ T parallel [100], where the Néel order probably changes to a spin-liquid state.

BaCo2V2O8 is a nice example of a quasi-one-dimensional quantum spin system that can be described in terms of Tomonaga-Luttinger liquid physics. This is explored in the present study where the magnetic field-temperature phase diagram is thoroughly established up to 12 T using single-crystal neutron diffraction. The transition from the Neel phase to the incommensurate longitudinal spin density wave (LSDW) phase through a first-order transition, as well as the critical exponents associated with the paramagnetic-Neel phase transition, and the magnetic order both in the Neel and in the LSDW phase are determined, thus providing a stringent test for the theory. DOI: 10.1103/PhysRevB.87.054408

Er2Ti2O7 is believed to be a realization of an XY antiferromagnet on a frustrated lattice of corner-sharing regular tetrahedra. It is presented as an example of the order-by-disorder mechanism in which fluctuations lift the degeneracy of the ground state, leading to an ordered state. Here we report detailed measurements of the low-temperature magnetic properties of Er2Ti2O7, which displays a second-order phase transition at T-N similar or equal to 1.2 K with coexisting short- and long-range orders. Magnetic susceptibility studies show that there is no spin-glass-like irreversible effect. Heat capacity measurements reveal that the paramagnetic critical exponent is typical of a 3-dimensional XY magnet while the low-temperature specific heat sets an upper limit on the possible spin-gap value and provides an estimate for the spin-wave velocity. Muon spin relaxation measurements show the presence of spin dynamics in the nanosecond time scale down to 21 mK. This time range is intermediate between the shorter time characterizing the spin dynamics in Tb2Sn2O7, which also displays long- and short-range magnetic order, and the time scale typical of conventional magnets. Hence the ground state is characterized by exotic spin dynamics. We determine the parameters of a symmetry-dictated Hamiltonian restricted to the spins in a tetrahedron, by fitting the paramagnetic diffuse neutron scattering intensity for two reciprocal lattice planes. These data are recorded in a temperature region where the assumption that the correlations are limited to nearest neighbors is fair.