We present a theoretical study of field-induced magnetic phases in the honeycomb Kitaev-Heisenberg model, which is believed to describe the essential physics of Mott insulators with strong spin-orbit coupling such as $A_2$IrO$_3$ and $α$-RuCl$_3$. We obtain a finite temperature phase diagram based on extensive Monte Carlo simulations and analytical calculations. We show that, while Zeeman coupling favors a symmetric non-coplanar magnetic order, thermal fluctuations enhances the stability of a collinear zigzag phase that breaks the rotational symmetry of the lattice. Our large-scale simulations also uncover intriguing commensurate-incommensurate transitions and multiple-$\mathbf Q$ incommensurate phases at high field. Experimental implications are also discussed.
Low temperature dependence of specific heat of one- dimensional multicomponent systems at the commensurate- incommensurate phase transition point is studied. It is found that for canonical systems, with a fixed total number of particles, low temperature specific heat linearly depends on temperature with a diverging prefactor.
We analyze the anomalous behavior in hole-doped cuprates near 1/8 doping in terms of the commensurate-incommensurate transition of a stripe phase. Based on an effective Ginzburg-Landau theory appropriate for weak pinning, we calculate the commensurate-incommensurate transition point and the energies of the phason and amplitudon collective modes. Using experimentally available parameters, we estimate the phason gap (pinning frequency), the conductivity and the contribution of the phason mode to the dielectric function.
X-ray scattering measurements on single crystals of TiOCl reveal the presence of commensurate dimerization peaks within both the incommensurate spin-Peierls phase and the so-called pseudogap phase above T_c2. This scattering is relatively narrow in Q-space indicating long correlation lengths exceeding ~ 100 A below T* ~ 130 K. It is also slightly shifted in Q relative to that of the commensurate long range ordered state at the lowest temperatures, and it coexists with the incommensurate Bragg peaks below T_c2. The integrated scattering over both commensurate and incommensurate positions evolve…
Neutron diffraction has been used to determine the magnetic structure of Na$_8$Cu$_5$O$_{10}$, a stoichiometric compound containing chains based on edge-sharing CuO$_4$ plaquettes. The chains are doped with 2/5 hole per Cu site and exhibit long-range commensurate charge order with an onset well above room temperature. Below $T_N = 23$ K, the neutron data indicate long-range collinear magnetic order with a spin density modulation whose propagation vector is commensurate along and incommensurate perpendicular to the chains. Competing interchain exchange interactions are discussed as a possible o…
We report an observation of a commensurate-incommensurate phase transition in the Dzyaloshinskii-Moriya spiral antiferromagnet Ba_2 Cu Ge_2 O_7. The transition is induced by an external magnetic field applied along the c-axis of the tetragonal structure, i. e., in the plane of spin rotation. Bulk magnetic measurements and neutron diffraction experiments show that the transition occurs in a critical field Hc=2.1T. Experimental results for the period of the magnetic structure and magnetization as functions of magnetic field are in quantitative agreement with our exact analytical solution for Dzy…
Neutron scattering studies of single-crystal LiNiPO$_4$ reveal a spontaneous first-order commensurate-incommensurate magnetic phase transition. Short- and long-range incommensurate phases are intermediate between the high temperature paramagnetic and the low temperature antiferromagnetic phases. The modulated structure has a predominant antiferromagnetic component, giving rise to satellite peaks in the vicinity of the fundamental antiferromagnetic Bragg reflection, and a ferromagnetic component giving rise to peaks at small momentum-transfers around the origin at $(0,\pm Q,0)$. The wavelength …
We present calculations of the magnetic ground state of Cs_2CuCl_4 in an applied magnetic field, with the aim of understanding the commensurately ordered state that has been discovered in recent experiments. This layered material is a realization of a Heisenberg antiferromagnet on an anisotropic triangular lattice. Its behavior in a magnetic field depends on field orientation, because of weak Dzyaloshinskii-Moriya interactions.We study the system by mapping the spin-1/2 Heisenberg Hamiltonian onto a Bose gas with hard core repulsion. This Bose gas is dilute, and calculations are controlled, cl…
The behavior in an external magnetic field is studied for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate-incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent. A scenario for the transition from one to two space dimensions for the integrable multichain models is proposed. The similarities in the external field behavior for the quant…
Materials that realize Kitaev spin models with bond-dependent anisotropic interactions have long been searched for, as the resulting frustration effects are predicted to stabilize novel forms of magnetic order or quantum spin liquids. Here we explore the magnetism of $γ$-Li$_2$IrO$_3$, which has the topology of a 3D Kitaev lattice of inter-connected Ir honeycombs. Using resonant magnetic x-ray diffraction we find a complex, yet highly-symmetric incommensurate magnetic structure with non-coplanar and counter-rotating Ir moments. We propose a minimal Kitaev-Heisenberg Hamiltonian that naturally …
Single-crystals of Cr and Cr3%Mn doped with ca. 0.2 at.% 119Sn were studied by means of 119Sn-site Mössbauer spectroscopy. Mössbauer spectra recorded in the temperature range of 78-300 K were analyzed using a hyperfine field distribution method. Derived therefrom values of a center shift, CS, analyzed in terms of the Debye model yielded values of the Debye temperature, T_D = 477(56)K for Cr and T_D=282(16)K for Cr3%Mn. The difference in the T_D-value can be regarded as evidence that a spin-phonon interaction is different for the incommensurate and commensurate antiferromagnetic structure of ch…
Synchrotron x-ray diffraction and resonant magnetic scattering experiments on single crystal DyMnO3 have been carried out between 4 and 40 K. Below TN(Dy) = 5K, the Dy magnetic moments order in a commensurate structure with propagation vector 0.5 b*. Simultaneous with the Dy magnetic ordering, an incommensurate lattice modulation with propagation vector 0.905 b* evolves while the original Mn induced modulation is suppressed and shifts from 0.78 b* to 0.81 b*. This points to a strong interference of Mn and Dy induced structural distortions in DyMnO3 besides a magnetic coupling between the Mn an…
The recently discovered coexistence of incommensurate antiferromagnetic neutron scattering peaks and commensurate resonance in underdoped YBa$_2$Cu$_3$O$_{6+x}$ is calling for an explanation. Within the t-J model, the doping and energy dependence of the spin dynamics of the underdoped bilayer cuprates in the normal state is studied based on the fermion-spin theory by considering the bilayer interactions. Incommensurate peaks are found at $[(1\pmδ)π,π] $ and $[π,(1\pmδ)π]$ at low energies with $δ$ initially increasing with doping at low dopings and then saturating at higher dopings. These incom…
Single crystal neutron diffraction studies have been performed on the S = 3/2 kagome staircase compound Co3V2O8 with a magnetic field applied along the magnetization easy-axis (H || a). Previous zero field measurements [Y. Chen, et al., Phys. Rev. B 74, 014430 (2006)] reported a rich variety of magnetic phases, with a ferromagnetic ground state as well as incommensurate, transversely polarized spin density wave (SDW) phases (with a propagation vector of k = (0 delta 0)) interspersed with multiple commensurate lock-in transitions. The magnetic phase diagram with H || a adds further complexity. …
The theoretical inception of the Kitaev honeycomb model has had defining influence on the experimental hunt for quantum spin liquids, bringing unprecedented focus onto the synthesis of materials with bond-directional interactions. Numerous Kitaev materials, which are believed to harbor ground states parametrically close to the Kitaev spin liquid, have been investigated since. Yet, in these materials the Kitaev interaction often comes hand in hand with off-diagonal $Γ$ interactions -- with the competition of the two potentially giving rise to a magnetically ordered ground state. In an attempt t…
We investigate the physical properties of two coupled chains of electrons, with a nearly half-filled band, as a function of the interchain hopping t_\perp and the doping. We show that upon doping, the system undergoes a metal-insulator transition well described by a commensurate-incommensurate transition. By using bosonization and renormalization we determine the full phase diagram of the system, and the physical quantities such as the charge gap. In the commensurate phase two different regions, for which the interchain hopping is relevant and irrelevant exist, leading to a confinement-deconfi…
The melting process of the orbital order in Pr0.5Ca0.5MnO3 single crystal has been studied in detail as a function of temperature by neutron diffraction. It is demonstrated that a commensurate-incommensurate (C-IC) transition of the orbital ordering takes place in a bulk sample, being consistent with the electron diffraction studies. The lattice structure and the transport properties go through drastic changes in the IC orbital ordering phase below the charge/orbital ordering temperature Tco/oo, indicating that the anomalies are intimately related to the partial disordering of the orbital orde…
We present a theoretical study of the response of $β$-$\text{Li}_2\text{IrO}_3$ under external magnetic fields in the $ab$, $bc$ and $ac$ crystallographic planes. The results are based on the minimal nearest-neighbor $J$-$K$-$Γ$ model and reveal a rich intertwining of field-induced phases and magnetic phase transitions with distinctive signatures that can be probed directly via torque magnetometry. Most saliently, we observe: i) an unusual reentrance of the incommensurate counter-rotating order for fields in the $ab$-plane, and ii) a set of abrupt torque discontinuities which are particularly …
We study the evolution of the d-wave neutron cross-section with variable frequency ωand fixed T (below and above Tc) in two different cuprate families. The evolution from incommensurate to commensurate to incommensurate peaks is rather generic within an RPA-like scheme. This behavior seems to be in reasonable accord with experiments, and may help distinguish between this and the "stripe" scenario.
We report an observation of a commensurate-incommensurate phase transition in a Dzyaloshinskii-Moriya spiral magnet Ba_2CuGe_2O_7. The transition is induced by applying a magnetic field in the plane of spin rotation. In this experiment we have direct control over the strength of the commensurate potential, while the preferred incommensurate period of the spin system remains unchanged. Experimental results for the period of the soliton lattice and bulk magnetization as a function of external magnetic field are in quantitative agreement with theory.
The pressure ($p$) -- temperature ($T$) phase diagram for microscopic magnetism in the multiferroic compound HoMn$_{2}$O$_{5}$ was established using neutron diffraction measurements under a hydrostatic pressure up to 1.25 GPa. At ambient pressure, incommensurate--commensurate--incommensurate magnetic phase transitions occur successively with decreasing temperature. Upon applying pressure, the incommensurate phase at the lowest temperature almost decreases and the commensurate phase appears. The $p$ -- $T$ phase diagram established shows excellent agreement with the recently reported $p$ -- $T$…
We study untwisted heterobilayers of ferromagnetic and antiferromagnetic van der Waals materials, with in particular a Dzyaloshinskii-Moriya interaction in the ferromagnetic layer. A continuum low energy field theory is utilized to study such systems. We develop a phase diagram as a function of the strength of inter-layer exchange and Dzyaloshinskii-Moriya interactions, combining perturbative and strong coupling analyses with numerical simulations using Landau-Lifshitz-Gilbert equations. Various moiré-periodic commensurate phases are found, and the commensurate-incommensurate transition is dis…
The layered honeycomb magnet $α$-Li$_2$IrO$_3$ has been theoretically proposed as a candidate to display novel magnetic behaviour associated with Kitaev interactions between spin-orbit entangled $j_{\rm eff}=1/2$ magnetic moments on a honeycomb lattice. Here we report single crystal magnetic resonant x-ray diffraction combined with powder magnetic neutron diffraction to reveal an incommensurate magnetic order in the honeycomb layers with Ir magnetic moments counter-rotating on nearest-neighbour sites. This type of magnetic structure has not been reported experimentally before in honeycomb magn…
The zero temperature phase diagram of the mono-axial chiral helimagnet in the magnetic field plane formed by the components parallel and perpendicular to the helical axis is thoroughly analyzed. The nature of the transition to the commensurate state depends on the angle between the field and the helical axis. For field directions close to the directions parallel or perpendicular to the helical axis the transition is continuous, while for intermediate angles the transition is discontinuous and the incommensurate and commensurate states coexist on the transition line. The continuous and disconti…
Magnetic properties of single crystalline SmRu$_{2}$Al$_{10}$ have been investigated by electrical resistivity, magnetic susceptibility, and specific heat. We have confirmed the successive magnetic phase transitions at $T_{\text{N}}=12.3$ K and $T_{\text{M}}=5.6$ K. Resonant x-ray diffraction has also been performed to study the magnetic structures. Below $T_{\text{N}}$, the Sm$^{3+}$ moments order in an incommensurate structure with $q_1=(0, 0.759, 0)$. The magnetic moments are oriented along the orthorhombic $b$ axis, which coincides with the magnetization easy axis in the paramagnetic phase…
We study the evolution of the neutron cross-section with variable frequency $ω$ and fixed $T$ below $T_c$ in two different cuprate families. Our calculations, which predominantly probe the role of d-wave pairing, lead to generic features, independent of Fermi surface shapes. Among our findings, reasonably consistent with experiment, are (i) for $ω$ near the gap energy $Δ$, both optimal {LaSrCuO} and slightly underdoped YBCO exhibit (comparably) incommensurate peaks (ii) peak sharpening below $T_c$ is seen in {LaSrCuO}, (iii) quite generically, a frequency evolution from incommensurate to comme…
The B20-type cobalt germanide CoGe was investigated by measuring the specific heat, resistivity, and $^{59}$Co nuclear magnetic resonance (NMR). We observed a phase transition at $T_Q=13.7$ K, evidenced by a very narrow peak of the specific heat and sharp changes of the nuclear spin-spin ($T_2^{-1}$) and spin-lattice ($T_1^{-1}$) relaxation rates. The fact that the entropy release is extremely small and the Knight shift is almost independent of temperature down to low temperatures as anticipated in a paramagnetic metal indicates that the $T_Q$ transition is of non-magnetic origin. In addition,…
Commensurate-incommensurate change on the one-dimensional S=1 bilinear-biquadratic model (${\cal H}(α)=\sum_i \{{\bf S}_i\cdot {\bf S}_{i+1} +α({\bf S}_i\cdot{\bf S}_{i+1})^2\}$) is examined. The gapped Haldane phase has two subphases (the commensurate Haldane subphase and the incommensurate Haldane subphase) and the commensurate-incommensurate change point (the Affleck-Kennedy-Lieb-Tasaki point, $α=1/3$). There have been two different analytical predictions about the static structure factor in the neighborhood of this point. By using the Sørensen-Affleck prescription, these static structure f…
As a method beyond the mean-field analysis, a matrix product state (MPS) with incommensurate periodicity is applied to detect phase transitions accompanied with periodicity change, where the incommensurate MPS is generated by acting local-spin-rotation operators with the incommensurate periodicity on a uniform MPS. As a commensurate/commensurate change, we calculate the partial ferro -- perfect ferro phase transition in the $S=1/2$ Heisenberg model and its critical exponent of the magnetization curve. As a commensurate/incommensurate change, we calculate the S=1 Heisenberg model with bilinear …
We performed elastic neutron scattering experiments on solid solution CeRh1-xCoxIn5 with x=0.4 to clarify the nature of the antiferromagnetic (AF) phase in the vicinity of the quantum critical point. We observed the incommensurate AF order below T_Nh=3.5 K. The structure of the incommensurate AF order is basically unchanged from that for pure CeRhIn5. We further found the evolution of a new commensurate AF order with the modulation of q_c=(1/2,1/2,1/2) below T_Nc=2.9 K. The volume-averaged moments for the incommensurate and commensurate AF phases are 0.38 mu_B/Ce and 0.21 mu_B/Ce, respectively…
We analyze the onset of incommensurabilities around the VBS point of the S=1 bilinear-biquadratic model. We propose a simple effective field theory which is capable of reproducing all known properties of the commensurate-incommensurate transition at the disorder point $θ_{\rm vbs}$. Moreover, the theory predicts another special point $θ_{\rm disp}$, distinct from the VBS point, where the Haldane gap behaves singularly. The ground state energy density is an analytic function of the model parameters everywhere, thus we do not have phase transitions in the conventional sense.
We have performed x-ray scattering measurements on single crystals of the doped spin-Peierls compound Ti(1-x)Sc(x)OCl (x = 0, 0.01, 0.03). These measurements reveal that the presence of non-magnetic dopants has a profound effect on the unconventional spin-Peierls behavior of this system, even at concentrations as low as 1%. Sc-doping suppresses commensurate fluctuations in the pseudogap and incommensurate spin-Peierls phases of TiOCl, and prevents the formation of a long-range ordered spin-Peierls state. Broad incommensurate scattering develops in the doped compounds near Tc2 ~ 93 K, and persi…
The nature of competition between incommensurate (IC) and commensurate (C) antiferromagnetic (AF) orders in UPd2Si2 was investigated by performing elastic neutron scattering experiments under uniaxial stress sigma. It is found that applying sigma along tetragonal [010] direction reduces the IC-AF order, and then stabilizes the C-AF order. The transition temperature from IC- to C-AF phases T_Nl is enhanced from 109 K (sigma=0) to 112.5 K (0.8 GPa), while the onset of IC-AF transition T_Nh is unchanged from 132 K under sigma. In addition, c-axis component q_z of the IC-AF modulation at 115 K als…
We investigate the interplay between commensurate lock-in and incommensurate supersolid phases of the hardcore bosons at half-filling with anisotropic nearest-neighbor hopping and repulsive interactions on triangular lattice. We use numerical quantum and variational Monte Carlo as well as analytical Schwinger boson mean-field analysis to establish the ground states and phase diagram. It is shown that, for finite size systems, there exist a series of jumps between different supersolid phases as the anisotropy parameter is changed. The density ordering wavevectors are locked to commensurate valu…
Incommensurate charge order in hole-doped oxides is intertwined with exotic phenomena such as colossal magnetoresistance, high-temperature superconductivity, and electronic nematicity. Here, we map at atomic resolution the nature of incommensurate order in a manganite using scanning transmission electron microscopy at room temperature and cryogenic temperature ($\sim$ 93K). In diffraction, the ordering wavevector changes upon cooling, a behavior typically associated with incommensurate order. However, using real space measurements, we discover that the underlying ordered state is lattice-comme…
Synchrotron X-ray diffraction investigations of two single crystals of Na_xCoO_2 from different batches with composition x = 0.525-0.530 reveal homogeneous incommensurate sodium ordering with propagation vector (0.53 0.53 0) at room-temperature. The incommensurate (qq0) superstructure exists between 220 K and 430 K. The value of q varies between q = 0.514 and 0.529, showing a broad plateau at the latter value between 260 K and 360 K. On cooling, unusual reversible phase segregation into two volume fractions is observed. Below 220 K, one volume fraction shows the well-known commensurate orthorh…
Field-induced transitions from incommensurate to commensurate phases in helical antiferromagnets
National Research University Higher School of Economics（国立高等经济大学）；Petersburg Nuclear Physics Institute named by B.P. Konstantinov of National Research Center “Kurchatov Institute”（国立库尔恰托夫研究所彼得堡核物理研究所）
A scheme for making ab-initio calculations of the dynamic paramagnetic spin susceptibilities of solids at finite temperatures is described. It is based on Time-Dependent Density Functional Theory and employs an electronic multiple scattering formalism. Incommensurate and commensurate anti-ferromagnetic spin fluctuations in paramagnetic Cr and compositionally disordered Cr95V5 and Cr95Re5 alloys are studied together with the connection with the nesting of their Fermi surfaces. We find that the spin fluctuations can be described rather simply in terms of an overdamped oscillator model. Good agre…
Sr$_2$RuO$_4$, an unconventional superconductor, is known to possess an incommensurate spin density wave instability driven by Fermi surface nesting. Here we report a static spin density wave ordering with a commensurate propagation vector $q_c$ = (0.25 0.25 0) in Fe-doped Sr$_2$RuO$_4$, despite the magnetic fluctuations persisting at the incommensurate wave vectors $q_{ic}$ = (0.3 0.3 L) as in the parent compound. The latter feature is corroborated by the first principles calculations, which show that Fe substitution barely changes the nesting vector of the Fermi surface. These results sugges…
The bond-dependent Kitaev model on the honeycomb lattice with anyonic excitations has recently attracted considerable attention. However, in solid state materials other spin interactions are present, and among such additional interactions, the off-diagonal symmetric Gamma interaction, another type of bond-dependent term, has been particularly challenging to fully understand. A minimal Kitaev-Gamma (KG) model has been investigated by various numerical techniques under a magnetic field, but definite conclusions about field-induced spin liquids remain elusive and one reason may lie in the limited…
The Fe1+y Te1-x Sex compounds belong to the family of iron-based high temperature superconductors, in which superconductivity often appears upon doping antiferromagnetic parent compounds. Unlike other Fe-based superconductors (in which the antiferromagnetic order is at the Fermi surface nesting wavevector [1/2,1/2,1]), the Fe1+y Te1-x Sex parent compound Fe1+y Te orders at a different wavevector, [1/2, 0, 1/2]. Furthermore, the ordering wavevector depends on y, the occupation of interstitial sites with excess iron; the origin of this behavior is controversial. Using inelastic neutron scatterin…
We investigate the classical chiral Ashkin-Teller model on a square lattice with the corner transfer matrix renormalisation group (CTMRG) algorithm. We show that the melting of the period-4 phase in the presence of a chiral perturbation takes different forms depending on the coefficient of the four-spin term in the Ashkin-Teller model. Close to the clock limit of two decoupled Ising models, the system undergoes a two-step commensurate-incommensurate transition as soon as the chirality is introduced, with an intermediate critical floating phase bounded by a Kosterlitz-Thouless transition at hig…
We report results of 23Na and 75As nuclear magnetic resonance (NMR) experiments on a self-flux grown high-quality single crystal of stoichiometric NaFeAs. The NMR spectra revealed a tetragonal to twinned-orthorhombic structural phase transition at T_O = 57 K and an antiferromagnetic (AF) transition at T_AF = 45 K. The divergent behavior of nuclear relaxation rate near T_AF shows significant anisotropy, indicating that the critical slowing down of stripe-type AF fluctuations are strongly anisotropic in spin space. The NMR spectra at low enough temperatures consist of sharp peaks showing a comme…
Recent scattering experiments in the 3D Kitaev magnet $β$-Li$_2$IrO$_3$ have shown that a relatively weak magnetic field along the crystallographic ${\bf b}$-axis drives the system from its incommensurate counter-rotating order to a correlated paramagnet, with a significant uniform `zigzag' component superimposing the magnetization along the field. Here it is shown that the zigzag order is not emerging from its linear coupling to the field (via a staggered, off-diagonal element of the ${\bf g}$-tensor), but from its intertwining with the incommensurate order and the longitudinal magnetization.…
Magnetic susceptibility, specific heat, and neutron powder diffraction measurements have been performed on polycrystalline Li2Co(WO4)2 samples. Under zero magnetic field, two successive magnetic transitions at TN1 ~ 9.4 K and TN2 ~ 7.4 K are observed. The magnetic ordering temperatures gradually decrease as the magnetic field increases. Neutron diffraction reveals that Li2Co(WO4)2 enters an incommensurate magnetic state with a temperature dependent k between TN1 and TN2. The magnetic propagation vector locks-in to a commensurate value k = (1/2, 1/4, 1/4) below TN2. The antiferromagnetic struct…
Detailed spin-wave spectra of magneto-electric LiNiPO4 have been measured by neutron scattering at low temperatures in the commensurate (C) antiferromagnetic (AF) phase with ordering temperature 20.8 K. An anomalous low-energy mode is observed at the modulation vector of the incommensurate (IC) AF phase appearing above the 20.8 K. A linear spin-wave model based on Heisenberg exchange couplings and single ion anisotropies accounts for all the observed spin-wave dispersions and intensities. Along the b axis an unusually strong next-nearest-neighbor AF coupling competes with the dominant nearest-…
We have synthesized single crystalline sample of Mn$_2$V$_2$O$_7$ using floating zone technique and investigated the ground state using magnetic susceptibility, heat capacity and neutron diffraction. Our magnetic susceptibility and heat capacity reveal two successive magnetic transitions at $T_{N1} =$ 19 K and $T_{N2} =$ 11.8 K indicating two distinct magnetically ordered phases. The single crystal neutron diffraction study shows that in the temperature ($T$) range 11.8 K $\le T \le$ 19 K the magnetic structure is commensurate with propagation vector $k_1 = (0, 0.5, 0)$, while upon lowering te…
We prove numerically and by dualities the existence of modulated, commensurate and incommensurate states of topological quantum matter in simple systems of parafermions, motivated by recent proposals for the realization of such systems in mesoscopic arrays. In two space dimensions, we obtain the simplest representative of a topological universality class that we call Lifshitz. It is characterized by a topological tricritical point where a non-locally ordered homogeneous phase meets a disordered phase and a third phase that displays modulations of a non-local order parameter.
In this work, we study strongly interacting spinor atoms in a lattice subject to a 2 dimensional (2d) anisotropic Rashba type of spin orbital coupling (SOC) and an Zeeman field. We find the interplay between the Zeeman field and the SOC provides a new platform to host rich and novel classes of quantum commensurate and in-commensurate phases, excitations and phase transitions. These commensurate phases include two collinear states at low and high Zeeman field, two co-planar canted states at Mirror reflected SOC parameters respectively. Most importantly, there are non-coplanar incommensurate Sky…
A comprehensive analysis of optical second harmonic generation (SHG) on an incommensurate (IC) magnetically ordered state is presented using multiferroic MnWO4 as model compound. Two fundamentally different SHG contributions coupling to the primary IC magnetic order or to secondary commensurate projections of the IC state, respectively, are distinguished. Whereas the latter can be described within the formalism of the 122 commensurate magnetic point groups the former involves a breakdown of the conventional macroscopic symmetry analysis because of its sensitivity to the lower symmetry of the l…
We consider the spin-1/2 two-leg ladders with ferromagnetic (FM) interactions along legs and rungs. Using the stochastic series expansion QMC method, we study the low-temperature magnetic behavior of the system. An isolated spin-1/2 FM two-leg ladder is in the gapped saturated FM phase at zero temperature. As soon as the spin-1/2 FM two-leg ladders are connected with antiferromagnetic (AFM) inter-ladder interaction, a first-order commensurate-incommensurate quantum phase transition occurs in the ground state magnetic phase diagram. In fact a jump in the magnetization curve is observed. We foun…
We have used the Path Integral Monte Carlo method to simulate a monolayer of molecular hydrogen on graphite above 1/3 submonolayer coverage. We find that at low temperature and as the coverage increases the system undergoes a series of transformations starting from the $\sqrt{3} \times \sqrt{3}$ commensurate solid near 1/3 coverage. First, a phase is formed which is characterized by a uniaxially compressed incommensurate solid with additional mass density modulations along the same direction which can be viewed as an ordered domain-wall solid with a characteristic domain-wall distance which de…
The structural distortion and magnetoelastic coupling induced through commensurate magnetism has been investigated by neutron diffraction in structurally related MnWO$_4$ and NaFe(WO$_4$)$_2$. Both systems exhibit a competition of incommensurate spiral and commensurate spin up-up-down-down ordering along the magnetic chains. In the latter commensurate phases, the alternatingly parallel and antiparallel arrangement of Fe$^{3+}$ respectively Mn$^{2+}$ moments leads to sizeable bond-angle modulation and thus to magnetic dimerization. For NaFe(WO$_4$)$_2$ this structural distortion has been determ…
Incommensurate spiral order is a common occurrence in frustrated magnetic insulators. Typically, all magnetic moments rotate uniformly, through the same wavevector. However the honeycomb iridates family Li2IrO3 shows an incommensurate order where spirals on neighboring sublattices are counter-rotating, giving each moment a different local environment. Theoretically describing its spin dynamics has remained a challenge: the Kitaev interactions proposed to stabilize this state, which arise from strong spin-orbit effects, induce magnon umklapp scattering processes in spin-wave theory. Here we pro…
Structural behaviour of PbMn$_{7}$O$_{12}$ has been studied by high resolution synchrotron X-ray powder diffraction. This material belongs to a family of quadruple perovskite manganites that exhibit an incommensurate structural modulation associated with an orbital density wave. It has been found that the structural modulation in PbMn$_{7}$O$_{12}$ onsets at 294 K with the incommensurate propagation vector $\mathbf{k}_s=(0,0,\sim2.08)$. At 110 K another structural transition takes place where the propagation vector suddenly drops down to a \emph{quasi}-commensurate value $\mathbf{k}_s=(0,0,2.0…
