Theory of field-induced quantum phase transition in spin dimer system Ba3_3Cr2_2O8_8

Motivated by recent experiments on Ba$_3$Cr$_2$O$_8$, we propose a theory describing low-temperature properties in magnetic field $h$ of dimer spin-$\frac12$ systems on a stacked triangular lattice with spatially anisotropic exchange interactions. Considering the interdimer interaction as a perturbation we derive in the second order the elementary excitations (triplon) spectrum and the effective interaction between triplons at the quantum critical point $h=h_c$ separating the paramagnetic phase ($h<h_c$) and a magnetically ordered one ($h_c<h<h_s$, where $h_s$ is the saturation field). Expressions are derived for $h_c(T)$ and the staggered magnetization $M_\perp(h)$ at $h$ close to $h_c$. We apply the theory to Ba$_3$Cr$_2$O$_8$ and determine exchange constants of the model by fitting the triplon spectrum obtained experimentally. It is demonstrated that in accordance with experimental data the system follows the 3D BEC scenario at $T<1$ K only due to a pronounced anisotropy of the spectrum near its minimum. Our expressions for $h_s$, $h_c(T)$ and $M_\perp(h)$ fit well available experimental data.Comment: 9 pages, 6 figure

Cascades of phase transitions in spiral magnets caused by dipolar forces

We present a mean-field theory describing the influence of long-range dipolar forces on the temperature transition from the paramagnetic to ordered phases in frustrated Heisenberg spiral magnets. It is shown that the dipolar interaction produces a cascade of first- and second- order phase transitions between the paramagnetic and the spiral states upon temperature decreasing. Depending on system parameters, the following intermediate phases can arise: an incommensurate and a commensurate sinusoidally modulated states, spiral phases in which perpendicular spin components have different amplitudes and are modulated with the same and with different wave vectors. We distinguish six possible sequences of phase transitions upon temperature decreasing at least four of which were observed before experimentally in specific compounds. It is found that the action of dipolar forces cannot always be modeled even qualitatively by small one-ion anisotropic spin interactions. We demonstrate that the dipolar interaction is responsible for successive phase transitions in the triangular-lattice multiferroic MnI$_2$: almost all available experimental findings are described quantitatively within the mean-field theory by taking into account the exchange, the dipolar and small symmetry-allowed anisotropic spin interactions.Comment: 12 pages, 5 figure

Spiral plane flops in frustrated helimagnets in external magnetic field

We discuss theoretically frustrated Heisenberg spiral magnets in magnetic field $\bf H$. We demonstrate that small anisotropic spin interactions (single-ion biaxial anisotropy or dipolar forces) select the plane in which spins rotate (spiral plane) and can lead to the spiral plane flop upon in-plane field increasing. Expressions for the critical fields $H_{flop}$ are derived. It is shown that measuring of $H_{flop}$ is an efficient and simple method of quantifying the anisotropy in the system (as the measurement of spin-flop fields in collinear magnets with axial anisotropy). Corresponding recent experiments are considered in spiral magnets some of which are multiferroics of spin origin.Comment: 8 pages, 1 figur

Control of multiferroic order by magnetic field in frustrated helimagnet MnI2_2. Theory

We provide a theoretical description of frustrated multiferroic $\rm MnI_2$ with a spiral magnetic ordering in magnetic field $\bf h$. We demonstrate that subtle interplay of exchange coupling, dipolar forces, hexagonal anisotropy, and the Zeeman energy account for the main experimental findings observed recently in this material (Kurumaji, et al., Phys.\ Rev.\ Lett.\ {\bf 106}, 167206 (2011)). We describe qualitatively the non-trivial evolution of electric polarization $\bf P$ upon $\bf h$ rotation, changing $\bf P$ direction upon $h$ increasing, and disappearance of ferroelectricity at $h>h_c$, where $h_c$ is smaller than the saturation field.Comment: 5 pages, 5 figure

Cubic B20 helimagnets with quenched disorder in magnetic field

We theoretically address the problem of cubic B20 helimagnets with small concentration ${c \ll 1}$ of defect bonds in external magnetic field $\bf H$, which is relevant to mixed B20 compounds at small dopant concentrations. We assume that Dzyaloshinskii-Moriya interaction and the exchange coupling constant are changed on imperfect bonds which leads to distortion of the conical spiral ordering. In one-impurity problem, we find that the distortion of the spiral pitch is long-ranged and it is governed by the Poisson equation for an electric dipole. The variation of the cone angle is described by the screened Poisson equation for two electric charges with the screening length being of the order of the spiral period. We calculate corrections to the spiral vector and to the cone angle at finite $c$. The correction to the spiral vector is shown to be independent of $H$. We demonstrate that diffuse neutron scattering caused by disorder appears in the elastic cross section as power-law decaying tails centered at magnetic Bragg peaks.Comment: 8 pages, 2 figure

Effective interactions in a quantum Bose-Bose mixture

We generalize the Beliaev diagrammatic theory of an interacting spinless Bose-Einstein condensate to the case of a binary mixture. We derive a set of coupled Dyson equations and find analytically the Green's functions of the system. The elementary excitation spectrum consists of two branches, one of which takes the characteristic parabolic form in the limit of a spin-independent interaction. We observe renormalization of the magnon mass and the spin-wave velocity due to the Andreev-Bashkin entrainment effect. For a 3D weakly-interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to the second-quantized Hamiltonian in which the microscopic two-body potentials in each channel are replaced by the corresponding off-shell scattering amplitudes. The superfluid drag density can be calculated by considering a mixture of phonons and magnons interacting via the effective potentials. We show that this problem is identical to the second-order perturbative treatment of a Bose polaron. In 2D the drag contributes to the magnon dispersion already in the first approximation. Our consideration provides a basis for systematic study of emergent phases in quantum degenerate Bose-Bose mixtures.Comment: 14 pages, 5 figure

Spiral magnets with Dzyaloshinskii-Moriya interaction containing defect bonds

We present a theory describing spiral magnets with Dzyaloshinskii-Moriya interaction (DMI) subject to bond disorder at small concentration $c$ of defects. It is assumed that both DMI and exchange coupling are changed on imperfect bonds. Qualitatively the same physical picture is obtained in two models which are considered in detail: B20 cubic helimagnets and layered magnets in which DMI leads to a long-period spiral ordering perpendicular to layers. We find that the distortion of the spiral magnetic ordering around a single imperfect bond is long-range: values of additional turns of spins decay with the distance $r$ to the defect as $1/r^2$ being governed by the Poisson's equation for electric dipole. At finite concentration of randomly distributed imperfect bonds, we calculate correction to the spiral vector. We show that this correction can change the sign of spin chirality even at $c\ll1$ if defects are strong enough. It is demonstrated that impurities lead to a diffuse elastic neutron scattering which has power-law singularities at magnetic Bragg peaks positions. Then, each Bragg peak acquires power-law decaying tails. Corrections are calculated to the magnon energy and to its damping caused by scattering on impurities.Comment: 19 pages, 7 figure

Phase competition in frustrated anisotropic antiferromagnet in strong magnetic field

We discuss theoretically a frustrated Heisenberg antiferromagnet in magnetic field close to the saturation one. It is demonstrated that a small biaxial anisotropy and/or the magnetic dipolar interaction produce a delicate balance between phases with a commensurate canted, incommensurate helical (conical), and fan spin orderings. As a result, different sequences of phase transitions are realized depending on values of these small anisotropic interactions. We derive analytical expressions for critical fields and ground-state energies of the phases which are in a quantitative agreement with our and previous Monte-Carlo simulations.Comment: 10 pages, 2 figure

Self-localization of magnons and magnetoroton in a binary Bose-Einstein condensate

We consider a two-component Bose-condensed mixture characterized by positive s-wave scattering lengths. We assume equal densities and intra-species interactions. By doing the Bogoliubov transformation of an effective Hamiltonian we obtain the lower energy magnon dispersion incorporating the superfluid entrainment between the components. We argue that p-wave pairing of distinct bosons should be accompanied by self-localization of magnons and formation of a magnetoroton. We demonstrate the effect on a model system of particles interacting via step potentials.Comment: 5 pages, 1 figur

Formation of spiral ordering by magnetic field in frustrated anisotropic antiferromagnets

We discuss theoretically phase transitions in frustrated antiferromagnets with biaxial anisotropy or dipolar forces in magnetic field applied along the easy axis at $T=0$. There are well-known sequences of phase transitions upon the field increasing: the conventional spin-flop transition and the flop of the spiral plane at strong and weak easy-axis anisotropy, respectively. We argue that much less studied scenarios can appear at moderate anisotropy in which the magnetic field induces transitions of the first order from the collinear state to phases with spiral orderings. Critical fields of these transitions are derived in the mean-field approximation and the necessary conditions are found for the realization of these scenarios. We show that one of the considered sequences of phase transitions was found in multiferroic MnWO$_4$ both experimentally and numerically (in a relevant model) and our theory reproduces quantitatively the numerical findings.Comment: 6 pages, 2 figure