Magnon BEC and various phases of 3D quantum helimagnets under high magnetic field

We study high-field phase diagram and low-energy excitations of three-dimensional quantum helimagnets. Slightly below the saturation field, the emergence of magnetic order may be viewed as Bose-Einstein condensation (BEC) of magnons. The method of dilute Bose gas enables a quantitative analysis of quantum effects in these helimagnets and thereby three phases are found: cone, coplanar fan and a phase-separated one. As an application, we map out the phase diagram of a 3D helimagnet which consists of frustrated J1-J2 chains as a function of frustration and an interchain coupling. Moreover, we also calculate the stability of the 2-magnon bound state to investigate the possibility of the bound-magnon BEC.Comment: 9pages, 6figure

Dilute-Bose-Gas Approach to ground state phases of 3D quantum helimagnets under high magnetic field

We study high-field phase diagram and low-energy excitations of three-dimensional quantum helimagnets. Slightly below the saturation field, the emergence of magnetic order may be mathematically viewed as Bose-Einstein condensation (BEC) of magnons. The method of dilute Bose gas enables an unbiased quantitative analysis of quantum effects in three-dimensional helimagnets and thereby three phases are found: cone, coplanar fan and an attraction-dominant one. To investigate the last phase, we extend the usual BEC approach so that we can handle 2-magnon bound states. In the case of 2-magnon BEC, the transverse magnetization vanishes and long-range order occurs in the quadrupolar channel (spin-nematic phase). As an application, we map out the phase diagram of a 3D helimagnet which consists of frustrated J1-J2 chains coupled by an interchain interaction J3.Comment: 4pages, 3figures, International Conference on Magnetism (ICM) 2009 (Karlsruhe, Germany, July 26-31, 2009)

Motion of the Tippe Top : Gyroscopic Balance Condition and Stability

We reexamine a very classical problem, the spinning behavior of the tippe top on a horizontal table. The analysis is made for an eccentric sphere version of the tippe top, assuming a modified Coulomb law for the sliding friction, which is a continuous function of the slip velocity $\vec v_P$ at the point of contact and vanishes at $\vec v_P=0$. We study the relevance of the gyroscopic balance condition (GBC), which was discovered to hold for a rapidly spinning hard-boiled egg by Moffatt and Shimomura, to the inversion phenomenon of the tippe top. We introduce a variable $\xi$ so that $\xi=0$ corresponds to the GBC and analyze the behavior of $\xi$. Contrary to the case of the spinning egg, the GBC for the tippe top is not fulfilled initially. But we find from simulation that for those tippe tops which will turn over, the GBC will soon be satisfied approximately. It is shown that the GBC and the geometry lead to the classification of tippe tops into three groups: The tippe tops of Group I never flip over however large a spin they are given. Those of Group II show a complete inversion and the tippe tops of Group III tend to turn over up to a certain inclination angle $\theta_f$ such that $\theta_f<\pi$, when they are spun sufficiently rapidly. There exist three steady states for the spinning motion of the tippe top. Giving a new criterion for stability, we examine the stability of these states in terms of the initial spin velocity $n_0$. And we obtain a critical value $n_c$ of the initial spin which is required for the tippe top of Group II to flip over up to the completely inverted position.Comment: 52 pages, 11 figures, to be published in SIAM Journal on Applied Dynamical Syste