Magnetic-field-induced phase transition in a two-dimensional quantum magnet with plaquette distortion
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TURE SOLID-STATE PHYSICS
Magnetic-Field-Induced Phase Transition in a Two-Dimensional Quantum Magnet with Plaquette Distortion V. V. Val’kova, b, c, * and V. A. Mitskana, b a
Kirenskiœ Institute of Physics, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 660036 Russia b Krasnoyarsk State University, Krasnoyarsk, 660075 Russia c Krasnoyarsk State Technical University, Krasnoyarsk, 660074 Russia *e-mail: [email protected]
Abstract—Magnetic field effect on the structure of the ground state of a two-dimensional quantum Heisenberg magnet is analyzed. A plaquette representation is used to solve the self-consistent problem and calculate the collective excitation spectrum in a magnetic field. Conditions are found for quantum transition between nonmagnetic and oblique antiferromagnetic phases. The change in the ground state of the system is associated with disappearance of the gap in the spin excitation spectrum. Effects of frustration and magnetic field on the spectrum are analyzed. A phase diagram of stable singlet and magnetically ordered phases is presented. PACS numbers: 73.22.Lp, 75.10.Dg, 75.50.Ee DOI: 10.1134/S1063776107070199
angle θ (as shown in Fig. 1), which can be found by exact treatment of the intraplaquette (strong) interactions. Thus, the magnetic order parameter is determined by the x z mean spin projections σx = 〈 S 1〉 and σz = 〈 S 1〉 at the first site (see site numbering in Fig. 1).
The introduction of a magnetic mechanism of the Cooper instability in high-temperature superconductors by Anderson [1] stimulated experimental and theoretical studies of quasi-low-dimensional magnets [2, 3]. Due to low dimension and bond frustration, quantum spin fluctuations in these materials can be sufficiently strong to change both the structure of the ground state and the low-temperature behavior of these systems. In particular, a sharp drop in magnetic susceptibility with decreasing temperature occurs in various quasi-twodimensional magnetic systems, such as CaV4O9 [4], Cu3B2O6 [5], SrCu4(BO3)2 [6], and (C4H12N2)Cu2Cl6 [7]. Analogous behavior is observed in quasi-onedimensional systems undergoing the spin-Peierls transition [8], which consists in the low-temperature dimerization of an antiferromagnetic (AF) chain into a spinsinglet phase driven by magnetoelastic coupling.
Magnetoelastic coupling is described by taking into account the dependence of exchange integrals on the intersite distance [9]. When an external magnetic field is applied, a modified self-consistent field is introduced as a vector with components parallel and perpendicular to the applied field, H z = (2Iex – (2J + J1))σz and H x = (2Iex – (2J + J1))σx. The plaquette Hamiltonian is then written as H 0 = –2H x σ x + H x D + 2H z σ z – H z F x
In [9], the one-dimensional scenario of spin-singlet pairing was extended to two-dimensional systems. As AF long-range order breaks down in a square-lattice Heisenberg magnet with plaquette distortion (see [9, Fig. 1]), a gap opens in its excitation spectrum. The gap width depends on the interaction
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