Metamagnetism in the<b><i>XXZ</i></b>model with next-to-nearest-neighbor coupling

Gerhardt, C.; Mütter, K.-H.; Kröger, H.

doi:10.1103/physrevb.57.11504

Cited by 42 publications

(72 citation statements)

References 26 publications

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“…This seems confirmed by recent numerical work [10]. The effects of magnetic field and magnetization jumps (metamagnetism) have also been studied recently [11][12][13][14]. Metamagnetism is more likely to occur in nature for ferromagnetic J 1 , because smaller anisotropies are required [13].…”

Section: Introductionsupporting

confidence: 61%

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Phase diagram of theXXZchain with next-nearest-neighbor interactions

Somma

Aligia

2001

Phys. Rev. B

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We calculate the quantum phase diagram of the XXZ chain with nearestneighbor (NN) J 1 and next-NN exchange J 2 with anisotropies ∆ 1 and ∆ 2 respectively. In particular we consider the case ∆ 1 = −∆ 2 to interpolate between the XX chain (∆ i = 0) and the isotropic model with ferromagnetic J 2 . For ∆ 1 < −1, a ferromagnetic and two antiferromagnetic phases exist. For |∆ i | < 1, the boundary between the dimer and spin fluid phases is determined by the method of crossing of excitation spectra. For large J 2 /J 1 , this method seems to indicate the existence of a second spin fluid critical phase. However, an analysis of the spin stiffness and magnetic susceptibility for ∆ 1 = ∆ 2 = 1 suggest that a small gap is present.

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Section: Introductionsupporting

confidence: 61%

“…In addition, there has been a renewed interest in this XXZ model (which is equivalent to a zig-zag ladder) recently [5][6][7][8][9][10][11][12][13][14][15][16]. In particular, for the XX chain (∆ 1 = ∆ 2 = 0), field theoretical methods predicted a critical (gapless) phase with incommensurate correlations for J 2 >> J 1 > 0.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of theXXZchain with next-nearest-neighbor interactions

Somma

Aligia

2001

Phys. Rev. B

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“…Such jumps can arise for different reasons. One possibility is a first-order transition between different ground states like the spin flop transition in classical magnets or in strongly anisotropic quantum chains [11]. Here we discuss another possibility, namely a macroscopically large degeneracy in the exact ground states of the full quantum system for a certain value of the applied field.…”

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confidence: 99%

Macroscopic Magnetization Jumps due to Independent Magnons in Frustrated Quantum Spin Lattices

Schulenburg¹,

et al. 2002

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For a class of frustrated spin lattices including the kagomé lattice we construct exact eigenstates consisting of several independent, localized one-magnon states and argue that they are ground states for high magnetic fields. If the maximal number of local magnons scales with the number of spins in the system, which is the case for the kagomé lattice, the effect persists in the thermodynamic limit and gives rise to a macroscopic jump in the zero-temperature magnetization curve just below the saturation field. The effect decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.In frustrated quantum spin lattices the competition of quantum and frustration effects promises rich physics. A reliable description of such systems often constitutes a challenge for theory. A famous example is the kagomé lattice antiferromagnet. In spite of extensive studies during the last decade its ground state properties are not fully understood yet. Classically it has infinite continuous degeneracies. In the quantum case (s=1/2), the system is likely to be a spin liquid with a gap for magnetic excitations and a huge number of singlet states below the first triplet state (see [1,2,3] and references therein).In this Letter we will focus on the zero-temperature magnetic behavior of highly frustrated lattices, in particular for high magnetic fields. One aspect is given by the observation of nontrivial magnetic plateaus in frustrated two dimensional (2D) quantum antiferromagnets like SrCu 2 (BO 3 ) [4,5], which has stimulated theoretical interest (see e.g. [6]). Also the kagomé lattice has a plateau at one third (m = 1/3) of the saturation magnetization [7,8]. Since this plateau can be found also in the Ising model and in the classical Heisenberg model with additional thermal fluctuations [9] it can be considered to be of classical origin. However, the structure of the ground state in the classical model is highly non-trivial at m = 1/3 [10] and has not been clarified yet for the quantum model.Another aspect is given by unusual jumps seen in magnetization curves. Such jumps can arise for different reasons. One possibility is a first-order transition between different ground states like the spin flop transition in classical magnets or in strongly anisotropic quantum chains [11]. Here we discuss another possibility, namely a macroscopically large degeneracy in the exact ground states of the full quantum system for a certain value of the applied field. We argue that this is a general phenomenon in highly frustrated systems. This is remarkable in so far as one can exactly write down ground states at a finite density of magnons in a strongly correlated system which is neither integrable, nor has any apparent non-trivial conservation laws. Such jumps represent a genuine macroscopic quantum effect which is also of possible experimental relevance since it occurs in many wellknown models like the kagomé lattice. This jump occurs just below saturation and should be observable in...

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“…Quasi one-dimensional magnetic systems have been identified and studied experimentally [1][2][3][4], and new theoretical studies of the spin-1/2 XXZ chain with nearest-neighbor (NN) and next-NN exchange coupling (which is equivalent to a two-leg zig-zag ladder) were presented [4][5][6][7][8][9][10][11][12][13][14] (1)…”

Section: Introductionmentioning

confidence: 99%

Magnetization jump in theXXZchain with next-nearest-neighbor exchange

Aligia

2000

Phys. Rev. B

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We study the dependence of the magnetization M with magnetic field B at zero temperature in the spin-1/2 XXZ chain with nearest-neighbor (NN) J1 and next-NN J2 exchange interactions, with anisotropies ∆1 and ∆2 respectively. The region of parameters for which a jump in M (B) exists is studied using numerical diagonalization, and analytical results for two magnons on a ferromagnetic background in the thermodynamic limit. We find a line in the parameter space (J2/J1, ∆1/J1, ∆2/J1) (determined by two simple equations) at which the ground state is highly degenerate. M (B) has a jump near this line, and at or near the isotropic case with ferromagnetic J1 and antiferromagnetic J2, with |J2/J1| ∼ 1/4. These results are relevant for some systems containing CuO chains with edge-sharing CuO4 units.

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Metamagnetism in theXXZmodel with next-to-nearest-neighbor coupling

Cited by 42 publications

References 26 publications

Phase diagram of theXXZchain with next-nearest-neighbor interactions

Phase diagram of theXXZchain with next-nearest-neighbor interactions

Macroscopic Magnetization Jumps due to Independent Magnons in Frustrated Quantum Spin Lattices

Magnetization jump in theXXZchain with next-nearest-neighbor exchange

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