arXiv:cond-mat/0307126 · Physical Review B

Universal scaling at field-induced magnetic phase transitions

Omid Nohadani, Stefan Weßel, Bruce Normand, Stephan Haas

Published Jun 7, 2004• 74 citations

Abstract

We study field-induced magnetic order in cubic lattices of dimers with antiferromagnetic Heisenberg interactions. The thermal critical exponents at the quantum phase transition from a spin liquid to a magnetically ordered phase are determined from stochastic series expansion quantum Monte Carlo simulations. These exponents are independent of the interdimer coupling ratios, and converge to the value obtained by considering the transition as a Bose-Einstein condensation of magnons, ${\ensuremath{\alpha}}_{\mathrm{BEC}}=\frac{3}{2}.$ The scaling results are of direct relevance to the spin-dimer systems ${\mathrm{TlCuCl}}_{3}$ and ${\mathrm{KCuCl}}_{3},$ and explain the broad range of exponents reported for field-induced ordering transitions.

DOI: 10.1103/physrevb.69.220402

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arXiv:cond-mat/0307126 · Physical Review B

Universal scaling at field-induced magnetic phase transitions

Omid Nohadani, Stefan Weßel, Bruce Normand, Stephan Haas

Published Jun 7, 2004• 74 citations

arXiv HTML PDF

Abstract

{\ensuremath{\alpha}}_{\mathrm{BEC}}=\frac{3}{2}.

The scaling results are of direct relevance to the spin-dimer systems

{\mathrm{TlCuCl}}_{3}

and

{\mathrm{KCuCl}}_{3},

and explain the broad range of exponents reported for field-induced ordering transitions.

DOI: 10.1103/physrevb.69.220402

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arXiv:1006.1598Physical Review BNov 19, 201022 citations

{\ensuremath{\alpha}}_{\mathrm{BEC}}=\frac{3}{2}.

The scaling results are of direct relevance to the spin-dimer systems

{\mathrm{TlCuCl}}_{3}

and

{\mathrm{KCuCl}}_{3},

and explain the broad range of exponents reported for field-induced ordering transitions.

H=H_{C}

T\to0

) where

H

is a longitudinal external magnetic field and

H_{C}

the critical value at which the transition occurs. We consider transitions from a spin liquid at a critical field

H_{C1}

and from a fully polarized paramagnet, at

H_{C2}

, into phases with long range order in the transverse components. The transitions at

H_{C1}

and

H_{C2}

can be viewed as Bose-Einstein condensations of magnons which however belong to different universality classes since they have different values of the dynamic critical exponent

z

. Finally, we use that the magnetic susceptibility is an entanglement witness to discuss how this type of correlation sets in as the system approaches the quantum critical point along the critical trajectory,

H=H_{C2}

T\to0

S=1/2

Heisenberg antiferromagnet on a site-diluted cubic lattice, which lends itself to efficient quantum Monte Carlo simulations. Our results show that the model exhibits a percolation transition in zero applied field, with the correlation length exponent $\ensuremath{\nu}=0.87(8)$ and $\ensuremath{\phi}=1.1(1)$ consistent with

3d

percolation. When applying a sufficiently strong magnetic field, the dilution-induced transition decouples from geometric percolation, and it becomes a SF-BG transition; nonetheless, the $\ensuremath{\nu}$ and $\ensuremath{\phi}$ exponents maintain values consistent with those of the percolation transition. These results contradict the conventional scaling, which predicts $\ensuremath{\phi}\ensuremath{\geqslant}2$; and they suggest a possible relationship between the SF-BG transition and percolation of phase coherence.

We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio $g=J/{J}^{\ensuremath{'}}$ in square-lattice dimerized

S=1/2

Heisenberg antiferromagnets with intradimer and interdimer couplings

J

and ${J}^{\ensuremath{'}}$. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy $\ensuremath{\nu}\ensuremath{\ge}1$. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where $\ensuremath{\nu}\ensuremath{\approx}0.71$). We discuss special circumstances which allow $\ensuremath{\nu}<1$ for the type of disorder considered here.