Critical Behaviour of Heisenberg Ferromagnets with Dipolar Interactions and Uniaxial Anisotropy

Kaul, S. N.

doi:10.1007/11417255_2

Cited by 2 publications

(3 citation statements)

References 43 publications

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“…The critical exponents reported in the above papers were β = 1 2 and α = 0 for both cases: in both cases the configurational specific heat C V /k B was found to remain constant at 3 2 for T ≤ T c,SM , and to change continuously but with a discontinuous slope at T = T c,SM .…”

Section: Resultsmentioning

confidence: 77%

“…Long-range dipolar interactions [1] between magnetic moments are ubiquitous in experimentally studied magnetic systems, although often dominated by exchange couplings (for more details see Refs. [2][3][4][5] and references therein), and, over decades, a number of theoretical studies, based on Renormalization group techniques, has addressed interaction models containing both dipolar and short-range isotropic or anisotropic exchange interactions (see, e.g., Refs [2,[6][7][8][9][10][11]); on the other hand, lattice models involving only the longrange dipolar term have also long been studied by various approaches, including spin-wave treatments and simulation (see, e.g., Refs. [12][13][14][15][16][17][18][19], and others quoted in the following).…”

Section: Introductionmentioning

confidence: 99%

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Nematic order in a simple-cubic lattice-spin model with full-ranged dipolar interactions

Chamati

Romano

2016

Phys. Rev. E

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In a previous paper [Phys. Rev. E 90, 022506 (2014)PLEEE81539-375510.1103/PhysRevE.90.022506], we studied the thermodynamic and structural properties of a three-dimensional simple-cubic lattice model with dipolarlike interaction, truncated at nearest-neighbor separation, for which the existence of an ordering transition at finite temperature had been proven mathematically; here we extend our investigation, addressing the full-ranged counterpart of the model, for which the critical behavior had been investigated theoretically and experimentally. In addition, the existence of an ordering transition at finite temperature had been proven mathematically as well. Both models exhibited the same continuously degenerate ground-state configuration, possessing full orientational order with respect to a suitably defined staggered magnetization (polarization), but no nematic second-rank order; in both cases, thermal fluctuations remove the degeneracy, so that nematic order does set in at low but finite temperature via a mechanism of order by disorder. On the other hand, there were recognizable quantitative differences between the two models as for ground-state energy and critical exponent estimates; the latter were found to agree with early renormalization-group calculations and with experimental results.

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Section: Resultsmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Nematic order in a simple-cubic lattice-spin model with full-ranged dipolar interactions

Chamati

Romano

2016

Phys. Rev. E

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“…The long-standing (spanning nearly four decades) controversy [9] about the asymptotic critical behaviour of Gd near the ferromagnetic-to-paramagnetic phase transition has finally been put to rest by demonstrating [10,11] that single power laws alone cannot adequately describe the observed temperature variations of spontaneous magnetization, M(T, 0), and intrinsic susceptibility, χ (T ), in the asymptotic critical region (ACR), but do so only when the multiplicative logarithmic correctionsto these power laws, predicted by the renormalization group (RG) calculations for a d = 3 uniaxial dipolar ferromagnet [12,13], are taken into account. To be more specific, zero-field electrical resistivity/specific heat C H =0 [14,15], M(T, 0) and χ (T ), taken along the c axis (easy direction of magnetization) of a high-purity Gd single crystal, respectively follow the RG-predicted temperature variations,…”

Section: Introductionmentioning

confidence: 99%

Critical behaviour of nanocrystalline gadolinium: evidence for random uniaxial dipolar universality class

Ferdinand¹,

Probst²,

Michels³

et al. 2014

J. Phys.: Condens. Matter

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We report on how nanocrystal size affects the critical behaviour of the rare-earth metal Gd near the ferromagnetic-to-paramagnetic phase transition. The asymptotic critical behaviour of the coarse-grained polycrystalline sample (with an average crystallite size of L≅100 μm) is that of a (pure) uniaxial dipolar ferromagnet, as is the case with single crystal Gd, albeit the width of the asymptotic critical region (ACR) is reduced. As the grain size approaches ∼30 nm, the ACR is so narrow that it could not be accessed in the present experiments. Inaccessibly narrow ACR for L ∼ 30 nm and continuous increase in the width of the ACR as L decreases from 16 to 9.5 nm basically reflect a crossover to the random uniaxial dipolar fixed point caused by the quenched random exchange disorder prevalent at the internal interfaces (grain boundaries).

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Critical Behaviour of Heisenberg Ferromagnets with Dipolar Interactions and Uniaxial Anisotropy

Cited by 2 publications

References 43 publications

Nematic order in a simple-cubic lattice-spin model with full-ranged dipolar interactions

Nematic order in a simple-cubic lattice-spin model with full-ranged dipolar interactions

Critical behaviour of nanocrystalline gadolinium: evidence for random uniaxial dipolar universality class

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