On high temperature susceptibilities of Heisenberg model ferromagnetics and anti-ferromagnetics

Pirnie, K.; Wood, P.J.; Eve, J.

doi:10.1080/00268976600101381

Cited by 43 publications

(11 citation statements)

References 8 publications

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“…It remains puzzling, however, why the ordered state was not observed at TϾ0 either. When the mean-field prediction for the ordering temperature, T N MF =1.5 nK, is corrected for fluctuations according to the high-temperature expansions (Pirnie et al, 1966), one obtains a theoretical T N around 1.0 nK, much higher than the lowest temperature of 0.28 nK reached in the experiments. Perhaps rhodium exhibits behavior similar to that of silver (so far unexplained):…”

Section: B Exchange Constants and Ordered Spin Structuresmentioning

confidence: 79%

“…Padé approximations provide a way of continuing the HTE to lower temperatures and can be used to obtain a reliable estimate of the ordering temperature (Rushbrooke et al, 1974). Pirnie et al (1966) have reported an HTE analysis of ferromagnetic and antiferromagnetic Heisenberg models with nearest-neighbor and next-nearest-neighbor interactions. The seven leading terms in the high-T expansions for the uniform (k=0) as well as the appropriate staggered (k 0) 18 susceptibilities were calculated as a function of I. Divergence of the staggered susceptibility at TϭT N is an indication of a second-order transition to an antiferromagnetic state modulated by the corresponding k vector.…”

Section: B High-t Expansions and Other Quantum-spin Theoriesmentioning

confidence: 99%

“…The simulations were done for classical spins with magnetic moments ϭ␥បI. An estimate of T c for the corresponding quantum-spin system can be made using the result obtained from the high-temperature expansions of Pirnie et al (1966), according to which T c (I)/T c MF (I) is nearly spin independent for Heisenberg systems in an fcc lattice. In other words, T c scales approximately with I as predicted by the mean-field theory.…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

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Nuclear magnetic ordering in simple metals at positive and negative nanokelvin temperatures

1997

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This paper is a comprehensive review of almost twenty years of research on nuclear magnetic ordering, first in copper and later in silver and rhodium metals. The basic principles of nuclear magnetism and the measurement of positive and negative spin temperatures are discussed first. Cascade nuclear refrigeration techniques, susceptibility and nuclear-magnetic-resonance (NMR) measurements, and arrangements for neutron-diffraction experiments at nanokelvin and picokelvin temperatures are described next. Comprehensive magnetic-susceptibility and neutron-diffraction measurements on copper, which led to the discovery of at least three antiferromagnetic phases, one displaying the novel (0 2 3 2 3 ) spin structure and the other two showing the type-I order of the fcc system, are then described in detail. NMR data on silver, at TϾ0 and TϽ0, are presented next leading to the observation that silver orders antiferromagnetically at positive spin temperatures and ferromagnetically at negative spin temperatures. The authors discuss recent neutron-diffraction measurements that show that the antiferromagnetic structure at TϾ0 is in a single-k type-I state. NMR data on rhodium at TϾ0 and TϽ0 are also described. Results obtained on Tl, Sc, AuIn 2 , and metallic Pr compounds and on insulators like CaF 2 are then discussed briefly. The paper is concluded by an extensive theoretical section. Calculations of conduction-electron mediated exchange interactions are described, and the mean-field theory of nuclear magnetic ordering is presented. The role of thermal and quantum fluctuations is then discussed, particularly in the selection of the antiferromagnetic ground state. Finally, theoretically calculated magnetic phase diagrams and ordered spin structures of copper and silver are presented in detail and compared with experimental results. The overall agreement is good, affirming the value of nuclear magnets in Cu and Ag as realizations of simple physical models. [S0034-6861(97)00301-2] ogy,

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Section: B Exchange Constants and Ordered Spin Structuresmentioning

confidence: 79%

Section: B High-t Expansions and Other Quantum-spin Theoriesmentioning

confidence: 99%

Section: Monte Carlo Simulationsmentioning

confidence: 99%

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Nuclear magnetic ordering in simple metals at positive and negative nanokelvin temperatures

1997

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“…At T < 0, the corresponding ferromagnetic dependence is displayed by the dashed line. At low temperatures, the Curie-Weiss approximation is known to deviate, especially when I = 1/2, from the more accurate results based on hightemperature series expansions (25). For negative temperatures, the measured data show a crossover from ferro-to antiferromagnetic behavior around -5 nK.…”

Section: Rhodium Prefers Antiferromagnetismmentioning

confidence: 93%

Negative Absolute Temperatures: "Hot" Spins in Spontaneous Magnetic Order

Hakonen

Lounasmaa

1994

Science

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Depending on the sign of the spin temperature in the picokelvin range, antiferromagnetic nuclear and ferromagnetic nuclear orders in silver are caused by the same interactions. In rhodium, the antiferromagnetic state is preferred both at temperatures greater than and temperatures less than zero. The lowest and "highest" temperatures ever produced on this scale and measured, 280 and –750 picokelvin, respectively, have been reached in the course of these experiments. The results on silver, in particular, show that negative temperatures are real, not fictitious, quantities.

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“…Several values of j ␣S were taken from Ref. 25, namely, those for ␣ Ͻ 0, S =1/2, because they were not given in Ref. 24.…”

Section: ͑5͒mentioning

confidence: 99%

Factors determining the shape of the temperature dependence of the spontaneous magnetization of a ferromagnet

Kuz’min

Richter

Yaresko³

2006

Phys. Rev. B

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On high temperature susceptibilities of Heisenberg model ferromagnetics and anti-ferromagnetics

Cited by 43 publications

References 8 publications

Nuclear magnetic ordering in simple metals at positive and negative nanokelvin temperatures

Nuclear magnetic ordering in simple metals at positive and negative nanokelvin temperatures

Negative Absolute Temperatures: "Hot" Spins in Spontaneous Magnetic Order

Factors determining the shape of the temperature dependence of the spontaneous magnetization of a ferromagnet

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