Critical two- and three-spin correlations in EuS: An investigation with polarized neutrons

Abstract

The critical magnetic scattering has been investigated in EuS by means of small-angle scattering with polarized neutrons using an inclined magnetic field geometry, allowing the determination of three-spin correlation functions. Two contributions to the critical magnetic scattering I ⌺ ͑q͒ = I ↑ ͑q͒ + I ↓ ͑q͒ and ⌬I͑q͒ = I ↑ ͑q͒ − I ↓ ͑q͒ were studied for temperatures near T C = 16.52 K. The I ↑ ͑q͒ and I ↓ ͑q͒ are the scattering intensities for the incident neutron beam polarized along ͑↑͒ and opposite ͑↓͒ to the magnetic field. The symmetric contribution, namely I ⌺ ͑q͒, comes from the pair-spin correlation function. The scattering intensity is well described by the Ornstein-Zernike expression I ⌺ ͑q͒ = A͑q 2 + 2 ͒ −1 , where = −1 is the inverse correlation length of the critical fluctuations. The correlation length obeys the scaling law = a 0 − , where = ͑T − T C ͒ / T C is the reduced temperature, a 0 = 0.17 nm, and = 0.68± 0.01. The difference contribution ⌬I͑q͒ is caused by the three-spin chiral dynamical spin fluctuations that represent the asymmetric part of the polarization dependent scattering. The q dependence of ⌬I͑q͒ follows closely 1 / q 2 . ⌬I͑q͒ depends on the temperature as − with = 0.64± 0.05. The exponents as determined by means of the static measurements by and the dynamic measurements ͑using the chirality͒ are in excellent agreement with each other, demonstrating the internal consistency of the theory and the experiment. Therefore, our results confirm the principle of the critical factorization, which is known as Polyakov-Kadanoff-Wilson operator algebra.

Magnetic cluster excitations

“…There has been ample experimental evidence for many-body interactions in the past, notably in studies of ultra-cold gases of alkaline atoms (Büchler et al, 2007), the stability of molecules like ozone (Zhaunerchyk et al, 2007), four-atom exchange in 3 He (McMahan and Wilkins, 1975), chirality in magnetic compounds (Grigoriev et al, 2005), ring-exchange (Coldea et al, 2001) and three-body correlations of vortex states (Menon et al, 2006) in high-temperature superconductors, or domain-wall fluctuations in (anti-) fer-romagnets (Shpyrko et al, 2007). Novel quantum phases with intriguing physical properties can arise from manybody interactions which are usually described on the basis of pair potentials G(r, t).…”

Magnetic Cluster Excitations

“…There has been ample experimental evidence for many-body interactions in the past, notably in studies of ultra-cold gases of alkaline atoms (Büchler et al, 2007), the stability of molecules like ozone (Zhaunerchyk et al, 2007), four-atom exchange in 3 He (McMahan and Wilkins, 1975), chirality in magnetic compounds (Grigoriev et al, 2005), ring-exchange (Coldea et al, 2001) and three-body correlations of vortex states (Menon et al, 2006) in high-temperature superconductors, or domain-wall fluctuations in (anti-) ferromagnets (Shpyrko et al, 2007). Novel quantum phases with intriguing physical properties can arise from manybody interactions which are usually described on the basis of pair potentials G(r, t).…”

Magnetic small-angle neutron scattering of bulk ferromagnets

“…Since the vast majority of magnetic SANS experiments are carried out by employing the two scattering geometries where the externally applied magnetic field H 0 is either perpendicular (figure 6(a)) or parallel (figure 6(b)) to the wave vector k 0 of the incoming neutron beam, we restrict our attention to these two specific situations. We refer the reader to [194] (and references therein) for a study of critical two and three-spin correlations in EuS which employs an inclined magnetic field geometry (H 0 at 45 • to k 0 ).…”