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{sub {sigma}}(q)=I{sup {up_arrow}}(q)+I{sup {down_arrow}}(q) and {delta}I(q)=I{sup {up_arrow}}(q)-I{sup {down_arrow}}(q) were studied for temperatures near T{sub C}=16.52 K. The I{sup {up_arrow}}(q) and I{sup {down_arrow}}(q) are the scattering intensities for the incident neutron beam polarized along ({up_arrow}) and opposite ({down_arrow}) to the magnetic field. The symmetric contribution, namely I{sub {sigma}}(q), comes from the pair-spin correlation function. The scattering intensity is well described by the Ornstein-Zernike expression I{sub {sigma}}(q)=A(q{sup 2}+{kappa}{sup 2}){sup -1}, where {kappa}={xi}{sup -1} is the inverse correlation length of the critical fluctuations. The correlation length {xi} obeys the scaling law {xi}=a{sub 0}{tau}{sup -{nu}}, where {tau}=(T-T{sub C})/T{sub C} is the reduced temperature, a{sub 0}=0.17 nm, and {nu}=0.68{+-}0.01. The difference contribution {delta}I(q) is caused by the three-spin chiral dynamical spin fluctuations that represent the asymmetric part of the polarization dependent scattering. The q dependence of {delta}I(q) follows closely 1/q{sup 2}. {delta}I(q) depends on the temperature as {tau}{sup -{nu}} with {nu}=0.64{+-}0.05. The exponents {nu} as determined by means of the static measurements by {xi} and the dynamic measurementsmore » (using the chirality) 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.« less