Neutron-diffraction studies of the nuclear magnetic phase diagram of copper

Abstract

We have studied the spontaneous antiferromagnetic (AF) order in the nuclear spin system of copper by use of neutron-diffraction experiments at nanokelvin temperatures. Copper is an ideal model system as a nearest-neighbor-dominated spin-2 fcc antiferromagnet. The phase diagram has been investigated by measuring the magnetic-field dependence of the (100) reflection, characteristic of a type-I AF structure, and of a Bragg peak at {0 3 3 ). The results suggest the presence of high-field (100) phases at 0. 12 (8 (B,=0.26 mT, for B along either the [100] or [011]crystalline axes, intermediate-field (0 -, -', )structures around 8 =0.09 mT for all field directions, and a zero-field (100) phase. No reflection corresponding to a high-field phase for B~i [111]has been found. The phase transition between the high-field phase and the intermediate-field structure is of first order. The change from {0 3 3 ) at intermediate fields to (100) at zero field is associated with a large region (0.02~B &0.06 mT) of coexisting-(100) and ( 0 3 3 )-type Bragg peaks, and can be interpreted as either a two-phase region with a first-order transition at -0.06 mT and huge hysteresis effects or as a single multiple-k phase which continuously transforms from being determined by (0 3 3 ) at -0.1 mT and (100) at zero field. The neutron-diffraction data have been compared with results of earlier susceptibility measurements in order to identify the translational periods of the three previously found antiferromagnetic phases for B~~ [100]. Recent theoretical work has yielded results in agreement with our experimental data.allows an accurate modeling and analysis of the spin assemblies. Antiferromagnetic order in a fcc lattice is a phenomenon characterized by intrinsic frustration. The requirement of oppositely aligned magnetic moments in a network of equilateral triangles is seemingly difficult to achieve. The structure of this system has puzzled theorists for decades but still remains unsolved. ' Nuclear magnets in certain metals, most notably copper, silver, and gold, are model systems for studies of the frustration problem. These three elements constitute a series with increasing strength of the antiferromagnetic coupling between adjacent nuclei.In noble metals, nuclear spins interact via the ordinary dipolar force, which is known accurately, and via the indirect, conduction-electron-mediated Ruderman-Kittel (RK) interaction, which can be calculated from electronic wave functions and the band structure. An external magnetic field also causes a Zeeman term, but quadrupolar forces are quenched by the cubic symmetry. Therefore, the Hamiltonian consists of only three terms, viz. , di +~RK+~ZThe anisotropic dipolar force favors ferromagnetism whereas the spin-rotation-invariant Ruderman-Kittel interaction tends to align neighboring spins antiparallel. In copper these competing interactions are of comparable strength. Experimentally, the parameter which is related to the average molecular field, can be measured in order to compare the strengths of the s...

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

“…Subsequent susceptibility and neutron-diffraction measurements on a single-crystal specimen have given more insight into the process by which irreversibility occurs. The entropy increase ⌬Sϭ0.12R ln4 was found to occur in a field around 0.1 mT Huiku et al, 1986;Annila et al, 1992), where a phase transition also takes place from the antiferromagnetic phase AF2 to AF1; see the phase diagram of Fig. 1.…”

“…This time, however, polarization losses were attributed to the ordering process rather than thermal mixing, and field sweeps between Bϭ1 mT and zero field in the disordered state, at entropies above 0.61R ln4, were found to be adiabatic. Neutrondiffraction experiments (Annila et al, 1992) have clearly shown that, indeed, during the transition from the (1 0 0) phase to the (0 2 3 2 3 ) phase in fields around B ϭ0.11 mT, a large nonadiabaticity occurs. There should, however, be some polarization loss caused by thermal mixing, too, although it may occur in fields above Bϭ1 mT.…”

“…The most recent series of neutron-diffraction experiments at Risø (Annila et al, 1992) were performed by varying the direction of the external magnetic field with respect to the crystalline axis. It was found that the intensities of the (0 2 3 2 3 ) and the (1 0 0) Bragg reflections depended sensitively on the alignment of the field.…”

“…Subsequent experiments ) on a single-crystal specimen, during which the longitudinal susceptibility was measured as well, revealed a third antiferromagnetic phase, AF3. Recent neutron-diffraction experiments (Annila et al, 1992), also performed on a single-crystal specimen, have further shown that the antiferromagnetic ordering vectors, and hence also the spin structures, strongly depend on the alignment of the external magnetic field with respect to the crystalline axes. It is therefore remarkable that the data on a polycrystalline sample do not smear out the evidence for phase changes, especially at the AF1 ↔ AF2 transition.…”

Static and Dynamic Spin Organization in Magnetic Semiconductor Nanostructures

“…The face centered cubic (fcc) Heisenberg antiferromagnet with short-ranged exchange is a problem which first attracted theoretical attention several decades ago [11], and still continues to be of contemporary interest because the frustration inherent to the fcc lattice leads to a rich variety of magnetic phases [12]. The fabrication by MBE of stuctures containing the zinc-blende phase of MnSe [13] and MnTe [14] provides an opportunity to revisit the problem of the fcc antiferromagnet in the context of symmetry-breaking strain fields and dimensional crossover.…”