Spin Correlations Among Narrow-Band Electrons

Abstract

In order to study the properties of narrow-band d electrons, it is convenient to study primarily ionic transition-metal compounds in which the broad-band states are separated into a filled valence band, an empty conduction band. A general Hamiltonian for this class of compound is presented. Since there is no analytic expression for the many-body spin-correlation energy of collective electrons, the Heisenberg exchange Hamiltonian for localized electrons is extrapolated continuously to the narrow-band case. In order to test the validity and power of this approach, it is used to construct a schematic energy diagram for orthorhombic MnP. The signs and relative magnitudes of the different exchange interactions follow from this diagram. The interaction along the orthorhombic c axis is predicted to be particularly sensitive to c-axis spacing, and therefore to increase with decreasing temperature and to induce significant exchange striction. The ground-state spin configurations are calculated from the Heisenberg exchange Hamiltonian, given these interactions. The antiferromagnetic⇌ferromagnetic transition found at 50°K and the metamagnetism of the low-temperature phase are found to follow from the model. The low-temperature magnetic phase is predicted to be a simple cycloidal spiral propagating along the orthorhombic c axis with spins in the b-c plane. However, the spiral is distorted by anisotropy and exchange striction, so that the turn angle is not uniform but is modulated with a wavelength half the spiral wavelength. The c-axis spacing is similarly modulated with a strain amplitude ε0∼0.015.