Spin Correlations Among Narrow-Band Electrons

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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.

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