Using the Landau–Ginzburg–Devonshire approach, the longitudinal piezoelectric coefficient in an arbitrary direction, d33*(θ), was calculated as a function of temperature in tetragonal BaTiO3 crystals. The direction along which d33*(θ) is maximum is a function of piezoelectric dij coefficients referred to the crystallographic coordinate system. Below a critical ratio of the shear and longitudinal coefficients, d15/d33, the maximum d33*(θ) lies along the [001] axis. As the low-temperature orthorhombic phase is approached on cooling, the d15 increases, reflecting softening of the lattice along the axis of the incipient orthorhombic distortion, and the direction of maximum d33*(θ) deviates significantly from the [001] axis. Our results suggest that the enhanced d33*(θ) coefficient along a direction other than the polar axis recently reported in some ferroelectrics is at least in part controlled by these intrinsic lattice effects.

Iron is a central element in the metabolism of normal and malignant cells. Abnormalities in iron and ferritin expression have been observed in many types of cancer. Interest in characterizing iron compounds in the human brain has increased due to advances in determining a relationship between excess iron accumulation and neurological and neurodegenerative diseases. In this work, four different magnetic methods have been employed to characterize the iron phases and magnetic properties of brain tumour (meningiomas) tissues and non-tumour hippocampal tissues. Four main magnetic components can be distinguished: the diamagnetic matrix, nearly paramagnetic blood, antiferromagnetic ferrihydrite cores of ferritin and ferrimagnetic magnetite and/or maghemite. For the first time, open hysteresis loops have been observed on human brain tissue at room temperature. The hysteresis properties indicate the presence of magnetite and/or maghemite particles that exhibit stable single-domain (SD) behaviour at room temperature. A significantly higher concentration of magnetically ordered magnetite and/or maghemite and a higher estimated concentration of heme iron was found in the meningioma samples. First-order reversal curve diagrams on meningioma tissue further show that the stable SD particles are magnetostatically interacting, implying high-local concentrations (clustering) of these particles in brain tumours. These findings suggest that brain tumour tissue contains an elevated amount of remanent iron oxide phases.

The growth of the nanotechnology industry has led to an increased interest in characterizing magnetic nanoparticles. A natural material with well-defined grain size in the nanoparticle range is commercially available—horse spleen ferritin, an iron storage protein. Modeling of the magnetic properties of commercial horse spleen ferritin is often based on the assumption of a single-phase core of ferrihydrite (5Fe2O3∙9H2O). Low temperature hysteresis measurements indicate, however, that the ferritin cores contain at least two magnetic phases. Initial magnetization curves measured at temperatures between 50 and 300K have been modeled using four methods. A model that used a sum of two Langevin functions fitted the data 70% better on average than a model that used a single Langevin function. It was also superior to both a random mean orientation model and a model that takes account of crystalline anisotropy. The two-phase model consists of a phase with a high coercivity that does not undergo saturation and a second phase with a low coercivity and a saturation field of 300mT. The high-coercivity phase is compatible with antiferromagnetic ferrihydrite, while the low-coercivity phase could be magnetite, maghemite, or a mixture of both. The results from this study are consistent with earlier microscopic studies that characterize horse spleen ferritin as a multiphase system with up to 30% of magnetite-maghemitelike cores.

Magnetic properties of a two-component system, consisting of horse spleen ferritin ͑HoSF͒ which contains a 5 -8 nm sized antiferromagnetic ferrihydrite ͑5Fe 2 O 3 •9H 2 O͒ core and ferrimagnetic magnetite ͑Fe 3 O 4 ͒ nanoparticles ͑MNP͒ with an average size of 10-20 nm, have been investigated by using four different methods: induced magnetization versus ͑1͒ temperature and ͑2͒ field; ͑3͒ AC susceptibility; and ͑4͒ first-order reversal curves ͑FORC͒. All measurements were done on a mixed system of HoSF and MNP, as well as separately on the individual components. The average blocking temperature ͑T B ͒ of the mixed system at 50 mT is 15.6 K, which is a shift towards higher temperatures compared to pure HoSF ͑T B =12 K͒. The contribution of the MNP component to magnetic ordering is evident only as a separation of the zero-field-cooled and field-cooled measurement curves. ac susceptibility is dominated by the ferrimagnetic MNP and shows strong frequency dependence. The peak ac susceptibilities can be described by the Vogel-Fulcher law, indicating the influence of interactions within the system. Hysteresis measurements at 5 K show a wasp-waisted shape due to the mixture of a high coercivity phase ͑HoSF͒ with a low coercivity phase ͑MNP͒. Initial magnetization curves above T B can be fitted by a sum of Langevin functions, showing superparamagnetic behavior of both components. FORC diagrams are effective in illustrating the change from that of blocked MNP particles together with the superparamagnetic HoSF at 20 K to purely superparamagnetic behavior in both components above 50 K. We conclude that the mixed nanoparticle system is a good model for complex natural samples, such as human brain tissue.

Excess iron accumulation in the brain has been shown to be related to a variety of neurodegenerative diseases. However, identification and characterization of iron compounds in human tissue is difficult because concentrations are very low. For the first time, a combination of low temperature magnetic methods was used to characterize iron compounds in tumour tissue from patients with mesial temporal lobe epilepsy (MTLE). Induced magnetization as a function of temperature was measured between 2 and 140 K after cooling in zero-field and after cooling in a 50 mT field. These curves reveal an average blocking temperature for ferritin of 10 K and an anomaly due to magnetite at 48 K. Hysteresis measurements at 5 K show a high coercivity phase that is unsaturated at 7 T, which is typical for ferritin. Magnetite concentration was determined from the saturation remanent magnetization at 77 K. Hysteresis measurements at various temperatures were used to examine the magnetic blocking of magnetite and ferritin. Our results demonstrate that low temperature magnetic measurements provide a useful and sensitive tool for the characterisation of magnetic iron compounds in human tissue.