There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Magnetocaloric effect: From materials research to refrigeration devices

H E Stanley Oxford: University Press 1971 pp xx + 308 price ?5 In the past fifteen years or so there has been a lot of experimental and theoretical work on the nature of critical phenomena in the neighbourhood of second order phase transitions. It has not been easy to get a good overall view of this work without digging through the rather complex original literature, although there are some good review articles covering particular aspects of the work.

https://iopscience.iop.org/article/10.1088/0031-9112/23/4/018/pdf

Introduction to Phase Transitions and Critical Phenomena

Extensive calculations based on density functional theory have been carried out to understand the origin of magnetism in undoped ZnO thin films as found in recent experiments. The observed magnetism is confirmed to be due to Zn, instead of O, vacancy. The main source of the magnetic moment, however, arises from the unpaired 2p electrons at O sites surrounding the Zn vacancy with each nearest-neighbor O atom carrying a magnetic moment ranging from 0.490 to 0.740 B. Moreover, the study of vacancy-vacancy interactions indicates that in the ground state, the magnetic moments induced by Zn vacancies prefer to ferromagnetically couple with the antiferromagnetic state lying 44 meV higher in energy. Since this is larger than the thermal energy at room temperature, the ferromagnetic state can be stable against thermal fluctuations. Calculations and discussions are also extended to ZnO nanowires that have larger surface to volume ratio. Here, the Zn vacancies are found to lead to the ferromagnetic state too. The present theoretical study not only demonstrates that ZnO samples can be magnetic even without transition-metal doping but also suggests that introducing Zn vacancy is a natural and an effective way to fabricate magnetic ZnO nanostructures. In addition, vacancy mediated magnetic ZnO nanostructures may have certain advantages over transition-metal doped systems in biomedical applications.

https://absimage.aps.org/image/MAR08/MWS_MAR08-2007-004197.pdf

Zinc Vacancy induced magnetism in ZnO thin films and nanowires

We report here enhancement of ferromagnetism in pure ZnO upon thermal annealing with the ferromagnetic transition temperature Tc above room temperature. We observe a finite coercive field upto 300K and a finite thermoremanent magnetization upto 340K for the annealed sample. We propose that magnetic moments can form at anionic vacancy clusters. Ferromagnetism can occur due to either superexchange between vacancy clusters via isolated F+ centers, or through a limited electron delocalization between vacancy clusters. Isolated vacancy clusters or isolated F+ centers give rise to a strong paramagnetic like behaviour below 10K.

Enhancement of ferromagnetism upon thermal annealing in pure ZnO

We prepared BaTi1-xMnxO3 samples (x = 0 and 0.05) by standard solid-state reaction at 700°C and 900°C in an Ar ambient to change oxidation number of Mn dopants. The fabricated samples were then studied structural characterization and electronic structures by means of X-ray diffraction and absorption, and Raman scattering and electron-spin-resonance spectrometers. We found oxidation numbers 2+ and 3+ of Mn ions coexisting in BaTi1-xMnxO3 with x = 0.05, where the Mn2+/Mn3+ ratio is about one for the sample annealed at 700°C. These Mn ions prefer locating at the Ti site in the tetragonal BaTiO3 host lattice. In particular, there is a change in the oxidation number of Mn2+ → Mn3+ when the annealing temperature changes from 700°C to 900°C. Their magnetic properties are accordingly changed. Meanwhile, annealing pure BaTiO3 in an Ar ambient at 700°C and 900°C does not lead to ferromagnetic (FM) order; they are almost diamagnetic. With the obtained results, we believe that FM order in Mn-doped BaTiO3 annealed in an Ar ambient is associated with exchange interactions of Mn2+ ions mediated by oxygen vacancies rather than associated with Mn3+ ions.

Influence of the Change in Oxidation Number of Mn on Magnetic Properties of ${\rm BaTi}_{{1}-{x}}{\rm Mn}_{x}{\rm O}_{3}$

We fabricated Huesler alloy ingots of Ni50−x Pr x Mn37Sn13 with x = 0 − 5 by using an arcmelting method. Crystalline-structural analyses revealed the coexistence of austenitic and martensitic phases in the samples with x = 0 and 1, in which the volume fraction of the austenitic phase for x = 1 was higher than that for x = 0. With higher Pr concentrations, x > 1, Pr- and Ni3Sn-related secondary phases, which reduced the magnetic order of the alloys, were formed. Thus, only the sample with x = 1 was more suitable for studying the critical behavior. Based on Landau’s phase-transition theory and Banerjee’s criteria, we found that this sample undergoes a second-order magnetic phase transition (SOMT) at a temperature around the Curie temperature T C ≈ 299 K. Using the modified Arrott plots, asymptotic relations, and a universal scaling law, we determined the values of the critical exponents β = 0.501 ± 0.009 and γ = 1.045 ± 0.006. These values are very close to those expected for the mean-field theory with β = 0.5 and γ = 1, proving the existence of long-range ferromagnetic (FM) order in the sample with x = 1. Particularly, around at temperature T C , the magnetic-entropy change reaches the maximum value (∆S max ). Its magnetic-field dependences can be described by using a power law |∆S max | ∝ H n , where n = 0.687 is close to the value 0.677 calculated from the theoretical relation n = 1 + (β − 1)/(β + γ). We believe that the doping of a suitable Pr amount in Ni50−x Pr x Mn37Sn13 (x ≈ 1) promotes the formation of the austenitic phase and results in long-range FM order. However, the persistence of the martensitic phase and secondary phases favors short-range FM order and thus decreases the FM order in Ni50−x Pr x Mn37Sn13.

Critical behavior and exponent parameters of the austenitic phase in Ni 50- x Pr x Mn 37 Sn 13 alloys with x = 1

We have studied the magnetic properties and magnetocaloric effect of rhombohedral $({\rm La}_{0.9}{\rm Dy}_{0.1})_{1\hbox{-}x}{\rm Pb}_{x}{\rm MnO}_{3}$ ( $x={0.1}$ , 0.2, and 0.3) fabricated by solid-state reaction. Thermomagnetization curve reveals that the increase of Pb doping in $({\rm La}_{0.9}{\rm Dy}_{0.1})_{1\hbox{-}x}{\rm Pb}_{x}{\rm MnO}_{3}$ shifts the ferromagnetic (FM)–paramagnetic (PM) phase-transition temperature $(T_{C})$ toward room temperature; the $T_{C}$ values determined for $x={0.1}$ , 0.2, and 0.3 are about 172, 249, and 322 K, respectively. Based on magnetic-field dependencies of magnetization, $M(H)$ , the magnetic entropy changes $(\Delta S_{m})$ of the samples were calculated. Under an applied magnetic field of $H={10}~{\rm kOe}$ , the $\vert\Delta S_{\rm max}\vert$ value slightly increases from 0.74 ${\rm J}/{\rm kg}\cdot~{\rm K}$ for $x={\rm 0.1}$ to about 1.1 ${\rm J}/{\rm kg}\cdot~{\rm K}$ for $x={\rm 0.2}$ and 0.3. These results correspond to a relative cooling power of ${\sim}{\rm 50}~{\rm J}/{\rm kg}$ , which is comparable with some perovskite manganites, indicating the applicability of $({\rm La}_{0.9}{\rm Dy}_{0.1})_{1\hbox{-}x}{\rm Pb}_{x}{\rm MnO}_{3}$ in magnetic refrigeration devices working around room temperature. Particularly, we find that the variation of $\vert\Delta S_{\rm max}\vert$ versus the magnetic field $H$ can be described by a power law $\vert\Delta S_{\rm max}\vert\propto H^{n}$ , where the magnetic-ordering parameter $(n)$ decreases from 0.861 for $x={0.1}{-}0.834$ for $x={\rm 0.3}$ . A deviation of the $n$ values estimated from the mean-field theory $(n=2/3)$ demonstrates an existence of short-range FM order in the samples.

Magnetic Properties and Magnetocaloric Effect in Pb-Doped ${\rm La}_{0.9}{\rm Dy}_{0.1}{\rm MnO}_{3}$ Manganites

It has been known that A 2 B'B"O 6 typed compounds (A is an alkaline-earth or rare-earth element, B' and B" are different transition-metal elements) belong to the double perovskite family, which have attacted considerable interes due to their complex electrical-magnetic properties. Among these, La 2 NiMnO 6 is a ferromagnetic (FM) semiconductor, and considered as one of the most promising materials for applications in spintronic devices [1]. Though the crystal structure, electromagnetic, and magnetic properties of this material have been widely studied, the nature of FM interactions and magnetocaloric effect (MCE) has not been fully understood yet. Within this context, it is essential to investigate the correlation between the MCE and critical behavior near the FM-para-magnetic (PM) transition in this material.

Tran Dang Thanh

Papers

Influence of the Change in Oxidation Number of Mn on Magnetic Properties of ${\rm BaTi}_{{1}-{x}}{\rm Mn}_{x}{\rm O}_{3}$

Critical behavior and exponent parameters of the austenitic phase in Ni 50- x Pr x Mn 37 Sn 13 alloys with x = 1

Magnetic Properties and Magnetocaloric Effect in Pb-Doped ${\rm La}_{0.9}{\rm Dy}_{0.1}{\rm MnO}_{3}$ Manganites

Critical behaviour and magneticaloric effect in La 2 NiMnO 6 nanoparticles