Magnetic ordering

The spinors further commute with the Kohn-Sham Hamiltonian and obey a commutative multiplication law, thereby making them an Abelian group isomorphic to the usual translation group [133]. But this means that they have the same irreducible representation, which is the Bloch theorem. So, we therefore have the generalized Bloch theorem  

It should also be noted that if we denote by the k-vector ko the Bloch function for the non-magnetic state, then Eq.(7.17) and the usual Bloch law give us, in the case of 0V = 0 

The multiplication of the rotation matrices comes from the need to transform the potential function matrices to the global spin quantization axis. Instead of doing this, the whole secular equation is rotated, meaning that the potential functions become constant, but the structure constants have to be rotated instead. This has been implemented in both the EMTO method and the BGFM and is used in Papers VI, VII, and VIII. 

Given the very considerable literature on molecule based magnets (MBMs), which includes a number of detailed books and reviews, 167-169, 172] pj-incipal attention here is given to describing the recent emergence of porous magnets. 

In utilising hydroxo bridges between metal ions, approaches have focused 

Principal attention in the incorporation of radical multitopic ligands into MOF phases has focused on the well known Tt-acceptors TCNE (tetracya-noethylene) and TCNQ (7,7,8,8-tetracyanoquinodimethane), which in their mononegative forms have an unpaired spin that can couple with 

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Yields bulk information of macro-sized samples (thin films for determining magnetic ordering)... 

Compounds with Sc, Y, lanthanoids and actinoids are of three types. Those with composition ME have the (6-coordinated) NaCl structure, whereas M3E4 (and sometimes M4E3) adopt the body-centred thorium phosphide structure (Th3P4) with 8-coordinated M, and ME2 are like ThAsi in which each Th has 9 As neighbours. Most of these compounds are metallic and those of uranium are magnetically ordered. Full details of the structures and properties of the several hundred other transition metal-Group 15 element compounds fall outside the scope of this treatment, but three particularly important structure types should be mentioned because of their widespread occurrence and relation to other structure types, namely C0AS3,... 

At the same time, the relatively low energy and ionic character of the chemical bonds between metal and fluorine cause some difficulties in the application of fluoride compounds. First, fluorides typically have a tendency towards thermolysis and hygroscopicity. In addition, fluoride compounds usually display relatively low temperatures of electrostatic and magnetic ordering. 

Magnetic ordering, 746 Magnetic point groups, 738, 739 international notation, 739 properties of, 740 Schonflies notation, 739 Shubnikov notation, 739 Magnetic point symmetry, determination of, 744... 

P. Hakonen, O. V. Lounasmaa and A. Oja. "Spontaneous Nuclear Magnetic Ordering in Copper and Silver at Nano- and Picokelvin Temperatures". J. Magn. Magn. Mater.. 100, 394-412 (1991). 

Contrary to other oxidation states most of the compounds of trivalent plutonium that have been investigated show magnetic ordering at low temperatures. 

The rare earths in their dodecaborides have the 3 + oxidation state except for Yb and Tm which have an intermediate valence state. A recoilless y-ray emission spectrum study of TmB,2 shows no magnetic ordering at 1.35 K the spectra of YbB,2 reveal no magnetic structure to 1.35 K. The compounds HoB,2, ErB,2 order antiferromagnetically, and ZrB,2 and LuB,2 become superconducting < 5.8 K and < 0.48 K, respectively. ... 

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