A Mean-Field Analysis of the Exchange Coupling (J) for Noncubic Prussian Blue Analogue Magnets

Abstract

Mean field expressions based on the simple Heisenberg model were derived to correlate the intra- and interlayer exchange couplings to the critical temperatures, T c, for three metallocyanide-based magnets with extended 2- and 3-D structure types. These expressions were used to estimate the exchange coupling, J, for 2-D ferrimagnetic [NEt4]2MnII 3(CN)8, 3-D antiferromagnetic [NEt4]MnII 3(CN)7, and 3-D antiferromagnetic interpenetrating 3-D MnII(CN)2. The type and magnitude of the exchange coupling are in accord with the previously reported magnetic data.

Anomalous Stoichiometry, 3-D Bridged Triangular/Pentagonal Layered Structured Artificial Antiferromagnet for the Prussian Blue Analogue A3MnII5(CN)13(A = NMe4, NEtMe3). A Cation Adaptive Structure

“…The cusp in the χ­( T ) data is additional evidence for antiferromagnetic ordering. − The temperature at which the maximum in χ­( T ) occurs lies above T c , , and T c can be determined from the temperature at which the maximum in d­(χ T )/d T occurs, i.e., Fisher’s specific heat. , The d­(χ T )/d T data for 1·H 2 O , 1·MeOH , and 2·H 2 O have peaks at 11, 8.8, and 14 K, respectively, Figure top inset, which are their antiferromagnetic ordering temperatures, T c , respectively. The higher T c for 2·H 2 O is in accord with 10% more high-spin S = 5/2 Mn­(II) and less low-spin S = 1/2 Mn­(II) being present with respect to 1·H 2 O , as T c ∝ S ( S + 1). ,, …”

“…The higher T c for 2•H 2 O is in accord with 10% more high-spin S = 5/2 Mn(II) and less low-spin S = 1/2 Mn(II) being present with respect to 1•H 2 O, as T c ∝ S(S + 1). 1,29,30 The field-dependent magnetization, M(H), at 5 K from ±90 kOe is linear and is still increasing with applied field and is 27 000, 28 750, and 38 700 emu Oe/mol at 90 kOe for 1•H 2 O, 1•MeOH, and 2•H 2 O respectively, with no evidence of a saturation or a remnant magnetization, or a coercive field, Figure 7, as is expected for an antiferromagnet.…”

Pressure Induced Crossover between a Ferromagnetic and a Canted Antiferromagnetic State for [Bis(pentamethylcyclopentadienyl)-iron(III)][Tetracyanoethenide], [FeCp2*][TCNE]

“…The rate of increase of T c (P) for the FeCp 2 *-based magnets, 0.24 ± 0.04 K/kbar (Table 1), however, is substantially reduced from 6.6 to 7.1 K/kbar reported for Mn II (TCNE)I(OH 2 ) and Mn II (TCNE) 3/2 (I 3 ) 1/2 . 19 In contrast, in addition to having a substantially larger dT…”

“…Furthermore, the pressure dependent behavior of [FeCp 2 *][TCNE] is more complex than that observed for 1-D [MnTRPP][TCNE] [H 2 TRPP = meso -tetrakis(4-R-substitutedphenyl)porphyrin; R = OC 10 H 21 , OC 14 H 29 , F], which undergoes a decrease in T c ( P ) with a small applied pressure, before reaching a minimum, and then T c ( P ) increases with additional increasing pressure, or 2-D, layered Mn II (TCNE)I(OH 2 ) and 3-D structured Mn II (TCNE) 3/2 (I 3 ) 1/2 · z THF for which T c ( P ) increases with increasing pressure but does not have pressure dependent magnetic transition to a different magnetic state. The rate of increase of T c ( P ) for the FeCp 2 *-based magnets, 0.24 ± 0.04 K/kbar (Table ), however, is substantially reduced from 6.6 to 7.1 K/kbar reported for Mn II (TCNE)I(OH 2 ) and Mn II (TCNE) 3/2 (I 3 ) 1/2 . In contrast, in addition to having a substantially larger d T c ( P )/d T , 3-D network structured Mn II (TCNE)[C 4 (CN) 8 ] 1/2 · z CH 2 Cl 2 and [Ru 2 (O 2 CMe) 4 ] 3 [Cr(CN) 6 ] undergo different types of magnetic transitions.…”

“…In addition, the pressure dependence for [FeCp 2 *][TCNE] is compared with that recently reported for the similarly structured ferromagnetic ( FO ) and metamagnetic ( MM ) polymorphs of [FeCp 2 *][TCNQ], [FeCp 2 *][C 4 (CN) 6 ], [FeCp 2 *][DDQ], and [FeCp 2 *][DCNQ], as well as other TCNE-based magnets including 1-D [MnTRPP][TCNE] [H 2 TRPP = meso -tetrakis(4-R-substitutedphenyl)porphyrin; R = OC 10 H 21 , OC 14 H 29 , F], 2-D Mn II (TCNE)I(OH 2 ), and 3-D Mn II (TCNE) 3/2 (I 3 ) 1/2 · z THF and Mn II (TCNE)[C 4 (CN) 8 ] 1/2 · z CH 2 Cl 2 . In addition to these materials, pressure also has been used to study other organic-based magnets, and both the enhancement of T c , e.g., β-4′-cyanotetrafluorophenyldithiadiazolyl] and benzo(1,2-d′:bis[1,3,2]dithiazole) tetrachlorogallate, and the reduction of T c , e.g., 4-nitrophenylnitronyl nitroxide and [TDAE] + [C 60 ] − [TDAE = tetrakis(dimethylamino)ethane], have been observed.…”