Structure and magnetic properties of the two-dimensional ferrimagnet (NEt4)[[Mn(salen)]2Fe(CN)6]: investigation of magnetic anisotropy on a single crystal

The title compound, (NEt(4))[[Mn(salen)](2)Fe(CN)(6)] (1), was synthesized via a 1:1 reaction of [Mn(salen)(H(2)O)]ClO(4) with (NEt(4))(3)[Fe(CN)(6)] in a methanol/ethanol medium (NEt(4)(+) = tetraethylammonium cation, salen(2)(-) = N,N'-ethylenebis(salicylidene)iminate). The two-dimensional layered structure of 1 was revealed by X-ray crystallographic analysis: 1 crystallizes in monoclinic space group P2(1)/c with cell dimensions of a = 12.3660(8) A, b = 15.311(1) A, c = 12.918(1) A, beta = 110.971(4) degrees, Z = 2 and is isostructural to the previously synthesized compound, (NEt(4))[[Mn(5-Clsalen)](2)Fe(CN)(6)] (5-Clsalen(2-) = N,N'-ethylenebis(5-chlorosalicylidene)iminate; Miyasaka, H.; Matsumoto, N.; Re, N.; Gallo, E.; Floriani, C. Inorg. Chem. 1997, 36, 670). The Mn ion is surrounded by an equatorial salen quadridentate ligand and two axial nitrogen atoms from the [Fe(CN)(6)](3-) unit, the four Fe[bond]CN groups of which coordinate to the Mn ions of [Mn(salen)](+) units, forming a two-dimensional network having [[bond]Mn[bond]NC[bond]Fe[bond]CN[bond]](4) cyclic repeating units. The network is spread over the bc-plane of the unit cell, and the layers are stacked along the a-axis. The countercation NEt(4)(+) is located between the layers. Compound 1 is a ferrimagnet with T(c) = 7.7 K and exhibits hysteresis with a remnant magnetization of 13.44 cm(3).mol(-1) (M/N mu(B) = 2.4) at zero field and a coercivity of 1000 Oe when the powder sample was measured at 1.9 K. Magnetic measurements of a direction-arranged single crystal were also carried out. The orientation of the crystallographic axes of a selected single crystal was determined by X-ray analysis, and magnetization was measured when an external field was applied in the a*, b, and c directions. The magnetization in the a* direction increased more easily than those in the b and c directions below the critical temperature. No hysteresis was observed only for the measurement in the a* direction, indicating the presence of strong structural anisotropy with potential anisotropy on Mn(III) ions.     

Photoinduced ferrimagnetic systems in Prussian blue analogues C(I)xCo4[Fe(CN)6]y (C(I) = alkali cation). 4. Characterization of the ferrimagnetism of the photoinduced metastable state in Rb1.8Co4[Fe(CN)6]3.3-13H2O by K edges X-ray magnetic circular dichroism.

In Part 2 of this work, the electronic and local structure of the photoinduced metastable magnetic state of the Prussian blue analogue Rb1.8Co4[Fe(CN)6]3.3-13H2O were characterized. To determine directly the relative orientation of the magnetic moments of Co(II) and Fe(III) ions in the metastable state, and the nature of the exchange interaction between them, we performed X-ray magnetic circular dichroism (XMCD) experiments at the cobalt and iron K edges. We present the first direct experimental evidence of the antiferromagnetic interaction between the cobalt and the iron ions, leading to the ferrimagnetism of the photoinduced metastable state.     

Comment on "Theoretical study of the photoinduced transfer among the ground state and two metastable states in [Fe(CN)5NO]2-" [J. Chem. Phys. 122, 074314 (2005)

We discuss the computational results of the "Theoretical study of the photoinduced transfer among the ground state and two metastable states in [Fe(CN)5NO]2-" [J. Chem. Phys. 122, 074314 (2005)] with respect to our previously reported polarized absorption study on the metastable states SI and SII in Na2[Fe(CN)5NO]2H2O [D. Schaniel, J. Schefer, B. Delley, M. Imlau, and Th. Woike, Phys. Rev. B 66, 085103 (2002)].     

Formation of abundant [Pb(H2O)]2+ by ligand-exchange reaction between [Pb(N2)n]2+ (n = 1-3) and H2O

Doubly charged lead monohydrate, [Pb(H2O)]2+, was predicted to be unstable in the gas phase, but it has recently been observed to form in low yield via ligand change between [Pb(CH3CN)]2+ and H2O [Shi, T.; Orlova, G.; Guo, J.; Bohme, D. K.; Hopkinson, A. C.; Siu, K. W. M. J. Am. Chem. Soc. 2004, 126, 7975-7980]. Here we report that abundant [Pb(H2O)]2+ is formed in the gas phase by ligand-exchange reaction between [Pb(N2)n]2+ (n = 1-3) and water after collisional activation. Density functional theory has been used to examine the ligand-exchange reaction profile. A comparison of the potential-energy surfaces between [Pb(N2)]2+ and [Pb(CH3CN)]2+ reacting with H2O provides strong evidence that the ligand-exchange reaction of [Pb(N2)]2+ with H2O to form [Pb(H2O)]2+ is more efficient than that of [Pb(CH3CN)]2+ with H2O.     

Fe L-edge XAS studies of K4[Fe(CN)6] and K3[Fe(CN)6]: a direct probe of back-bonding

Distinct spectral features at the Fe L-edge of the two compounds K3[Fe(CN)6] and K4[Fe(CN)6] have been identified and characterized as arising from contributions of the ligand pi orbitals due to metal-to-ligand back-bonding. In addition, the L-edge energy shifts and total intensities allow changes in the ligand field and effective nuclear charge to be determined. It is found that the ligand field term dominates the edge energy shift. The results of the experimental analysis were compared to BP86 DFT calculations. The overall agreement between the calculations and experiment is good; however, a larger difference in the amount of pi back-donation between Fe(II) and Fe(III) is found experimentally. The analysis of L-edge spectral shape, energy shift, and total intensity demonstrates that Fe L-edge X-ray absorption spectroscopy provides a direct probe of metal-to-ligand back-bonding.     

Preparation of57Fe enriched K4[Fe(CN)6] and K3[Fe(CN)6]

A simple method to prepare⁵⁷Fe enriched K₄[Fe(CN)₆] and K₃[Fe(CN)₆] is described. The yields of the products are much better than those reported in the literature so far. The enrichment is essential for⁵⁷Fe Mössbauer investigation in a variety of Prussiate type complexes and other inorganic compounds which are conveniently prepared from K₄[Fe(CN)₆] and K₃[Fe(CN)₆]. K₄[Fe(CN)₆] was obtained by reacting freshly prepared Fe(OH)₃ with glacial acetic acid and treating with iron acetate in boiling aqueous solution of KCN. The novel feature of the procedure to obtain K₃[Fe(CN)₆] is that the oxidation of K₄[Fe(CN)₆] has been carried out in the solid state by passing chlorine gas over the powdered specimen. K₃[Fe(CN)₆] was crystallised from alkaline solution of this oxidised powder. The compounds were characterised by Mössbauer spectroscopy.     

Structure of an I- x (H2O)6 anion cluster in a 3D anion crystal host [I x (H2O)6Fe(CN)6 x H2O]4-

A planar structure of an anion cluster I- x (H2O)6 in a 3D supramolecular complex [Ru(bpy)3]2[I x (H2O)6Fe(CN)6 x H2O] has been determined by single-crystal X-ray analysis. In the supramolecule, the anion cluster I- x (H2O)6, together with the anion [Fe(CN)6 x H2O]2-, acts as a 3D crystal host, and the [Ru(bpy)3]2+ cations, as the guest molecules, occupy the vacancies of the 3D host framework. This is the first crystal example of the anion cluster I- x (H2O)6.     

Application of a universal force field to mixed Fe/Mo-S/Se cubane and heterocubane clusters. 1. Substitution of sulfur by selenium in the series [Fe4X4(YCH3)4]2-; X = S/Se and Y = S/Se

A series of Fe-S and Fe-Se cubane clusters containing all four combinations of the general formula [Fe(4)X(4)(Y-CH(3))(4)](2)(-) (X = S/Se, Y = S/Se) is investigated with FTIR and Raman spectroscopy. The terminally selenolate coordinated clusters (Y = Se) are prepared by a new synthetic route. All four cluster compounds are structurally characterized by X-ray single-crystal structure determination. Infrared and Raman spectra of all compounds are presented and interpreted with normal coordinate analysis. The corresponding force fields are based on that developed for the Fe(4)S(4)-benzyl cluster (Czernuszewicz, R. S.; Macor, K. A.; Johnson, M. K.; Gewirth, A.; Spiro, T. G. J. Am.Chem. Soc. 1987, 109, 7178-7187). An empirical procedure is presented to convert Fe-S into Fe-Se force constants. Only minor changes in force constants are found upon S --> Se exchange, reflecting the similarity of the Fe-S and Fe-Se bonds. The drastic frequency shifts in the metal-ligand region observed upon substitution of sulfur by selenium are, therefore, primarily due to the corresponding mass changes.     

Syntheses, structures, and magnetic properties of cyano-bridged heterobimetallic complexes based on [Fe(bpca)(CN)3]-

Two new cyano-bridged one-dimensional heterobimetallic coordination polymers, [(bpca)(2)Fe(III)(2)(CN)(6)Cu(H(2)O)(2).1.5H(2)O](n)() (2) and [(bpca)Fe(III)(CN)(3)Cu(bpca)(H(2)O).H(2)O](n)() (3), and a trinuclear complex, [(bpca)(2)Fe(III)(2)(CN)(6)Mn(CH(3)OH)(2)(H(2)O)(2)].2H(2)O (4), have been synthesized using the tailored tricyanometalate precursor (Bu(4)N)[Fe(bpca)(CN)(3)].H(2)O (1) (Bu(4)N(+) = tetrabutylammonium cation; bpca = bis(2-pyridylcarbonyl)amidate anion) as a building block and structurally characterized. In complex 2, the Cu(II) ions are six-coordinated in an elongated distorted octahedral environment, and they are linked by distorted octahedrons of [Fe(bpca)(CN)(3)](-) to form 1D chain of squares. Complex 3 is an unexpected chiral heterobimetallic helical chain complex, in which the helical chain consists of the asymmetric unit of [(bpca)Fe(CN)(3)Cu(bpca)(H(2)O)]. In complex 4, there are two independent trinuclear clusters in one asymmetric unit, and the coordination modes of the two methanol and two water molecules coordinating to the central Mn(II) ion are different (cis and trans). Complex 2 shows metamagnetic behavior with a Neel temperature of T(N) = 2.2 K and a critical field of 250 Oe at 1.8 K, where the cyanides mediate the intrachain ferromagnetic coupling between the Cu(II) and Fe(III) ions. Complex 3 shows ferromagnetic coupling between Cu(II) and Fe(III) ions, the best-fit for chi(M)T versus T using a 1D alternating chain model leads to the parameters J(1) = 7.9(3) cm(-)(1), J(2) = 1.03(2) cm(-)(1), and g = 2.196(3). Complex 4 exhibits ferrimagnetic behavior caused by the noncompensation of the local interacting spins (S(Mn) = 5/2 and S(Fe) = 1/2) which interact antiferromagnetically through bridging cyano groups.     

掠射椭圆偏振术对K4[Fe(CN)6]/K3[Fe(CN)6]表面溶液层性质的研究

目前广泛应用于表面反应现场研究的椭圆偏振技术都采用反射式测量方案[1，2]，这种方法通过测量光在电极表面反射时描述偏振光相位变化的参量和振幅变化的参量．以及上述两个参量的变化趋势并结合预先设定的表面膜模型计算表面膜厚度和复折射系数等光学参量[3]反射式椭圆偏振测     

Photoinduced magnetic properties of sequentially deposited thin films of RbjCok[Fe(CN)6]l · nH2O

Using sequential deposition methods, we have generated two different films of Rb_jCo_k[Fe(CN)₆]_l · nH₂O for magneto-optical studies. The synthesis protocol was intentionally varied in order to generate samples with different degrees of surface homogeneity. As a consequence, film 1 possessed a powder-like rough surface, while film 2 was a smooth, quasi-two-dimensional film. Upon irradiation at 5 K with an external magnetic field of 200 G perpendicular to the film surface, the magnetization of film 1 increased, whereas the magnetization of film 2 decreased. This contrasting behavior is consistent with a dipolar field model describing the phenomena and is related to the novel anisotropy of the photoinduced magnetism in film 2, where the photoinduced magnetization increases or decreases depending on the orientation of the film with respect to the external field.     

Fe(bpym)(CN)4]-: a new building block for designing single-chain magnets

We herein present the preparation, crystal structure, magnetic properties, and theoretical study of new heterobimetallic chains of formula {[Fe(III)(bpym)(CN4)]2M(II)(H2O)2}.6H2O [bpym = 2,2'-bipyrimidine; M = Zn (2), Co (3), Cu (4), and Mn (5)] which are obtained by using the building block PPh4[Fe(bpym)(CN)4].H2O (1) (PPh4+= tetraphenylphosphonium) as a ligand toward the fully solvated MII ions. The structure of complex 1 contains mononuclear [Fe(bpym)(CN)4]- anions. Compounds 2-5 are isostructural 4,2-ribbonlike bimetallic chains where the [Fe(bpym)(CN)4]- unit acts as a bis-monodenate ligand through two of its four cyanide ligands toward the M atom. Water hexamer clusters (4) and regular alternating fused six- and four-membered water rings with two dangling water molecules (2, 3, and 5) are trapped between the cyanide-bridged 4,2-ribbonlike chains. 1 and 2 behave as magnetically isolated low-spin iron(III) centers. 3 behaves as a single-chain magnet (SCM) with intrachain ferromagnetic coupling, slow magnetic relaxation, hysteresis effects, and frequency-dependent ac signals at T < 7 K). As expected for a thermally activated process, the nucleation field (Hn) in 3 increases with decreasing T and increasing v. Below 1.0 K, Hn becomes temperature independent but remains strongly sweep rate dependent. In this temperature range, the reversal of the magnetization may be induced by a quantum nucleation of a domain wall that then propagates due to the applied field. 4 and 5 are ferro- and ferrimagnetic chains respectively, with metamagnetic-like behavior (4). DFT-type calculations and QMC methodology provided a good understanding of the magnetic properties of 3-5.     

Cyano-bridged bimetallic assemblies from hexacyanometalate, [M(CN)6](3-) (M = Mn(III) and Fe(III)), and [M(N4-macrocycle)]2+ (M=Fe(III), Ni(II) and Zn(II)) building blocks. Syntheses, multidimensional structures, and magnetic properties

Reactions between [M(N(4)-macrocycle)](2+) (M = Zn(II) and Ni(II); macrocycle ligands are either CTH = d,l-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane or cyclam = 1,4, 8, 11-tetrazaazaciclotetradecane) and [M(CN)(6)](3-) (M = Fe(III) and Mn(III)) give rise to cyano-bridged assemblies with 1D linear chain and 2D honeycomblike structures. The magnetic measurements on the 1D linear chain complex [Fe(cyclam)][Fe(CN)(6)].6H(2)O 1 points out its metamagnetic behavior, where the ferromagnetic interaction operates within the chain and the antiferromagnetic one between chains. The Neel temperature, T(N), is 5.5 K and the critical field at 2 K is 1 T. The unexpected ferromagnetic intrachain interaction can be rationalized on the basis of the axially elongated octahedral geometry of the low spin Fe(III) ion of the [Fe(cyclam)](3+) unit. The isostructural substitution of [Fe(CN)(6)](3-) by [Mn(CN)(6)](3-) in the previously reported complex [Ni(cyclam)](3)[Fe(CN)(6)](2).12H(2)O 2 leads to [Ni(cyclam)](3)[Mn(CN)(6)](2).16 H(2)O 3, which exhibits a corrugated 2D honeycomblike structure and a metamagnetic behavior with T(N) = 16 K and a critical field of 1 T. In the ferromagnetic phase (H > 1 T) this compound shows a very important coercitive field of 2900 G at 2 K. Compound [Ni(CTH)](3)[Fe(CN)(6)](2).13H(2)O 4, C(60)H(116)Fe(2)N(24)Ni(3)O(13), monoclinic, A 2/n, a = 20.462(7), b = 16.292(4), c = 27.262(7) A, beta = 101.29(4) degrees, Z = 4, also has a corrugated 2D honeycomblike structure and a ferromagnetic intralayer interaction, but, in contrast to 2 and 3, does not exhibit any magnetic ordering. This fact is likely due to the increase of the interlayer separation in this compound. ([Zn(cyclam)Fe(CN)(6)Zn(cyclam)] [Zn(cyclam)Fe(CN)(6)].22H(2)O.EtOH) 5, C(44)H(122)Fe(2)N(24)O(23)Zn(3), monoclinic, A 2/n, a = 14.5474(11), b = 37.056(2), c = 14.7173(13) A, beta = 93.94(1) degrees, Z = 4, presents an unique structure made of anionic linear chains containing alternating [Zn(cyclam)](2+) and [Fe(CN)(6)](3)(-) units and cationic trinuclear units [Zn(cyclam)Fe(CN)(6)Zn(cyclam)](+). Their magnetic properties agree well with those expected for two [Fe(CN)(6)](3-) units with spin-orbit coupling effect of the low spin iron(III) ions.     

Thermally induced linkage isomerization in KCd[Fe(CN)6]

Heating KCd[Fe(CN)₆]-5H₂O, either isothermally or in a differential scanning calorimeter, results in dehydration and linkage isomerization of the cyanides. In accord with hard—soft acid—base predictions, the product contains cyanide C-bonded to Cd₂₊. The integrated intensity of the peaks corresponding to the CN stretching vibrations indicates that two of the cyanides change bonding mode more readily than the others. Cyanide isomerization does not occur when KCd[Fe(CN)₆]-5H₂O is dehydrated at room temperature under vacuum conditions.     

Magnetic Properties of M3[Fe(Cn)6]2Xh2O (M = Co (II), Ni(II), Cu(II), Zn(II))

Compounds of the type M₃[Fe(CN)₆]₂XH₂O (M = Co(II), Ni(II), Cu(II), and Zn(II)) were prepared and magnetic properties of their powders were investigated by means of EPR spectra, Mössbauer effect and magnetic susceptibility measurements. The temperature dependence of the magnetization for the complexes Co₃[Fe(CN)₅]₂- 10H₂O, Ni₃[Fe(CN)₆]₂-10H₂O and Cu₃[Fe(CN)₆]₂-4H₂O revealed that below the critical temperatures 15, 22 and 20 K respectively, these complexes have zero-field magnetization. The magnetic hysteresis at 10 K for Co(II), Ni(II) and Cu(II) complexes was observed. Mössbauer spectra at 4.2 K for the compounds are discussed.     

Effect of film thickness on the photoinduced decrease in magnetism for thin films of the cobalt iron Prussian blue analogue Rb0.7Co4[Fe(CN)6]3.0

Films of the photomagnetic Prussian blue analogue Rb_0.7Co₄(Fe(CN)₆)_3.0(Co–Fe PBA) were deposited onto a Melinex^® substrate using two different multiple sequential adsorption methods. Film thickness, measured using atomic force microscopy, was controlled by the number of deposition cycles. The photoinduced magnetism known for the bulk Co–Fe PBA at low temperatures is also seen in the thin films, although the response is anisotropic. A photoinduced increase in magnetization is observed when the film is parallel (∥) to the applied magnetic field (H_E), while a photoinduced decrease is observed when the film is perpendicular (⊥) to a weak H_E. The relationship between the film thickness and the photoinduced decrease in magnetization is explored in this article. The photoinduced decrease is observed for films less than ∼200 nm thick. The behavior is explained by invoking a dipolar interaction between primordial ferrimagnetic domains and the photoswitchable pairs arrayed in the quasi-2D thin film.     

Mechanism for interplay between electron and ionic fluxes in KhFek[Fe(CN)6]l.mH2O compounds

This paper develops a framework for the interpretation of ionic insertion/deinsertion reactions in an aqueous environment taking place in transition-metal hexacyanoferrates of the general formula K(h)[Fe(2+) (CN)(6)](l).mH(2)O, also called Prussian Blue. Three different processes were fully separated in the electrochemistry of these films. It was clearly identified that one of these electrochemical processes involves the insertion/deinsertion of H(3)O(+) (hydrated protons) through the channels of the K(h)[Fe(2+) (CN)(6)](l).mH(2)O structure to reach the film electroneutrality during the electron transfer between Everitt's Salt and Prussian Blue. The other electrochemical processes involve K(+) or H(+) (proton) exchange through the water crystalline structure existing in the channels of the K(h)[Fe(2+)(CN)(6)](l).mH(2)O structure.     

Synthesis of Isotope Enriched (CN3H6)2[57Fe(CN)5NO] starting from 57Fe

A high‐yield, mmolar‐scale synthesis of pure guanidinium nitroprusside, (CN₃H₆)₂[⁽⁵⁷⁾Fe(CN)₅NO] (GNP) from iron metal is described. The iron metal contained pieces of 95.3% ⁵⁷Fe together with normal iron so that an isotope enrichment in ⁵⁷Fe of 25% was achieved. Single‐crystals of GNP could be grown in cubic shape and dimensions of about 3 × 4 × 4 mm³. The purity of the GNP product and the intermediates K₄[⁽⁵⁷⁾Fe(CN)₆] · 3 H₂O and Na₂[⁽⁵⁷⁾Fe(CN)₅NO] · 2 H₂O was ascertained by ⁵⁷Fe Mössbauer spectroscopy as well as ¹³C, ¹⁴N and ⁵⁷Fe NMR spectroscopy. The ⁵⁷Fe NMR chemical shift for [⁽⁵⁷⁾Fe(CN)₅NO]^2– in GNP was detected at +2004.0 ppm [vs Fe(CO)₅].     

Single-chain magnet (NEt4)[Mn2(5-MeOsalen)2Fe(CN)6] Made of Mn(III)-Fe(III)-Mn(III) trinuclear single-molecule magnet with an S(T) = 9/2 spin ground state

The cyano-bridged trinuclear compound, (NEt(4))[Mn(2)(salmen)(2)(MeOH)(2)Fe(CN)(6)] (1) (salmen(2)(-) = rac-N,N'-(1-methylethylene)bis(salicylideneiminate)), reported previously by Miyasaka et al. (ref 19d) has been reinvestigated using combined ac and dc susceptibility measurements. The strong frequency dependence of the ac susceptibility and the slow relaxation of the magnetization show that 1 behaves as a single-molecule magnet with an S(T) = (9)/(2) spin ground state. Its relaxation time (tau) follows an Arrhenius law with tau(0) = 2.5 x 10(-)(7) s and Delta(eff)/k(B) = 14 K. Moreover, below 0.3 K, tau saturates around 470 s, indicating that quantum tunneling of the magnetization becomes the dominant process of relaxation. (NEt(4))[Mn(2) (5-MeOsalen)(2)Fe(CN)(6)] (2) (5-MeOsalen(2)(-) = N,N'-ethylenebis(5-methoxysalicylideneiminate)) is a heterometallic one-dimensional assembly made of the trinuclear [Mn(III)(SB)-NC-Fe(III)-CN-Mn(III)(SB)] (SB is a salen-type Schiff-base ligand) motif similar to 1. Compound 2 has two types of bridges, a cyano bridge (-NC-) and a biphenolate bridge (-(O)(2)-), connecting Mn(III) and Fe(III) ions and the two Mn(III) ions, respectively. Both bridges mediate ferromagnetic interactions, as shown by modeling the magnetic susceptibility above 10 K with g(av) = 2.03, J(Mn)(-)(Fe)/k(B) = +6.5 K, and J'/k(B) = +0.07 K, where J' is the exchange coupling between the trimer units. The dc magnetic measurements of a single crystal using micro-SQUID and Hall-probe magnetometers revealed a uniaxial anisotropy (D(T)/k(B) = -0.94 K) with an easy axis lying along the chain direction. Frequency dependence of the ac susceptibility and time dependence of the dc magnetization have been performed to study the slow relaxation of the magnetization. A mean relaxation time has been found, and its temperature dependence has been studied. Above 1.4 K, both magnetic susceptibility and relaxation time are in agreement with the dynamics described in the 1960s by R. J. Glauber for one-dimensional systems with ferromagnetically coupled Ising spins (tau(0) = 3.7 x 10(-)(10) s and Delta(1)/k(B) = 31 K). As expected, at lower temperatures below 1.4 K, the relaxation process is dominated by the finite-size chain effects (tau'(0) = 3 x 10(-)(8) s and Delta(2)/k(B) = 25 K). The detailed analysis of this single-chain magnet behavior and its two regimes is consistent with magnetic parameters independently estimated (J'and D(T)) and allows the determination of the average chain length of 60 nm (or 44 trimer units). This work illustrates nicely a new strategy to design single-chain magnets by coupling ferromagnetically single-molecule magnets in one dimension.