Strategies to Design Single-Molecule Toroics Using Triangular {Ln3} n Motifs.

In this mini-review, we highlight the research advanced in the field of single-molecule toroics (SMTs) with a specific focus on the triangular Ln3-based SMTs. SMTs are molecules with a toroidal magnetic state and are insensitive to homogeneous magnetic fields but cooperate with charge and spin currents. The rapid growth in the area of SMTs witnessed in recent years is correlated not only to the interest to understand the fundamental physics of these molecules but also to the intriguing potential applications proposed, as the SMTs have several advantages compared to other classes of molecules such as single-molecule magnets (SMMs). The important chemico-structural strategy in SMT chemistry is to choose and design ligand and bridging species that will help to attain toroidal behavior. Considering this primarily, all the Dy3 SMTs reported so far are summarized, showing how utilizing different peripheral ligands influences the toroidal nature beyond the role of the symmetry of the molecule and stronger dipolar interactions. Likewise, linking Dy3 toroidal units through 3d ions with suitable peripheral/bridging ligands enhances the toroidal magnetic moment and leads to fascinating physics of ferrotoroidal/antiferrotoridal behavior. Further, we have also summarized the recently reported non-Dy triangular SMTs.

Introduction

Single-molecule toroics (SMTs) are bistable molecules similar to single-molecule magnets (SMMs) but with a toroidal magnetic state. The noncollinear arrangement of the magnetic moments of each metal center in SMTs can lead to interesting magnetic behavior.[1−12] SMTs have possible wide-ranging applications in quantum computing, memory storage, and spintronics devices and the development of magneto–electric coupling for multiferroic materials.[13−15] Noteworthily, the magnetic field produced by toroidal moments decays more rapidly than the field produced by a magnetic dipole; thus, the memory storage devices or qubits designed utilizing toroidal moments will be more densely packed than SMMs or spin qubits, respectively.[3] For a molecule to show SMT behavior, it should possess the following criteria: (a) high molecular symmetry, (b) local magnetic moment, and (c) strong intramolecular magnetic interactions.[11,12] Both experiments and theory have played a vital role in detecting the presence of toroidal magnetic moments. Particularly ab initio calculations based on the CASSCF/RASSI-SO method offered significant insights into the SMT behavior.[11,12] Usually, SMT complexes display a stepped hysteresis profile and a pronounced S-shaped curve in the magnetization isotherm plots at low fields and low temperatures; however, these profiles are not witnessed in some cases.[1−12] Additionally, single-crystal magnetic studies, EPR, and Torque magnetometry offer clues on the SMT molecules,[11] though unambiguous confirmation requires accurate spectral methods such as NMR, which can probe the magnetic dynamics of individual Ln(III) ions via line broadening.[16,17]

There are different shaped SMTs with numerous examples of Dy3 triangles,[1−5,9] planar/cubic Dy4,[18,19] wheel Dy6,[17,20] a snub-square Dy8,[21] and double Dy3 + Dy3 triangles.[6,7,22,23] Toroidal moments are reported for dysprosium (DyIII) complexes; however, recently we reported the SMTs possessing TbIII and HoIII ions as well.[20,24] SMTs have been reported by connecting two molecular triangles, for example, via a 3d ion, and such systems offer a chance to observe properties such as ferrotoroidicity in 3d–4f-based complexes,[25] which in turn is of interest for the strategy of molecule-based multiferroics with a magneto–electric coupling.[13−15] A con-rotating ferrotoroidal ground-state behavior in a series of heptanuclear {CrLn6} complexes (Ln = Dy, Tb, Ho) has been observed by us.[24,25] The ferrotoroidal moments were recently observed in another large {Fe18Dy6} cluster where two molecular Dy3 triangles are connected by a {Fe18} ring.[26] Though several SMTs have been reported to date, the most seen archetype system is the triangular Dy3 motif (Figure ). Therefore, here we represented mainly the triangle-shaped SMTs and classified them based on their peripheral ligands. Moreover, how toroidicity is enhanced by connecting two Dy3 triangles through bridging ligands or via a 3d ion and the other lanthanide-based Ln3 triangular SMTs is also discussed in this mini-review, using representative examples (see Table ).

Figure 1

Schematic representation of a different type of triangular SMTs discussed here. Red arrows are Dy(III) local g magnetization axes. Middle and right pictures are representing ferrotoroidal (FT) and antiferrotoroidal (AFT) behavior.[24,25]

Table 1

Summary of All Triangular Shaped SMTs Discussed in This Mini-Review

molecular formula (complex no.)	peripheral ligandsa	ϕ (deg)b	θ (deg)c	SMT type	M/μB	ref
[Dy3L3(μ3-OH)2Cl(H2O)5]Cl (1-Dy3)	o-vanillin	8.72–9.49	2.4–8.8	mixed moment	0.56	(1, 2, 5)
[Dy3(H2L)(HL)(NO3)4] (2-Dy3)	N,N,N′,N′-tetrakis(2-hydroxyethyl)-ethylene-diamine	0.57–10.4		mixed moment	11.5	(9)
[Dy3(Hpovh)3(μ3-OH)2(NO3)3(CH3 OH)2H2O]·NO3·3CH3OH·2H2O (3-Dy3)	N-(pyridyl-methylene)-o-vanilloyl-hydrazone (H2povh)					(27)
[Dy3(H2vovh)3(μ3-OH)2Cl2(CH3OH)(H2O)3][Dy3 (H2vovh)3(μ3-OH)2Cl2(H2O)4]·Cl4·2CH3OH·2CH3CN·7H2O (4-Dy3)	N-vanillidene-o-vanilloylhydrazone (H3vovh)					(27)
[DyIII3(teaH2)3(OH)(paa)3]Cl2 (5-Dy3)	triethanolamine (teaH3) and N-(2-pyridyl)-acetoacetamide (paaH)		13	mixed moment	6.4	(20)
[Dy3(o-dppd)3(OH)2Cl2(H2O)4]Cl2·7H2O (6-Dy3)	1,3-bis(pyridin-2-yl)propane-1,3-dione (o-dppdH)		2.8–5.7	mixed moment		(28)
[CrIIIDyIII6(o-tol)12(OH)8(NO3)(MeOH)5]·3MeOH (7-Cr{Dy3}2)	ortho-toluate	1.1–7.9	0.3–4.7	enhanced FT	9.75	(25)
[DyIII6MnIII(OH)8(o-tol)12(MeOH)5(NO3)]·4MeOH (8-Mn{Dy3}2)	ortho-toluate	–2.23		enhanced FT		(29)
[DyIII6FeIII(OH)8(o-tol)12(MeOH)5(NO3)]·4MeOH (9-Fe{Dy3}2)	ortho-toluate	–3.82		enhanced AFT	4.4	(29)
[DyIII6CoIII(OH)8(o-tol)12(MeOH)5(NO3)]·4MeOH (10-Co{Dy3}2)	ortho-toluate	–3.63		enhanced FT	0.01	(29)
[DyIII6AlIII(OH)8(o-tol)12(MeOH)5(NO3)]·4MeOH (11-Al{Dy3}2)	ortho-toluate	4.58		enhanced FT		(29)
[DyIII6CrIII(OH)8(o-tol)12(MeOH)6]Cl·6MeOH (7′-Cr{Dy3}2)	ortho-toluate	0.22		enhanced FT		(29)
[DyIII6MnIII(OH)8(o-tol)12(MeOH)6]Cl·6MeOH (8′-Mn{Dy3}2)	ortho-toluate	–3.66		enhanced AFT		(29)
[DyIII6FeIII(OH)8(o-tol)12(MeOH)6]Cl·6MeOH (9′-Fe{Dy3}2)	ortho-toluate	1.17		enhanced FT	0.01	(29)
[DyIII6CoIII(OH)8(o-tol)12(MeOH)6]Cl·6MeOH (10′-Co{Dy3}2)	ortho-toluate	–1.68		enhanced FT		(29)
[DyIII6AlIII(OH)8(o-tol)12(MeOH)6]Cl·6MeOH (11′-Al{Dy3}2)	ortho-toluate	–6.40		enhanced FT		(29)
{[Cu(Val)2CH3OH][Dy3L3(μ3-OH)2(NO3)4]}n (12-Cun{Dy3}n)	enantiopure valine (l- or d-Val), o-vanillin	10.3–15.61	0.1–10.2	zero toroidal moment	0.8	(8)
[Fe18Dy6(ampd)12(Hampd)12(μ-OH)6(PhCO2)24](NO3)6·38MeCN (13-{Fe18}{Dy3}2)	2-amino-2-methyl-1,3-propanediol (H2ampd)			enhanced FT		(26)
[Dy6L4L′2(μ3-OH)4(H2O)9Cl]Cl5·15H2O (14-{Dy3}2)	o-vanillin, 2-hydroxymethyl-6-methoxyphenol	82.1–82.5	<3 and 10	mixed moment		(6)
[Dy6(μ4-O)L4(NO3)4(CH3OH)]·CH3OH (15-{Dy3}2)	2,6-bis((2-hydroxyethylimino)methyl)-4-methylphenol		5.6–9.8	enhanced FT		(7)
[Dy6L2(μ3-OH)4(μ2-OH)2(H2O)12]·8Br·2CH3CN· 6CH3OH (16-{Dy3}2)	4,6-dihydrazinopyrimidine, o-vanillin,	2.9–6.9	3.2–7.0	mixed moment		(22)
[Dy6L′4(μ4-O)(NO3)4]·4CH3OH (17-{Dy3}2	2,6-bis((2-hydroxypropyl-imino)methyl)-4-methylphenol					(23)
[CrIIITbIII6(OH)8(o-tol)12(NO3)(MeOH)5]·2MeOH (7-Cr{Tb3}2)	ortho-toluate		5.3–13.9	enhanced FT		(24)
[CrIIIHoIII6(OH)8(o-tol)12(NO3)(MeOH)5]·2MeOH (7-Cr{Ho3}2)	ortho-toluate		5.9–32.4	enhanced FT		(24)
[TbIII3(teaH2)3(OH)(paa)3]Cl2 (5-Tb3)	triethanolamine (teaH3) and N-(2-pyridyl)-acetoacetamide (paaH)		≈2	mixed moment	0.9	(20)
[HoIII3(teaH2)3(OH)(paa)3]Cl2 (5-Ho3)	triethanolamine (teaH3) and N-(2-pyridyl)-acetoacetamide (paaH)		17.7–19.7	mixed moment	6.0	(20)
[Tb3(o-dppd)3(CH3CH2OH)3(μ3-OH)2Cl3][Tb3(μ3-OH)2(o-dppd)3(H2O)(CH3CH2OH)2Cl3]Cl2·H2O (6-Tb3)	1,3-bis(pyridin-2-yl)propane-1,3-dione (o-dppdH)		3.5–35.4	mixed moment		(28)
[Ho3(OH)2(o-dppd)3Cl(H2O)5]Cl3·3H2O (6-Ho3)	1,3-bis(pyridin-2-yl)propane-1,3-dione (o-dppdH)		1.9–3.9	mixed moment		(28)
[Zn3Dy3(μ6-CO3)(μ3-OH)3(L)3(H2O)3]·3(ClO4)·NO3 (18-Zn3Dy3)	6,6′-{[2-(dimethylamino) ethylazanediyl]bis(methylene)}bis(2-methoxy-4-methylphenol)	8.9	2.6	net toroidal moment	3.62	(30)
[Zn3Tb3(μ6-CO3)(μ3-OH)3(L)3(H2O)3]·3(ClO4)·NO3 (18-Zn3Tb3)	6,6′-{[2-(dimethylamino) ethylazanediyl]bis(methylene)}bis(2-methoxy-4-methylphenol)	2.4–7.6	4.4–11.2			(30)

Structure of pheripheral ligands presented in each triangle is shown in their respective figures.

ϕ is the angles of magnetic anisotropy axes with tangential direction of the Ln3 triangle. See Figure , right, inset.

θ is the angle of magnetic anisotropy axes that deviate from the Ln3 triangle.

Figure 2

(Left) Structure of the triangular unit in 1-Dy with the calculated anisotropy axes (dashed lines) on the Dy sites and the local magnetization (blue arrows) in the ground state. (Right) M vs H calculated and the experimental powder magnetization at T = 1.8 K for 1-Dy. Inset: the same simulations for T = 0.1 K and scheme of the two components of the ground Kramers doublet (KD). The arrows show the direction of magnetization on Dy(III) sites. The angles ϕI represent the deviation of the resultant anisotropy g axis from the tangential direction. Reprinted with permission from ref (5). Copyright 2009, The Royal Society of Chemistry.

Comparing Dy3 SMTs by Peripheral Ligands

Many Dy triangular-based motifs have been reported in the literature, and in general, the majority of them have either one or two μ3-hydroxide or μ3-oxide as bridging ligands, with a notable structural difference being the peripheral ligands. A quick Cambridge Structural Database (CSD) reveal more than 250 {Dy3} structures reported in the literature, but only a handful of these structures exhibit toroidal moments. As the peripheral ligands are the major difference among the structures reported, the nature and position of donor atoms at the peripheral ligand play a critical role in determining the presence/absence of toroidal moments in the {Dy3} motif. These peripheral ligands connect two Dy centers in each molecule peripherally through their two or three coordination sites. The first Dy3 toroidal example has been reported by Powell and co-workers that have the ortho-vanillin as a peripheral ligand.[1] This complex has the noncollinear alignment of the local anisotropy axes on the three Dy(III) sites and a nonmagnetic ground state that helped them to achieve the SMT behavior predicted by theory and verified by experiments.[2,5] The thorough investigation of the toroidal magnetic moment in the ground state for this parent Dy3 triangle by experimental and theoretical studies offered an interesting archetype system to explore further and discover other new SMTs and opened up new frontiers in the broader area of SMMs.

Using the o-vanillin ligand, Powell and co-workers have synthesized the parent triangular Dy3 SMT having the formula of [Dy3L3(μ3-OH)2Cl(H2O)5]Cl (see Table , 1-Dy, HL = o-vanillin, Figure , left).[1] The three Dy(III) centers are connected by two μ3-OH groups. Furthermore, two Dy(III) ions are bridged by three μ2-phenoxo groups of o-vanillin ligands along each side of the triangle. Likewise, two Cl– ions and two H2O molecules coordinate to three DyIII ions above and below the triangle plane. Notably, the vanishing susceptibility at low temperature and an S-shaped curve in the M vs H plot at a lower field at 1.8 K (Figure , right) hint at the possibility of a triangular arrangement of the magnetic anisotropy (g) axes of each Dy(III) ion. The presence of an S-shaped curve at the magnetization isotherm plot and opening up the hysteresis at low temperature despite having a diamagnetic ground state were puzzling, and the presence of excited states and their associated slow relaxation was suggested as the reason for the puzzling observations.

Chibotaru et al. performed the complete active space self-consistent-field (CASSCF) ab initio calculations on the parent Dy3 triangle molecule to interpret the nature of the nonmagnetic ground state.[2,5] They found that the magnetic anisotropy axes are nearly tangential to the vertices of the triangle (the ϕ angles with the tangential direction are 8.72–9.49°, Figure , right, inset) and a small-angle deviation (θ = −4.3°, 8.8°, and −2.4° for Dy1–Dy3, respectively) with the Dy3 plane. Moreover, the magnetic axes in each Dy site make angles of ca. 120° with each other, and the lowest excited states are illustrated by a large magnetic moment of ca. 20 μB. The presence of the ∼D2 symmetry in each Dy(III) site causes the main magnetic anisotropy axes to point outward the Dy3 triangle. Moreover, the two oxygen atoms lying adjacent to the tangential axis (the OH oxygens of the o-vanillin ligands) have a higher negative charge and thus break the D2 symmetry. These results suggested that the deviation of magnetization vectors was primarily influenced by the o-vanillin ligand in 1-Dy that causes the nonmagnetic ground state and the toroidal arrangement of magnetic moments in each Dy center. The magnetic interaction (exchange and dipolar) between Dy sites supports the noncollinear Ising type that actually preserves the states of maximal magnetizations.

Furthermore, Sessoli et al. performed the single-crystal magnetic measurements combined with theoretical studies to confirm further the magnetic ground state of the 1-Dy.[4] Using an ideal model of trigonal symmetry the single-crystal magnetic data were fitted by considering magnetic moments on Dy sites lying in the plane of the molecule. The directions of the magnetic moments on Dy sites have been extracted with the angles ϕ = ±17° + n60° (n = 0, 1, 2, etc.) with respect to the tangential directions at each Dy center, and the best simulation was achieved corresponding to n = 1. The intramolecular dipolar interaction of magnetic exchange was evaluated as a function of ϕ, and 50% of the contribution was found to come from the most favorable configuration (ϕ = 90°). These results are, in general, in agreement with the results reported by Chibotaru and co-workers.

In 2012, Cheng and co-workers synthesized another triangular Dy3 SMT different from 1-Dy with the formula [Dy3(H2L)(HL)(NO3)4] (2-Dy, H4L = N,N,N′,N′-tetrakis(2-hydroxyethyl)-ethylene-diamine) using an amino-polyalcohol ligand (H4L) with four −OH arms.[9] Excluding Dy1···Dy3, sets of Dy(III) ions are singly bridged by a μ2-O from the H4L ligand; furthermore, three Dy(III) ions are doubly bridged by two μ3-O from ligands forming a pseudoisosceles triangle rather than the equilateral triangle, and overall two H4L ligands and four NO3– form this triangle. The transformation of triangular shape owing to the amino-polyalcohol ligand as a peripheral ligand also causes the different magnetic moments and anisotropy axes. Both low-temperature susceptibility and low-field magnetization (Figure , right) show non-negligible positive slopes that suggest a nonvanishing magnetic moment in the KD of 2-Dy (see Table ). This condition varies from the parent 1-Dy triangle, where the ground state was found to be nonmagnetic;[1] however, this is not the reason for the observation of toroidicity in 2-Dy. The orientations of the main magnetic anisotropy axes lie almost in the plane of the Dy3 triangles where the ϕ angles with the tangential direction are 0.57–10.40°, while these ϕ angles are found to be smaller (∼9°) in 1-Dy. The angles between the main anisotropy in Dy centers are found to be in the range of 25.10–77.97°, whereas this was found to be 120° in 1-Dy. As a result, the local magnetic moments in the ground KD do not compensate each other (ca. 11.5 μB); thus, the 2-Dy remains magnetic until very low temperatures. Overall, the amino-polyalcohol ligand might not be helpful for the nonmagnetic ground state; however, the presence of toroidal magnetic moments was attained. Moreover, ab initio calculations suggested that the dipolar interaction alone helps the toroidal alignment of the local magnetic moments. As the dipolar interactions are strongly correlated to the Dy···Dy distance, we envisage that the difference in dipolar interaction and hence the observed toroidicity is likely to be correlated to the presence of an amino-polyalcohol ligand in 2-Dy. A similar sign of exchange interactions further stabilizes the circular pattern of local magnetic moments in 2-Dy.

Figure 3

(Left) Molecular structure of 2-Dy with g axes (dashed lines) and local magnetizations (arrows) in the ground state. (Right) Temperature dependence of the χT. The red line is the ab initio calculated curve. Inset: molar magnetization at 2 K for 2-Dy. Reprinted with permission from ref (9). Copyright 2012, The Royal Society of Chemistry.

In 2012, Tang and co-workers synthesized two more Dy3 SMTs using the derivatives of the o-vanillin ligand.[27] These compounds have been assembled by attaching bulky hydrazine onto the vanillin group, maintaining the vortex-spin structure (Figure a and 4b). The two compounds, viz., [Dy3(Hpovh)3(μ3-OH)2(NO3)3(CH3OH)2H2O]·NO3·3CH3OH·2H2O (3-Dy, H2povh = N-(pyridylmethylene)-o-vanilloylhydrazone) and [Dy3(H2vovh)3(μ3-OH)2Cl2(CH3OH)(H2O)3][Dy3(H2vovh)3(μ3-OH)2Cl2(H2O)4]·Cl4·2CH3OH·2CH3CN·7H2O (4-Dy, H3vovh = N-vanillidene-o-vanilloylhydrazone), have a similar two μ3-OH bridged triangular archetype as observed in 1-Dy. The observed structural differences between these two structures and the parent 1-Dy structure resulted in different dynamic magnetic behavior revealed by their AC susceptibility. Even though the theoretical calculations are not performed on these complexes, both the vanishing susceptibility at low temperature and the noticeable S-shaped curve at the lower field in M vs H plots suggest a nonmagnetic ground state (Figure c and 4d). This might suggest that these two complexes possess a toroidal magnetic moment. Since these two complexes possess the derivative of the o-vanillin ligand, we envisage that they could also show similar kinds of magnetic anisotropy axes tangential to the vertices of the Dy3 triangle and a small-angle deviation to the Dy3 plane; however, this can not be confirmed as ab initio calculations or experimental verifications are lacking.

Figure 4

Molecular structure of (a) 3-Dy and (b) 4-Dy. Field dependences of magnetization for (c) 3-Dy and (d) 4-Dy. Reprinted with permission from ref (27). Copyright 2012, Americal Chemical Society.

In 2019, Langley et al. reported the magnetic and theoretical characteristics of a triangular Dy complex (Figure a), [DyIII3(teaH2)3(OH)(paa)3]Cl2 (5-Dy; teaH3 = triethanolamine and paaH = N-(2-pyridyl)-acetoacetamide], along with their Tb and Ho analogues.[20] The three Dy ions are bridged by a μ3-OH ligand, and the three triethanolamine ligands connecting Dy ions via one O-atom of the singly deprotonated −OH arm and two protonated −OH arms and the N-atom chelate. Each paa– ligand chelates to one DyIII ion through the β-diketonate functionality. An essential structural alteration between the parent 1-Dy and 5-Dy is the presence of two μ3-OH bridging ligands in 1-Dy, whereas this complex has just one central μ3-OH bridge. An S-shaped curve was not observed for 5-Dy in the M vs H plots in low fields (Figure , right, inset); however, ab initio CASSCF calculations predict that this 5-Dy molecule exhibits SMT behavior. The magnetic anisotropy axes are found to lie closer to the Dy3 plane, with a deviation angle (θ) of 13° observed, and the same is found to be in the range of 2.4–8.8° for 1-Dy.[1] These axes are almost tangential to the vertices of the Dy3 triangle, similar to 1-Dy, which affirms the presence of a toroidal magnetic moment. As a consequence, noncollinear arrangement between localized magnetic moments owing to the presence of dipolar interactions does not compensate each other, resulting in a small magnetic moment (ca. 6.4 μB), which is three times smaller compared to the value calculated for the 1-Dy (∼20 μB). This result agrees well with the observation of nonvanishing susceptibility at low temperature (Figure , right) as observed in 2-Dy.[9] In this example as well, the toroidal magnetic moments are found to be favored by both dipolar and exchange interactions, both of which are controlled by the peripheral triethanolamine ligand. As triethanolamine is also an amino-polyalcoholic ligand, it appears that such ligands favor mixed magnetic moments of the toroidal ground state, as observed in 2-Dy having a similar ligand framework.[9,10]

Figure 5

(Left) Molecular structure and the orientations of the magnetic anisotropy axes in the ground doublets on the DyIII sites in 5-Dy. (Right) χT vs T plots for 5-Dy in an applied dc field of 0.1 and 1 T. (Inset) The molar magnetization data for 5-Dy. The solid lines are calculated data. Reprinted with permission from ref (20). Copyright 2019, The Royal Society of Chemistry.

In 2020, Caporale et al. have reported a different Dy3 SMT and characterized their toroidal behavior using magnetic instruments and ab initio calculations.[28] This complex having the formula of [Dy3(o-dppd)3(OH)2Cl2(H2O)4]Cl2·7H2O (6-Dy, Figure , left) has been synthesized using a pyridyl-containing β-diketonate, 1,3-bis(pyridin-2-yl)propane-1,3-dione (o-dppdH). Each β-diketonate ligand chelates two DyIII centers where one O-atom is shared (μ2-O) between the two DyIII centers, and the other O-atom binds solely to one DyIII atom. Likewise, a pyridyl nitrogen atom coordinates to each DyIII center; however, the other pyridyl nitrogen atom is left unbound. Importantly, all three DyIII centers are bridged by two central μ3-OH ligands that lie above and below the Dy3 plane. Like o-vanillin Dy3 systems (1-Dy), this complex also possesses a triangular dodecahedron geometry with D2 symmetry. The S-shaped curve in the M vs H plot at low fields is not observed. However, ab initio calculations predict that orientations of the magnetic anisotropy axes in each Dy center in the ground state form a circular pattern, suggesting SMT behavior for 6-Dy. The localized molecular polarizability charge is higher at the bridging O of the diketo group and less for μ3-O, which makes the g axis lie in the direction of the bridging keto oxo group and helps to form the circular pattern of the anisotropy axis in 6-Dy. Moreover, with the small energy gap at the first excited state, the 6-Dy loses its toroidal arrangement due to the alteration of direction of the anisotropy axis in one of the Dy centers, which could be the reason for not observing the S-shaped curve in the M vs H plot. The ground-state magnetization vectors are found to lie nearly in the Dy3 plane with a small angle of deviation (θ = 2.8°, 3.0°, and 5.7° for Dy–Dy, respectively), and these are similar to the values obtained for the o-vanillin Dy3 systems (1-Dy).[1] The presence of the D2 symmetry at each Dy(III) site and a huge negative charge on the O atom of the diketo group enforce the anisotropic g axis to lie along with this bond which is tangential to the vertices of the Dy3 triangle. This observation is very similar to the one found for 6-Dy.

Figure 6

(Left) Molecular structure and arrangement of the anisotropic axis (green and black arrows) for the ground-state KDs in 6-Dy. Violet = Dy, Red = O, Gray = C, Blue = N, Green = Cl. (Right) Magnetization isotherms (2–20 K) in applied fields 0–5 T for 6-Dy. Reprinted with permission from ref (28). Copyright 2020, The Royal Society of Chemistry.

Double {Dy3} Triangles Connecting via 3d Ions

It is reported that two Dy3 triangles displaying toroidal states are connected via a 3d ion or by peripheral ligands. In that case, the two toroidal moments can lead to enhanced toroidal moments, an essential criterion for realizing potential applications proposed for molecular ferrotoroidicity and the development of molecule-based multiferroics.[7,8,10,15,25] There are a few examples where two Dy3 triangles connected by the peripheral ligands have been reported.[6,7,22,23] In order to isolate a complex with a ferrotoroidal ground state, we have focused our attention on {3d–4f} coordination complexes containing anisotropic Dy ions and transition metal ions such as Cr(III).[25]

{Dy3}–Cr–{Dy3} Motif to Achieve Ferrotoroidicity

We have synthesized and theoretically studied a heptanuclear {CrDy6} complex, viz., [CrIIIDyIII6(o-tol)12(OH)8(NO3)(MeOH)5]·3MeOH (7-Cr{Dy}, o-tol = ortho-toluate).[25] It has been found that the metallic core is two triangular DyIII motifs that lie above and below a single central CrIII ion (Figure a and 7b), and it is stabilized by 8 μ3-OH and 12 o-tol, MeOH, and [NO3]− ligands. Two μ3-OH ligands bridge the three DyIII ions and form each triangle, whereas the other six μ3-OH ligands bridge two DyIII ions to the central CrIII ion. The 7-Cr{Dy} displays an S-shaped curve at 2 and 3 K at low fields in M vs H plots (Figure c) and a stepped shape of the magnetization in single-crystal micro-SQUID measurements (Figure d), which proposes the presence of a toroidal moment.[10,12] This {CrDy6} complex displays slow magnetic relaxation and SMM behavior at temperatures below 2 K. Theoretical studies predict that the 7-Cr{Dy} complex shows a very rare ferrotoroidically (FT) coupled ground state determined by dipolar coupling between the two con-rotating toroidal Dy3 triangles. A pseudo S6 axis passes via the CrIII ion and the center of both of the {DyIII3} triangular motifs (Figure b). The calculated anisotropy axes are found to lie in the Dy3 plane with an out-of-plane angle (θ) of 0.3, 4.5, and 4.7° for Dy1, Dy2, and Dy3, respectively. These calculated g axes are perfectly aligned with the tangents to an ideal circumference enclosing the triangles (the ϕ angle of the anisotropy axis with these tangential directions is in the range of 1.1–7.9°). These values are almost similar to the values calculated for the parent 1-Dy. By comparing the hysteresis profile of 7-Cr{Dy} with the parent 1-Dy toroidal complex,[1] we find that the profile is superior for the former, particularly comparing the coercitivity. This finding suggests that coupling between the two Dy3 triangles in 7-Cr{Dy} enhances the toroidal magnetic moment due to the presence of the ferrotoroidically coupled ground state.[25] The dipolar-induced FT/AFT (antiferrotoroidal) splitting is calculated as ∼0.28 cm–1, and the spin of Cr(III) is freely fluctuating.

Figure 7

(a) Molecular structure of 7-Cr{Dy}. (b) The orientations of the g axes in the ground KD on each Dy site (dotted lines) in 7-Cr{Dy}. Blue arrows are the local magnetic moment in the ground KD. The con-rotation of the toroidal magnetic moment is shown by black arrows, and the yellow arrow is the S6 symmetry axis. (c) The measured (blue circles) and simulated (orange solid line) plot of an M vs H isotherm at 2 K for 7-Cr{Dy}. (Inset) M vs H isotherms for 7-Cr{Dy} at 2, 3, 4, 5.5, 10, and 20 K. (d) MicroSQUID magnetization (M) vs applied field plot for 7-Cr{Dy} at a 0.03–0.8 K with the scan rate of 0.14 T s–1. Reprinted with permission from ref (25). Copyright 2017, Nature Publishing Group.

While ferrotoroidal behavior was achieved in 7-Cr{Dy}, the next reasonable question was how the connecting 3d ion would affect the ferrotoroidal behavior. Some of us have isolated another {CrDy6} complex with a different counteranion (chloride) and other 3d/p block ions as a central metal that connects two Dy3 triangles to enhance the ferrotoroidal coupling.[29] The family of complexes may differ in the counteranion and has the general molecular formula of [DyIII6MIII(OH)8(o-tol)12(MeOH)5(NO3)]·4MeOH (M = Mn (8-Mn{Dy}), Fe (9-Fe{Dy}), Co (10-Co{Dy}), and Al (11-Al{Dy}); o-tol = o-toluate) and [DyIII6MIII(OH)8(o-tol)12(MeOH)6]Cl·6MeOH (M = Cr (7′-Cr{Dy}), Mn (8′-Mn{Dy}), Fe (9′-Fe{Dy}), Co (10′-Co{Dy}), and Al (11′-Al{Dy}), see Table ). Despite that the Cr(III) ion is substituted by various metal ions, the core {Dy3O} structure is found to be retained in all geometries, offering a possibility to observe ferro-/antiferrotoroidicity in this class of molecule. Each DyIII ion’s magnetic anisotropy axis almost lies in-plane and tangentially to a {Dy3} triangle in all the complexes. The DyIII magnetic axes form circular patterns, suggesting toroidal ground states in both the triangles (Figure ). Complexes Cr(Cl)/Mn(NO3)/Fe(Cl)/Co(Cl)/Co(NO3)/Al(Cl)/Al(NO3) have their magnetic moments oriented clockwise in both the triangles, leading to the FT ground state, but the complexes Mn(Cl)/Fe(NO3) have their magnetic moment oriented anticlockwise in one of the Dy3 triangles leading to an AFT ground state. Importantly, the theoretical calculations confirmed that the ground-state toroidal behavior depends on the nature of the magnetic coupling between the DyIII ions, which is consistent with the experimental observation. Above all, we have revealed that: (i) the ferrotoroidic coupling between Dy3 motifs can be enhanced by small, diamagnetic M linking ions; (ii) a paramagnetic M ion is able to stabilize the antiferrotoroidic states only if the anisotropy is held up; and (iii) by choosing a better M ion, a complex’s hysteresis profile can be fine-tuned to increase the remnant magnetization and/or coercive field. Moreover, a model to simulate microSQUID hysteresis plots was developed for the first time in this work. This tool helps to validate the presence/absence of the ferro/antiferrotoroidal arrangement.[29]

Figure 8

Orientations of magnetic anisotropy axes (dotted lines and blue arrows) in each MDy6 complex.

Cu{Dy3} Polymer Exhibiting Antiferrotoroidicity

The coupling of two or more triangular Dy3 rings via a 3d ion, each stabilizing a toroidal moment in their ground state, has been first explored by Powell and co-workers in a chiral heterometallic polymer having the formula of {[Cu(Val)2CH3OH][Dy3L3(μ3-OH)2(NO3)4]} (12-Cu{Dy}, Val = enantiopure valine (l- or d-Val), HL = o-vanillin; Figure a).[8] They have reported the first CuII/DyIII 1D polymers built from an alternating trinuclear Dy3 SMT-building motif and a Cu(II) bisvalinate complex with the chiral spin state propagating along the chain, which exhibits the exchange coupling between the toroidal moments. The 12-Cu{Dy} displays an S-shaped curve in magnetization isotherm plots at low fields and low temperatures (Figure b) and a stepped hysteresis of the magnetization (Figure c) in single-crystal studies. Ab initio calculations predict the antiferromagnetic coupling between Dy ions, thus allowing the local magnetic moments to be arranged in a toroidal fashion (Figure a and 9d). The main g axes on Dy sites are adjacent to tangential directions with angles (ϕ) of 10.3–15.61° (Figure d), and they lie nearly in the Dy3 plane with a deviation (θ) of 0.1–10.2°. These values are comparable to the values found for the ground state of the parent 1-Dy triangle, thus showing well-maintained toroidal moments within the individual {Dy3} motif despite the polymerization of the Dy3 units, and they have uncompensated moments (0.8 μB). They also showed how to induce strong toroidal magnetization by applying a magnetic field at low temperature in single crystals of these compounds. The ground state of such a system is found to be antiferrotoroidic, and it is argued there that the ferrotoroidic first excited state, having a magnetic component, can be stabilized by a magnetic field, so that in an applied magnetic field condition in the appropriate direction the ground state would become ferrotoroidic (but not degenerate).

Figure 9

(a) Molecular structure of 12-Cu{Dy} along with the calculated g axes for the lowest KDs on Dy ions in the D-chain; (b) measured and calculated magnetic susceptibility data and molar magnetization at 3.0 K for the D-chain; (c) microSQUID magnetization (M) vs applied field plot for the D-chain (bottom) with different field sweep rates at 0.04 K; and (d) two components of the toroidal state τ = 1/2 of the Dy3 triangles. Blue dashed lines show the tangential directions, and red dashed lines are the anisotropy axes. Reprinted with permission from ref (8). Copyright 2012, The Royal Society of Chemistry.

{Fe18}{Dy3}2 Exhibiting Ferrotoroidicity

Recently, Powell and co-workers reported a large {Fe18Dy6} cyclic coordination cluster, viz., [Fe18Dy6(ampd)12(Hampd)12(μ-OH)6(PhCO2)24](NO3)6·38MeCN (13-{Fe}{Dy}, H2ampd = 2-amino-2-methyl-1,3-propanediol).[26] In this molecule, two giant Dy3 triangles were sandwiched by a strongly antiferromagnetically coupled Fe18 ring, and it shows a ferrotoroidal behavior in the ground state (Figure , left). The cluster is possibly fragmented into repeating {Fe2Dy} triangles connected via a benzoate-bridged Fe ion to form a “modified delta-chain”. Therefore a {Fe3Dy} moiety is a repeating unit within the chain. Though the dominant interaction in the Fe18 ring is antiferromagnetic, the six Dy ions arrange themselves toroidally. No clear evidence for an S-shaped curve in the M vs H plots was noted; however, the toroidal arrangement was ascertained by microSQUID measurements (Figure , right). If we compare the microSQUID data for the ferrotoroidal 7-Cr{Dy} complex[25] and that of the 13-{Fe}{Dy}, very similar features are observed. The microSQUID hysteresis loops display a plateau between −0.5 and 0.5 T, which is representative of a nonmagnetic toroidal ground state. Quantum calculations found that the moments are arranged ferrotoroidally. Moreover, the field needed to break the toroidal arrangement in the 13-{Fe}{Dy} system is nearly as large as that for the 7-Cr{Dy} (vide infra).

Figure 10

(Left) Fe18Dy6 metallic core with the arrangement of g axis (dark blue) within the Dy3 triangles sandwiching the Fe18 ring. (Right) MicroSQUID magnetic hysteresis of 13-{Fe}{Dy} at 30 mK under varying field sweep rates and derivative. (Inset) The loops show a plateau between −0.5 and 0.5 T. Reprinted with permission from ref (26). Copyright 2020 Americal Chemical Society.

Double {Dy3} Triangles Connected via Peripheral Ligands

After the remarkable observation of SMT behavior in the parent Dy3 triangle, in 2010, Powell and co-workers purposely added a 2-hydroxymethyl-6-methoxyphenol ligand and discovered a {Dy6} cluster with two Dy3 units coupled with each other (Dy3 + Dy3 connected by an inversion center in a vertex-to-vertex fashion) having the formula of [Dy6L4L′2(μ3-OH)4(H2O)9Cl]Cl5·15H2O (14-{Dy}, HL = o-vanillin, and H2L′ = 2-hydroxymethyl-6-methoxyphenol).[6] This Dy6 structure results from the formal linkage by the alkoxides of the reduced form of the ligand (−CH2OH from H2L′) of two Dy3 triangles in 1-Dy with the associated formal loss of the two terminal Cl– ligands (Figure a). In the M vs H plots, an S-shaped curve is observed at 1.8 K at 0.5 kOe (Figure b), and this behavior is mostly comparable to that of the parent 1-Dy cluster; however, the antiferromagnetism is less pronounced due to the presence of an even number of interacting Dy centers.

Figure 11

(a) Structure of the {Dy6}5+ cation in 14-{Dy}. (b) Field dependence of the molar magnetization measured of 14-{Dy} at T = 1.8 K (□) and T = 4.0 K (●). Inset: Ellipsoidal representation of the experimental (top) and calculated (bottom) susceptibility tensors of Dy6 at two different temperatures. The tensors are superimposed onto the molecular structure of the magnetic core (Dy violet, O red); the orientation of the Dy easy axes estimated from ab initio calculations is also shown. Reprinted with permission from ref (6). Copyright 2010, John Wiley & Sons Ltd.

The calculated directions of the anisotropy axes for Dy1 and Dy2 centers in 14-{Dy} lie almost in the Dy3 plane (deviation (θ) of <3°) and are tangential to the triangle. These outcomes are consistent with the 1-Dy when the similar ligand environments of Dy1 and Dy2 are found in both the compounds. However, for the central Dy3 ions, the g easy-axis deviates by about 10° from the plane of the triangle, replicating the slightly different coordination surroundings resulting from the alkoxo bridges to the second triangle (Figure b, inset). Furthermore, the weak interaction between the two triangles could not stabilize the con-rotating or counter-rotating of the magnetic moments in each triangle. It means that the total toroidal moment of 14-{Dy} is not maximized by such coupling, as the antiferromagnetic interwheel interaction is such that it cancels the contribution arising from the Dy magnetic moment of the two coupled vertices to the overall vortex magnetization. In terms of con-rotating and counter-rotating toroidal moments on the two triangular subunits, the FT and/or AFT nature of such states was not explicitly discussed. Given that FT and AFT states are nonmagnetic, they make little contribution to the magnetic response of the system. In this respect, the fact that the Hamiltonian used in this work contains four fitting parameters and neglects dipolar coupling suggests that more detailed investigations of 14-{Dy} are necessary to affirm the presence/absence of the FT ground state.

After succeeding in linking the two Dy3 units in a vertex-to-vertex fashion in the 14-{Dy} molecule, in 2012, Powell and co-workers have reported another Dy6 molecule (Figure , left) coupling two Dy3 units ([Dy3(μ3-O)2(μ2-O)2]) but in an edge-to-edge fashion, viz., [Dy6(μ4-O)L4(NO3)4(CH3OH)]·CH3OH (15-{Dy}, H3L = 2,6-bis((2-hydroxyethylimino)methyl)-4-methylphenol).[7] The alcohol μ2-O atoms from the same ligands (H3L) bridge the edges of the triangles. Notably, the μ4-O2– ion connects two Dy3 triangles in the center, and four deprotonated phenol oxygen atoms further merge the Dy6 molecule in the edge to organize the two Dy3 triangles in an edge-to-edge arrangement. The measured magnetization with a variable field at 1.9 K shows a pronounced S-shape around 9 kOe, and a stepped shape of the magnetization hysteresis in the microSQUID technique indicates the presence of toroidal behavior (Figure , right). The reason for the presence of a large magnetic moment is due to the orientations of local anisotropy axes (perfectly arranged in a toroidal fashion in both triangles), which vary much more from an equilateral triangle in this compound than in the parent 1-Dy, and the presence of much lower symmetry for this Dy6. Thus, this Dy6 construction enhanced the toroidal magnetic moment of the molecule.

Figure 12

(Left) Molecular structure of 15-{Dy} with the main anisotropy axes (dashed lines) on Dy ions and local magnetizations (arrows) in the ground state. (Right) M vs H at 1.9 K. The solid line corresponds to the best fit. Inset: Hysteresis loops for 15-{Dy} at different field sweep rates at 0.03 K. Reprinted with permission from ref (7). Copyright 2012, John Wiley & Sons Ltd.

In particular, we note that while antiferromagnetic coupling between DyIII ions belonging to the same triangle is known to stabilize a toroidal moment, given the geometry of 15-{Dy}, antiferromagnetic coupling between nearest-neighbor ions on different triangles will in fact stabilize counter-rotating toroidal states on different triangles, hence an antiferrotoroidic ground state. The lack of low-lying antiferrotoroidic excitations renders this system a somewhat less clear-cut case of a well-defined magnetic coupling between separate toroidal subunits, such as the case presented in 7-Cr{Dy},[25] albeit an exciting example of how to achieve a large toroidal moment in the ground state.

In 2016, Cheng and co-workers also had reported a Dy6 molecule by linking two Dy3 triangles, viz., [Dy6L2(μ3-OH)4(μ2-OH)2(H2O)12]·8Br·2CH3CN·6CH3OH (16-{Dy}, Figure , left). Among the Dy6 family of compounds, all six DyIII ions are found to coordinate with a neutral H2O axial ligand only in this structure. Additionally, the two [Dy3(μ3-O)2(μ2-O)3] triangles connected via an organic space ligand in an edge-to-edge fashion.[22] Each of the triangular units is connected by two μ3-OH atoms, two bridging O atoms from the phenolic oxygen of the ligands, and one bridging −OH atom. The vanishing low-temperature χT and a clear S-shape at around 7 kOe of the M(H) plot suggest possible antiferromagnetic interactions and a toroidal magnetic moment in each triangle (Figure , right). A nonmagnetic ground state found for each of the {Dy3} units in this complex is similar to the parent 1-Dy molecule. Ab initio calculations predict that the anisotropic g axes in all the Dy centers align in the plane of the triangle leading to the toroidal magnetic moment in the molecule (Figure , left). The con-rotating and counter-rotating toroidal moments on the two triangular subunits were not evidently discussed for this molecule as well. We stress here that more detailed studies of 16-{Dy} are essential to ascertain the FT/AFT nature of its ground state.

Figure 13

(Left) Structure with main anisotropy axes (dashed lines) and local magnetizations (arrows) in the ground state and (right) magnetic plots of 16-{Dy}. Reprinted with permission from ref (22). Copyright 2016, The Royal Society of Chemistry.

In 2017, Xu and co-workers reported a new Dy6 complex, [Dy6L′4(μ4-O)(NO3)4]·4CH3OH (17-{Dy}, H3L′ = 2,6-bis((2-hydroxypropylimino)methyl)-4-methylphenol, Figure a) using a methyl-modified Schiff-base ligand.[23] This complex possesses a similar μ4-O-bridged Dy6 core as the 15-{Dy}, though the coordination geometries and magnetic interactions are marginally different, which results in different SMT behavior. The measured magnetization under a variable field at 1.9 K shows an S- shaped (Figure b) curve, and this indicates that the 17-{Dy} molecule is likely to possess a toroidal moment in its ground state with its conventional magnetic moment larger than 15-{Dy}. The orientation of magnetic anisotropy axes calculated by the electrostatic potential model predicts toroidal arrangement of spins; however, detailed ab initio calculations are not provided to discuss the con-rotating and counter-rotating toroidal moments on the two Dy3 triangles to disprove/prove the FT and/or AFT ground state.

Figure 14

(a) Structure with main anisotropy axes (dashed lines) and local magnetizations (arrows) in the ground state and (b) M vs H plot of 17-{Dy}. Reprinted with permission from ref (23). Copyright 2017, The Royal Society of Chemistry.

Non-DyIII Triangular SMTs

Although limited, other than DyIII ions were also found to exhibit toroidal moments, and this is at the moment restricted to TbIII and HoIII ions, both of which have oblate electron density similar to DyIII ions, and there are no examples from lanthanide ions having prolate electron density stabilized as ground state (such as ErIII ion). When we have extended our studies on 7-Cr{Dy} to other lanthanide ions such as TbIII, HoIII, and ErIII in place of DyIII and examined the magnetic behavior in these complexes and also in other triangular and wheel-shaped complexes, toroidal magnetic moments were detected in some examples.[20,24] These findings are summarized in this section.

Cr{Ln3}2 (Ln = Tb, Ho, and Er)

Focusing on the triangular complexes and the effect changing the DyIII ion would have on the toroidal behavior in the 7-Cr{Dy} complex, we reported the experimental and theoretical studies on three heptanuclear [CrIIILnIII6(OH)8(o-tol)12(NO3) (MeOH)5]·2MeOH (Ln = Tb (7-Cr{Tb}), Ho(7-Cr{Ho}), and Er(7-Cr{Er})) complexes.[24] The S-shaped curves in M vs H at lower T as well as opening up of the hysteresis in single-crystal measurements were absent in these examples. Since both TbIII and HoIII ions are non-Kramers in nature, this encourages stronger tunnelling between the levels and has been suggested to diminish the expected steps in the single-crystal measurements. However, ab initio calculations predict toroidal magnetic moments in Tb and Ho analogues but not in the Er analogue (Figure ). The angle (θ) of magnetic anisotropy axes with the plane of the Ln3 triangle is in the range of 5.3°–13.9° in 7-Cr{Tb} and 5.9°–32.4° in 7-Cr{Ho}. For 7-Cr{Tb} and 7-Cr{Ho} complexes, a con-rotating ferrotoroidal ground state is observed due to the presence of the ferromagnetic dipolar coupling between the Ln(III) ions and the presence of S6 symmetry of the complexes.[24]

Figure 15

Metallic core with the direction of the local anisotropy axes (green dotted lines) and the local magnetic moment (blue arrows) in the ground Ising doublet on each TbIII and HoIII site in 7-Cr{Tb} (a) and 7-Cr{Ho} (b). The blue arrows show the con-rotation of the toroidal magnetic moment, and and the yellow arrow is the S6 symmetry axis. Low-lying exchange spectrum for (c) 7-Cr{Tb} and (d) 7-Cr{Ho}. The exchange-coupled states (KDs) are placed on the diagram according to their magnetic moments (bold black lines). For various energy states, a graphical representation of one of the corresponding noncollinear Ising quantum states, where the red/blue thick arrows at the LnIII sites indicate the direction of the magnetic moment in toroidal form. Reprinted with permission from ref (24). Copyright 2018, John Wiley & Sons Ltd.

As the ground-state electron density of the TbIII and HoIII ions in the ligand field has oblate character and the μ3-O atom has the largest negative charges, the electrostatic repulsion clearly favors the corresponding g axes of the {Ln3} triangle to lie outward in a circular pattern, leading to the presence of toroidal moments. For the 7-Cr{Er} complex, the ErIII ion in the ligand field stabilizes mJ = ±15/2 as the ground state and therefore has prolate electron density. Hence, the corresponding g axis tends to orient perpendicular to the {Er3} triangular plane and results in a nontoroidal arrangement. If the 7-Cr{Dy}, 7-Cr{Tb}, and 7-Cr{Ho} complexes intertriangle dipolar-induced splittings are analyzed, it is clear that ΔE(FT-AFT) is 0.28 cm–1, 0.65 cm–1, and 0.1 cm–1, respectively, with the largest gap detected for the 7-Cr{Tb} complex rewarding such LnIII ions substitution strategy.

Similarly, Langley et al. have synthesized and magnetically and theoretically characterized the Tb and Ho analogues of 5-Dy, viz., [LnIII3(OH)(teaH2)3(paa)3]Cl2 (Ln = Tb (5-Tb), Ho (5-Ho), Figure ), to investigate their toroidal nature.[20] Remarkably, M vs H plots show an S-shaped curve at low magnetic fields at 2 K for 5-Tb (Figure , right), but it was absent for 5-Ho. The ab initio calculations furthermore support toroidal behavior for both 5-Tb and 5-Ho triangles (Figure ). These two molecules belong to mixed moment SMTs due to the presence of uncompensated magnetic moments of 0.9 μB and 6.0 μB for 5-Tb and 5-Ho, respectively.[10] For non-Kramer ions, the toroidal behavior is rare; however, the toroidal moments in 5-Tb and 5-Ho are favored by the oblate nature of TbIII and HoIII ions, allowing the magnetic axes to lie in the plane of the Ln3 triangles as observed for 5-Dy.

Figure 16

Molecular structure and the orientations of the magnetic anisotropy axes in the ground doublets on the LnIII sites in (left) 5-Tb, (middle) 5-Ho, and (right) the molar magnetization data for 5-Tb. The solid lines are calculated data. Reprinted with permission from ref (20). Copyright 2019, The Royal Society of Chemistry.

Recently, along with the Dy analogue (6-Dy), Caporale et al. have reported another set of Ln3 triangles, viz., [Tb3(μ3-OH)2(o-dppd)3(CH3CH2OH)3Cl3][Tb3(μ3-OH)2(o-dppd)3(H2O)(CH3CH2OH)2Cl3]Cl2·H2O (6-Tb), [Ho3(OH)2(o-dppd)3Cl(H2O)5]Cl3·3H2O (6-Ho), and [Er3(OH)2(o-dppd)3Cl2(H2O)3(CH3OH)]Cl2·3H2O·CH3OH (6-Er) and characterized their toroidal behavior (Figure ).[28] The metal array is the same as seen in 6-Dy. No S-shaped profile at a low-field M vs H plot is observed for these complexes as well. Theoretical calculations predict that the Ho analogue has a toroidal arrangement of spins the same as 6-Dy, but 6-Tb does not support a toroic spin state owing to the changes in the coordination environment. The prolate nature of the ErIII centers in 6-Er yields significant transverse anisotropy and hence a strong QTM that leads to the absence of toroidal moments (Figure ) and suggests that it is hard to witness toroidal moments in ErIII ions.

Figure 17

Molecular structure and the orientations of the magnetic anisotropy axes in the ground doublets on the LnIII sites in (left) 6-Ho, (middle) 6-Tb, and (right) 6-Er. Reprinted with permission from ref (28). Copyright 2020, The Royal Society of Chemistry.

Apart from the complexes discussed here, Chandrasekhar and co-workers have reported a Zn3Ln3 SMT,[30] [Zn3Ln3(μ6-CO3)(μ3-OH)3(L)3(H2O)3]·3(ClO4)·NO3 (Ln = Dy (18-ZnDy), Tb (18-ZnTb), LH2 = 6,6′-{[2-(dimethylamino)ethylazanediyl]bis(methylene)}bis(2-methoxy-4-methylphenol), Figure , left), with a μ6-CO3– bridging ligand which bridges all three Ln(III) centers in these molecules. These molecules are formed by the coordination realization of three [L]2–, three μ3-OH–, and one μ6-CO3– ligands. The metallic core is a Dy3 triangle surrounded by a Zn3 triangle. Both nonvanishing low-temperature susceptibility and the S-shaped curve at low-field magnetization plots suggest a magnetic ground doublet state for both 18-ZnDy and 18-ZnTb. Similarly, the first step around the zero field in microSQUID measurements and the loops have an S-shape with a large coercive field opening upon cooling (Figure , right), which indicates the presence of toroidal moments. Moreover, ab initio calculations predict the orientation of the magnetic moment of the lowest Kramers doublets in 18-ZnDy (Figure , left), and Ising doublets in 18-ZnTb are also almost coplanar with the Dy3 and Tb3 plane, respectively, which confirms the presence of toroidal behavior in these complexes.[30] As Zn(II) ions are placed on the same plane as that of Dy(III), this tends to polarize the oxygen atom, which in turn coordinates with the Dy(III) ion. This ensures larger negative charges on these oxygen atoms, and therefore the g axis points toward the Zn(II) ion. This is also a design strategy to obtain toroidal moments in the Dy3 motif.

Figure 18

(Left) Molecular structure and the orientations of the magnetic anisotropy axes in the ground doublets on the DyIII sites in 18-ZnDy and (right) magnetization (M) vs field hysteresis loops for a single crystal of 18-ZnDy at 0.03 K and the indicated field sweep rates. Reprinted with permission from ref (30). Copyright 2017, John Wiley & Sons Ltd.

Conclusions

Though a significant number of molecules with SMT behavior have been reported to be in common, the realization of SMTs is majorly found in Dy3 systems. In this mini-review, we attempt to give an overview of various structural topologies related to the {Ln3} core that were found to yield SMT properties. Particularly, the peripheral ligands were found to be crucial in dictating the direction of the g axis, which in turn strongly correlated to the presence and absence of toroidal moments. The main conclusions observed from this mini-review are summarized below.

: To attain toroidal moments in Dy3 systems, it is clear that the peripheral ligand design plays an important role. As the anisotropic axis needs to be aligned tangential to the μ3-O/OH groups, it is important to have ligands that have significantly larger negative charges compared to μ3-O/OH groups. In this respect, having multifunctional groups such as aldehyde and phenol binding each Dy(III) site in bidentate fashion yield the desired results. Additionally, diamagnetic ions can also be used to enhance the negative charge on the ligand if these ions are placed on the same plane as that of {Ln3}.

: Both the site symmetry of the Dy(III) coordination environment and the overall symmetry of the {Dy3} core were found to help attain toroidal moments. In the {Dy3} family of molecules, the majority of the Dy(III) coordination environment has a C2 or pseudo C2 or higher rotational axis passing tangentially to the Dy-μ3-O/OH vertices, and this helps to reduce the ϕ angle, though the charges on all coordinated atoms and not only the dominant ones play an important role here. Dy3 SMTs with peripheral ligands containing multifunctional groups such as aldehyde and phenol were found to have a similar type of toroidal magnetic moments, and the tangential angles are similar in examples 1-Dy, 3-Dy, 4-Dy, and 6-Dy. These complexes also have vanishing susceptibility at low T and display an S-shaped curve in the M vs H plot. At the same time, Dy3 SMTs with amino-polyalcohol ligands such as 2-Dy and 5-Dy lead to mixed moment toroidal examples and therefore remain magnetic at very low temperatures. For this class of SMTs, a finite susceptibility at low T is typical, and an S-shaped curve in magnetizations was not witnessed in all the examples.

: While several structural motifs beyond {Dy3} to enhance toroidal moments were attempted, many of these polynuclear clusters are made serendipitously, leaving little room for controlling the charges on the peripheral ligands to engineer toroidal moments. On the other hand, enhancing the toroidal magnetic moments by linking two Dy3 units via 3d ions is found to be a superior strategy compared to linking them via organic ligands. Complexes 7-Cr{Dy}, 7-Cr{Tb}, 7-Cr{Ho}, and 13-{Fe}{Dy} show a fascinating ferrotoroidal behavior, whereas two Dy3 units connecting via organic ligands 15-{Dy} exhibit antiferrotoroidal behavior due to antiferromagnetic interactions in intratriangles, and in some cases, the toroidal magnetic moments are not maximized (14-{Dy}).

: Moreover, recently reported non-Dy SMTs suggest that lanthanide ions with oblate electron densities at their ground state are also suitable candidates for engineering toroidal moments, though the success rate of getting toroidal moments with prolate ions appears to be small. Although more than half-filled ions with oblate electron densities are so far proven to be suitable candidates for engineering toroidal moments, the possibility of such states in other Ln(III) examples cannot be ruled out, and thorough studies covering both experiments and theory are needed to uncover such examples.