Single-molecule magnet

A single-molecule magnet (SMM) is a metal-organic compound that has superparamagnetic behavior below a certain blocking temperature at the molecular scale. In this temperature range, a SMM exhibits magnetic hysteresis of purely molecular origin.[1][2] In contrast to conventional bulk magnets and molecule-based magnets, collective long-range magnetic ordering of magnetic moments is not necessary.[2]

Although the term "single-molecule magnet" was first employed in 1996,[3] the first single-molecule magnet, [Mn12O12(OAc)16(H2O)4] (nicknamed "Mn12") was reported in 1991.[4][5][6] This manganese oxide compound features a central Mn(IV)4O4 cube surrounded by a ring of 8 Mn(III) units connected through bridging oxo ligands, and displays slow magnetic relaxation behavior up to temperatures of ca. 4 K.[7][8]

Efforts in this field primarily focus on raising the operating temperatures of single-molecule magnets to liquid nitrogen temperature or room temperature in order to enable applications in magnetic memory. Recent acceleration in this field of research has resulted in significant enhancements of single-molecule magnet operating temperatures to above 60 K.[9][10][11][12]

Measurement

Arrhenius behavior of magnetic relaxation

Because of single-molecule magnets' magnetic anisotropy, the magnetic moment has usually only two stable orientations antiparallel to each other, separated by an energy barrier. The stable orientations define the molecule's so called “easy axis”. At finite temperature, there is a finite probability for the magnetization to flip and reverse its direction. Identical to a superparamagnet, the mean time between two flips is called the Néel relaxation time and is given by the following Néel–Arrhenius equation:[13]

where:

  • τ is the magnetic relaxation time, or the average amount of time that it takes for the molecule's magnetization to randomly flip as a result of thermal fluctuations
  • τ0 is a length of time, characteristic of the material, called the attempt time or attempt period (its reciprocal is called the attempt frequency); its typical value is between 10−9 and 10−10 second
  • Ueff is the energy barrier associated with the magnetization moving from its initial easy axis direction, through a “hard plane”, to the other easy axis direction. The barrier Ueff is generally reported in cm−1 or in kelvins.
  • kB is the Boltzmann constant
  • T is the temperature

This magnetic relaxation time, τ, can be anywhere from a few nanoseconds to years or much longer.

Magnetic blocking temperature

The so-called magnetic blocking temperature, TB, is defined as the temperature below which the relaxation of the magnetization becomes slow compared to the time scale of a particular investigation technique.[14] Historically, the blocking temperature for single-molecule magnets has been defined as the temperature at which the molecule's magnetic relaxation time, τ, is 100 seconds. This definition is the current standard for comparison of single-molecule magnet properties, but otherwise is not technologically significant.

Intramolecular magnetic exchange

The magnetic coupling between the spins of the metal ions is mediated by superexchange interactions and can be described by the following isotropic Heisenberg Hamiltonian:

where is the coupling constant between spin i (operator ) and spin j (operator ). For positive J the coupling is called ferromagnetic (parallel alignment of spins) and for negative J the coupling is called antiferromagnetic (antiparallel alignment of spins): a high spin ground state, a high zero-field-splitting (due to high magnetic anisotropy), and negligible magnetic interaction between molecules.

The combination of these properties can lead to an energy barrier, so that at low temperatures the system can be trapped in one of the high-spin energy wells.[2][15][16][17][18]

Performance

The performance of single-molecule magnets is typically defined by two parameters: the effective barrier to slow magnetic relaxation, Ueff, and the magnetic blocking temperature, TB. While these two variables are linked, only the latter variable, TB, directly reflects the performance of the single-molecule magnet in practical use. In contrast, Ueff, the thermal barrier to slow magnetic relaxation, only correlates to TB when the molecule's magnetic relaxation behavior is perfectly Arrhenius in nature.

The table below lists representative and record 100-s magnetic blocking temperatures and Ueff values that have been reported for single-molecule magnets.

Complex Type TB (100-s; K) Ueff (cm−1) Ref.
[Mn12O12(OAc)16(H2O)4] cluster 3 K 42 cm−1 [6]
[K(18-crown-6)(THF)2][{[(Me3Si)2N]2(THF)Tb}2(μ-η2:η2-N2)] cluster 14 K 227 cm−1 [19]
Tb(CpiPr5)2 single-ion 52 K 1205 cm−1 [20]
[Dy(Cpttt)2][B(C6F5)4] (Cpttt=1,2,4‐tri(tert‐butyl)cyclopentadienide) single-ion 53 K 1277 cm−1 / 1223 cm−1 [9]/[10]
[Dy(CpiPr4Me)2][B(C6F5)4] single-ion 62 K 1468 cm−1 [11]
[Dy(CpiPr5)(CpMe5)][B(C6F5)4] single-ion 65 K 1541 cm−1 [12]

Types

Metal clusters
Ferritin

Metal clusters formed the basis of the first decade-plus of single-molecule magnet research, beginning with the archetype of single-molecule magnets, "Mn12".[4][5][6] This complex is a polymetallic manganese (Mn) complex having the formula [Mn12O12(OAc)16(H2O)4], where OAc stands for acetate. It has the remarkable property of showing an extremely slow relaxation of their magnetization below a blocking temperature. [Mn12O12(OAc)16(H2O)4]·4H2O·2AcOH, which is called "Mn12-acetate" is a common form of this used in research.[21]

Single-molecule magnets are also based on iron clusters[14] because they potentially have large spin states. In addition, the biomolecule ferritin is also considered a nanomagnet. In the cluster Fe8Br the cation Fe8 stands for [Fe8O2(OH)12(tacn)6]8+, with tacn representing 1,4,7-triazacyclononane.

The ferrous cube complex Fe4C40H52N4O12 (commonly called [Fe4(sae)4(MeOH)4]) was the first example of a single-molecule magnet involving an Fe(II) cluster, and the core of this complex is a slightly distorted cube with Fe and O atoms on alternating corners.[22] Remarkably, this single-molecule magnet exhibits non-collinear magnetism, in which the atomic spin moments of the four Fe atoms point in opposite directions along two nearly perpendicular axes.[23] Theoretical computations showed that approximately two magnetic electrons are localized on each Fe atom, with the other atoms being nearly nonmagnetic, and the spin–orbit-coupling potential energy surface has three local energy minima with a magnetic anisotropy barrier just below 3 meV.[24]

Applications
One possible use of SMMs is superior magnetic thin films to coat hard disks.

There are many discovered types and potential uses.[25][26] Single-molecule magnets represent a molecular approach to nanomagnets (nanoscale magnetic particles).

Due to the typically large, bi-stable spin anisotropy, single-molecule magnets promise the realization of perhaps the smallest practical unit for magnetic memory, and thus are possible building blocks for a quantum computer. Consequently, many groups have devoted great efforts into synthesis of additional single-molecule magnets.

In addition, single-molecule magnets have provided physicists with useful test-beds for the study of quantum mechanics. Macroscopic quantum tunneling of the magnetization was first observed in Mn12O12, characterized by evenly spaced steps in the hysteresis curve.[27] The periodic quenching of this tunneling rate in the compound Fe8 has been observed and explained with geometric phases.[28]

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See also

References
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  2. Introduction to Molecular Magnetism by Dr. Joris van Slageren.
  3. Aubin, Sheila M. J.; Wemple, Michael W.; Adams, David M.; Tsai, Hui-Lien; Christou, George; Hendrickson, David N. (1996). "Distorted MnIVMnIII3Cubane Complexes as Single-Molecule Magnets". Journal of the American Chemical Society. 118 (33): 7746. doi:10.1021/ja960970f.
  4. Caneschi, Andrea; Gatteschi, Dante; Sessoli, Roberta; Barra, Anne Laure; Brunel, Louis Claude; Guillot, Maurice (1991). "Alternating current susceptibility, high field magnetization, and millimeter band EPR evidence for a ground S = 10 state in [Mn12O12(Ch3COO)16(H2O)4].2CH3COOH.4H2O". Journal of the American Chemical Society. 113 (15): 5873. doi:10.1021/ja00015a057.
  5. Sessoli, Roberta; Tsai, Hui Lien; Schake, Ann R.; Wang, Sheyi; Vincent, John B.; Folting, Kirsten; Gatteschi, Dante; Christou, George; Hendrickson, David N. (1993). "High-spin molecules: [Mn12O12(O2CR)16(H2O)4]". Journal of the American Chemical Society. 115 (5): 1804–1816. doi:10.1021/ja00058a027. ISSN 0002-7863.
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  14. Gatteschi, Dante (2000). "Single-molecule magnets based on iron(iii) oxo clusters". Chemical Communications (9): 725–732. doi:10.1039/a908254i..
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