Single-molecule magnet

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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, an 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]

Contents

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. Along with raising the blocking temperature, efforts are being made to develop SMMs with high energy barriers to prevent fast spin reorientation. [9] Recent acceleration in this field of research has resulted in significant enhancements of single-molecule magnet operating temperatures to above 70 K. [10] [11] [12] [13]

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: [14]

where:

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. [15] 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. There is typically a correlation between increasing an SMM's blocking temperature and energy barrier. The average blocking temperature for SMMs is 4K. [16] Dy-metallocenium salts are the most recent SMM to achieve the highest temperature of magnetic hysteresis, greater than that of liquid nitrogen. [9]

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] [17] [18] [19] [20]

Barrier to magnetic relaxation

A single-molecule magnet can have a positive or negative magnetic moment, and the energy barrier between these two states greatly determines the molecule's relaxation time. This barrier depends on the total spin of the molecule's ground state and on its magnetic anisotropy. The latter quantity can be studied with EPR spectroscopy. [21]

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.

ComplexTypeTB (100-s; K)Ueff (cm−1)Ref.Year Reported
[Mn12O12(OAc)16(H2O)4]cluster3 K42 cm−1 [5] [4] [6] 1991
[K(18-crown-6)(THF)2][{[ (Me3Si)2N]2(THF)Tb}2(μ-η2:η2-N2)]cluster14 K227 cm−1 [22] 2011
Tb(CpiPr5)2single-ion52 K1205 cm−1 [23] 2019
[Dy(Cpttt)2][B(C6F5)4]*single-ion56 K1219 cm−1 [10] [11] 2017
[Dy(CpiPr4Me)2][B(C6F5)4]single-ion62 K1468 cm−1 [12] 2018
[tBuPO(NHiPr)2Dy(H2O)][I3]single-ion2.4 K452 cm−1 [24] 2016
[Dy(CpiPr4H)2][B(C6F5)4]single-ion17 K1285 cm−1 [12] 2018
[Dy(CpiPr5)(CpMe5)][B(C6F5)4]single-ion67 K1541 cm−1 [13] 2018
[Dy(CpiPr4Et)2][B(C6F5)4]single-ion59 K1380 cm−1 [12] 2018
[Dy(CpiPr5)2][B(C6F5)4]single-ion56 K1334 cm−1 [12] 2018
[Dy(OtBu)2(py)5][BPh4]single-ion12 K1264 cm−1 [25] 2016

Abbreviations: OAc=acetate, Cpttt=1,2,4‐tri(tert‐butyl)cyclopentadienide, CpMe5= 1,2,3,4,5-penta(methyl)cyclopentadienide, CpiPr4H= 1,2,3,4-tetra(isopropyl)cyclopentadienide, CpiPr4Me= 1,2,3,4-tetra(isopropyl)-5-(methyl)cyclopentadienide, CpiPr4Et= 1-(ethyl)-2,3,4,5-tetra(isopropyl)cyclopentadienide, CpiPr5= 1,2,3,4,5-penta(isopropyl)cyclopentadienide

*indicates parameters from magnetically dilute samples [26]

Types

Metal clusters

Ferritin Ferritin.png
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. [27]

Single-molecule magnets are also based on iron clusters [15] 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 [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. [28] 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. [29] 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. [30]

Applications

One possible use of SMMs is superior magnetic thin films to coat hard disks. Hard disk.jpg
One possible use of SMMs is superior magnetic thin films to coat hard disks.

There are many discovered types and potential uses. [31] [32] 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. [1] Consequently, many groups have devoted great efforts into synthesis of additional single-molecule magnets. Single-molecule magnets have been considered as potential building blocks for quantum computers. [33] A single-molecule magnet is a system of many interacting spins with clearly defined low-lying energy levels. The high symmetry of the single-molecule magnet allows for a simplification of the spins that can be controllable in external magnetic fields. Single-molecule magnets display strong anisotropy, a property which allows a material to assume a variation of properties in different orientations. Anisotropy ensures that a collection of independent spins would be advantageous for quantum computing applications. A large amount of independent spins compared to a singular spin, permits the creation of a larger qubit and therefore a larger faculty of memory. Superposition and interference of the independent spins also allows for further simplification of classical computation algorithms and queries.

Theoretically, quantum computers can overcome the physical limitations presented by classical computers by encoding and decoding quantum states. Single-molecule magnets have been utilized for the Grover algorithm, a quantum search theory. [34] The quantum search problem typically requests for a specific element to be retrieved from an unordered database. Classically the element would be retrieved after N/2 attempts, however a quantum search utilizes superpositions of data in order to retrieve the element, theoretically reducing the search to a single query. Single molecular magnets are considered ideal for this function due to their cluster of independent spins. A study conducted by Leuenberger and Loss, specifically utilized crystals to amplify the moment of the single spin molecule magnets Mn12 and Fe8. Mn12 and Fe8 were both found to be ideal for memory storage with a retrieval time of approximately 10−10 seconds. [34]

Another approach to information storage with SMM Fe4 involves the application of a gate voltage for a state transition from neutral to anionic. Using electrically gated molecular magnets offers the advantage of control over the cluster of spins during a shortened time scale. [33] The electric field can be applied to the SMM using a tunneling microscope tip or a strip-line. The corresponding changes in conductance are unaffected by the magnetic states, proving that information storage could be performed at much higher temperatures than the blocking temperature. [16] The specific mode of information transfer includes DVD to another readable medium, as shown with Mn12 patterned molecules on polymers. [35]

Another application for SMMs is in magnetocaloric refrigerants . A machine learning approach using experimental data has been able to predict novel SMMs that would have large entropy changes, and therefore more suitable for magnetic refrigeration. Three hypothetical SMMs are proposed for experimental synthesis:, , . [36] The main SMM characteristics that contribute to the entropy properties include dimensionality and the coordinating ligands.

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. [37] The periodic quenching of this tunneling rate in the compound Fe8 has been observed and explained with geometric phases. [38]

See also

Related Research Articles

<span class="mw-page-title-main">Ferromagnetism</span> Mechanism by which materials form into and are attracted to magnets

Ferromagnetism is a property of certain materials that results in a significant, observable magnetic permeability, and in many cases, a significant magnetic coercivity, allowing the material to form a permanent magnet. Ferromagnetic materials are familiar metals that are noticeably attracted to a magnet, a consequence of their substantial magnetic permeability. Magnetic permeability describes the induced magnetization of a material due to the presence of an external magnetic field. This temporarily induced magnetization, for example, inside a steel plate, accounts for its attraction to the permanent magnet. Whether or not that steel plate acquires a permanent magnetization itself depends not only on the strength of the applied field but on the so-called coercivity of the ferromagnetic material, which can vary greatly.

<span class="mw-page-title-main">Magnetism</span> Class of physical phenomena

Magnetism is the class of physical attributes that occur through a magnetic field, which allows objects to attract or repel each other. Because both electric currents and magnetic moments of elementary particles give rise to a magnetic field, magnetism is one of two aspects of electromagnetism.

<span class="mw-page-title-main">Superparamagnetism</span>

Superparamagnetism is a form of magnetism which appears in small ferromagnetic or ferrimagnetic nanoparticles. In sufficiently small nanoparticles, magnetization can randomly flip direction under the influence of temperature. The typical time between two flips is called the Néel relaxation time. In the absence of an external magnetic field, when the time used to measure the magnetization of the nanoparticles is much longer than the Néel relaxation time, their magnetization appears to be in average zero; they are said to be in the superparamagnetic state. In this state, an external magnetic field is able to magnetize the nanoparticles, similarly to a paramagnet. However, their magnetic susceptibility is much larger than that of paramagnets.

<span class="mw-page-title-main">Magnet</span> Object that has a magnetic field

A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, cobalt, etc. and attracts or repels other magnets.

<span class="mw-page-title-main">Hysteresis</span> Dependence of the state of a system on its history

Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of the moment often form a loop or hysteresis curve, where there are different values of one variable depending on the direction of change of another variable. This history dependence is the basis of memory in a hard disk drive and the remanence that retains a record of the Earth's magnetic field magnitude in the past. Hysteresis occurs in ferromagnetic and ferroelectric materials, as well as in the deformation of rubber bands and shape-memory alloys and many other natural phenomena. In natural systems, it is often associated with irreversible thermodynamic change such as phase transitions and with internal friction; and dissipation is a common side effect.

<span class="mw-page-title-main">Antiferromagnetism</span> Regular pattern of magnetic moment ordering

In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism. The phenomenon of antiferromagnetism was first introduced by Lev Landau in 1933.

<span class="mw-page-title-main">Ferrimagnetism</span> Type of magnetic phenomenon

A ferrimagnetic material is a material that has populations of atoms with opposing magnetic moments, as in antiferromagnetism, but these moments are unequal in magnitude so a spontaneous magnetization remains. This can for example occur when the populations consist of different atoms or ions (such as Fe2+ and Fe3+).

Exchange bias or exchange anisotropy occurs in bilayers of magnetic materials where the hard magnetization behavior of an antiferromagnetic thin film causes a shift in the soft magnetization curve of a ferromagnetic film. The exchange bias phenomenon is of tremendous utility in magnetic recording, where it is used to pin the state of the readback heads of hard disk drives at exactly their point of maximum sensitivity; hence the term "bias."

<span class="mw-page-title-main">Spin ice</span>

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In magnetism, a nanomagnet is a nanoscopic scale system that presents spontaneous magnetic order (magnetization) at zero applied magnetic field (remanence).

<span class="mw-page-title-main">Nuclear magnetic resonance</span> Spectroscopic technique based on change of nuclear spin state

Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field and respond by producing an electromagnetic signal with a frequency characteristic of the magnetic field at the nucleus. This process occurs near resonance, when the oscillation frequency matches the intrinsic frequency of the nuclei, which depends on the strength of the static magnetic field, the chemical environment, and the magnetic properties of the isotope involved; in practical applications with static magnetic fields up to ca. 20 tesla, the frequency is similar to VHF and UHF television broadcasts (60–1000 MHz). NMR results from specific magnetic properties of certain atomic nuclei. Nuclear magnetic resonance spectroscopy is widely used to determine the structure of organic molecules in solution and study molecular physics and crystals as well as non-crystalline materials. NMR is also routinely used in advanced medical imaging techniques, such as in magnetic resonance imaging (MRI). The original application of NMR to condensed matter physics is nowadays mostly devoted to strongly correlated electron systems. It reveals large manybody couplings by fast broadband detection and it should not to be confused with solid state NMR, which aims at removing the effect of the same couplings by Magic Angle Spinning techniques.

Quantum spin tunneling, or quantum tunneling of magnetization, is a physical phenomenon by which the quantum mechanical state that describes the collective magnetization of a nanomagnet is a linear superposition of two states with well defined and opposite magnetization. Classically, the magnetic anisotropy favors neither of the two states with opposite magnetization, so that the system has two equivalent ground states.

<span class="mw-page-title-main">Spinterface</span>

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<span class="mw-page-title-main">David P. Mills</span> British chemist

David Paul Mills is a British chemist and a Professor in the Department of Chemistry at The University of Manchester. His research typically investigates the chemistry of the lanthanide and actinide f-block elements. This is generally based on the synthesis of new f-block complexes, structural and bonding properties and their uses in different fields including in nuclear fuel cycles, energy and single molecule magnets.

Nicholas Frederick Chilton is an Australian chemist and a Professor in the Department of Chemistry at the University of Manchester. His research is in the areas of magnetochemistry and computational chemistry, and includes the design of high-temperature single molecule magnets, molecular spin qubits for quantum information science, methods and tools for modelling magnetic calculations.

Richard Eric Parry Winpenny FRSC FLSW is a British chemist and a professor in the Department of Chemistry at the University of Manchester. Winpenny's research is within the fields of inorganic chemistry and magnetochemistry, specifically the areas of single-molecule magnetism, inorganic synthesis, supramolecular chemistry and polymetallic caged complexes.

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<span class="mw-page-title-main">Danna Freedman</span> American inorganic chemist

Danna Freedman is an American chemist and the Frederick George Keyes Professor of Chemistry at the Massachusetts Institute of Technology. Her group's research focuses on applying inorganic chemistry towards questions in physics, with an emphasis on quantum information science, materials with emergent properties, and magnetism. Freedman was awarded the 2019 ACS Award in Pure Chemistry and a MacArthur Fellowship in 2022.

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