Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance

Not all noise in experimental measurements is unwelcome. Certain fundamental noise sources contain valuable information about the system itself-a notable example being the inherent voltage fluctuations (Johnson noise) that exist across any resistor, which allow the temperature to be determined. In magnetic systems, fundamental noise can exist in the form of random spin fluctuations. For example, statistical fluctuations of N paramagnetic spins should generate measurable noise of order N spins, even in zero magnetic field. Here we exploit this effect to perform perturbation-free magnetic resonance. We use off-resonant Faraday rotation to passively detect the magnetization noise in an equilibrium ensemble of paramagnetic alkali atoms; the random fluctuations generate spontaneous spin coherences that precess and decay with the same characteristic energy and timescales as the macroscopic magnetization of an intentionally polarized or driven ensemble. Correlation spectra of the measured spin noise reveal g-factors, nuclear spin, isotope abundance ratios, hyperfine splittings, nuclear moments and spin coherence lifetimes-without having to excite, optically pump or otherwise drive the system away from thermal equilibrium. These noise signatures scale inversely with interaction volume, suggesting a possible route towards non-perturbative, sourceless magnetic resonance of small systems.     

Single-shot read-out of an individual electron spin in a quantum dot

Spin is a fundamental property of all elementary particles. Classically it can be viewed as a tiny magnetic moment, but a measurement of an electron spin along the direction of an external magnetic field can have only two outcomes: parallel or anti-parallel to the field. This discreteness reflects the quantum mechanical nature of spin. Ensembles of many spins have found diverse applications ranging from magnetic resonance imaging to magneto-electronic devices, while individual spins are considered as carriers for quantum information. Read-out of single spin states has been achieved using optical techniques, and is within reach of magnetic resonance force microscopy. However, electrical read-out of single spins has so far remained elusive. Here we demonstrate electrical single-shot measurement of the state of an individual electron spin in a semiconductor quantum dot. We use spin-to-charge conversion of a single electron confined in the dot, and detect the single-electron charge using a quantum point contact; the spin measurement visibility is approximately 65%. Furthermore, we observe very long single-spin energy relaxation times (up to approximately 0.85 ms at a magnetic field of 8 T), which are encouraging for the use of electron spins as carriers of quantum information.     

Artificial 'spin ice' in a geometrically frustrated lattice of nanoscale ferromagnetic islands

Frustration, defined as a competition between interactions such that not all of them can be satisfied, is important in systems ranging from neural networks to structural glasses. Geometrical frustration, which arises from the topology of a well-ordered structure rather than from disorder, has recently become a topic of considerable interest. In particular, geometrical frustration among spins in magnetic materials can lead to exotic low-temperature states, including 'spin ice', in which the local moments mimic the frustration of hydrogen ion positions in frozen water. Here we report an artificial geometrically frustrated magnet based on an array of lithographically fabricated single-domain ferromagnetic islands. The islands are arranged such that the dipole interactions create a two-dimensional analogue to spin ice. Images of the magnetic moments of individual elements in this correlated system allow us to study the local accommodation of frustration. We see both ice-like short-range correlations and an absence of long-range correlations, behaviour which is strikingly similar to the low-temperature state of spin ice. These results demonstrate that artificial frustrated magnets can provide an uncharted arena in which the physics of frustration can be directly visualized.     

Pressure-induced crystallization of a spin liquid

Liquids are expected to crystallize at low temperature. The only exception is helium, which can remain liquid at 0 K, owing to quantum fluctuations. Similarly, the atomic magnetic moments (spins) in a magnet are expected to order at a temperature scale set by the Curie-Weiss temperature theta(CW) (ref. 3). Geometrically frustrated magnets represent an exception. In these systems, the pairwise spin interactions cannot be simultaneously minimized because of the lattice symmetry. This can stabilize a liquid-like state of short-range-ordered fluctuating moments well below theta(CW) (refs 5-7). Here we use neutron scattering to observe the spin liquid state in a geometrically frustrated system, Tb(2)Ti(2)O(7), under conditions of high pressure (approximately 9 GPa) and low temperature (approximately 1 K). This compound is a three-dimensional magnet with theta(CW) = -19 K, where the negative value indicates antiferromagnetic interactions. At ambient pressure Tb(2)Ti(2)O(7) remains in a spin liquid state down to at least 70 mK (ref. 8). But we find that, under high pressure, the spins start to order or 'crystallize' below 2.1 K, with antiferromagnetic order coexisting with liquid-like fluctuations. These results indicate that a spin liquid/solid mixture can be induced by pressure in geometrically frustrated systems.     

Quantum simulation of antiferromagnetic spin chains in an optical lattice

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications for systems ranging from high-temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers, owing to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we use a degenerate Bose gas of rubidium atoms confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary a magnetic field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase, the interaction between the spins is overwhelmed by the applied field, which aligns the spins. In the antiferromagnetic phase, the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, thereby improving our understanding of real magnetic materials.     

Chiral magnetic order at surfaces driven by inversion asymmetry

Chirality is a fascinating phenomenon that can manifest itself in subtle ways, for example in biochemistry (in the observed single-handedness of biomolecules) and in particle physics (in the charge-parity violation of electroweak interactions). In condensed matter, magnetic materials can also display single-handed, or homochiral, spin structures. This may be caused by the Dzyaloshinskii-Moriya interaction, which arises from spin-orbit scattering of electrons in an inversion-asymmetric crystal field. This effect is typically irrelevant in bulk metals as their crystals are inversion symmetric. However, low-dimensional systems lack structural inversion symmetry, so that homochiral spin structures may occur. Here we report the observation of magnetic order of a specific chirality in a single atomic layer of manganese on a tungsten (110) substrate. Spin-polarized scanning tunnelling microscopy reveals that adjacent spins are not perfectly antiferromagnetic but slightly canted, resulting in a spin spiral structure with a period of about 12 nm. We show by quantitative theory that this chiral order is caused by the Dzyaloshinskii-Moriya interaction and leads to a left-rotating spin cycloid. Our findings confirm the significance of this interaction for magnets in reduced dimensions. Chirality in nanoscale magnets may play a crucial role in spintronic devices, where the spin rather than the charge of an electron is used for data transmission and manipulation. For instance, a spin-polarized current flowing through chiral magnetic structures will exert a spin-torque on the magnetic structure, causing a variety of excitations or manipulations of the magnetization and giving rise to microwave emission, magnetization switching, or magnetic motors.     

Minority spin condensate in the spin-polarized superfluid 3He A1 phase

The magnetic properties of (3)He in its various phases originate from the interactions among the nuclear spins. The spin-polarized 'ferromagnetic' superfluid (3)He A(1) phase (which forms below 3 mK between two transition temperatures, T(c1) and T(c2), in an external magnetic field) serves as a material in which theories of fundamental magnetic processes and macroscopic quantum spin phenomena may be tested. Conventionally, the superfluid component of the A(1) phase is understood to contain only the majority spin condensate, having energetically favoured paired spins directed along the external field and no minority spin condensate having paired spins in the opposite direction. Because of difficulties in satisfying both the ultralow temperature and high magnetic field required to produce a substantial phase space, there exist few studies of spin dynamics phenomena that could be used to test the conventional view of the A(1) phase. Here we develop a mechanical spin density detector that operates in the required regime, enabling us to perform measurements of spin relaxation in the A(1) phase as a function of temperature, pressure and magnetic field. Our mechanical spin detector is based in principle on the magnetic fountain effect; spin-polarized superfluid motion can be induced both magnetically and mechanically, and we demonstrate the feasibility of increasing spin polarization by a mechanical spin filtering process. In the high temperature range of the A(1) phase near T(c1), the measured spin relaxation time is long, as expected. Unexpectedly, the spin relaxation rate increases rapidly as the temperature is decreased towards T(c2). Our measurements, together with Leggett-Takagi theory, demonstrate that a minute presence of minority spin pairs is responsible for this unexpected spin relaxation behaviour. Thus, the long-held conventional view that the A(1) phase contains only the majority spin condensate is inadequate.     

Transient ferromagnetic-like state mediating ultrafast reversal of antiferromagnetically coupled spins

Ferromagnetic or antiferromagnetic spin ordering is governed by the exchange interaction, the strongest force in magnetism. Understanding spin dynamics in magnetic materials is an issue of crucial importance for progress in information processing and recording technology. Usually the dynamics are studied by observing the collective response of exchange-coupled spins, that is, spin resonances, after an external perturbation by a pulse of magnetic field, current or light. The periods of the corresponding resonances range from one nanosecond for ferromagnets down to one picosecond for antiferromagnets. However, virtually nothing is known about the behaviour of spins in a magnetic material after being excited on a timescale faster than that corresponding to the exchange interaction (10-100?fs), that is, in a non-adiabatic way. Here we use the element-specific technique X-ray magnetic circular dichroism to study spin reversal in GdFeCo that is optically excited on a timescale pertinent to the characteristic time of the exchange interaction between Gd and Fe spins. We unexpectedly find that the ultrafast spin reversal in this material, where spins are coupled antiferromagnetically, occurs by way of a transient ferromagnetic-like state. Following the optical excitation, the net magnetizations of the Gd and Fe sublattices rapidly collapse, switch their direction and rebuild their net magnetic moments at substantially different timescales; the net magnetic moment of the Gd sublattice is found to reverse within 1.5 picoseconds, which is substantially slower than the Fe reversal time of 300 femtoseconds. Consequently, a transient state characterized by a temporary parallel alignment of the net Gd and Fe moments emerges, despite their ground-state antiferromagnetic coupling. These surprising observations, supported by atomistic simulations, provide a concept for the possibility of manipulating magnetic order on the timescale of the exchange interaction.     

一维亚铁磁无序混合自旋链的磁特性的Monte Carlo模拟

基于一维自旋链模型,采用Monte Carlo方法模拟研究了具有反铁磁相互作用的自旋S-1和自旋S-3/2混合的亚铁磁系统的磁特性,重点研究了自旋的无序排列对此混合系统磁特性的影响.研究发现,基态时,当自旋S-1和自旋S-3/2交替混合(有序排列)时,系统存在M-H磁化曲线的阶梯效应;而当自旋S-1和自旋S-3/2无序混合时,系统的阶梯效应出现涨落,台阶甚至消失.最后,通过对系统自旋组态和能量的研究,解释了该混合系统中所产生的阶梯效应和相图.     

Quantum annealing with manufactured spins

Many interesting but practically intractable problems can be reduced to that of finding the ground state of a system of interacting spins; however, finding such a ground state remains computationally difficult. It is believed that the ground state of some naturally occurring spin systems can be effectively attained through a process called quantum annealing. If it could be harnessed, quantum annealing might improve on known methods for solving certain types of problem. However, physical investigation of quantum annealing has been largely confined to microscopic spins in condensed-matter systems. Here we use quantum annealing to find the ground state of an artificial Ising spin system comprising an array of eight superconducting flux quantum bits with programmable spin-spin couplings. We observe a clear signature of quantum annealing, distinguishable from classical thermal annealing through the temperature dependence of the time at which the system dynamics freezes. Our implementation can be configured in situ to realize a wide variety of different spin networks, each of which can be monitored as it moves towards a low-energy configuration. This programmable artificial spin network bridges the gap between the theoretical study of ideal isolated spin networks and the experimental investigation of bulk magnetic samples. Moreover, with an increased number of spins, such a system may provide a practical physical means to implement a quantum algorithm, possibly allowing more-effective approaches to solving certain classes of hard combinatorial optimization problems.     

Quantum oscillations in a molecular magnet

The term 'molecular magnet' generally refers to a molecular entity containing several magnetic ions whose coupled spins generate a collective spin, S (ref. 1). Such complex multi-spin systems provide attractive targets for the study of quantum effects at the mesoscopic scale. In these molecules, the large energy barriers between collective spin states can be crossed by thermal activation or quantum tunnelling, depending on the temperature or an applied magnetic field. There is the hope that these mesoscopic spin states can be harnessed for the realization of quantum bits--'qubits', the basic building blocks of a quantum computer--based on molecular magnets. But strong decoherence must be overcome if the envisaged applications are to become practical. Here we report the observation and analysis of Rabi oscillations (quantum oscillations resulting from the coherent absorption and emission of photons driven by an electromagnetic wave) of a molecular magnet in a hybrid system, in which discrete and well-separated magnetic clusters are embedded in a self-organized non-magnetic environment. Each cluster contains 15 antiferromagnetically coupled S = 1/2 spins, leading to an S = 1/2 collective ground state. When this system is placed into a resonant cavity, the microwave field induces oscillatory transitions between the ground and excited collective spin states, indicative of long-lived quantum coherence. The present observation of quantum oscillations suggests that low-dimension self-organized qubit networks having coherence times of the order of 100 micros (at liquid helium temperatures) are a realistic prospect.     

在分子自旋量子系统中的可控多体纠缠态

在由N＋1个相互作用的反铁磁分子环构成的量子自旋系统中,可以调控1种多体纠缠态。N个周边分子环的电子自旋和1个中心分子环的电子存在相互交换,从而在分子间形成可调的相互作用。通过整个系统的有效自旋哈密顿量解析得出系统的量子动力学行为。研究发现在量子涨落的条件下,1种高精度的形纠缠态可以被制备出来。通过控制分子间的相互作用,这种多体纠缠态也可以从一些分子环传输到其他分子环上。     

Nanoscale imaging magnetometry with diamond spins under ambient conditions

Magnetic resonance imaging and optical microscopy are key technologies in the life sciences. For microbiological studies, especially of the inner workings of single cells, optical microscopy is normally used because it easily achieves resolution close to the optical wavelength. But in conventional microscopy, diffraction limits the resolution to about half the wavelength. Recently, it was shown that this limit can be partly overcome by nonlinear imaging techniques, but there is still a barrier to reaching the molecular scale. In contrast, in magnetic resonance imaging the spatial resolution is not determined by diffraction; rather, it is limited by magnetic field sensitivity, and so can in principle go well below the optical wavelength. The sensitivity of magnetic resonance imaging has recently been improved enough to image single cells, and magnetic resonance force microscopy has succeeded in detecting single electrons and small nuclear spin ensembles. However, this technique currently requires cryogenic temperatures, which limit most potential biological applications. Alternatively, single-electron spin states can be detected optically, even at room temperature in some systems. Here we show how magneto-optical spin detection can be used to determine the location of a spin associated with a single nitrogen-vacancy centre in diamond with nanometre resolution under ambient conditions. By placing these nitrogen-vacancy spins in functionalized diamond nanocrystals, biologically specific magnetofluorescent spin markers can be produced. Significantly, we show that this nanometre-scale resolution can be achieved without any probes located closer than typical cell dimensions. Furthermore, we demonstrate the use of a single diamond spin as a scanning probe magnetometer to map nanoscale magnetic field variations. The potential impact of single-spin imaging at room temperature is far-reaching. It could lead to the capability to probe biologically relevant spins in living cells.     

Spin-torque diode effect in magnetic tunnel junctions

There is currently much interest in the development of 'spintronic' devices, in which harnessing the spins of electrons (rather than just their charges) is anticipated to provide new functionalities that go beyond those possible with conventional electronic devices. One widely studied example of an effect that has its roots in the electron's spin degree of freedom is the torque exerted by a spin-polarized electric current on the spin moment of a nanometre-scale magnet. This torque causes the magnetic moment to rotate at potentially useful frequencies. Here we report a very different phenomenon that is also based on the interplay between spin dynamics and spin-dependent transport, and which arises from unusual diode behaviour. We show that the application of a small radio-frequency alternating current to a nanometre-scale magnetic tunnel junction can generate a measurable direct-current (d.c.) voltage across the device when the frequency is resonant with the spin oscillations that arise from the spin-torque effect: at resonance (which can be tuned by an external magnetic field), the structure exhibits different resistance states depending on the direction of the current. This behaviour is markedly different from that of a conventional semiconductor diode, and could form the basis of a nanometre-scale radio-frequency detector in telecommunication circuits.     

Persistent sourcing of coherent spins for multifunctional semiconductor spintronics.

Recent studies of n-type semiconductors have demonstrated spin-coherent transport over macroscopic distances, with spin-coherence times exceeding 100 ns; such materials are therefore potentially useful building blocks for spin-polarized electronics ('spintronics'). Spin injection into a semiconductor (a necessary step for spin electronics) has proved difficult; the only successful approach involves classical injection of spins from magnetic semiconductors. Other work has shown that optical excitation can provide a short (<500 ps) non-equilibrium burst of coherent spin transfer across a GaAs/ZnSe interface, but less than 10% of the total spin crosses into the ZnSe layer, leaving long-lived spins trapped in the GaAs layer (ref. 9). Here we report a 'persistent' spin-conduction mode in biased semiconductor heterostructures, in which the sourcing of coherent spin transfer lasts at least 1-2 orders of magnitude longer than in unbiased structures. We use time-resolved Kerr spectroscopy to distinguish several parallel channels of interlayer spin-coherent injection. The relative increase in spin-coherent injection is up to 500% in the biased structures, and up to 4,000% when p-n junctions are used to impose a built-in bias. These experiments reveal promising opportunities for multifunctional spin electronic devices (such as spin transistors that combine memory and logic functions), in which the amplitude and phase of the net spin current are controlled by either electrical or magnetic fields.     

Magnetic and non-magnetic phases of a quantum spin liquid

A quantum spin-liquid phase is an intriguing possibility for a system of strongly interacting magnetic units in which the usual magnetically ordered ground state is avoided owing to strong quantum fluctuations. It was first predicted theoretically for a triangular-lattice model with antiferromagnetically coupled S = 1/2 spins. Recently, materials have become available showing persuasive experimental evidence for such a state. Although many studies show that the ideal triangular lattice of S = 1/2 Heisenberg spins actually orders magnetically into a three-sublattice, non-collinear 120° arrangement, quantum fluctuations significantly reduce the size of the ordered moment. This residual ordering can be completely suppressed when higher-order ring-exchange magnetic interactions are significant, as found in nearly metallic Mott insulators. The layered molecular system κ-(BEDT-TTF)(2)Cu(2)(CN)(3) is a Mott insulator with an almost isotropic, triangular magnetic lattice of spin-1/2 BEDT-TTF dimers that provides a prime example of a spin liquid formed in this way. Despite a high-temperature exchange coupling, J, of 250 K (ref. 6), no obvious signature of conventional magnetic ordering is seen down to 20 mK (refs 7, 8). Here we show, using muon spin rotation, that applying a small magnetic field to this system produces a quantum phase transition between the spin-liquid phase and an antiferromagnetic phase with a strongly suppressed moment. This can be described as Bose-Einstein condensation of spin excitations with an extremely small spin gap. At higher fields, a second transition is found that suggests a threshold for deconfinement of the spin excitations. Our studies reveal the low-temperature magnetic phase diagram and enable us to measure characteristic critical properties. We compare our results closely with current theoretical models, and this gives some further insight into the nature of the spin-liquid phase.     

Detecting excitation and magnetization of individual dopants in a semiconductor

An individual magnetic atom doped into a semiconductor is a promising building block for bottom-up spintronic devices and quantum logic gates. Moreover, it provides a perfect model system for the atomic-scale investigation of fundamental effects such as magnetism in dilute magnetic semiconductors. However, dopants in semiconductors so far have not been studied by magnetically sensitive techniques with atomic resolution that correlate the atomic structure with the dopant's magnetism. Here we show electrical excitation and read-out of a spin associated with a single magnetic dopant in a semiconductor host. We use spin-resolved scanning tunnelling spectroscopy to measure the spin excitations and the magnetization curve of individual iron surface-dopants embedded within a two-dimensional electron gas confined to an indium antimonide (110) surface. The dopants act like isolated quantum spins the states of which are governed by a substantial magnetic anisotropy that forces the spin to lie in the surface plane. This result is corroborated by our first principles calculations. The demonstrated methodology opens new routes for the investigation of sample systems that are more widely studied in the field of spintronics-that is, Mn in GaAs (ref. 5), magnetic ions in semiconductor quantum dots, nitrogen-vacancy centres in diamond and phosphorus spins in silicon.     

Controlled multiple quantum coherences of nuclear spins in a nanometre-scale device

The analytical technique of nuclear magnetic resonance (NMR) is based on coherent quantum mechanical superposition of nuclear spin states. Recently, NMR has received considerable renewed interest in the context of quantum computation and information processing, which require controlled coherent qubit operations. However, standard NMR is not suitable for the implementation of realistic scalable devices, which would require all-electrical control and the means to detect microscopic quantities of coherent nuclear spins. Here we present a self-contained NMR semiconductor device that can control nuclear spins in a nanometre-scale region. Our approach enables the direct detection of (otherwise invisible) multiple quantum coherences between levels separated by more than one quantum of spin angular momentum. This microscopic high sensitivity NMR technique is especially suitable for probing materials whose nuclei contain multiple spin levels, and may form the basis of a versatile multiple qubit device.     

Triplet-singlet spin relaxation via nuclei in a double quantum dot

The spin of a confined electron, when oriented originally in some direction, will lose memory of that orientation after some time. Physical mechanisms leading to this relaxation of spin memory typically involve either coupling of the electron spin to its orbital motion or to nuclear spins. Relaxation of confined electron spin has been previously measured only for Zeeman or exchange split spin states, where spin-orbit effects dominate relaxation; spin flips due to nuclei have been observed in optical spectroscopy studies. Using an isolated GaAs double quantum dot defined by electrostatic gates and direct time domain measurements, we investigate in detail spin relaxation for arbitrary splitting of spin states. Here we show that electron spin flips are dominated by nuclear interactions and are slowed by several orders of magnitude when a magnetic field of a few millitesla is applied. These results have significant implications for spin-based information processing.     

Coupling of spin and orbital motion of electrons in carbon nanotubes

Electrons in atoms possess both spin and orbital degrees of freedom. In non-relativistic quantum mechanics, these are independent, resulting in large degeneracies in atomic spectra. However, relativistic effects couple the spin and orbital motion, leading to the well-known fine structure in their spectra. The electronic states in defect-free carbon nanotubes are widely believed to be four-fold degenerate, owing to independent spin and orbital symmetries, and also to possess electron-hole symmetry. Here we report measurements demonstrating that in clean nanotubes the spin and orbital motion of electrons are coupled, thereby breaking all of these symmetries. This spin-orbit coupling is directly observed as a splitting of the four-fold degeneracy of a single electron in ultra-clean quantum dots. The coupling favours parallel alignment of the orbital and spin magnetic moments for electrons and antiparallel alignment for holes. Our measurements are consistent with recent theories that predict the existence of spin-orbit coupling in curved graphene and describe it as a spin-dependent topological phase in nanotubes. Our findings have important implications for spin-based applications in carbon-based systems, entailing new design principles for the realization of quantum bits (qubits) in nanotubes and providing a mechanism for all-electrical control of spins in nanotubes.