logo 复旦大学周磊老师课题组 Research Group of Metamaterials  

(Ⅰ) Wave-functional Materials

Wave-functional materials include electromagnetic metamaterials, photonic crystals and plasmonic materials. Based upon local resonance and/or Bragg scattering mechanisms, these wave-functional materials possess many unusual wave transmission/scattering properties, making them good candidates for applications in information & communication technologies. Starting from 2001, our group has conducted extensive researches within this area, which are highlighted in the following.

11. Discovery of the perfect conversion of propagating waves and surface waves resorting to the gradient-index meta-surface

9. Nonlinear responses in optical metamaterials: theory and experiment

8. Fractal plasmonic metamaterials for subwavelength imaging

7. New mechanism for directive electromagnetic wave emissions based on metamaterials

6. Resolving the puzzles of image instabilities in the super lensing process

5. Discovery of the anomalous Brewster angle effect

4. Subwavelength band gaps from planar fractal structures based on local resonance.

3. Discovery of the zero- n-bar gap

2. Discoveries of two novel mechanisms for perfect photonic transparency

1. Manipulating electromagnetic wave polarizations by anisotropic metamaterials

(Ⅱ) Magnetism

2. Crucial role of the "orbital correlation" effect in low-dimensional magnetic systems

1. Resolving the hot debates on the ground states of magnetorheological fluids

(Ⅰ) Wave-functional Materials

1. Manipulating electromagnetic wave polarizations by anisotropic metamaterials

It is always desirable to have full control of the polarization states of electromagnetic (EM) waves. Conventional methods to manipulate polarization include using optical gratings, dichroic crystals, or employing the Brewster and birefringence effects, etc.. These methods, each possessing its own characteristics, share a common shortcoming of signal loss since all these materials are not perfectly transparent (reflective) for EM waves. In 2007, collaborating with Zhejiang University and HKUST, we proposed an alternative approach based on metamaterials. We show the polarization states of EM waves can be manipulated through reflections by an anisotropic metamaterial plate, and all possible polarizations are realizable via adjusting material parameters. In particular, a linearly polarized light converts its polarization completely to the cross direction after reflection under certain conditions. Microwave experiments were performed to realize these ideas and results are in excellent agreement with numerical simulations.

Schematic I1-1

We further push our study to visible wavelength. Although there are quite some progresses in metamaterial research, and many theories have been proposed and verified in microwave frequency regime, very few are realized at optical frequencies. The challenges come from two sides. On the one hand, fabrications of optical metamaterials need sophisticated nanofabrication techniques; on the other hand, theoretical modeling of metamaterials becomes more difficult at higher frequencies due to the loss and frequency dispersion of material. Recently, combining efforts from theoretical designs, material fabrications, and experimental characterizations, we, in collaborations with two other groups in Fudan and a group in Sweden, succeeded in fabricating our optical metamaterials working at visible frequencies (see left figure), and experimentally verified that they can convert light polarizations at wavelength around 700nm with an efficiency as high as 96% (see right figure). Theoretical results are in semi-quantitative agreement with experimental measurements.

Schematic I1-2 Schematic I1-3

We design an anisotropic ultrathin metamaterial to allow perfect transmissions of electromagnetic (EM) waves for two incident polarizations within a common frequency interval. The transparencies are governed by different mechanisms, resulting in significant differences in transmission phase changes for two polarizations. The system can thus manipulate EM wave polarizations efficiently in transmission geometry, including polarization conversion and rotation. Microwave experiments performed on realistic samples are in excellent agreement with numerical simulations.

Schematic I1-4 Schematic I1-5

Related publications:
[1]"Manipulating electromagnetic wave polarizations through anisotropic meta-materials",
Jiaming Hao, Yu Yuan, Lixin Ran, Tao Jiang, J. A. Kong, C. T. Chan, and L. Zhou,
Phys. Rev. Lett. 99, 063908 (2007).
[2]"Optical metamaterial for polarization control",
Jiaming Hao, Qijun Ren, Zhenghua An, Xueqin Huang, Zhanghai Chen, Min Qiu, and Lei Zhou,
Phys. Rev. A 80, 023807 (2009).
[3]"Electromagnetic wave scatterings by anisotropic metamaterials: Generalized 4×4 transfer-matrix method",
Jiaming Hao and Lei Zhou,
Phys. Rev. B 77, 094201 (2008).
[4]"Manipulate light polarizations with metamaterials: From microwave to visible",
Jiaming Hao, Min Qiu, Lei Zhou,
Front. Phys. China 5, 291(2010). (Review Article)
[5]"A transparent metamaterial to manipulate electromagnetic wave polarizations",
Wujiong Sun, Qiong He, Jiaming Hao, and Lei Zhou,
Opt. Lett. 36, 927 (2011).

2. Study of mechanisms for perfect photonic transparency

In 2005, collaborating with HKUST, we employed theory, numerical simulations and microwave experiments to demonstrate two novel mechanisms for perfect photonic transparency. We found that, for an optically opaque slab with a negative permittivity, if we attach two identical metamaterial slabs with particular permittivity to both sides of the slab or drill some fractal slit patterns through the slab, the structure then becomes perfect transparent for EM waves at particular frequencies. These two mechanisms differ fundamentally from the existing mechanisms. For example, here the working frequency is independent of the wave incidence angles (different from the surface-plasmon resonance mechanism) and the slab thickness (different from the Fabry-Perot mechanism). In addition, for mechanism 1, we found that extraordinarily high magnetic field exists inside the structure accompanying the transparency. These discoveries could result in various applications in practice, such as making a high-frequency high-magnetic-field generator, EM wave filters, or subwavelength waveguides, etc..

Schematic I2-1

Making a high-conducting metal transparent has drawn lots of attention recently. The problem is of great scientific curiosity since a bare metal itself is opaque for light. On the application side, transparent conducting metals (TCMs) with both high DC conductivity and high light transmission are desired in optoelectronic devices. Transparency of a metal film can also be achieved with help of certain resonances such as surface plasmon polaritons (SPPs) or Fabry-Perot (FP) resonances. However, in such schemes, the targeted metals should be perforated with holes or slits. Moreover, the SPP approach is sensitive to structural order while the FP one requires samples with thicknesses comparable to wavelength, both are inconvenient for practical realizations. Here, we propose a scattering cancellation scheme to make a continuous (apertureless) metal film transparent at optical frequencies. Our approach retains the full electric and mechanical properties of a natural metal, and the transparency is robust against structural disorder and incidence angle. We demonstrate the idea by full-wave simulations and proof-of-concept microwave experiments. Due to the enormous difficulty in fabricating this free-standing and multilayers sample if we want expanding this phenomenon to terahertz (THz) or optical region, subsequently we realized the similar transparent effect via another multilayers structure deposited on Si substrate. The experimental results in THz domain agree very well with numerical calculations.

Schematic I2-2

Related publications:
[1]"Electromagnetic wave tunneling through negative-permittivity media with high magnetic fields",
Lei Zhou, W. J. Wen. C. T. Chan, and P. Sheng,
Phys. Rev. Lett. 94, 243905 (2005).
[2]"Resonant transmission of microwaves through subwavelength fractal slits in a metal plate",
W. J. Wen, L. Zhou, B. Hou, C. T. Chan, and P. Sheng,
Phys. Rev. B 72, 153406 (2005).
[3]"Making a continuous metal film transparent via scattering cancellations",
Zhengyong Song, Qiong He, Shiyi Xiao, and Lei Zhou,
Appl. Phys. Lett. 101, 181110 (2012).
[4]"A new method for obtaining transparent electrodes",
Radu Malureanu, Maksim Zalkovskij, Zhengyong Song, Claudia Gritti, Andrei Andryieuski, Qiong He, Lei Zhou, Peter Uhd Jepsen, and Andrei V. Lavrinenko,
Opt. Express 20, 22770 (2012).

3. Discovery of the zero-n gap

In 2003 when I was still working in HKUST, we proposed a novel mechanism to open a photonic band gap that is different from the conventional Bragg mechanism. We rigorously proved that a photonic band gap opens when the volume averaged refraction index is zero inside a periodic structure. This new gap is usually termed as a "zero- n-bar gap" in literature. Apparently, such a gap can only be realized in a composite consisting of both ordinary materials and negative-index materials. We demonstrated many unique properties related to such a new gap: 1)its central wavelength is independent of the periodicity of the photonic crystal; 2)it is rather insensitive to impurities or weak disorders. We employed the finite-different-time-domain method to successfully design a realistic structure that supports such a new type of photonic gap, and the results obtained based on the full-wave simulations were in perfect agreement with those based on theoretical calculations. This new mechanism breaks many limitations imposed by the conventional Bragg mechanism. For example, the Bragg gap requires that the sample thickness should be several times larger than the wavelength, but in principle the zero- n-bar gap can be realized in an ultra-thin sample. Moreover, impurities and disorders inevitably exist in any realistic samples. While they do affect the Bragg gap significantly, their influences on the zero- n-bar gap are less pronounced. Therefore, the fabrication requirements could be much released for this new type of band gap systems.

Schematic I3

Immediately after its appearance, the zero- n-bar gap mechanism began to attract extensive attention. Many research groups studied lots of other unusual properties of this zero- n-bar gap, such as its omni-directional reflectivity, the gap solitons, the light reshaping effects, and so on. Similar gaps were also found in anisotropic structures as well as quasi-periodic structures. It is worth noting that the theoretical prediction of a zero- n-bar gap was finally verified experimentally by a research group in Zhejiang University in 2006.

Related publications:
[1]"Photonic band gap from a stack of positive and negative index materials",
Jensen Li, Lei Zhou, C. T. Chan, Ping Sheng,
Phys. Rev. Lett. 90, 083901 (2003).

4. Subwavelength band gaps from planar fractal structures based on local resonance.

In 2002 when I was still in HKUST, we found by both experiment and theory that a specific class of H-shaped planar conducting fractals possesses a series of self-similar resonances, leading to multiple gaps and pass bands for electromagnetic waves over an ultra-wide frequency range, with the property that the transmittance can be modulated by an external current source. A double stack of these fractal patterns exhibits polarization-independent absolute gaps over a wide range of incidence angles. These characteristics are retained even when the fractal patterns are significantly subwavelength in all dimensions. When attaching a perfect metallic sheet to the back of such a plate, the whole structure behaves as a multi-band magnetic reflector at a series of frequencies (reflecting EW waves in phase). Compared with the conventional Bragg mechanism, our mechanism possesses the following obvious merits: (1) the periodicity is not required; (2) subwavelength functionality. This class of structure should be useful in reflecting EM waves at microwave and far infra-red frequency regimes, compared with the conventional reflectors.

Schmatic I4

Related publications:
[1]"Subwavelength photonic band gaps from planar fractals",
Weijia Wen, Lei Zhou, Jensen Ji, Weigun Ge, C. T. Chan, Ping Sheng,
Phys. Rev. Lett. 89, 223901 (2002).
[2]"Reflectivity of planar metallic fractal patterns",
Lei Zhou, Weijia Wen, C. T. Chan, Ping Sheng,
Appl. Phys. Lett. 82, 1012 (2003).
[3]"Multiband subwavelength magnetic reflectors based on fractals",
Lei Zhou, Weijia Wen, C. T. Chan, P. Sheng,
Appl. Phys. Lett. 83, 3257 (2003).

5. Discovery of the anomalous Brewster angle effect

In 2003 when I was still in HKUST, we found that when an electromagnetic wave strikes on the surface of a particular anisotropic negative index materials at a certain incidence angle, the reflection disappears. Such an oblique-angle transparency is completely different from the conventional Brewster effect, but is rather dictated by the anisotropy and the frequency dispersion of the meta-material. Such an effect is subsequently termed as the "anomalous Brewster angle effect" in literature. Finite-difference-time-domain simulation of realistic negative-n structures confirms the analytic results based on effective indices.

Schematic I5

Related publications:
[1]"Anisotropy and oblique total transmission at a planar negative-index interface",
Lei Zhou, C. T. Chan, and P. Sheng,
Phys. Rev. B 68, 115424 (2003).

6. Resolving the puzzles of image instabilities in the super lensing process

Russia scientist V. G. Veselago proposed that a flat slab of material with ε=μ=-1 could function as a lens to focus electromagnetic (EM) waves. UK scientis Jr. J. Pendry showed that the proposed lens was in fact a perfect one. It was then argued that a small deviation in material properties results in a super lens with imaging resolution beyond the usual diffraction limit. However, pioneering numerical simulation studies revealed that the image formed by such a perfect lens varies dramatically over time, and a stable image can be obtained only when the absorption is added, which unfortunately degrades the obtained image resolution. Why such a beautiful prediction of perfect lens is not supported by numerical simulations? How to reach a stable image within a short time period? These puzzles have greatly frustrated scientists before 2005.

Schematic I6

Collaborating with Prof. C. T. Chan in HKUST, we resolved these puzzles in 2005-2006. We showed that a slab of meta-material (with ε=μ=-1+iΔ) possesses a vortex-like surface wave with no ability to transport energy, whose nature is completely different from a localized mode or a standing wave. Through computations based on a rigorous time-dependent Green's function approach, we demonstrated that such a mode inevitably generates characteristic image oscillations in two-dimensional focusing with even a monochromatic source, which were observed in many numerical simulations, but such oscillations are weak in three-dimensional focusing. We further analyzed the relationships between image oscillations and various factors, and predicted a new type of image oscillations. More recently, we proposed that changing the source' "switch-on" time can efficiently modulate the image oscillations. Computations show that an optimized "switch-on" time can help reach a stable image within the shortest duration, without scarifying the image quality.

Related publications:
[1]"Vortex-like surface wave and its role in the transient phenomena of meta-material focusing",
Lei Zhou and C. T. Chan,
Appl. Phys. Lett. 86, 101104 (2005).
[2]"Relaxation mechanisms in three dimensional meta-material lens focusing",
Lei Zhou and C. T. Chan,
Opt. Lett. 30, 1812 (2005).
[3]"Modulating image oscillations in focusing by a meta-material lens: Time-dependent Green's function approach",
Xueqin Huang, Lei Zhou, and C. T. Chan,
Phys. Rev. B 74, 045123 (2006).

7. New mechanism for directive electromagnetic wave emissions based on metamaterials

Conventionally, the directive emission is realized through using an electromagnetic wave resonator. However, such a mechanism requires that the thickness of the cavity should larger than half wavelength, so that its application to low-frequency situations is quite unfavorable since the resonator is too bulky. In 2005, collaborating with Tongji University and HKUST, we employed theory, simulations and experiments to demonstrate a new mechanism for directive emission based on metamaterials. Using the extraordinary reflection phase properties of metamaterials, we have successfully constructed a resonance cavity, with size unbounded by the half wavelength, to achieve directive radiations. The directivity index of the radiation pattern is as high as 129. Such a new mechanism breaks the strict restriction of the conventional mechanism imposed on the sample size, so that it could be helpful in device-miniaturizations required by modern technologies.

Schematic I7

Related publications:
[1]"Directive emissions from subwavelength metamaterial-based cavities",
Lei Zhou, H. Q. Li, Y. Q. Qin, Z. Y. Wei and C. T. Chan,
Appl. Phys. Lett. 86, 101101 (2005).

8. Fractal plasmonic metamaterials for subwavelength imaging, slow wave and total absorption

Surface plasmon polaritons (SPPs) attracted considerable attention recently. The plasmon frequency ωp of a natural material is fixed by its electron density, which limits the applications significantly. In 2004, Pendry et al. demonstrated that a metallic plate with periodic square holes can mimic a plasmonic material in terms of SPP properties, with effective ωp dictated by the structure. However, to make the idea work, one has to fill the holes with high-index materials which is not easy to realize in practice, particularly at higher frequencies. Here, we demonstrate that a metallic plate drilled with fractal-shaped slits (see left figure) exhibits SPPs with ωp dictated by the fractal geometry. Without using high-index insertions, the system can homogenized as a plasmonic metamaterial to support transverse-magnetic and transverse-electric SPPs simultaneously.

Our plasmonic metamaterial possesses many interesting applications. We show it works as a super lens to focus light sources with all dimensional subwavelength resolutions. Microwave experiments and FDTD simulations were performed to verify the super imaging effect in microwave frequency regime (see right figure below) successfully.

Schematic I10-1 Schematic I10-2

Available approaches to slow down light include the photonic crystals and EIT. In this paper, we demonstrate by both experiment and theory that an ultra-thin MTM supports slow-wave propagations, which can perfectly couple to external fast waves. We show that an ultrathin metamaterial can trap photons for a long time. Such photon-trapping effect is governed by the anomalous dispersion and surface plasmon excitations of the system. Light-matter interactions are remarkably enhanced inside these structures, leading to perfect omnidirectional light absorption and dramatically enhanced nonlinear generations.

Schematic I10-3 Schematic I10-4

Related publications:
[1]"Fractal plasmonic metamaterials for subwavelength imaging",
Xueqin Huang, Shiyi Xiao, Dexin Ye, Jiangtao Huangfu, Zhiyu Wang, Lixin Ran, and Lei Zhou,
Opt. Express 18, 10377 (2010).
[2]"Enhancement of light-matter interactions in slow-wave metasurfaces",
Shiyi Xiao, Qiong He, Xueqin Huang, Shiwei Tang, and Lei Zhou,
Phys. Rev. B 85, 085125 (2012).

9. Nonlinear responses in optical metamaterials: theory and experiment

Since the invention of LASER in 1960s, nonlinear optics has grown up to be a very active research field, and the nonlinear spectroscopy has become a very powerful technique to study material properties. However, the nonlinear signals are typically too small in conventional materials, which limit the applications of such techniques to a wider range of physical problems. With help of the electromagnetic resonances in metamaterials, one expects that the local fields, and in turn, the nonlinear generation efficiency, can be significantly enhanced in such materials. However, prior works are mostly theoretical in nature and experiments are relatively rare. In addition, convincing theoretical explanations were lacking for those existing experimental measurements.
In collaboration with Prof. Y. R. Shen’s group in UC Berkeley, we employed both theoretical calculations and experiments to study the nonlinear responses in optical metamaterials. The spectra of second-harmonic generations measured on a fishnet metamaterial are in quantitative agreements with calculations based on full-wave numerical simulations combined with field integrations. We found that the stimulated nonlinear signals are strongly enhanced when the incidence wavelength hits the magnetic resonance of the double fishnet structure. Both of the spectra exhibit ~80 times enhancements at the magnetic resonance frequency. Our calculations explained several interesting features observed experimentally, and suggested an optimal metamaterial structure to yield the strongest nonlinear signals.

Schematic I11-1 Schematic I11-2

Related publications:
[1]"Nonlinear responses in optical metamaterials: theory and experiment",
Shiwei Tang, David J. Cho, Hao Xu, Wei Wu, Y. Ron Shen, and Lei Zhou,
Opt. Express 19, 18283 (2011).


Schematic I12-1

Schematic I12-2 Schematic I12-3

Related publications:
[1]"Tight-binding analysis of coupling effects in metamaterials",
Hao Xu, Qiong He, Shiyi Xiao, Bin Xi, Jiaming Hao, and Lei Zhou,
J. Appl. Phys. 109, 023103 (2011).
[2]"Theory of coupling in dispersive photonic systems",
Bin Xi, Hao Xu, Shiyi Xiao, and Lei Zhou,
Phys. Rev. B 83, 165115 (2011).

11. Discovery of the perfect conversion of propagating waves and surface waves resorting to the gradient-index meta-surface

The arbitrary control of electromagnetic waves is a key aim of photonic research. Although, for example, the control of freely propagating waves and surface waves has separately become possible using transformation optics and metamaterials, a bridge linking both propagation types has not yet been found. We demonstrate theoretically and experimentally that a specific gradient-index meta-surface can convert a PW to a SW with nearly 100% efficiency. Distinct from conventional devices such as prism or grating couplers, the momentum mismatch between PW and SW is compensated by the reflection-phase gradient of the meta-surface, and a nearly perfect PW–SW conversion can happen for any incidence angle larger than a critical value. Experiments in the microwave region, including both far-field and near-field characterizations, are in excellent agreement with full-wave simulations. Our findings may pave the way for many applications, including high-efficiency surface plasmon couplers, anti-reflection surfaces, light absorbers, and so on.

Schematic I13-1

Recently, many efforts were devoted to utilizing metamaterials to focus a plane wave to a point image. However, so far, most proposed lenses were realized through optimizing the local transmission phase only, and therefore, there are significant energy losses due to reflections at surfaces caused by the impedance mismatch. Here, inspired by our previous work of gradient meta-surfaces supporting anomalous reflection, we propose a new structure with a parabolic reflection-phase profile, which can focus a plane electromagnetic wave to a point image in reflection geometry. We first employed the dyadic Green's function method to identify the designing criterion of the proposed device, and then designed a realistic device based on full wave simulations. Collaborating with Tie Jun Cui's group in Southeast University, and combing microwave experiments, full-wave simulations as well as analytical results based on dyadic Green's function method, the excellent agreements show the good functionalities of our proposed device. Our lens also works well for obliquely incident EM waves. Compared to conventional devices with similar functionality, our device is much thinner than wavelength and makes full use of the incidence energy.

Schematic I13-2

In 2011, Prof. Capasso's group introduced a meta-surface which supported anomalous reflections/refractions for impinging light at wavelength λ=8μm, governed by a generalized Snell's law. Here an additional parallel wavevector is provided by the radiation phase gradient of the meta-surface. The idea was soon pushed to near infra-red (IR) regime (λ~2μm) by down scaling the sizes of those optical antennas, and the functionality of the device was found to be broadband. In the above systems, the impinging light will be converted to both normal and anomalous modes for its reflection and refraction. And the conversion efficiency to the anomalous mode is quite limited and the polarization will be changed to the cross direction. All these properties will influence the real applications of meta-surfaces. Recently, in collaboration with NTU, we designed and fabricated a gradient meta-surface supporting high-efficiency (~80%) anomalous reflections in a shorter wavelength regime with a broad bandwidth (750-900nm). Finite-difference-time-domain (FDTD) simulations are in excellent agreement with experiments. Compared to previously studied meta-surfaces working in the IR regime, our meta-surface is more easily designed and fabricated, works in a shorter wavelength regime, can reflect the incident waves to a single anomalous reflection channel with a high conversion efficiency, and keeps its polarization unchanged. Our findings may lead to many interesting applications, such as anti-reflection coating, polarization and spectral beam splitters, high-efficiency light absorber, and surface plasmon coupler, etc.

Schematic I13-3

Related publications:
[1]"Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves",
Shulin Sun, Qiong He, Shiyi Xiao, Qin Xu, Xin Li & Lei Zhou,
Nature Materials 11, 426-431 (2012).
[2]"Flat metasurfaces to focus electromagnetic waves in reflection geometry",
Xin Li, Shiyi Xiao, Bengeng Cai, Qiong He, Tie Jun Cui, and Lei Zhou,
Opt. Lett. 37, 4940 (2012).
[3]"High-Efficiency Broadband Anomalous Reflection by Gradient Meta-Surfaces",
Shulin Sun, Kuang-Yu Yang, Chih-Ming Wang, Ta-Ko Juan, Wei Ting Chen, Chun Yen Liao, Qiong He, Shiyi Xiao, Wen-Ting Kung, Guang-Yu Guo, Lei Zhou, and Din Ping Tsai,
Nano Lett. 12, 6223−6229 (2012).

(Ⅱ) Magnetism

1. Resolving the hot debates on the ground states of magnetorheological fluids

Magnetorheological (Electrorheological) fluids, generally consisting of small magnetic (dielectric) particles dispersed in a liquid, are material systems whose rheological properties are controllable through the application of an external magnetic (electric) field. Before 1997, hot debates and puzzles exist about the ground states of the Magnetorheological (MR) fluids --- 1) why elongated clusters are formed in the solid phase of a MR fluid but the same thing does not happen for an Electrorheological (ER)? 2) conflicting experimental data were reported for the index of the power-law relation between the length and the width of the cluster; 3) what is the internal structure inside the cluster? Collaborating with Prof. W. J. Wen and Prof. P. Sheng in HKUST, we established a unified picture to resolve these debates and puzzles in 1997. We found that 1) the demagnetization field is the key factor to lead the formation of clusters with ellipsoidal shape; 2)priors experimental data on the index are correct only in specific conditions 3)the microstructure inside each cluster is BCT. Our theoretical calculations were supported by our own experimental results (performed by Prof. Wen), and explained the conflicting experimental data published previously, so that they form a unified framework to understand the ground states of MR fluids.

Schematic II1

Related publications:
[1]"Ground states of magnetorheological fluids",
Lei Zhou, Weijia Wen and Ping Sheng,
Phys. Rev. Letts. 81, 1509 (1998).

2. Crucial role of the "orbital correlation" effect in low-dimensional magnetic systems

When computing the magnetic properties of transition-metal systems, we usually assume that the "orbital polarization" is completely quenched by the crystal field, and the calculations based on such an assumption have achieved great successes. However, when dealing with the problem of magnetocrystalline anisotropy energy (MAE), such a method faces great challenges – the computations can not even yield a correct sign of the MAE. Collaborating with Prof. D. S. Wang from Institute of Physics, we studied this problem by using a tight-binding model. We found that the orbital correlation (OC) effect, which is often omitted in a conventional method, plays a crucial role in the calculations for the MAE, especially in a low-dimensional magnetic system. This work points out a possible route for correctly computing the MAE in a low-dimensional system in the future. Based on this work, Dr. X. G. Wan from Nanjing University and Prof. D. S. Wang continued to study the magnetic properties of magnetic nanoclusters. Their results showed that calculations with OC effects correctly considered were in quantitative agreements with the experiments. On the contrary, calculations with only spin correction included deviate from the experimental data drastically. These studies reinforced the notion that the OC effect does play a crucial role in determining the magnetic properties of low-dimensional magnetic systems.

Schematic II2

Related publications:
[1]"Orbital correlation and magnetocrystalline anisotropy in one-dimensional transition metal systems",
Lei Zhou, Dingsheng Wang, and Yoshiyuki Kawazoe,
Phys. Rev. B 60, 9545 (1999).
[2]"Orbital polarization, surface enhancement, and quantum confinement in nanocluster magnetism",
Xiangang Wan, Lei Zhou, Jinming Dong, T. K. Lee, Ding-sheng Wang,
Phys. Rev. B 69, 174414 (2004).

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