Giant Magnetoresistance in Hubbard Chains
Update: 2019-10-22 09:13:12      Author:

Giant magnetoresistance (GMR) is a good example of how an unexpected fundamental scientific research can quickly give rise to new technologies and commercial products. After its discovery in 1988 [1,2], less than 10 years later, in around 1997, GMR-type sensors were introduced as reading elements in hard disk drives. Since then, the applications of GMR effect not only have greatly increased storage capacities, but also paved the way for the new storage technologies.

The GMR effect is observed as a significant change in the electrical resistance of composed magnetic-nonmagnetic multilayers. Depending on the magnetization direction of adjacent ferromagnetic layers, the overall resistance is relatively low for parallel alignment and relatively high for antiparallel alignment. Here the magnetization direction can be controlled, for example, by applying an external magnetic field. The physical explanation of this purely quantum mechanical effect relies on the fact that electrons traveling through a ferromagnetic conductor scatter differently depending on the relative orientation of their spin to the magnetization direction of the conductor—with those oriented parallel scattering less often than those oriented antiparallel [3-5]. In a band picture, this is explained by the imbalance of charge populations with spin parallel and antiparallel to an external magnetic field, which translates into very different local density of states in the magnetic regions for both spin states at the Fermi energy [5]. For the antiparallel component, the reduced density of states results in a higher resistance for this channel, compared to a lower resistance for the parallel one.


Fig. 1: (a) Schematic representation of the superlattice with the picture for transport and magnetism, in the absence or presence of an external magnetic field B. (b) [(c)] The spin-resolved density of states of the superlattice at zero temperature for h = 0 [h ≠ 0]. In the absence of the field, the Mott gap renders an insulating behavior, while the latter, a metal induced by the field.

A recent investigation [6] involving Jian Li, Cheng Chen, Hai-Qing Lin and Rubem Mondaini from CSRC, and Thereza Paiva from Federal University of Rio de Janeiro, investigates GMR effect in a pure quantum scenario, with full interacting setting. The researchers start from one of the simplest possible interacting quantum model describing the interacting electrons hopping on a lattice, namely the Hubbard model. By applying site-dependent interactions on a one-dimensional lattice, one can mimic the nonmagnetic-magnetic multilayer structure in GMR material with periodic distributed nonmagnetic (without Hubbard U) and magnetic (with finite Hubbard U) sites, as shown in Fig.1 (a). By means of unbiasedly numerical methods, a combination of exact diagonalization and density matrix renormalization group techniques, the obtained transport properties as well as the spin correlations of this simplified quantum system show the essential features of the GMR effect. In the absence of external field, the adjacent magnetic sites show antiferromagnetic correlations and the system behaves as a perfect insulator [See Fig.1(b)]. In the contrary, in the presence of a sufficient magnetic field, the adjacent magnetic sites show ferromagnetic correlation, and the system has finite conductivity [See Fig.1(c)].

The authors have connected the GMR effect, which is usually explained in a single-particle picture, to the strongly-correlated lattice model in a purely interacting setting. Therefore, to artificially distinguish the identical electrons to two types, localized and delocalized ones, is no longer necessary in this work. Moreover, the implementation has the possibility of being emulated using cold atoms trapped in optical lattices experimentally and could inspire experimentalists in exploring GMR effects in highly tunable cold atom experiments.


[1]     M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, Giant Magnetoresistance of (001)Fe/(001Cr Magnetic Superlattices, Phys. Rev. Lett. 61, 2472 (1988).

[2]     G. Binasch, P. Grünberg, F. Saurenbach, and W. Zinn, Enhanced magnetoresistance in layered magnetic structures with antiferromagnetic interlayer exchange, Phys. Rev. B 39, 4828 (1989).

[3]     E. Gerstner, Nobel prize 2007: Fert and Grünberg, Nat. Phys. 3, 754 (2007).

[4]     P. A. Grünberg, Nobel lecture: From spin waves to giant magnetoresistance and beyond, Rev. Mod. Phys. 80, 1531 (2008).

[5]     Nobel Media AB, The Nobel prize in physics 2007—Advanced information,

J. Li, C. Chen, T. Paiva, H.-Q. Lin, and R. Mondaini, Giant Magnetoresistance in Hubbard Chains, Phys. Rev. Lett. 121, 020403 (2018).

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