Gong'
title: 'Magnetism of 3d Transition Metals and Magnetic Anisotropy of one-dimension Ni Chains on Au(110)-(1$\times2$): A Noncollinear $ab-initio$ Density-Functional-Theory Study'
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Non-Collinear Density Functional Theory ,Surface Magnetism , one-dimensional Magnetism ,Magnetic Crystalline Anisotropy 75.70.Ak ,75.30.Gw ,75.75.+a ,71.15.Mb

\[Intro\] Introduction
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The high-density magnetic recording and the memory devices require the strong magnetic anisotropy. The low-dimensional materials due to the reduced dimensionality generally have a favorable direction and the physical properties along this direction are generally different from the other directions. Thus we have the most possibilities to find the strong magnetic anisotropy materials from these low-dimensional materials. On the other hand, the reduced dimensionality reduces the atomic coordination number and enhances the spin and orbital magnetic moments of the materials. Since the pioneering experiments for the magnetism of Fe strips on the W(110) and Cu(111) surfaces [@Elmers1; @Shen1; @Hauschild1; @Pratzer1], the researches along this direction have been extended to others quasi-one-dimensional systems such as the monatomic magnetic chains on vicinal surface [@Gambardella1; @Gambardella2; @Gambardella3] and Co magnetic dot-chain on Ru(0001) surface [@Li1]. The transition from in-plane to out-of-plane magnetic anisotropy had been found in Fe nano-structure when it is approach to one-dimensional limit [@Boeglin1]. Besides the celebrating properties 