  Tuning the electronic and magnetic properties of a material through strain
engineering is an effective strategy to enhance the performance of electronic
and spintronic devices. Recently synthesized two-dimensional transition metal
carbides M$_2$C (M=Hf, Nb, Sc, Ta, Ti, V, Zr), known as MXenes, has aroused
increasingly attentions in nanoelectronic technology due to their unusual
properties. In this paper, first-principles calculations based on density
functional theory are carried out to investigate the electronic and magnetic
properties of M$_2$C subjected to biaxial symmetric mechanical strains. At the
strain-free state, all these MXenes exhibit no spontaneous magnetism except for
Ti$_2$C and Zr$_2$C which show a magnetic moment of 1.92 and 1.25 $\mu_B$/unit,
respectively. As the tensile strain increases, the magnetic moments of MXenes
are greatly enhanced and a transition from nonmagnetism to ferromagnetism is
observed for those nonmagnetic MXenes at zero strains. The most distinct
transition is found in Hf$_2$C, in which the magnetic moment is elevated to 1.5
$\mu_B$/unit at a strain of 15%. We further show that the magnetic properties
of Hf$_2$C are attributed to the band shift mainly composed of Hf(5$d$) states.
This strain-tunable magnetism can be utilized to design future spintronics
based on MXenes.
