Hole- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi mathvariant="normal">Cr</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math> nanomagnet in a semiconductor quantum dot

We study a new diluted magnetic semiconductor system based on the spin of ionized acceptor Cr$^+$. show that negatively charged Cr$^+$ ion, an excited state Cr in II-VI semiconductor, can be stable when inserted CdTe quantum dot (QD). The attracts heavy-hole QD and form hole-Cr$^+$ complex. Optical probing this reveals ferromagnetic coupling between heavy-holes spins. At low temperature, thermalization ground with parallel spins prevents optical recombination excess electron 3$d$ shell atom. dynamics nano-magnet formed by exchange interaction. states M$_z$=$\pm$4 controlled resonant pumping relaxation time 20 $\mu$s range is obtained at T=4.2 K. This memory zero field limited interaction phonons.