Charge ordering in Ni$^{1+}$/Ni$^{2+}$ nickelates: La$_4$Ni$_3$O$_8$ and La$_3$Ni$_2$O$_6$

Ab initio calculations have been performed to unravel the origin of the recently found superlattice peaks in the trilayer nickelate La $_{4}$ Ni $_{3}$ O $_{8}$ . These peaks arise from static charge ordering of Ni $^{2 +}$ / Ni $^{1 +}$ stripes oriented at 45 $^{\circ}$ to the Ni-O bonds. An insulating state originates from a combination of structural distortions and magnetic order, with the gap being formed solely within the d $_{x^{2} - y^{2}}$ manifold of states. When doped, electrons or holes would go into these states, in a similar fashion to what occurs in the cuprates. Analogous calculations suggest that checkerboard charge order should occur in the bilayer nickelate La $_{3}$ Ni $_{2}$ O $_{6}$ . These results reveal a close connection between La $_{4}$ Ni $_{3}$ O $_{8}$ and La $_{3}$ Ni $_{2}$ O $_{6}$ with La $_{2 - x}$ Sr $_{x}$ NiO $_{4}$ for x=1/3 and x=1/2, respectively.

Charge ordering in Ni $^{1 +}$ /Ni $^{2 +}$ nickelates: La $_{4}$ Ni $_{3}$ O $_{8}$ and La $_{3}$ Ni $_{2}$ O $_{6}$

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Charge ordering in Ni $^{1 +}$ /Ni $^{2 +}$ nickelates: La $_{4}$ Ni $_{3}$ O $_{8}$ and La $_{3}$ Ni $_{2}$ O $_{6}$

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Charge ordering in Ni1+1+/Ni2+2+ nickelates: La44​Ni33​O88​ and La33​Ni22​O66​

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Charge ordering in Ni1+1+/Ni2+2+ nickelates: La44​Ni33​O88​ and La33​Ni22​O66​

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Charge ordering in Ni $^{1 +}$ /Ni $^{2 +}$ nickelates: La $_{4}$ Ni $_{3}$ O $_{8}$ and La $_{3}$ Ni $_{2}$ O $_{6}$

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Charge ordering in Ni $^{1 +}$ /Ni $^{2 +}$ nickelates: La $_{4}$ Ni $_{3}$ O $_{8}$ and La $_{3}$ Ni $_{2}$ O $_{6}$

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