Electronic Structure Calculations of Transition Metal
Work funded by ONR and NSF
and Rare Earth Nitrides Using LSDA+U
Paul Larson, Aditi Herwadkar, W. R. L. Lambrecht
Department of Physics
Chromium Nitride: 3d orbitals FP-LMTO LSDA
Case Western Reserve University FP-LMTO LSDA FP-LMTO LSDA+Uf
Structural and Magnetic properties
Rare-earth nitrides – 4f
CrN forms in the rocksalt crystal structure.
It undergoes a transition from paramagnetic to anti-ferromagnetic 2 at the The rare-earth nitrides have two main problems in
LSDA. First, the position of the 4f orbitals is too close to
Néel temperature, TN ~ 283 K. Motivation: What is the Fermi level. The value of Uf was scaled from
This transition is accompanied by a structural distortion from cubic to
orthorhombic. LSDA+U? photoemission data to fit their experimental positions.
The transformation is first order with transition width (of 2-3 K) and Electronic structure calculations solve Schrodinger's equations for the For GdN Uf = 8.0 eV and Jf = 1.2 eV.
transition temperature extremely sensitive on N composition.
Band structure of CrN (Non-spin-
electrons in a solid. Here we use the full-potential linear muffin-tin orbital
Magnetic stress is the driving force for lattice distortion. (FP-LMTO) method.
Second, the band gap is underestimated as in the F
transition-metal nitrides. The band gap of 0.98 eV at the FP-LMTO LSDA+Uf,d
Most calculations assume the nature of the electrons depend only upon X point was measured above the Curie temperature in
the density (and spin) of electrons at any point in space - Local Spin the paramagnetic regime. Since our calculations cannot
Temperature dependent resistivity and corresponding band-gap for CrN available in literature.
Density Approximation (LSDA). be done for this limit, we take the average of the spin-
Chemical Synthesis of CrN1 Molecular Beam Epitaxy2 Magnetron Sputter Deposition3 majority and spin-minority bands. We expect a
Many-body effects become important for d and f orbitals which have reduction (red-shift) in the band gap (0.67 eV 0.12
narrow energy bands. Hopping small compared to Coulomb interaction. eV) through Tc, possibly a metal insulator transition.
For GdN Ud = 3.4 eV and Jd = 0.0 eV.
The density for specified orbitals is treated in a hybrid manner - additional Cubic Symmetry Broken Symmetry
localized potential added as a Hubbard U correction - LSDA+U.
Symmetry also plays an important role. If we force the
Two parameters are needed - U which describes the shift of the center of cubic symmetry of the lattice on the 4f states, they split to
CrNx=1±0.03 the band and J which describes the splitting of the m states for each l. two triply degenerate (t1u and t2u) and a nondegenerate
Semiconductor Metal -Semiconductor transition Semiconductor (a2u) state. For certain band fillings, these bands become
fixed at the Fermi level. Hund's rules forces the lowest
Band gap 0.09 eV calculated using resistivity measurement
Optical band gap of 0.7eV ●H0LSDA+U = U/2 mm'' nm nm'' - J/2 m m', nm nm' energy state to have largest orbital momentum, allowing
D. Gall suggested that CrN is a Mott insulator. for all bands to be independent and moving bands away
1P.S. Herle et. al J.
Solid State Chem 134, 120 (1997) Based on the fact that LDA theory gives CrN to be a metal from the Fermi level.
et. al Appl. Phys. Lett. 85. 6371 (2004)
3D. Gall et. Al J. Appl. Phys. 91, 5882 (2002) but his results shows a semiconductor. Can we test
this? What will we study with
Hund's rules requires maximizing the orbital
LSDA+U? momentum, L. This reduces the energy
FP-LMTO LSDA Allrare-earth nitrides and many transition-metal nitrides form in the significantly for most of the rare-earth nitrides.
Band Structure AFM CrN2
DOS for AFM CrN2 Band Structure for FM CrN
DOS for FM CrN rocksalt crystal structure. The effect is less important for small L. EuN and
TbN prefer the cubic symmetry arrangement.
These materials have applications for spintronics (combining the spin Also important to note is that L lies opposite S
Metallic degree of freedom with electronics) for dilute doping of the transition metal for members lighter than GdN but lies parallel
for members heavier than GdN.
nitrides and in pure form for the rare earth nitrides.
The size of the band gap in LSDA is too small. The position of the rare-earth
4f orbitals is too close to the Fermi level. Adding LSDA+U corrections to both
the d and f orbitals may be necessary.
Rare-earth nitrides – magnetic
Black : undistorted CrN2 ● AFMI
Red: distorted CrN2 structure. Black :Non-spin-polarized
Total energies for 3 magnetic orderings were fit to a Heisenberg Hamiltonian in order to obtain the AFM
Red: AFM distorted CrN2 structure. III
magnetic exchange parameters Jij (not to be confused with Hubbard J). The choices were FM, AFMI,
The density of states is reduced slightly near EF compared to the non-spin-polarized d Questions solved using and AFMIII (at right) up to second neighbors. Positive J corresponds to ferromagnetic interactions,
calculation, leading to a dip in the density of states or a weak metal.
Conclusion t2g LSDA+U. negative J to antiferromagnetic interactions.
FP-LMTO LSDA+Ud What values of U and J are needed to find the proper band H = -i>j Jij Si . Sj
EFM = E0 – 6J1 – 3J2
structure? EAFMI = E0 + 2J1 – 3J2
Band Structure of FM Band Structure of AFM CrN2 LSDA+U provides support for the idea that CrN may be a Mott –
insulator. What are the positions of the 3d and 4f orbitals? EAFMIII = E0 + 2J1 – J2
U=3eV With a U value of 3eV (which seems a realistic value based on
U=3eV exited atom model estimates) we find What is the true ground state and how is it found?
AFM2 CrN gets a gap of 0.7 eV Cubic symmetry (first on right) shows that GdN has
FM CrN is metallic for U=3eV How good an approximation is LSDA+U to explain the experimental maximum J1 and J2 which drop off quickly for heavier
TiN and VN stay non-magnetic and metallic. results? rare-earth nitrides and not as fast for lighter rare-earth
Values of U larger than 5 are probably unrealistic because VN nitrides. Preliminary calculations for maximum L
Metallic becomes magnetic and the values of U would then be as large as in Are these materials being studied semiconductors or semimetals? symmetry (second on right) change many of the coupling
Semiconduct the oxides, which is unlikely. constants. While some values of J1 are similar, others
or Resistivity data on gaps are more difficult to explain but the large Are these materials useful for spintronics applications? change sign. More calculations need to be done, but GdN
variation among experimental data suggests that this is influenced
U is estimated to be about 3eV for the early transition metal nitrides. still has the largest value of J1 which makes it the best
primarily by defects, in particular N concentration.
candidate for a ferromagnetic semiconductor.
Further work on defects will be needed to address the resistivity