Alexander Edström, Uppsala University, 2016 1. Eq. 2.6 is incorrect and should be either

Erratum: Theoretical and Computational Studies on the Physics of Applied Magnetism

Alexander Edström, Uppsala University, 2016 1. Eq. 2.6 is incorrect and should be either

cos θ = k _z q k _⊥ ² + k _z ²

= k _z

k , sin θ = k _⊥ q k ² _⊥ + k ² _z

= k _⊥

k or tan θ = k _⊥ k z

2. In the bottom line on page 27, energy shit should be energy shift.

3. The sign convention for the uniaxial magnetic anisotropy followed is such that positive values of the magnetocrystalline anisotropy, or leading anisotropy constants, indicate that magnetisation along the crystal axis is favoured over in-plane magnetisation. Eq. 2.44 does not follow this convention and it would be better to write it as

H _MAE = − ^X

i

h K ₁ ( ˆ m _i · ˆ e _z ) ² + K ₂ ( ˆ m _i · ˆ e _z ) ^{4 i}

or (compare to Eq. 2.22)

H _MAE = ^X

i

h K ₁ sin ² θ + K ₂ sin ⁴ θ ⁱ .

4. In Sec. 3.1.2, it is not properly discussed that the Green’s function is not defined when E is an energy eigenvalue. Typically, retarded (+) and advanced (-) Green’s functions are defined by

G ^± (E) = lim

δ→0

G(E ± iδ).

In some equations, e.g. Eq. 3.12 or Eq. 3.13, it would be more correct to exchange G(E) for G ⁺ (E).

5. Page 57 states that finite temperature DFT is not widely used due to difficulties in formu- lating useful temperature dependent exchange-correlation functionals. Recent work, such as Phys. Rev. Lett. 112, 076403 (2014), does provide such functionals.

6. Eq. 3.33 should be

U = 1 − m ⁴

3 hm ² i ² . 7. In Eq. 4.6, it would be correct to write

ψ l,k

(r, φ, z) = ˜ N e ^ilφ f (r, z)

to allow variations in k _z and preservation of energy according to Eq. 4.4.

8. Paper XV has been published as Phys. Rev. B 94, 174414 (2016).