The tricritical point in the quantum IsingS= 1 spin glass with biaxial crystal-field effects

Abstract

We study a quantum generalization of the infinite-range Sherrington-Kirkpatrick spin-glass model with biaxial crystal-field effects described by two uniaxial anisotropy parameters Dx and Dy. For spin dimensionality S = 1 we report an analytical and numerical analysis in the (T, Dx, Dy) parameter space (with T being the temperature). For D ≡ Dx = Dy the model effectively becomes classical and identical with the crystal-field-split spin-glass Ising model (introduced by Ghatak and Sherrington) showing a discontinuous phase transition to the spin-glass phase on a portion of the T-D line.

Truncated forms of the second-rank orthorhombic Hamiltonians used in magnetism and electron magnetic resonance (EMR) studies are invalid—Why it went unnoticed for so long?

“…where 'biaxial crystal-field effects' 'D x and D y ' are 'two uniaxial anisotropy parameters' describing 'biaxial crystal-field effects' [88]. Note that in [88] the forms DS z 2 ÀD(S x 2 ÀS y 2 )+DS(S+1) and D P 2 have also been invoked.…”

“…Note that in [88] the forms DS z 2 ÀD(S x 2 ÀS y 2 )+DS(S+1) and D P 2 have also been invoked. The quote [88]: 'for DD x ¼ D y the model effectively becomes classical and identical with the crystal-field-split spin-glass Ising model' is pertinent for our discussion. (iii) Spin-S Ising model with 'transverse crystal field'…”

“…As discussed above, the terminology labeling the actual ZFS parameters as the 'crystal-field (terms or effects)' in [87][88][89][90][91][92], whereas as the 'anisotropy constant' in [93], indicates the CF ¼ ZFS and double MA ¼ CF( ¼ ZFS) confusion, respectively [21][22][23]. The latter cases consist in referring to purportedly 'CF' (in fact, actual ZFS) quantities by the names related to magnetic or magnetocrystalline anisotropy or equivalently single-ion anisotropy.…”

“…Each type of confusion is physically incorrect. In view of the potential applications to magnetic materials involving transition-metal ions invoked in [87][88][89][90][91][92][93], all terms in Eqs. (25)- (31) should be considered as pertaining, in fact, to the actual ZFS terms [8,9].…”

First-order quantum phase transition in an anisotropic Ising model with infinite-range random interaction

“…The TCP in the quantum anisotropic spin-1 glass Ising model has been investigated. 57 They showed that the disordered model possesses unusual features, manifesting both continuous and first-order phase transitions. This shows that the role of the biaxial crystal field is very important.…”