Strain-induced magnetic anisotropy in epitaxial thin films of the spinelCoCr2O4

Abstract

We show that the magnetic anisotropy in spinel-structure CoCr2O4 thin films exhibits a strain dependence in which compressive strain induces an out-of-plane magnetic easy axis and tensile strain an in-plane easy axis, exactly opposite to the behavior reported for the related compound CoFe2O4. We use density functional theory calculations within the LSDA+U approximation to reproduce and explain the observed behavior. Using second-order perturbation theory, we analyse the anisotropy tensor of the Co 2+ ions in both octahedral and tetrahedral coordination, allowing us to extend our results to spinels with general arrangements of Co 2+ ions. PACS numbers: 75.70.Ak, 75.80.+q, 75.30.Gw, 71.15.Mb Thin films with out-of-plane spontaneous magnetization, showing so-called perpendicular magnetic anisotropy, are of great interest for applications such as high density magnetic memories with fast switching 1 . Perpendicular magnetic anisotropy is also needed for spintronic applications, for example in magnetic tunnel junctions, and for low energy current-driven domain wall motion 2-5 .In a system of finite size, magnetic anisotropy is determined by the balance of magnetocrystalline and shape anisotropy. The former is a bulk property originating from spin-orbit interaction, while the latter originates from magnetic dipole-dipole interaction and depends on the geometry of the sample. For the case of thin films, where shape anisotropy always favors in-plane magnetization, it is interesting to understand how the strain affects the magnetocrystalline part. Indeed, the way in which epitaxial strain can affect the magnetocrystalline anisotropy has been the subject of intensive investigations 6-13 . A prominent example of such investigations is the spinel compound CoFe 2 O 4 , which has a strong magnetostriction coefficient 7,10,11,14 . In CoFe 2 O 4 thin films, it was shown that changing the sign of the strain leads from cooperation to competition of shape and magnetocrystalline anisotropies 7 .Compounds with spinel (MgAl 2 O 4 -type) structure have chemical formula AB 2 X 4 where A and B are cations and X represents the ligand anion (usually O, S or Se). In this structure, the cations occupy either the tetrahedrally coordinated 15 (T) site or the octahedrally coordinated (O) site. There are twice as many O sites as T sites. In a normal spinel, A and B cations occupy T and O sites, respectively, while in an inverse spinel, half of the B cations occupy the T sites and the remaining half occupy the O sites together with the A cations. In general, spinels can be characterised by the degree of inversion (i.e. the concentration of B cations occupying T sites).The bulk structure (unstrained case) of the inverse spinel CoFe 2 O 4 , with a disordered Co 2+ /Fe 3+ occu-pancy on the octahedrally coordinated sites, has cubic symmetry (space group F d3m). This enforces the quadratic magnetization terms in the magnetocrystalline anisotropy to vanish, leaving as lowest order terms the quartic ones, which are typically of smaller size, although ...

Strain-induced perpendicular magnetic anisotropy inLa2CoMnO6−ɛthin films and its dependence on film thickness

“…In the case of tensile strain, where basal distances of the octahedra are larger than apical ones, is positive and |30 is the state with higher energy while the other two sates of 4 T 1 triplet have lower energy. This is in agreement with the expected degeneration of the ground state under tensile stress [23]. In the case of compressive strain is negative, and |30 becomes the ground state (crystal field only).…”

“…On the contrary, CoFe 2 O 4 coincides with the behavior of LCMO reported here in the sense that a tensile stress induces PMA [24,25], while a compressive strain induces in-plane anisotropy [26,27]. In both systems, magnetic anisotropy is attributed to Co 2+ ions [23]. Theoretical calculations in Ref.…”

“…As mentioned, different magnetic epitaxial films show a change in the anisotropy direction under different strain [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Of special relevance is the dependence on strain of the magnetic anisotropy found in Co 2+ -containing spinels.…”

“…It has been proved in several material systems that the easy magnetization axis can be changed from in plane to out of plane by means of tensile strain as in (GaMn)As [14], (IrMn)As, [15], (GaMn)(PN) [16], Fe garnets [17]; or by means of compressive strain in La 0.7 Sr 0.3 MnO 3 [18] and SrRuO 3 [19]. Other interesting systems where strain-induced anisotropy changes have been revealed are Y 3 Fe 5 O 12, which is widely used in microwave applications [20], CoFeB based systems [13,21,22] that additionally have functional properties such as giant tunnel magnetoresistance or CoFe 2 O 4 and CoCr 2 O 4 spinel systems that also present large magnetostriction [23,24,25,26,27]. Interestingly, strain tunable magnetocrystalline anisotropy has been found in double perovskite systems such as Sr 2 FeMoO 6 [28] and Sr 2 CrReO 6 [29,30].…”

Structural and magnetic properties of [001] CoCr2O4 thin films

“…* cmagend@unizar.es † b.noheda@rug.nl For device applications, the integration of the material in the form of thin film is necessary. However, only a few studies have been focused on the epitaxial growth of CCO thin films [11,[22][23][24]. Recently, experiments and theory revealed a strain dependence of the magnetocrystalline anisotropy in CCO thin films, where compressive strain induces a perpendicular magnetization, while tensile strain induces an in-plane magnetization [24].…”