**Large exchange bias in tetragonal compensated ferrimagnets. **By following the rules of the chemical and magnetic ordering in Heusler materials, we have realized the compensated ferrimagnet (of approximately Mn_{2.6}Pt_{0.4}Ga composition) by substituting Mn to Pt in Mn_{3}Ga tetragonal ferrimagnet [1]. Since the whole Mn_{3-x}Pt_{x}Ga (0<*x*<1) series exhibit a tetragonal structure, the presence of the non-zero magnetorystalline anisotropy together with segregation of the deffect ferromagnetic phase into the grains with a small characteristic volume δ*V* and large magnetization *M*, results into a huge exchange-bias field *H*_{EB}~(*J·S*)/(*M·δV+M*_{res}) of several Tesla, where *J* - is the effective surface exchange coupling between the compensated host phase with the residual magnetization *M*_{res} and the ferromagnetic grains with the magnetization *M*, *S* - surface of the coupling area. The fit of the experimental data, based on this formula using the calculated magnetization *M*_{res}(*x*) as a function of Pt content *x* is shown in FIG.1.

*x*≈0.4) in Mn

_{3-x}Pt

_{x}Ga series.

Such systems might provide an alternative appoach to the magnetic harderning. In this case the *M*×*H* product will be maximized by increasing *H*_{EB} parameter. Further disorder engineering to maximize the coupling surface area *S* migh allow to increase the size of the ferromagnetic grains, and thus the magnetization *M* as well.

**Noncollinear magnetism in Heusler materials. **Antiparallel alignment of the magnetic moments in two different Mn sublattices is typically encountered in Mn_{2}YZ compounds (cubic or tetragonal) but not all of them exhibit noncollinearity. The most significant exchange coupling between the nearest Mn_{I} and Mn_{II} atoms in different Wyckoff sites is characterized by a large exchange constant (*J*_{I}_{-II}∼−20 meV) that leads to a typical collinear ferrimagnetic state. However, we have identified several systematic cases (e.g., the tetragonal Mn_{2}RhSn, Mn_{2}PtIn and Mn_{2}IrIn), in which the collinear ferrimagnetic order cannot explain the measured saturated magnetization, which appears to be two high. For this systems we figured out that their collinear order can be perturbed by the next important interaction *j* between the next-nearest planes, e.g., between pairs of Mn_{II}-Y planes, as shown in FIG.2. This interaction is antiparallel due to its indirect origin realized through the main-group element Z (superexchange). Since *j* tends to rotate the moments of the nearest Mn_{II}-Y planes antiparallel to each other, it competes with the strong antiparallel exchange *J* and may then result in a nontrivial canting angle (*θ*≠0°;180°). The relevant *θ*-dependent part of the Heisenberg Hamiltonian contains only two types of antiparallel interactions *H*(*θ*)=−*J ·*cos

*θ*−½

*·**j*cos2(π−

*·**θ*), where the first term is the coupling of the nearest planes (Mn

_{I}-Z with Mn

_{II}-Y) and the second is that of the next-nearest (Mn

_{II}-Y) planes. The extrema of

*H*(

*θ*),

*θ*

_{1,2}=180°±arccos(

*J*/2

*j*) correspond to a noncollinear solution for

*j*> ½

*·**J*, i.e. canting occurs only if the next-nearest antiparallel exchange

*j*is sufficiently strong. Parameterized by the

*ab-intio*calculated

*J*and

*j*exchange constants, this model reasonably describes the

*θ*-dependence of the total energy, also computed

*ab-initio*

*.*For Mn

_{2}RhSn, the plot of the total energy as a function of

*θ*(FIG.2) indeed exhibits two energy minima corresponding to the nontrivial canting angles

*θ*

_{1,2}=180°±55°, which was confirmed by neutron diffraction (

*θ*

_{1,2}=180° ± 58.9°) [2]. Similar plots were obtained for Mn

_{2}PtIn and Mn

_{2}IrIn

*.*

_{2}YZ Heusler compounds. Magnetocrystalline anisotropy induced by tetragonal distortion orients Mn

_{I}magnetic moments along the

*c*axis; on Mn

_{II }the moments are canted in an alternating manner with respect to the

*c*axis. Schematic picture shows the leading magnetic exchange interactions between different atomic layers in Mn

_{2}YZ (atomic planes containing Z and Y elements, in blue and red, respectively). Arrows show the orientation of the spin moments on Mn, and the springs - the exchange interactions between different planes. Assuming only the nearest antiparallel interactions

*J*(between Mn

_{I}-Z and Mn

_{II}-Y planes) leaves the magnetic structure collinear; introducing the next-nearest antiparallel coupling

*j*(between Mn

_{II}-Y planes) leads to the alternating canting of Mn

_{II}moments by

*θ*and 2

*π*−

*θ*. For the case of Mn

_{2}RhSn the total energy as a function of

*θ*for three different orientations of the easy axis is shown on the right.

The influence of the magnetocrystalline anisotropy is figured out by rotating the easy axis of magnetization as well with the plane of the canting moments, as shown in FIG.2. In agreement with neutron data, it follows that the easy axis in Mn_{2}RhSn coincides with the tetragonal *c*-axis, and the magnetocrystalline anisotropy energy is close to 2 meV/f.u. Further analysis of the micromagnetic model based on the computed Dzyaloshinski-Moriya interactions suggests the possibility for existance of the chiral skyrmions (see the supplemental in [2]).