单相材料在不同温度和磁场下可呈现不同的磁结构，即磁相，很多重要的磁现象都是磁相竞争产生的。在磁相线附近，由于形成两种相的自由能相差不大，中等的磁场即能导致磁相变，产生磁电阻等巨大的宏观效应。磁结构耦合的赝二元Laves化合物Hf_1-xTa_xFe₂是几何阻挫的六方MgZn₂结构，伴随其中磁相变存在一个与现在实用材料相当的巨大的负热膨胀效应。我们用不同温度和磁场下的中子衍射和密度泛函理论研究了Hf_0.86T_0.14Fe₂中阻挫点阵的铁磁和反铁磁竞争关系及负热膨胀效应。如图4(a)所示，随着温度升高， (002)峰的强度在255 K剧烈降低，而(300)峰连续向高Q方向移动，一个非常弱的峰突然出现在(103)峰旁边，这是与结构不相容的(111)峰，它的出现表明出现反铁磁性。在低温下(002)峰的增强表明低温相的磁矩在ab面内。进一步的分析表明2a和6h位Fe原子均有磁矩，且在面内大小相近。在中温反铁磁相中只有kagome面内6h位Fe原子具有磁矩，且磁矩远小于铁磁态的。在相转变温度，点阵常数a变化大约0.3%，从220-260 K体积V变化－123×10^-6/K。验证了加场或降温导致的反铁磁到铁磁相变造成面内点阵膨胀，出现负热膨胀效应。

Fig. 4 (a) The crystal structure of Hf_1-xTa_xFe₂. (b) The contour plot of neutron diffraction intensity. The features are pointed out by the arrows.

Fig. (a) and (b) The contour plots of diffraction intensity of Bragg peaks (002) and (300) at different magnetic fields, respectively. (c) The Bragg peak (002) at 200 (left) and 290 K (right) as a function of magnetic fields, respectively. (d) The phase diagram of the first-order transition. The phase boundary is well described by a linear relation with intercept of -37(2) T.

The magnetic phase competition is examined in the magnetic fields and temperature phase space by employing in situ neutron diffraction. The contour plots of the diffraction intensity of the (002) and (300) Bragg peaks are shown in Figs. 4(a) and 4(b), respectively. The crossover of the intensity of the (002) peak, an indication of AFM to FM transition, is prompted to higher temperatures with increasing magnetic fields. This means the AFM state is suppressed, in accordance with previous specific-heat values measured with magnetic fields and our diffraction data under applied magnetic fields. At 200 K, it is FM, so that the intensity is much less susceptible to magnetic fields than at 290 K where it is AFM. The intensity at 290 K becomes almost field independent beyond 4 T, which roughly defines the critical field inducing the AFM to FM transition. In response to the applied magnetic fields, the lattice is concomitantly expanded in the ab plane, as seen in the shift of the (300) peak. The detailed field dependencies of lattice dimensions are compared with their temperature dependencies. The diffraction under in situ magnetic fields enables us to directly determine the magnetic phase diagram. The transition temperature is defined as one where the lattice constant a of the FM state starts to sharply drop. There is a linear relationship, depicted by the fitting shown in Fig. ?(d), similar to the other systems with AFM to FM transitions. The intercept represents the extrapolated critical fields for the AFM to FM transition at 0 K.