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We theoretically investigate multiple-$Q$ spin textures, which are composedof superpositions of spin density waves with different wave numbers, for aneffective spin model of centrosymmetric itinerant magnets. Our focus is on theinterplay between biquadratic interactions arising from the spin-chargecoupling and magnetic anisotropy caused by the spin-orbit coupling. Taking intoaccount two types of the magnetic anisotropy, single-ion anisotropy andbond-dependent anisotropy, we elucidate magnetic phase diagrams for anarchetypal triangular-lattice system in the absence and presence of an externalmagnetic field. In the case of the single-ion anisotropy, we find a plethora ofmultiple-$Q$ instabilities depending on the strength and the sign of theanisotropy (easy plane or easy axis), including a skyrmion crystal withtopological number of two. In an external magnetic field, we find that askyrmion crystal with topological number of one is stabilized by the in-plane(out-of-plane) magnetic field under the easy-plane (easy-axis) anisotropy. Wealso examine the stability of the field-induced skyrmion crystal by rotatingthe field direction. As a biproduct, we show that a triple-$Q$ state withnonzero chirality appears in the presence of the biquadratic interaction andthe easy-axis anisotropy. Meanwhile, we find that the bond-dependent anisotropyalso stabilizes both types of skyrmion crystals. We show that, however, for theskyrmion crystal with topological number of one, Bloch- and N\'eel-typeskyrmion crystals are selectively realized depending on the sign of thebond-dependent anisotropy. Moreover, we find yet another multiple-$Q$ states,including two types of meron crystals with the skyrmion numbers of one and two.The systematic investigation will provide a reference to complex magnetictextures in centrosymmetric magnetic metals.

Noncoplanar multiple-$Q$ spin textures by itinerant frustration: Effects of single-ion anisotropy and bond-dependent anisotropy