Proximity induced spin density waves observed in PdCrO$_{\mathrm{2}}$

PdCrO$_{\mathrm{2}}$ with delafossite structure has an intriguing three-dimensional spin order in the layered triangular Cr lattices. We performed Spin-polarized scanning tunneling microscopy (SPSTM) study on the two equally possible cleaved surfaces terminated with CrO$_{\mathrm{2}}$ and Pd. On the CrO$_{\mathrm{2}}$-terminated surface where direct tunneling to the Cr verified, we could observe no long range magnetic order. The CrO$_{\mathrm{2}}$-terminated surface missing Pd upper layer has different super exchange interaction compared with the bulk CrO$_{\mathrm{2}}$ state, which can explain the suppression of long range magnetic order. However, on the Pd-terminated surface with irregular hexagonal surface reconstruction, we could observe a signature of spin density waves induced by proximity effect associated with the long range $\surd $3x$\surd $3 magnetic order in the CrO$_{\mathrm{2}}$ layer.